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-- Table structure for table `ai_users`
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CREATE TABLE `ai_users` (
  `ai_id` int(11) NOT NULL,
  `ai_fullname` varchar(500) NOT NULL,
  `ai_address` longtext NOT NULL,
  `ai_phone` varchar(20) NOT NULL,
  `ai_password` varchar(50) NOT NULL,
  `ai_account_type` int(2) NOT NULL,
  `ai_email` varchar(100) NOT NULL,
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  `status` int(2) NOT NULL,
  `start_status` timestamp NOT NULL DEFAULT current_timestamp() ON UPDATE current_timestamp(),
  `ai_city` varchar(100) DEFAULT NULL,
  `ai_state` varchar(100) DEFAULT NULL,
  `ai_zip` varchar(100) DEFAULT NULL,
  `ai_email_update` int(1) NOT NULL DEFAULT 1 COMMENT '0=not recieve email update,1=recieve email update',
  `ai_add_email` varchar(200) DEFAULT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4;

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INSERT INTO `ai_users` (`ai_id`, `ai_fullname`, `ai_address`, `ai_phone`, `ai_password`, `ai_account_type`, `ai_email`, `account_id`, `status`, `start_status`, `ai_city`, `ai_state`, `ai_zip`, `ai_email_update`, `ai_add_email`) VALUES
(37, 'Loveday Grace', 'Audu bako way', '09090846106', 'NU91enhDVmtEUEY2aUdBellObWdsUT09', 0, 'graceloveday@gmail.com', 'B2021-31', 0, '2021-10-20 09:36:10', NULL, NULL, NULL, 1, NULL),
(38, 'Damilola Aleyemi', '84 Dankaji, Badawa Layout', '07035664911', 'K2NtYlUzUHNIQnRFMGxZN0lPZy95Zz09', 0, 'damilolaaleyemi@steamledge.com', 'B2021-32', 0, '2021-10-20 09:36:50', NULL, NULL, NULL, 1, NULL),
(39, 'Victor Anawo', '45, Aviation Quarters, Murtala Mohammed Way', '2348164093044', 'Vks1d3YxTlRNQ3RVUXJWVUdoYnVlZz09', 0, 'anawovic@gmail.com', 'B2021-33', 0, '2021-10-20 09:37:02', NULL, NULL, NULL, 1, NULL),
(40, 'TOYIN AKIODE', 'STEAMLEDGE', '07038696101', 'UFowbVR1bVVja2tnZUhPZFphc0NZZz09', 0, 'toyinakiode@steamledge.com', 'B2021-34', 0, '2021-10-20 09:37:29', NULL, NULL, NULL, 1, NULL),
(41, 'Abubakar Bello', '', '', 'bzhLSWFmRklzVHM4Wk5TeHZ3YUUwdz09', 0, 'abubakarbello@steamledge.com', 'B2021-35', 0, '2021-10-20 10:15:47', NULL, NULL, NULL, 1, NULL),
(42, 'Adastra', 'constellation Orion', '1123344', 'UFowbVR1bVVja2tnZUhPZFphc0NZZz09', 1, 'anonymous@gmail.com', 'B2021-36', 0, '2021-10-20 15:01:11', NULL, NULL, NULL, 1, NULL);

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-- Table structure for table `assessment_exam`
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CREATE TABLE `assessment_exam` (
  `id` int(11) NOT NULL,
  `question_id` varchar(200) NOT NULL,
  `answer_id` varchar(200) NOT NULL,
  `package_id` varchar(200) NOT NULL,
  `subject_id` varchar(200) NOT NULL,
  `user_id` varchar(200) NOT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4;

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INSERT INTO `assessment_exam` (`id`, `question_id`, `answer_id`, `package_id`, `subject_id`, `user_id`) VALUES
(1, '13', '1', 'N2ZkMjJZVFRhOHVJcFVzNGkwY0tQQT09', 'VXRYK2RNZks5VmZrL2M1R0gzeGo3QT09', 'THdqMFBVY3JDQ3R4M091d3BubUpXUT09'),
(2, '14', '2', 'N2ZkMjJZVFRhOHVJcFVzNGkwY0tQQT09', 'VXRYK2RNZks5VmZrL2M1R0gzeGo3QT09', 'THdqMFBVY3JDQ3R4M091d3BubUpXUT09'),
(3, '15', '2', 'N2ZkMjJZVFRhOHVJcFVzNGkwY0tQQT09', 'VXRYK2RNZks5VmZrL2M1R0gzeGo3QT09', 'THdqMFBVY3JDQ3R4M091d3BubUpXUT09'),
(4, '16', '2', 'N2ZkMjJZVFRhOHVJcFVzNGkwY0tQQT09', 'VXRYK2RNZks5VmZrL2M1R0gzeGo3QT09', 'THdqMFBVY3JDQ3R4M091d3BubUpXUT09'),
(5, '17', '1', 'N2ZkMjJZVFRhOHVJcFVzNGkwY0tQQT09', 'VXRYK2RNZks5VmZrL2M1R0gzeGo3QT09', 'THdqMFBVY3JDQ3R4M091d3BubUpXUT09'),
(6, '18', '2', 'N2ZkMjJZVFRhOHVJcFVzNGkwY0tQQT09', 'VXRYK2RNZks5VmZrL2M1R0gzeGo3QT09', 'THdqMFBVY3JDQ3R4M091d3BubUpXUT09'),
(7, '19', '3', 'N2ZkMjJZVFRhOHVJcFVzNGkwY0tQQT09', 'VXRYK2RNZks5VmZrL2M1R0gzeGo3QT09', 'THdqMFBVY3JDQ3R4M091d3BubUpXUT09'),
(8, '20', '2', 'N2ZkMjJZVFRhOHVJcFVzNGkwY0tQQT09', 'VXRYK2RNZks5VmZrL2M1R0gzeGo3QT09', 'THdqMFBVY3JDQ3R4M091d3BubUpXUT09'),
(9, '21', '2', 'N2ZkMjJZVFRhOHVJcFVzNGkwY0tQQT09', 'VXRYK2RNZks5VmZrL2M1R0gzeGo3QT09', 'THdqMFBVY3JDQ3R4M091d3BubUpXUT09'),
(10, '22', '2', 'N2ZkMjJZVFRhOHVJcFVzNGkwY0tQQT09', 'VXRYK2RNZks5VmZrL2M1R0gzeGo3QT09', 'THdqMFBVY3JDQ3R4M091d3BubUpXUT09'),
(11, '23', '3', 'N2ZkMjJZVFRhOHVJcFVzNGkwY0tQQT09', 'VXRYK2RNZks5VmZrL2M1R0gzeGo3QT09', 'THdqMFBVY3JDQ3R4M091d3BubUpXUT09');

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-- Table structure for table `exam_simulation`
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CREATE TABLE `exam_simulation` (
  `id` int(11) NOT NULL,
  `examYear` varchar(200) NOT NULL,
  `questions` longtext NOT NULL,
  `options` longtext NOT NULL,
  `answer` longtext NOT NULL,
  `explaination` longtext NOT NULL,
  `imageDir` longtext NOT NULL,
  `topic` varchar(500) NOT NULL,
  `package_id` varchar(200) NOT NULL,
  `subject_id` varchar(200) NOT NULL,
  `status` int(1) NOT NULL DEFAULT 0
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4;

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-- Dumping data for table `exam_simulation`
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INSERT INTO `exam_simulation` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`, `status`) VALUES
(1, '2020', 'The period of a simple pendulum of length 80.0cm was found to have doubled when the length of the pendulum was increased by X. Calculate X.', '26.7cm~40.0cm~160.0cm~240.0cm', '240.0cm', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(2, '2020', 'A body of mass 5kg movimg with a velocity of 30ms-1 due east is suddenly hit by another body and changes its velocity to 50ms-1 in the same direction. Calculate the magnitude of the impulse received.', '100Ns~150Ns~250Ns~400Ns', '100Ns', 'I = Ft = m(v - u)\n\n= 5(50 - 30) = 100', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(3, '2020', 'Electric energy is measured in', 'ampere~coulomb~kilowatt-hour~kilowatt', 'kilowatt-hour', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(4, '2020', 'A stone of mass 0.5kg is dropped from a height of 12m. Calculate its maximum kinetic energy. [g = 10ms-1]', '3.0J~6.0J~30.0j~60.0J', '60.0J', 'K.E = P.E = mgh\n\n= 0.5 x 10 x 12 = 60J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(5, '2020', 'A machine of efficiency 80% is used to lift a box. If the effort applied by the machine is twice the weight of the box. Calculate the velocity ratio of the machine', '0.5~0.63~0.8~1.6', '0.63', 'Y = \\(\\frac{M.A}{V.R} \\times \\frac{100}{1}\\)\n\n= \\(\\frac{\\frac{1}{2}}{V.R} \\times \\frac{100}{1}\\)\n\nV.R = 0.625', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(6, '2020', 'A faulty thermometer registers 102.5oC t 100oC. If the thermometer has no zero hour, what will it register at 55oC?', '54.6oC~55.0oC~56.0oC~56.4oC', '56.4oC', 'x = \\(\\frac{102.5 \\times 55}{100}\\)\n\n= 56.375oC', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(7, '2020', 'A rod of initial lenght 2m at a temperature of 25oC is heated to 80oC. Calculate the increase in length of the rod if its linear expansivity is 4.0 x 10-3K-1', '0.26m~0.44m~0.53m~0.84m', '0.44m', '\\(l_2 - l_1 = \\alpha l_1 (\\theta_2 - \\theta_1) = 4.0 \\times 10^{-3} \\times 2(80 - 25)\\)\n\n= 0.44m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(8, '2020', 'as a bicycle Tyre was being pumped up, it was noticed that contrary to Boyle\'s law the volume increased as the pressure increased. The best explanation of this is that Boyle\'s law is only true for', 'ideal gases~a fixed mass of gas~a mixture of gases~a gas at variable temperature', 'ideal gases', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(9, '2020', 'It takes 4 minutes to boil a quantity of water using an electrical heating coil. How long will it take to boil the same quantity of water using the same coil if the current is doubled? [Neglect any external heat losses]', '8 minutes~4 minutes~2 minutes~1 minute', '2 minutes', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(10, '2020', 'When table salt is added to ice, the melting point of the ice', 'is raised~is lowered~remains unchanged~is first raised, then lowered', 'is lowered', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(11, '2020', 'Which of the following is used to measure relative humidity?', 'hydrometer~barometer~hypsometer~hygrometer', 'hygrometer', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(12, '2020', 'Which of the following factors affect the rate of evaporation of a liquid? i. Exposed surface area ii Temperature of the surroundings iii. Thermal capacity of the liquid iv. Relative humidity of the surroundings', 'ii and iii only~ii, iii and iv only~i, iii and iv only~i, ii amd iv only', 'i, ii amd iv only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(13, '2020', 'The maximum displacement of a vibrating tunning fork is its', 'amplitude~frequency~period~wavelength', 'amplitude', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(14, '2020', 'A boat is rocked by waves of speed 30ms-1 whose successive crest are 10m apart. Calculate the rate at which the boat recieves the waves', '30s-1~10s-1~3s-1~1s-1', '3s-1', 'F = \\(\\frac{v}{\\lambda} = \\frac{30}{10} = 3s^{-1}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(15, '2020', 'Which of the following waves is not transverse', 'light waves~sound waves~sea waves~radio waves', 'sound waves', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(16, '2020', 'Light travelling through a small pinhole usually does not make a shadow with a distinct sharp edge because of', 'diffraction~inteference~reflection~refraction', 'diffraction', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(17, '2020', 'The angle of incidence of a ray of light on a plane mirror is 55o. Determine the angle between the reflected ray and the mirror', '35o~45o~55o~110o', '35o', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(18, '2020', 'A concave mirror forms a magnified and errect image only when the object is placed', 'at the centre of curvature~at the focus~between the focus and the pole of the mirror~beyound the radius of curvature', 'between the focus and the pole of the mirror', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(19, '2020', 'A thin lens is placed 50cm from an illustrated object. The image produced has linear magnification of \\(\\frac{1}{4}\\). Calculate the power of the lens in dioptres', '2.5D~5.0D~10.0D~25.0D', '10.0D', '\\(\\frac{1}{v} = \\frac{1}{u}\\)\n\nm = \\(\\frac{v}{u} = \\frac{1}{4} = \\frac{v}{50}\\)\n\nv = 12.5\n\nBut \\(\\frac{1}{v} + \\frac{i}{u} = \\frac{1}{f}\\)\n\n= \\(\\frac{1}{50} + \\frac{1}{12.5} = f\\)\n\nf = 10m\n\nP = \\(\\frac{100}{10} = 10D\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(20, '2020', 'Which of the following characteristics of light determines its colour?', 'velocity~wavelength~amplitude~intensity', 'wavelength', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(21, '2020', 'Which of the following is not a part of the electro-magnetic spectrum?', 'x-rays~microwaves~infrared radiation~alpha rays', 'alpha rays', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(22, '2020', 'Sound interference is necessary to produce the phenomenon of', 'beats~doppler effect~acoustic resonance~echo', 'beats', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(23, '2020', 'A satellite in circular motion around the earth does not have', 'a gravitational force acting on it~a uniform velocity~an acceleration~a centripetal force acting on it', 'a uniform velocity', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(24, '2020', 'When a conductor mounted on an insulating stand is charged and left for sometime, the conductor eventually loses all its charges. This is because the', 'electric charges evaporate from the surface of the conductor~charges are connected to earth~charges on the conductor are neutralized by opposite charges from the surrounding air~charges ionize the surrounding air', 'charges on the conductor are neutralized by opposite charges from the surrounding air', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(25, '2020', 'An isolated metal sphere of radius R, carrying an electric charge Q, is situated in the medium of relative permitivity, Er. A test charge is placed at a point p, distance r from the surface of the sphere. Let Eo represent the permitivity of free space. The electric potential at p is given by the expression', '\\(\\frac{Q}{4 \\pi E_o E_r}\\)~\\(\\frac{Q}{4 \\pi E_o E_r (R +r)}\\)~\\(\\frac{Q}{4 \\pi E_o E_r(R - r)}\\)~\\(\\frac{Q}{4 \\pi E_o E_rR}\\)', '\\(\\frac{Q}{4 \\pi E_o E_rR}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(26, '2020', 'An isolated metal sphere of radius R, carrying an electric charge Q, is situated in the medium of relative permitivity, Er. A test charge is placed at a point p, distance r from the surface of the sphere. Let Eo represent the permitivity of free space. The magnitude of the electric field intensity at P is given by the expression', '\\(\\frac{Q}{4 \\pi E_o E_r r^2}\\)~\\(\\frac{Q}{4 \\pi E_o E_r(R + r)^2}\\)~\\(\\frac{Q}{4 \\pi E_o E_r(R - r)^2}\\)~\\(\\frac{Q}{4 \\pi E_o E_rR^2}\\)', '\\(\\frac{Q}{4 \\pi E_o E_rR^2}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(27, '2020', 'A resistor of resistance R is connected to a battery of negligible internal resistance. If a siilar resistor is connected in series with it the', 'effective resistance of the circuit is halved~total power dissipated is doubled~total current in the circuit is halved~terminal voltage is halved', 'total power dissipated is doubled', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(28, '2020', 'A cell of e.m.f. 1.5V is connected in series with a resistor of resistance 3.0\\(\\Omega\\). A voltmeter connected across the cell registers 0.9V. Calculate the internal resistance of the cell', '2.0\\(\\Omega\\).~3.0\\(\\Omega\\).~5.0\\(\\Omega\\).~6.0\\(\\Omega\\).', '2.0\\(\\Omega\\).', '\\(\\frac{V}{R} = \\frac{E}{R + r}\\)\n\n\\(\\frac{0.9}{3} = \\frac{1.5}{3 + r}\\)\n\nr = 2\\(\\Omega\\).', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(29, '2020', 'A wire of resistivity 4.40 x 10-5\\(\\Omega\\) cm has a cross sectional area of 7.50 x 10-4 cm2. Calculate the length of the wire that will be required to make a 4.0\\(\\Omega\\) resistor', '82.50 cm~68.18cm~15.90cm~11.95cm', '68.18cm', 'L = \\(\\frac{R.A}{e} = \\frac{4 \\times 7.50 \\times 106{-4}}{4.40 \\times 10^{-5}} = 68.18cm\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(30, '2020', 'A battery of e.m.f. 12.0V and internal resistance0.5\\(\\Omega\\) is connected to 1.5\\(\\Omega\\) and 4.0\\(\\Omega\\) series resistor. Calculate the terminal voltage of the battery.', '13.0V~11.0V~3.0V~1.0V', '11.0V', '\\(\\frac{V}{R} = \\frac{E}{R + r} = \\frac{V}{5.5} = \\frac{12}{6}\\)\n\nv = 11.0V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(31, '2020', 'If the direction of the curent in a straight wire is reversed, the magnetic field', 'remains the same~becomes parallel to the wire~ceases to exist~is oppositely directed', 'is oppositely directed', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(32, '2020', 'An inductor of inductance 1.0H is connected in series with a capacitor of capacitance 2.0\\(\\mu F\\) in an a.c. circuit. to resonate', '112.5Hz~225.0Hz~323.5Hz~707.1Hz', '112.5Hz', 'fo = \\(\\frac{1}{2 \\pi \\sqrt{LC}} = \\frac{1}{2 \\times 3.14 \\sqrt{1 \\times 2 \\times 10^{-6}}}\\)\n\n= 112.5Hz', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(33, '2020', 'An ammeter connected to an a.c circuit records 5.5. The peak current in the circuit is', '7.8A~7.1A~3.8A~3.5A', '7.8A', '\\(I_o = I_{rms} \\times \\sqrt{2} = 5.5 \\times 1.41 = 7.8A\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(34, '2020', 'Two isotopes of uranium are designed as \\(^{238}U\\) and \\(^{235}U\\). The numbers 238 and 235 represent their', 'atomic numbers~nucleon numbers~proton numbers~neutron numbers', 'nucleon numbers', 'neutrons + protons = the nucleus or mass numbers.\n\nU-238 has mass number(proton 92 + neutron 146=238)\nU-235 has mass number (proton 92 + neutron 143 =235)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(35, '2020', 'The main difference between between x-rays and \\(\\gamma-rays\\) lies in their', 'ionizing ability~absorption rate~mode of production~mode of propagation', 'mode of propagation', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(36, '2020', 'An electron of mass 9.1 x 10-31 kg moves with a speed of 107ms-1. Calculate the wavelength of the associates wave[h = 6.6 x 10-34Js]', '9.0 x 10-24m~4.55 x 10-17m~7.25 x 10-11m~6.20 x 10-8m', '7.25 x 10-11m', '\\(\\lambda = \\frac{hc}{\\frac{1}{2}mv^2}\\)\n\n= \\(\\frac{6.6 x 10^{-34} \\times 3 \\times 10^8}{0.5 \\times 9.1 \\times 10^{-3} (10^7)^2}\\)\n\n= 7.25 x 10-11m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(37, '2020', 'Which of the following properties of a long steel bar would alter if the bar were melted, recast into a cube and allowed to cool to its original temperature?', 'sensity~volume~specific heat capacity~electrical resistance', 'volume', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(38, '2020', 'Which of the following instruments is best for measuring the diameter of a thin constantan wire?', 'callipers~metre rule~micometer screw guage~vernier callipers', 'micometer screw guage', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(39, '2020', 'What is the density of a fuel of relative density 0.72? [Density of water = 1000kg m-3]', '72 kgm-3~720 kgm-3~7200 kgm-3~72000 kgm-3', '720 kgm-3', 'P = 0.72 x 1000 = 720', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(40, '2020', 'The types of motion which a cylindrical drum rolling down an inclined plane undergoes are', 'circular and translational~rotational and translational~rotational and circular~rectilinear and circular', 'rotational and translational', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(41, '2020', 'Which of the following statements about static friction is correct? It', 'is independent of the nature of the surface in contact~depends on the area of surface in contact~depends on the relative motion between the surface in contact~depends on the weight of the moving body', 'depends on the relative motion between the surface in contact', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(42, '2020', 'Which of the following statements about moving particle is correct?', 'if the resultant force acting on the particle is zero, then it is in dynamic equillibrium~If the resultant force acting on the acting on the particle is greater than zero, then it is moving with a uniform velocity~the rate of change of its momentum with time tales place in a direction opposite to that of its motion~the particle falling freely covers equal distances in equal time interval', 'the particle falling freely covers equal distances in equal time interval', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(43, '2020', 'Two cars X and Y travelling in opposite directions along the same high way at uniform velocities 110 kmh-1 and 90kmh-1 respectively pass each other at a certain point. The velocity of X relative to Y at the time they pass each other is', '200 kmh-1~100 kmh-1~40 kmh-1~20 kmh-1', '200 kmh-1', 'R = 110 + 90 = 200', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(44, '2020', 'The average speed of an object is determined by dividing the sum of its initial and final speeds by two only when the acceleration is', 'changing~uniform~increasing~decreasing', 'uniform', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(45, '2020', 'a body is projected horizonatlly from the top of a cliff 45m above the ground. if the body lands at a distance 30m from the foot of the cliff, calculate the speed of projection. [g = 10ms-2]', '10ms-1~15ms-1~20ms-1~30ms-1', '30ms-1', 'V2 = U2 + 2gh \n\n= 02 + 2 x 10 x 45 = 30', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(46, '2020', 'Which of the following statements best describes a rigid body? A body which', 'is not equally deformed~when deformed regains it shape~is brittle~when deformed remains deformed', 'is not equally deformed', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(47, '2020', 'simple harmonic oscillator has a period of 0.02s and amplitude of 0.25m. Calculate the speed in ms-1 at the centre of the oscillation', '125\\(\\pi\\)~25.00\\(\\pi\\)~100.00 \\(\\pi\\)~400.00\\(\\pi\\)', '25.00\\(\\pi\\)', 'V = WX = \\(\\frac{2\\pi \\times 0.25}{0.02} = 25\\pi\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(48, '2020', 'A vertical string, suspended from a fixed point and having a small mass attached to the free end is set into oscillations. Which of the following statements about the system are correct? i. The potential energy of the mass is a minimum at the middle of the swing ii. Its kinetic energy is a maximum at the middle of the swing iii. The sum of the potential and kinetic energies is constant throughout the swing', 'i,ii and iii~i and ii only~ii and iii only~i and iii only', 'ii and iii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(49, '2020', 'A moving body of mass 25.0kg undergoes a uniform retardation of 20.0ms-2. Calculate the magnitude of the retardating force', '1.25N~8.00N~45.00N~500.00N', '500.00N', 'F = MG \n\n= 25 x 20 = 500N', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(50, '2020', 'Which of the following sources of energy is', 'i, ii and iii~i and ii only~i and iii only~ii and iii only', 'ii and iii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(51, '2020', 'a machine is said to be a third class lever when the', 'load is between the fulcrum and effort~fulcrum is between the effort and the load~effort is between the fulcrum and load~fulcrum is directly below the load', 'effort is between the fulcrum and load', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(52, '2020', 'a thermometer records 680 mmHg at steam point and 440 mmHg at ice point. The temperature it records at 380 mmHg is', '-25oC~-20oC~20oC~25oC', '-25oC', '\\(\\frac{440 - 380}{680 - 380} = \\frac{0 - x}{100 - x}\\) \n\n= -25oC', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(53, '2020', 'The advantages of the thermoelectric thermometer include the following characteristics except that it', 'can measure rapidly changing temperatures~can measure high and low temperature~can measure high and low temperature almost at a point~is fairly sensitive', 'is fairly sensitive', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(54, '2020', 'In a thermos flask, heat loss by radiation is minimizes by the', 'silvered surfaces~vacuum within the doubled walls~plastic stopper~cork support', 'silvered surfaces', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(55, '2020', 'The pressure P, volume V, and absolute temperature T of a given mass of an ideal gas change simultaneously. Which of the followng equations is correct about the gas?', 'PV = \\(\\frac{constant}{T}\\)~\\(\\frac{P}{T} = Constant\\)~\\(\\frac{P}{V} = \\frac{constant}{T}\\)~\\(\\frac{I}{T} = \\frac{constant}{PV}\\)', '\\(\\frac{I}{T} = \\frac{constant}{PV}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(56, '2020', 'Specific heat capacity 36.4 Jkg-1 K-1 of a body means that when 36.4J of heat energy is supplied to a body of', 'mass 100kg the temperature rises by 1k~mass 1kg, the temperature by 1000K~mass 1kg, the temperature rises by 1K~mass 100kg, the temperature rises by 1000k', 'mass 1kg, the temperature rises by 1K', 'The specific heat capacity of a body is the heat energy required to raise a body of mass 1kg through a temperature of 1K.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(57, '2020', 'The diagram above shoes three forces F1, F2 and F3, which of the following ewuations is correct?', 'F3 = F1 + F2~F2 = F1 + F3~F1 = F2 - F3~F1 = F2 + F3', 'F1 = F2 + F3', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(58, '2020', 'An electric drill rated 400W is used to drill a hole in copper of mass 400g in 20s. Calculate the rise in temperature if all the heat produced is absorbed by the copper. [specific heat capacity of copper = 400Jkg-1K-1]', '100oC~75oC~50oC~45oC', '50oC', '\\(\\theta = \\frac{Pt}{MC} = \\frac{400 \\times 20}{0.4 \\times 400} = 50^o\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(59, '2020', 'A solid of mass 0.5kg initially at 50oC melts at 60oC. Calculate the quantity of heat required to melt it completely. [specific heat capacity of the solid =2.0KJ kg-1K-1][Specific latent heat of fusion of solid =1.0 KJ kg-1]', '1500J~10000J~10500J~15000J', '10500J', 'Q = ML + C\\(\\theta\\) \n\n= 0.5 x 1000 + 0.5 x 2000 x 10 \n\n= 10500', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(60, '2020', 'Dew point is not affected by', 'temperature~wind~the amount of water vapour in the atmosphere~atmospheric pressure', 'atmospheric pressure', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(61, '2019', 'A certain wave has a speed of 20ms-1. If the frequency of the wave is 0.25Hz, calculate the distance between successive crests of the wave', '5.0m~40.0m~50.0m~80.0m', '80.0m', '\\(\\lambda = \\frac{v}{f} = \\frac{20}{0.25} = 80\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(62, '2019', 'The ability of a wave to spread around corners is called', 'polarisation~dispersion~diffraction~reflection', 'diffraction', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(63, '2019', 'The following devices use plane mirrors in their operations, except', 'periscope~sextant~kaleidoscope~binoculars', 'binoculars', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(64, '2019', 'When an object is placed at the principal focus of a concave mirror, the location of the image formed is', 'between principal focus and pole~between principal focus and centre of curvature~at infinity~at centre of curvature', 'at infinity', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(65, '2019', 'From the diagram, the correct equation for the refractive index n of the medium is', 'n = tan i~n = \\(\\frac{sin i}{sin 90^o}\\)~n = \\(\\frac{sin i}{cos (90^o - i)}\\)~n = sin 90oC', 'n = \\(\\frac{sin i}{sin 90^o}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(66, '2019', 'A ray of light travels from air to water. The refeactive index of water is given by the expression', '\\(\\frac{\\text{velocity in water}}{\\text{velocity in air}}\\)~\\(\\frac{\\text{sine of angle of refraction}}{\\text{sine of angle of incidence}}\\)~\\(\\frac{\\text{apparent depth}}{\\text{real depth }}\\)~\\(\\frac{\\text{wavelength in air}}{\\text{wavelength in water}}\\)', '\\(\\frac{\\text{wavelength in air}}{\\text{wavelength in water}}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(67, '2019', 'A lens that is thinner at the middle and thicher at the edges is', 'diverging~converging~plano-convex~converging meniscus', 'diverging', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(68, '2019', 'Which of the following electromagnetic wave has the longest wavelength?', 'radio-waves~gamma rays~infrared waves~ultraviolet rays', 'radio-waves', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(69, '2019', 'The amplitude of a sound wave determines its', 'frequency~quality~loudness~pitch', 'loudness', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(70, '2019', 'As the air column of length L in an air pipe decreases, the frequency of the sationary wave emitted', 'decreases~increases~varies as L2~varies as \\(\\sqrt{L}\\)', 'decreases', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(71, '2019', 'A positively charged glass rod is placed near the cap of a positively charged electroscope. The divergence of the leaf is observed to', 'decrease~increase~remain the same~increase and collapse immediately', 'increase', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(72, '2019', 'Capacitors are used in the following devices, except', 'water pumping machines~ceiling fans~electric irons~television sets', 'electric irons', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(73, '2019', 'Use the diagram above to calculate the current, I.', '0.60A~0.97A~1.03A~5.00A', '0.97A', '\\(\\frac{1}{R} = \\frac{1}{R_1} + \\frac{1}{R_2}\\)\n\n= \\(\\frac{1}{6} + \\frac{1}{4}\\)\n\nR = \\(\\frac{12}{5} = 2.5\\Omega\\)\n\nR = 2.4 + 10 = 12.4\n\nV = IR\n\nI = \\(\\frac{v}{R} = \\frac{12}{12.4} = 0.97\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(74, '2019', 'Determine the potential difference. V across the parallel resistors', '2.0V~2.3V~3.0V~0.7V', '2.3V', 'V = IR \n\n= 0.97 x 2.4 = 2.3V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(75, '2019', 'A galvanometer of internal resistance 50\\(\\Omega\\) and full scale deflection of 20 mA is converted into a voltmeter by connecting a resistor of resistance 1950\\(\\Omega\\) in series to it. Calculate the maximum voltage that can be read by the voltmeter', '20V~30V~38V~40V', '40V', 'V = IR1 + IR2 \n\n= 0.02 x 50 + 0.02 x 1950 = 40V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(76, '2019', 'In the wiring of houses, the fuse is connected to the wire coloured', 'blue~brown~yellow~yellow and green', 'brown', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(77, '2019', 'Which of the following factors does not affect the electric resistance of wire?', 'length~mass~temperature~cross-sectional area', 'mass', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(78, '2019', 'Which of the following factors will increase the sensitivity of moving coil meter?', 'strong spring~low numbers of turns~small area of coil~soft iron core', 'soft iron core', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(79, '2019', 'In order to prevent bar magnets from losing their strength, they are stored wih keepers such that the two bars are placed with', 'like poles facing each other and the keepers placed between them~like poles facing each other and the keepers placed between them~unlike poles facing each other and the keepers placed at their ends~unlike poles facing each other and the keepers placed between them', 'unlike poles facing each other and the keepers placed at their ends', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(80, '2019', 'The energy, E stored in an inductor of inductance L when current I passes through it is given by the equation', 'E = \\(\\frac{1}{2} LI^2\\)~E = LI2~E \\(\\frac{1}{2}LI\\)~E = \\(\\frac{1}{2} L^2I\\)', 'E = LI2', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(81, '2019', 'The resonant frequency of an a.c circuit is 1000 kHz. If each of the capacitance and inductance in the circuit is reduced by 50%, and no other changes are made, the resonant frequency will become', '250kHz~750kHz~1000kHz~2000kHz', '2000kHz', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(82, '2019', 'Eddy currents can be reduced by', 'using coil of high resistance~winding the coil on a soft iron core~creating holes in the metal plates~using coil of low resistance', 'creating holes in the metal plates', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(83, '2019', 'an electron moves with a speed of 2.0 x 106ms-1 in a straight line. Calculate the wave length of the electron wave. [mass of an electron = 9.1 x 10-31 kg][Planck\'s constant = 6.6 x 10-34Js]', '3.63 x 10-19m~6.51 x 10-9m~4.24 x 10-8m~7.25 x 10-8m', '4.24 x 10-8m', '\\(\\lambda = \\frac{hc}{\\frac{1}{2}mv^2} = \\frac{6.6 \\times 10^{-38} \\times 3 \\times 10^8}{\\frac{1}{2} \\times 9.1 \\times 10^{-31} (2 \\times 10^6)^2}\\)\n\n= 4.24 x 10-8m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(84, '2019', 'Oxidation of the filament in a light bulb is prevented by the introduction of', 'hydrogen~oxygen~argon~mercury vapour', 'argon', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(85, '2019', 'In a cathode ray tube, the function of the x-plates is to', 'deflect the electron beam horizontally~deflect the electron beam vertically~reflect the electron beam~generate sinusoid waves', 'deflect the electron beam horizontally', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(86, '2019', 'A nuclide represented as \\(^{70}_{32}X\\) has a neutron-proton ratio of', '0.5~0.8~1.2~1.5', '1.2', '\\(\\frac{38}{32} = 1.2\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(87, '2019', 'Neutrons are used to induce artificial radioactivity because they', 'are energetic~have no charge~have no mass~are ionizing', 'have no charge', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(88, '2019', 'Which of the following statements is not correct?', '~molecules of ice, water and water vapour do not differ in the structure of their molecules~molecules of water vapour attract each other with forces far less than the forces of attraction between water molecules~water is less compressible than water vapour', '', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(89, '2019', 'The density P of a spherical ball of diameter d and mass m is given by', 'P = \\(\\frac{3m}{4 \\pi d^3}\\)~p = 4\\(\\pi md^3\\)~p = \\(\\frac{6m}{\\pi d^3}\\)~p = \\(\\frac{3m}{2 \\pi d^3}\\)', 'p = \\(\\frac{6m}{\\pi d^3}\\)', 'p = \\(\\frac{M}{V} = \\frac{M}{\\frac{4}{3} \\pi (\\frac{d}{\\pi})^3}\\)\n\n= \\(\\frac{6m}{\\pi d^3}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(90, '2019', 'A metal rod of density 7000 kgm-3 and cross-sectional area of 0.001257m2 has a mass of 1.76kg. Calculate its length.', '0.20m~0.25m~0.40m~0.50m', '0.20m', 'P = \\(\\frac{M}{AL}\\)\n\nL = \\(\\frac{M}{CA}\\)\n\n= \\(\\frac{1.76}{7000 \\times 0.001257}\\)\n\n= 0.2m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(91, '2019', 'The pressure in a liquid', 'is the same at all points in the liquid~decreases with depth~is the same in all directions at a given point~is equal to the atmospheric pressure', 'is the same in all directions at a given point', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(92, '2019', 'The property of a fluid that is used to determine its suitability as a lubricant is its', 'capillarity~viscocity~surface tension~relative density', 'viscocity', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(93, '2019', 'The area under a velocity-time graph represents', 'final velocity attained~distance covered~acceleration~workdone', 'distance covered', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(94, '2019', 'In the absence of gravitational force, the weight of the body is', 'its mass~zero~its density~its volume', 'zero', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(95, '2019', 'Which of the following propeties is not considered in choosing mercury as a thermomemetric liquid?', 'density~expansivity~conductivity~opacity', 'density', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(96, '2019', 'A stone of mass 300g is released from rest from the top of a bulding of height 100m. Determine the kinetic energy gained by the stone when it is a quarter way down from the point of release.[g = 10 ms-2]', '750.0J~225.0J~75.0J~22.5J', '75.0J', 'K.E = P.E = mgh \n\n= 0.3 x 10 x 100 - 0.3 x 10 x 75 \n\n= 75J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(97, '2019', 'A body of mass 120g placed at the 10cm mark on a uniform metre rule makes the rule settle horizontally on a fulcrum places at 35cm mark. Calculate the mass of the rule', '60g~80g~120g~200g', '200g', 'm = \\(\\frac{25 \\times 120}{15}\\)\n\n= 200g', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(98, '2019', 'Two simple pendulum A and B of equal lengths and of masses 5g and 20g respectively are located in the same environment. The periods TA and TB of their respective oscillations are related by the equations', 'TA = 4TB~TA = \\(\\frac{1}{4} T_B\\)~TA = TB~TA = 5TB', 'TA = TB', 'The period of a simple pendulum is dependent on the frequency. It is also dependent on the length of the pendulum but not the mass. Since the two pendulums have equal length, then their periods are equal as well.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(99, '2019', 'An object of mass 5.0 kg moves with a velocity of 10ms-1. Calculate its momentum.', '50.0 kgms-1~15.0 kgms-1~2.0 kgms-1~0.5 kgms-1', '50.0 kgms-1', 'Momentum = MV \n\n= 5 x 10 = 50', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(100, '2019', 'A coin is pushed from the edge of a laboratory bench with a horizontal velocity of 15.0 ms-1. If the height of the bench from the floor is 1.5m, calculate the distance from the foot of the bench to the point of impact with the floor [g = 10ms-2]', '0.75m~2.25m~8.22m~15.00m', '8.22m', 'S = U\\(\\sqrt{\\frac{2h}{g}}\\)\n\n= 15\\(\\sqrt{\\frac{2 \\times 1.5}{10}}\\)\n\n= 8.22m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(101, '2019', 'Which of the following statements correctly defines a simple machine? A device', 'that can produce electric current~which can only carry people from one place to another~with which work can be done easily~which changes the state of rest or of uniform motion of an object', 'with which work can be done easily', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(102, '2019', 'The radius of a wheel is 30.0 cm and that of its axle is 6.0cm. Calculate the effort required to lift a load of 120.0N using this machine. Assuming 100% efficiency', '600.0N~40.0N~24.0N~20.0N', '24.0N', 'V.R = \\(\\frac{R}{r} = \\frac{30}{6} = 5\\)\n\n\\(\\gamma = \\frac{M.A}{V.R} \\times \\frac{100}{1} \\)\n\nM.A = \\(\\frac{100 \\times 5}{100} = 5\\)\n\nEffort = \\(\\frac{L}{M.A} = \\frac{120}{5}\\)\n\n= 24N', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(103, '2019', 'A hypsometer is used for determining', 'steam point~relative humidity~ice point~relative density', 'steam point', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(104, '2019', 'Which of the following equations shows how how the linear expansivity (\\(\\alpha\\)) and the cubic expansivity (\\(\\gamma\\)) of a material are related?', '\\(\\gamma = \\alpha\\)~\\(\\gamma = 1 - \\alpha\\)~\\(\\gamma = 2 \\alpha\\)~\\(\\gamma = 3 \\alpha\\)', '\\(\\gamma = 3 \\alpha\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(105, '2019', 'Which of the following statements about anomalous expansion of water are correct? i. There is contraction between 0oC and 4oC. ii. There is expansion between 0oC and 100oC. iii. The volume is minimum at 4oC. iv. The volume is maximum at 4oC', 'i and ii only~ii and iii only~i and iii only~ii and iv only', 'i and iii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(106, '2019', 'Which of the following assumptions is not valid for an ideal gas ?', 'molecules of a particular gas are identical~molecules moves freely throughout the volume of the container~force of attraction between molecules is negligible~molecules move at constant speed between collisions', 'force of attraction between molecules is negligible', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(107, '2019', 'A body is pulled over a distance of 500m by a force of 20N. If the power developed is o.4 kW, calculate the time interval during which the force is applied', '0.2s~2.5s~25.0s~250.0s', '25.0s', 't = \\(\\frac{fs}{p} = \\frac{20 \\times 500}{0.4 \\times 1000} = 25s\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(108, '2019', 'A metal of mass 200g at a temperature of 100oC is placed in 100g of water at 25oC in a container of negligible heat capacity. If the final steady temperature is 30oC, calculate the specific heat capacity of the metal. [specific heat capacity of the water is 4200 Jkg-1 K-1]', '150 Jkg-1K-1~300 Jkg-1K-1~320 Jkg-1K-1~1960 Jkg-1K-1', '150 Jkg-1K-1', 'MC\\(\\theta\\)metal = MC\\(\\theta _{water}\\) \n\n0.2 x C x 70 = 0.1 x 4200 x 5\n\nC = 150', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(109, '2019', 'Ether produces a cooling effect when it is poured on the hand because it has', 'low conductivity~high conductivity~high latent heat of vaporization~low latent heat of vaporization', 'high latent heat of vaporization', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(110, '2019', 'Which of the following statements about the image formed by a plane mirror is not correct?', 'it is laterally inverted~it has unit magnifiation~it is formed by actual intersection of rays~its distance from the mirror is equal to that of the object from the mirror', 'it is formed by actual intersection of rays', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(111, '2019', 'The image formed by a convex mirror is always', 'real, erect and diminished~real, inverted and diminished~virtual, inverted and diminished~virtual, erect and diminshed', 'virtual, erect and diminshed', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(112, '2019', 'A ray undergoes a minimum deviation at 40o when it is incident on equilateral triangular glass prism. Calculate the refractive index of the prism', '1.48~1.5~1.53~1.67', '1.53', 'n = \\(\\frac{\\sin \\frac{1}{2} (dm + A)}{\\sin \\frac{1}{2} A}\\)\n\n= \\(\\frac{\\sin \\frac{1}{2} (40 + 60)}{\\sin \\frac{1}{2} \\times 60}\\)\n\n= 1.532', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(113, '2019', 'Total internal reflection occurs in an optical prism when light rays', 'travel from the prism into an optically denser medium~are incident in the prism at an angle greater than the critical angle~are incident normally in the prism~travel from the prism to the air', 'are incident in the prism at an angle greater than the critical angle', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1);
INSERT INTO `exam_simulation` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`, `status`) VALUES
(114, '2019', 'The speed of light in a certain medium is V while its speed in a vacuum is C. The absolute refractive index of the medium is', 'C + V~\\(\\frac{C}{V}\\)~\\(\\frac{V}{C}\\)~C - V', '\\(\\frac{C}{V}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(115, '2019', 'An object is placed 20.0cm in front of a converging lens of focal length 15.0cm. Calculate its image distance', '1.3cm~8.6cm~35.0cm~60.0cm', '60.0cm', '\\(\\frac{1}{v} = \\frac{1}{f} - \\frac{1}{U}\\)\n\n\\(\\frac{1}{15} - \\frac{1}{20} = 60cm\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(116, '2019', 'Presbyopia is a defect of the eye resulting from', 'weak ciliary muscles~short eyeball~loss of sphericity of the lens~long eyeball', 'weak ciliary muscles', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(117, '2019', 'The focal length of the eye-piece of an astronomical telescope is f1, while the focal length of the object is f2. Fro normal adjustment, the angular magnification is given by', '\\(\\frac{f_2}{f_1}\\)~1 - \\(\\frac{f_2}{f_1}\\)~\\(\\frac{f_2}{f_1}\\) - 1~\\(\\frac{f_1}{f_2}\\)', '\\(\\frac{f_2}{f_1}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(118, '2019', 'two sound waves have frequencies of 12Hz and 10Hz. Calculate their beats period', '0.5s~1.0s~1.2s~2.0s', '0.5s', '\\(f_1 - f_2 = \\frac{1}{T}\\)\n\n12 - 10 = \\(\\frac{1}{2}\\)\n\n= 0.5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(119, '2019', 'The main difference between echo and reverberation is that', 'reverberation is reflected sound while echo is refracted sound~the time interval between incident sound and reflecte sound is shorter for reverbration~the amplitude of an echo is greater~reverberation is from acoustic speakers while echo comes from clifts', 'the time interval between incident sound and reflecte sound is shorter for reverbration', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(120, '2019', 'Which of the following statements about the electromagnetic waves is correct?', 'radio waves have longer frequencies than x-rays~x-rays have the longest wavelength~some of the waves travel at 3.0 x 108ms-1~white light occupies a region beyond ultraviolet rays', 'some of the waves travel at 3.0 x 108ms-1', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(121, '2018', 'The correct relationship between \"G\" and \"g\" in a gravitational field is given by the equation (Where the symbols have their usual meanings)', 'g = \\(\\frac{GM}{R}\\)~g = \\(\\frac{GM}{R^2}\\)~g = \\(\\frac{GM^2}{R}\\)~g = \\(\\frac{GM^2}{R^2}\\)', 'g = \\(\\frac{GM}{R^2}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(122, '2018', 'The capacitance of a parallel-plate capacitor', 'decreases when the seperation between the plate decreases~increases when the optential difference between the plates is increased~is greater without a dielectric material between the plates than with a dielectric~is greater with a dielectric between the plates than without a dielectric.', 'is greater with a dielectric between the plates than without a dielectric.', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(123, '2018', 'When the pointed end of an uncharged optical pin is brought near the cap cf a positively charged electroscope, it is observed that the gold', 'collapse slowly~vibrate~are not affected~diverge rapidly', 'collapse slowly', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(124, '2018', 'Which of the following substances does not conduct electricity?', 'graphite~glass~sulphuric acid~table salt solution', 'glass', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(125, '2018', 'The unit of capacitance is', 'farad~coulomb~henry~ohms', 'farad', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(126, '2018', 'An ammeter with a full scale deflection of 10mA has an internal resistance 0.5\\(\\Omega\\). calculate the resistance of the shunt required to adapt it to read up to 3A', '0.0167\\(\\Omega\\)~0.0130\\(\\Omega\\)~0.0250\\(\\Omega\\)~0.1000\\(\\Omega\\)', '0.0167\\(\\Omega\\)', '\\(R_2 = \\frac{I_1R_1}{I_2} = \\frac{0.01 \\times 5}{2.99}\\)\n\n= 0.0167', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(127, '2018', 'The resistivity, \\(\\mathit{P}\\), of a material of length l, cross-sectional area A, resistance R, is given by the equation', '\\(\\mathit{P} = \\frac{RA}{l}\\)~\\(\\mathit{P} = \\frac{l}{RA}\\)~\\(\\mathit{P} = \\frac{Rl}{A}\\)~\\(\\mathit{P} = \\frac{R}{Al}\\)', '\\(\\mathit{P} = \\frac{RA}{l}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(128, '2018', 'A wire of length 30cm is moved with a speed of 2ms-1 at right angles to a magnetic field of flux density 0.4T. calculate the emf induced in the wire', '0.15V~0.24V~2.70V~24.00V', '0.24V', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(129, '2018', 'Which of the following practices will lead to losses in electrical power transmission?', 'using transmission cables of large diameter~transmitting at high voltage and low current~transmitting at relatively low voltage and high current~using a set-up transformer at the production end', 'transmitting at relatively low voltage and high current', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(130, '2018', 'For photoelectric emission, the threshold frequency is the', 'maximum frequency of incident radiation that will eject elecrons~minimum fraquency of incident radiation required to eject elecrons~frequency which results in the emission of the greater number of electrons~fraquency whch impacts greatest kinetic energy to emitte electrons', 'minimum fraquency of incident radiation required to eject elecrons', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(131, '2018', 'Which of the following properties is not applicable to X-rays? They', 'travel in straight lines~travel with the speed of light~are deflected by magnetic field~affect photographic films', 'are deflected by magnetic field', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(132, '2018', 'Uranium-234 disintegrated to form Thorium-230 by emitting', 'alpha particles~gamma rays~beta negative rays~beta positive rays', 'alpha particles', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(133, '2018', 'The change in mass of fuel during a nuclear reaction is 2.0 x 10-27 kg. Calculate the amount of energy released. (Speed of light = 2.0 x 108ms-1)', '1.8 x 10-10J~9.0 x 10-11J~6.0 x 10-19J~1.2 x 10-45J', '1.8 x 10-10J', 'Q = \\(\\Delta MC^2\\) \n\n= 2 x 10-27(3 x 10)2\n\n= 1.8 x 10-10J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(134, '2018', 'Nuclear fusion is not used as a source of enegy because', 'very high temperature is needed for the reaction~the fuel for the reaction is not easy to obtain~less energy is released~the reaction is too slow', 'very high temperature is needed for the reaction', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(135, '2018', 'Using the circuit diagram above. Calculate the total charge in the circuit', '80\\(\\mu C\\)~35\\(\\mu C\\)~20\\(\\mu C\\)~16\\(\\mu C\\)', '16\\(\\mu C\\)', 'C - \\(C_1 + C_2 = 2 + 6 = \\mu F\\)\n\n\\(\\frac{1}{C} = \\frac{1}{C_1} + \\frac{1}{C_1} + \\frac{1}{C_2} = \\frac{1}{8} + \\frac{1}{2}\\)\n\nC = \\(\\frac{8}{5 \\mu F}\\)\n\nQ = CV \n\n= \\(\\frac{8}{5} \\times 10 = 16\\mu C\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(136, '2018', 'Using the circuit diagram above. Calculate the potential difference across the capacitors in parallel', '10.0V~8.0V~6.7V~2.0V', '2.0V', 'V = \\(\\frac{Q}{V} = \\frac{16}{8} = 2\\Gamma\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(137, '2018', 'The derived unit of pressure can be expressed as', 'kgms-2~kg m-1s-2~kg m-2s-2~kg m-1s2', 'kg m-1s-2', 'Pressure = \\(\\frac{Force}{Area}\\)\nForce = mass x acceleration\n\\(\\therefore\\) Pressure = \\(\\frac{mass \\times acceleration}{Area}\\)\n= \\(\\frac{kg \\times m \\times s^{-2}}{m^2}\\)\n= kg m\\(^{-1}\\) s\\(^{-2}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(138, '2018', 'The diagram above illustrates trapped air in a syringe placed in water that is gradually heated. It is observed that the piston rises as the temperature of the water rises. Which of the following statements explains this observation?', 'frequency of collision of trapped air molecules with walls of the syringe is more~molecules of trapped air expands more~speed of the trapped air molecules decreases~number of molecules of trapped air increases', 'molecules of trapped air expands more', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(139, '2018', 'Which of the following devices is used to determine the relative density of an acid?', 'manometer~hydrometer~hypsometer~hygrometer', 'hydrometer', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(140, '2018', 'A block of wood of density 0.6 gcm\\(^{-3}\\), weighing 3.06N in air, floats freely in a liquid of density 0.9 gcm\\(^{-3}\\). Calculate volume of the portion immersed (g = 10ms\\(^{-2}\\))', '510cm3~340cm3~254cm3~170cm3', '340cm3', 'V = \\(\\frac{M}{D}\\)\n\n= \\(\\frac{3.06}{10} \\times \\frac{1000}{0.9} = 340\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(141, '2018', 'A metal ball of weight W falls through a column of glycerine of viscosity V. If the ball experiences an upthrust U and terminal velocity', 'W ~W = U + V~W = U - V~W ', 'W = U + V', 'When terminal velocity is attained, The equation of motion becomes\nmg - V - U = 0\n\\(\\therefore\\) mg = W = U + V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(142, '2018', 'The movement of fluid up or down a narrow tube is', 'osmosis~brownian motion~capillarity~diffusion', 'capillarity', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(143, '2018', 'Which of the following substances is the most volatile at room temperature?', 'water~diesel~petrol~kerosine', 'petrol', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(144, '2018', 'A bird flies at 10ms\\(^{-1}\\) for 3s, 15ms\\(^{-1}\\) for 3s and 20 ms\\(^{-1}\\) for 4s. Calculate the bird\'s average speed', '4.5 ms-1~15.0 ms-1~15.5 ms-1~51.7 ms-1', '15.5 ms-1', 'Av. speed = \\(\\frac{3 \\times 15 + 3 \\times 10 + 4 \\times 20}{3 + 3 + 4}\\)\n\n= 15.5 ms\\(^{-1}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(145, '2018', 'The time of flight for a projectile motion is given by the expression', '\\(\\frac{U sin \\theta}{g}\\)~\\(\\frac{U sin \\theta}{2g}\\)~\\(\\frac{2U sin \\theta}{g}\\)~\\(\\frac{U sin 2\\theta}{g}\\)', '\\(\\frac{2U sin \\theta}{g}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(146, '2018', 'An object is dropped from the top of a tower. If it takes 4s for it to reach the ground, calculate the height of the tower.(g = 10 ms-2, ignore air resistance)', '20m~40m~80m~160m', '80m', 'H = \\(\\frac{1}{2} gt^2\\)\n\n\\(\\frac{1}{2} \\times 10 \\times 4^2 = 80\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(147, '2018', 'When a body is slightly tilted, it is found that its centre of gravity is slightly raised. What is the state of equilibrium of the body?', 'unstable~stable~neutral~cannot be determined', 'stable', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(148, '2018', 'A simple pendulum makes 50 oscillations in one minute. Determine its period of oscillation', '0.02s~0.83s~1.20s~50.00s', '1.20s', 'T = \\(\\frac{t}{n} = \\frac{60}{50} = 1.2\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(149, '2018', 'The tendency for a stationary body to continue to remain at rest when a force is applied to it is known as', 'friction~impulse~inertia~momentum', 'inertia', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(150, '2018', 'A resultant force of magnitude 15N acts on a body of mass 250g. Calculate the magnitude of the acceleration', '0.06 ms-2~3.75ms-2~16.67ms-2~60.00ms-2', '60.00ms-2', 'a = \\(\\frac{F}{M} = \\frac{15}{0.25} = 60\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(151, '2018', 'A girl stands on a scale in a lift. If the reading on the scale is less than her weight, then the lift is moving', 'upward at uniform speed~upward with uniform acceleration~downward with uniform speed~downward with uniform acceleration', 'downward with uniform acceleration', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(152, '2018', 'The S.I unit of heat is', 'joule~kelvin~watt~ampere', 'joule', 'Heat is a form of energy (heat energy). The S.I unit of energy generally is Joules (J).', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(153, '2018', 'A body is pulled through a distance of 500m by a force of 20N. If the power developed is 0.4kW, calculate the time for which the force acts', '250.0s~25.0s~2.5s~0.5s', '25.0s', 'Force x Distance = Power x Time\nTime = \\(\\frac{Force \\times Distance}{Power}\\)\n= \\(\\frac{20 \\times 500}{0.4 \\times 1000}\\)\n= 25.0s', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(154, '2018', 'A metal sheet of area 100cm\\(^2\\) was heated through 70', '100.06 cm2~100.12cm2~100.24cm2~100.36cm2', '100.24cm2', 'Formula', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(155, '2018', 'The thermopile is a device for detecting', 'radioactive radiations~radiant energy~x-rays~the presence of electrons', 'radiant energy', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(156, '2018', 'In the formation of sea breeze. wind blows from', 'sky to land~sea to sky~land to sea~sea to land', 'sea to land', 'A sea breeze describes a wind that blows from the ocean (sea) inland towards land.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(157, '2018', 'A piece of copper of mass 20g at a temperature of 110', '0.37g~0.60g~2.40g~2.70g', '2.70g', 'Mice = \\(\\frac{MC}{\\theta}\\)\n\n= \\(\\frac{20 \\times 0.4 \\times 110}{330}', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(158, '2018', 'Which of the following factors decreases the rate of evaporation of a liquid?', 'increase in pressure over the liquid~lowering the boiling point~decreasing in humidity~wind', 'increase in pressure over the liquid', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(159, '2018', 'When two waves are superimposed on each other, the following occurrences are possible, except', 'nodal lins~anti nodal lines~stationary waves~dispersion', 'dispersion', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(160, '2018', 'Which of the following properties of waves is exclusive to transverse waves?', 'reflection~interference~diffraction~polarization', 'polarization', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(161, '2018', 'An object of height 2.5cm is places 20cm from a convex mirror of focal length 10cm. Calculate the height of its image.', '2.5 cm~3.0cm~5.0cm~25.0cm', '2.5 cm', '\\(\\frac{1}{v} = \\frac{1}{f} - \\frac{1}{u}\\)\n= \\(\\frac{1}{10} - \\frac{1}{2} = \\frac{1}{20}\\)\nv = 20\n\nbut h\\(_i\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(162, '2018', 'A ray of light passes from air to water to glass to air. Given that the refractive index for light passing from air to water is \\(\\frac{4}{3}\\) and air to glass is \\(\\frac{3}{2}\\), calculate the refractive index of glass relative to water', '0.5~0.67~0.75~1.13', '1.13', '\\(_{g} \\eta _{w} = \\frac{ _g', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(163, '2018', 'An object is placed at a point X between the focal point F and the optical centre C of a diverging lens. If F is the focal point on the other side of the lens, the image of the object is formed between', 'F and X~X and C~C and F~F and 2F', 'X and C', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(164, '2018', 'An object is placed 10cm from a converging lens of foal length 15cm. Calculate the magnification of the image formed', '3~1.5~0.6~0.3', '3', '\\(\\frac{1}{f} = \\frac{1}{v} + \\frac{1}{u}\\)\n\\(\\frac{1}{v} = \\frac{1}{f} - \\frac{1}{u}\\)\n\n\\(\\frac{1}{15} - \\frac{1}{10} = \\frac{2 -', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(165, '2018', 'A telescope is said to be in normal adjustment when the', 'focal length of he objective is greater than that of the eyepiece~focal length of the eyepiece is greater than that of the objective~focal length of the eyepiece is equal to that of the objective~objective focal point coincides wih that of the eyepiece', 'objective focal point coincides wih that of the eyepiece', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(166, '2018', 'The sound heard by a person after the reflection of the sound generated by him is called', 'reverberation~resonance~echo~audibility', 'echo', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(167, '2018', 'Which of the following sets of coloured light is', 'i and ii only~ii and iii only~iv only~i, ii and iv only', 'iv only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(168, '2018', 'When two like charges are brought together, the potential energy of the system formed will', 'increase because work is done against the field~increase because work is done by the field~decrease because work is done by the field~decrease because work is done against the field', 'decrease because work is done against the field', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(169, '2018', 'Two capacitors, each of capacitance 2\\(\\mu\\)F', '6.0 x 10-5C~1.2 x 10-4C~2.4 x 10-4C~4.8 x 10-4C', '2.4 x 10-4C', 'C = \\(C_1 + C_2 = 2 + 2 = 4 \\mu F\\)\n\nbut Q = CV\n\n= 4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(170, '2018', 'Which of the following properties is an advantage of lead-acid accumulator over an alkaline accumulator?', 'possesses low internal resistance~can be recharges~has shorter life span~possesses high e.m.f', 'possesses high e.m.f', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(171, '2018', 'Six dry cells each of e.m.f. 2.0 and internal resistance of 1.0\\(\\Omega\\) are connected in parallel across a load of 3.0\\(\\Omega\\). Calculate the effective current in the circuit.', '0.63A~0.50A~0.31A~0.22A', '0.63A', 'I = \\(\\frac{f}{n} = \\frac{1}{6 - 2}\\)\n\nI = \\(\\frac{v}{R + r} = \\frac{2}{3} + \\frac{1}{6} = 0.63\\)A', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(172, '2018', 'Two similar cells are used to light two similar lamps as illustrated in the diagrams above. In which of the circuit diagrams are the lamps brightest?', 'P~Q~R~S', 'P', 'The determinant of the brightness of a bulb is the power (watts) of the circuit.\nRecall that Power (P) = \\(\\frac{V^2}{R}\\).\nSince the resistance is to be used as a divisor, it means the smaller the resistance, the greater the power.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(173, '2018', 'A 120\\(\\Omega\\) resistor dissipates 8 kJ of heat in 20s. Calculate the current through the resistor', '5.8A~6.9A~30.0A~33.3A', '5.8A', 'Q = I2Rt\n\nI = \\(\\sqrt{\\frac{Q}{Rt}}\\)\n\n= \\(\\sqrt{\\frac{8000}{12 \\times 20}}\\)\n\n= 5.8', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(174, '2018', 'The magnetic relay is a device used for', 'timing in sports~storing magnetic field~readin the magnitude of magnetic flux~controlling another circuit carrying larger current', 'controlling another circuit carrying larger current', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(175, '2018', 'the core of a transformer is usually laminated in order to', 'reduce magnetic leakage~reduce eddy current~prevent vibration of the transformer~make magnetic reversal in the core much easier', 'reduce eddy current', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(176, '2018', 'Which of the following modes is the most economical method of transmitting electrical power over long distances?', 'alternating current at low voltage and high current~alternating current at high voltage and high current~alternating current at high voltage and low current~direct current at low voltage and high current', 'alternating current at high voltage and low current', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(177, '2018', 'An inductor is connected to a 24V, 50Hz mains supply. If the current through the inductor is 1.5A, calculate the inductance of the inductor (\\(\\pi = \\frac{22}{7}\\))', '8.0 x 102H~7.5 x 10oH~1.6 x 10oH~5.1 x 10-2H', '5.1 x 10-2H', '\\(X_L = \\frac{V}{I} = \\frac{24}{1.5} = 16\\Omega\\)\n\nL = \\(\\frac{XL}{2 \\pi f} = \\frac{16}{2 \\pi 50}\\)\n\n= 0.05H', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(178, '2018', 'In a R-C circuit', 'Irms leads Vrms by 60o~Irms slags Vrms by 60o~Vrms lags Irms by 90o~Vrms leads Irms by 90o', 'Vrms lags Irms by 90o', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(179, '2018', 'An atom in an excited state is one whose', 'potential energy is minimum~potential energy is maximum~electron are in the conduction band~electron have moved to higher energy level', 'electron have moved to higher energy level', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(180, '2018', 'A metal with a work function of 3.0ev is irradiated with ultraviolet light of energy 4.0 ev. The kinetic energy of the ejected electron is', '1.0eV~3.0eV~4.0eV~7.0eV', '1.0eV', 'K.E = hf - Wo\n\n= 4 - 3 = 1eV', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(181, '2017', 'Which of the following statements about X-rays is correct? X-rays', 'are produced when a metal surface is irradiated with ultraviolet light~are produced when a metal target is used to block fast miving electrons~have long wavelengths and are therefoer very penetrating~are not part of the electromagnetic spectrum', 'are produced when a metal target is used to block fast miving electrons', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(182, '2017', 'Which of the following arrangements of radiations is in the order of decreasing penetrating power?', '\\(\\alpha, \\beta, \\gamma\\)~\\(\\alpha, \\gamma, \\beta\\)~\\(\\gamma, \\beta, \\alpha\\)~\\(\\beta, \\gamma, \\alpha\\)', '\\(\\gamma, \\beta, \\alpha\\)', 'Thanks for your contribution, corrections have been made.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(183, '2017', 'Which of the following radiations emitted in radioactive decay has momentum, a fairly high penetrating power and is deflected by a magnet?', 'alpha particles~beta particle~gamma radiation ~X-radiation', 'beta particle', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(184, '2017', 'The rising of a liquid in an open and ended glass tube of narrow bore is', 'osmosis~adhesion~capillarity~surface tension', 'capillarity', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(185, '2017', 'Which of the following units is equivalent to the watt?', 'kgms-2~kgm2s-3~kgm2s-2~kgm2s-1', 'kgm2s-3', '\\(Power = \\frac{\\text{Work done}}{time}\\)\n= \\(\\frac{Force \\times distance}{time}\\)\n= \\(\\frac{mass \\times acceleration \\times distance}{time}\\)\n= \\(\\frac{kg \\times m \\times m}{s^{2} \\times s}\\)\n= \\(kgm^{2} s^{-3}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(186, '2017', 'Which of the following statements about pressure in a liquid is correct?', 'the pressure in a liquid increases with depth~the higher the density of a liquid, the lower the pressure it exerts~pressure in liquid act only in a direction perpendicular to the sides of the containing vessel~pressure is independent of the acceleration due to gravity', 'the pressure in a liquid increases with depth', 'At different depths, the pressure of a liquid differs.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(187, '2017', 'Solid friction, like viscosity is', 'independent of the surface area in contact~independent of the relative motion between layers~dependent on normal reaction~in opposition to motion', 'in opposition to motion', 'The force acting on a body due to the viscous resistance of the surrounding fluid is called the drag force and it acts in the direction opposite to the direction of motion. So also does friction.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(188, '2017', 'The slope of a linear distance-times graph represents', 'acceleration~displacement~speed~velocity', 'speed', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(189, '2017', 'A body of mass 2kg is released from rest on a plane inclined at an angle of 60', '3.1ms-2~5.2ms-2~6.0ms-2~8.7ms-2', '8.7ms-2', 'a = g sin \\(\\theta\\)\n\n= 10 sin 60\n\n= 8.7 ms\\(^{-2}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(190, '2017', 'The total area under a force-velocity graph represents', 'energy~momentum~power~pressure', 'power', 'Power = Force x Velocity.\nTherefore, the area under the force- velocity graph gives Power.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(191, '2017', 'A body of mass 20g projected vertically upwards in vacuum returns to the point of projection after 1.2s. [g = 10ms\\(^{-2}\\)]. Calculate the speed of projection', '1.2ms-1~6.0ms-1~12.0ms-1~0.6ms-1', '6.0ms-1', 'V = u - gt\n\nu = v + gt\n\n= 0 + 10 x 0.6\n\n= 6ms\\(^{-1}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(192, '2017', 'A body of mass 20g projected vertically upwards in vacuum returns to the point of projection after 1.2s. [g = 10ms-2]. Determine the potential energy of the body at the maximum height of its motion', '0.36J~0.72J~360.00J~720.00J', '0.36J', 'P.E at max = K.E on projection \n\n= \\(\\frac{1}{2}\\)mv2 = \\(\\frac{1}{2} \\times 0.02 \\times 6^2 = 0.36J\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(193, '2017', 'The maximum displacement on either side of the equilibrium position of an object in simple harmonic motion represents', 'period~amplitude~wavelength~frequency', 'amplitude', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(194, '2017', 'From Newton\'s first law of motion,', 'a body can only undergo translational motion~once a body remains at rest no force acts on it~the net force acting in uniform linear motion is zero~a body\'s inertia is its weight', 'the net force acting in uniform linear motion is zero', 'The key point of this law', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(195, '2017', 'A body of mass 11kg is suspended from a ceiling fan by an aluminum wire of length 2m and diameter 2mm. Calculate the elastic energy stored in the wire [Young\'s modulus of aluminum is 7.0 x 1010Nm-2, g = 10ms-2, \\(\\pi\\) = 3.142]', '1.1 x 10-1J~5.5 x 10-2J~1.1 x 10-4J~5.5 x 10-8J', '5.5 x 10-2J', 'e = \\(\\frac{4FI}{Y \\pi d^2} = \\frac{4 \\times 11 \\times 10 \\times 2}{7 \\times 10^3 \\times 3.14(2 \\times 10^{-2})^2}\\)\n\n= 0.001m\n\nE = \\(\\frac{1}{2} Fe = \\frac{1}{2} \\times 110 \\times 0.001\\)\n\n= 5.5 x 10-2J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(196, '2017', 'The velocity ratio of an inclined plane', 'increases with increase in the angle of inclination~increases with decrease in the angle of inclination~decreases with decrease in the angle of inclination~is independent of the angle of inclination', 'increases with increase in the angle of inclination', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(197, '2017', 'Which of the following types of thermometer is used for the calibration of other thermometers?', 'liqud-in-glass thermometer~constant volume gas thermometer~optical pyrometer~thermocouple', 'constant volume gas thermometer', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(198, '2017', 'The magnitude of the expansion or contraction of a substance depends on the i. temperature change ii. nature of the substance iii. size of the substance. Which of the statements above are correct?', 'i and ii only~ii and iii only~i and iii only~i, ii and iii', 'i and ii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(199, '2017', 'Highly polished silvery surfaces are', 'poor absorbers and poor emitters of radiation~poor absorbers and good emitters of radiation~good absorbers and poor emitters of radiation~good absorbers and good emitters of radiation', 'poor absorbers and good emitters of radiation', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(200, '2017', 'The volume of a given mass of gas at 27oC and 800 mmHg is 76cm2. Calculate its volume at s.t.p', '100.0 cm3~72.8 cm3~60.0 cm3~36.4 cm3', '72.8 cm3', '\\(V_2 = \\frac{P_1V_1T_2}{P_2T_1} = \\frac{800 \\times 76 \\times 273}{760 \\times 300}\\)\n\n= 72.8cm3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(201, '2017', 'Ice of mass 10g at 5', '105J~3255J~3465J~16821J', '3465J', 'Q = ML + MC\\(\\theta\\)\n\n= 10 x 335 + 10 x 2.1 x 5\n\n= 3465J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(202, '2017', 'An electric heater has a resistance of 50\\(\\Omega\\). When it is immersed in water and connected to mains source, it draws a current of 4.0A. Calculate the heat gained by the water if the heater is switched on for 2 minutes, assuming no heat losses to the surroundings', '4200J~1600J~24000J~96000J', '96000J', 'Q = I2RT\n\n= 42 x 50 x 2 x 60\n\n= 96000J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(203, '2017', 'When salt is dissolved in water, the freezing point of the water', 'increases~decreases~remains the same~increases and later decrease', 'decreases', 'The salt in the water (same for any other impurities)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(204, '2017', 'The equation of a certain progressive transverse wave is y = 2 sin 2 \\(\\pi ( \\frac{t}{0.01} - \\frac{x}{30})\\), where x and y are in cm and t in seconds. Calculate the period of the wave.', '0.001s~0.010s~10.000s~100.000s', '0.010s', 'Compare', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(205, '2017', 'At which position should an object be placed in front of a concave mirror in order to obtain an image which is of the same size as the object?', 'at the centre of curvature~at the principal focus~between the pole and principal focus~between the centre of curvature and principal focus', 'at the centre of curvature', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(206, '2017', 'Images formed by a convex mirror are always', 'magnified~behind the mirror~real~inverted', 'behind the mirror', 'Convex mirrors always form virtual images, which appear behind the mirror.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(207, '2017', 'The refractive index of a material is 1.5. Calculate the critical angle at the glass-air interface', '19o~21o~39o~42o', '42o', 'Sin C = \\(\\frac{1}{\\eta} = \\frac{1}{1.5} = 0.6667\\)\n\nC = sin\\(^{-1}\\) 0.6667\n\n= 42', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(208, '2017', 'A diverging lens of focal length 30cm produces an image 20cm from the lens. Determine the object distance', '10cm~12cm~50cm~60cm', '60cm', 'Lens formula', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(209, '2017', 'Which of the following statements about the Galilean telescope is not correct?', 'the final image is inverted~it is shorter than terrestial telescope~the final image is erect~it has a small field of view', 'the final image is inverted', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(210, '2017', 'Which of the following radiations has it\'s frequency lower than that of infrared radiation?', 'Utra-violet rays~gamma rays~x-rays~radio waves', 'radio waves', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(211, '2017', 'A string under tension produces a note of frequency 14Hz. Determine the frequency when the tension is quadrupled.', '14Hz~18Hz~28Hz~56Hz', '28Hz', 'The formula for the frequency in a stringed instrument ', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(212, '2017', 'Which of the following statements about waves in pipes is correct?', 'for open pipes, there is only one end correction to be accounted for~for closed pipes, there are two end corrections to be accounted for~only odd harmonics are possible in closed pipes~all harmonics are possible in closed pipes', 'only odd harmonics are possible in closed pipes', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(213, '2017', 'When a person holds a negatively charges metal rod and stands bare-footed on the ground, how will the charges leak?', 'negative charges flows to the ground through the person\'s body~positive charges flow from the ground through his body to neutralize the negative charges~positive charges in the air neutralizes the negative charges the person is holding~negative charges will leak through the air', 'negative charges flows to the ground through the person\'s body', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(214, '2017', 'A charge of 2.0 x 10\\(^{-5}\\) C experiences a force of 80N in a uniform electric field. Calculate the magnitude of the electric field intensity', '8.0 x 106 NC-1~4.0 x 106 NC-1~4.0 x 104 NC-1~2.0 x 104 NC-1', '4.0 x 106 NC-1', 'E = \\(\\frac{F}{Q} = \\frac{80}{2 \\times 10^{-5}}\\)\n\n= 4 x 10\\(^6\\) NC\\(^{-1}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(215, '2017', 'A potential difference of 12V is applied across the ends of a 6\\(\\Omega\\) resistor for 10 minutes. Determine the quantity of heat generated', '720J~1200J~14400J~43200J', '14400J', 'Q = \\(\\frac{V^2 t}{R}\n= \\frac{12^2 \\times 10 \\times 60}{6}\\)\n\n= 14400J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(216, '2017', 'Which of the following instruments is used to determine the accurate value of the electromotive force of a cell?', 'voltmeter~meterbridge~voltameter~potentiometer', 'potentiometer', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(217, '2017', 'The capacitance of parallel plates capacitors varies', 'inversely as the square of the distance between the plates~directly as the square of the distance between the plates~inversely as the distance between the plates~directly as the distance between the plate', 'inversely as the square of the distance between the plates', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(218, '2017', 'Which of the following devices does not makes use of eddy current for its action? A', 'galvanometer~speedometer~induction furnace~speedometer', 'galvanometer', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(219, '2017', 'A coil of inductance 0.12 H and resistance 4\\(\\Omega\\), is connected across a 240V, 50Hz supply. Calculate the current through it. [\\(\\pi\\) = 3.142]', '6.3A~33.3A~37.2A~40.0A', '6.3A', 'XL = \\(2\\pi f L\\)\n\n= = 2 x 3.142 x 50 x 0.12\n\n= 37.68\\(\\Omega\\)\n\nZ = \\(\\sqrt{R^2 + X_L^2} = \\sqrt{4^2 + 37.68^2}\\)\n\nI = \\(\\frac{V}{z} = \\frac{240}{37.89}\\)\n\n= 6.3A', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(220, '2017', 'The work function of a metal is 2.56 x 10-19J. Calculate the frequency of a photon whose energy is required to eject from the metal an electron with kinetic energy of 3.0ev. [1 eV = 1.6 x 10-19J, h = 6.6 x 10-34Js]', '5.56 x 1019Hz~1.66 x 1019Hz~1.12 x 1015Hz~8.42 x 1014Hz', '1.12 x 1015Hz', 'F = \\(\\frac{K.E + Wo}{h}\\)\n\n= \\(\\frac{3.0 \\times 1.6 \\times 10^{-19} + 2.56 \\times 106{-19}}{6.6 \\times 106{-34}}\\)\n\n- 1.12 x 10-15HZ', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(221, '2017', 'The minimum energy required to cause photoelectric emission when the surface of a metal is irradiated with electromagnetic radiation of suitable frequency is called', 'critical energy~ionization energy~work function~planck\'s constant', 'work function', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(222, '2017', 'Which of the following particles are termed nucleons in a neutral atom?', 'protons and neutrons~neutrons and electrons~protons and electrons~protons, electrons and neutrons', 'protons and neutrons', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(223, '2017', 'Which of the following statements about the use of radioisotopes is not correct? They are used to', 'induce mutations in plants and animals to obtain new and improved varieties~trace the paths of metabolic processes in plants and animals~estmate the age of rocks~locate broken bones', 'induce mutations in plants and animals to obtain new and improved varieties', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(224, '2017', 'Which of the following phenomena supports the theory that waves have a particle nature?', 'electron diffraction~photoelectric effect~diffraction of light~x-ray interference', 'diffraction of light', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(225, '2017', 'A block of wood of mass 5kg is pulled on a platform by a force of 40N as illustrated in the diagram above. If the frictional force, F experienced by the block is 12N, calculate the magnitude of the acceleration of the acceleration of the block', '2.4ms-2~5.6ms-2~8.0ms-2~2.4ms-2', '5.6ms-2', 'F + Ma = P\n\na = \\(\\frac{P - F}{m}\\)\n\n= \\(\\frac{40 - 12}{5} = 5.6ms^{-2}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(226, '2017', 'Four co-planar forces of magnitudes 10N, 17N, 6N and 20N act at point O as shown in the above diagram. Determine the magnitude of the resultant force', '53.N~21.0N~7.0N~5.0N', '5.0N', 'Vertical resultant = 10 - 6 = 4N\n\nHorizontal resultant = 20 - 17 = 3N\n\nR = \\(\\sqrt{3^2 + 4^2}\\)\n\n= 5N', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(227, '2017', 'The outlet of a bicycle pump is used to inflate a football as illustrated in the diagram above. Why does the pressure of the air inside the pump increases as the pump handle is slowly pushed downward at constant temperature?', 'momentum of the air molecules are increased~volume occupied by the molecules are increased~frequency of collision of the air molecules with the walls of the pump is increased~more air molecules are collidin with one another in the system', 'frequency of collision of the air molecules with the walls of the pump is increased', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(228, '2017', 'The diagram above illustrates a waveform. Which of the point on the waveform are in phase?', 'P and R~R and T~P and T~Q and S', 'Q and S', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(229, '2017', 'An electric circuit is connected as illustrated above. Determine the equivalent e.m.f and current flowing through the circuit respectively, neglecting the internal resistance of the cells', '2V, 1.0A~2V, 4.0A~6V, 0.3a~6V, 3.0a', '2V, 1.0A', 'cells in V = voltage of the cell \n\n= 2V\n\nI = \\(\\frac{v}{R} = \\frac{2}{3}\\)\n\n= 1A', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1);
INSERT INTO `exam_simulation` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`, `status`) VALUES
(230, '2017', 'A ball falling through a viscous liquid is acted upon by', 'upthrust only~upthrust and the ball\'s weight~the ball\'s weight and viscous force~upthrust, the ball\'s weight and viscous force', 'upthrust, the ball\'s weight and viscous force', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(231, '2017', 'An object of mass m moves with a uniform speed v round a circular path of radius r. If its angular speed is \\(\\omega\\), the magnitude of the centripetal force acting on it is', '\\(m \\omega^2 r\\)~\\(\\frac{mv^2}{r}\\)~\\(m \\omega r\\)~\\(\\frac{mv^2}{r^2}\\)', '\\(\\frac{mv^2}{r}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(232, '2017', 'When an elastic material is stretched by a force, the energy stored in it is', 'kinetic~potential~thermal~electrical', 'potential', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(233, '2017', 'When the linear momentum of a body is constant, the net force acting on it', 'is zero~increases~decreases~remains constant', 'is zero', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(234, '2017', 'If no net force acts on an object, the object maintains a state of rest or constant speed in a straight line. The above is a statement of Newton\'s', 'first law of motion~second law of motion~third law of motion~law of universal gravitation', 'first law of motion', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(235, '2017', 'Which of the following pairs of physical quantities is made up of vectors?', 'speed and displacement~mass and force~dislacement and acceleration~momentum and length', 'dislacement and acceleration', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(236, '2017', 'The knowledge of surface tension is applied in the following areas except in', 'manufacturing of rain coats~production of palm oil~floating of a needle on water~washing of plates with soapy water', 'production of palm oil', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(237, '2017', 'A body is projected vertically upwards with a speed of 10 ms-1 from a point 2m above the ground. Calculate the total time taken for the body to reach the ground. [g = 10ms-2]', '1.00s~2.00s~2.18s~3.00s', '2.00s', 'T = \\(\\frac{2u}{g} = \\frac{2 \\times 10}{10} = 2s\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(238, '2017', 'A car starts from rest and covers a distance of 40m in 10s. Calculate the magnitude of its acceleration', '0.25ms-2~0.80ms-2~3.20ms-2~4.00ms-2', '0.80ms-2', 'S = ut + \\(\\frac{1}{2} at^2\\)\n\n40 = 0 x 10 + \\(\\frac{1}{2}\\) x a x 102\n\n50a = 40\n\na = \\(\\frac{40}{50}\\)\n\n= 0.8ms-2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(239, '2017', 'The diagram above illustrates a uniform metre rule which is balanced on a pivot by some masses. Calculate the value of M', '500.0g~400.0g~44.4g~25.0g', '25.0g', 'clockwise moment = Anti-clock wise moment \n\n= M x 40 = 100 x 10\n\nM = \\(\\frac{1000}{40}\\)\n\n= 25g', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(240, '2017', 'The period of a simple pendulum X is 5s. What is the period of a simple pendulum Y which makes 50 vibrations in the same time it takes X to make 20 vibrations?', '12.5s~2.5s~2.0s~1.2s', '2.0s', 'It takes X 5s for 1 complete vibration.\n', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(241, '2016', 'Alcohol of mass 21g and density 0.7g cm-3 is mixed with 10g of water. Determine the density of the mixture [density of water = 1.0gcm-3]', '0.775gcm-3~0.875gcm-3~0.780gcm-3~0.880gcm-3', '0.775gcm-3', '\\(V_A = \\frac{M}{D} = \\frac{21}{0.7} = 30cm^3\\)\n\n\\(V_w = \\frac{M}{D} = \\frac{10}{1} = 10cm^3\\)\n\nVmixture = 30 + 10 = 40cm3\n\nMmixture = 21 + 10 = 31g\n\nDmixture = \\(\\frac{m}{v} = \\frac{31}{40} = 0.775\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(242, '2016', 'A device that converts mechanical energy into electrical energy is', 'a dynamo~an electric motor~an induction coil~a transformer', 'a dynamo', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(243, '2016', 'The S.I unit of power is', 'N~Pa~W~J', 'W', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(244, '2016', 'A screw-jack has the distance between its successive threads as P and the length of its tommy bar as r. Its velocity ratio is given by the expression', '\\(\\frac{2 \\pi r^2}{P}\\)~\\(\\frac{2 \\pi r}{P}\\)~\\(\\frac{2 \\pi}{rp}\\)~\\(\\frac{P}{2 \\pi r}\\)', '\\(\\frac{2 \\pi r}{P}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(245, '2016', 'Heat transfer by conduction is similar to wave motion because', 'there is increase in temperature~transfer of materials is involved~charged particles vibrates at right angles~no transfer of materials is involved', 'no transfer of materials is involved', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(246, '2016', 'The temperature at which the water vapor in the air saturates the air and begins to condense is known as', 'dew point~critical point~boiling point~triple point', 'dew point', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(247, '2016', 'The change of state from solid to liquid occurs', 'at constant temperature~when temperature is lower than the boiling point~when temperature is just near freezing point~when temperature is equal to the boiling point', 'at constant temperature', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(248, '2016', 'Which of the following types of thermometers can be used to measure a range of temperature from -50', 'i only~ii only~iii only~i and ii only', 'iii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(249, '2016', 'A body of mass M kg rests on a plane inclined at an angle \\(\\theta\\) to the horizontal. The component of the weight of the body parallel to the plane is', 'Mg sin \\(\\theta\\)~Mg cos \\(\\theta\\)~Mg tan \\(\\theta\\)~Mg sec \\(\\theta\\)', 'Mg sin \\(\\theta\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(250, '2016', 'A quantity of water at 20oC is mixed with another quantity of water at 70oC. The final steady temperature of the mixture is 40oC. Determine the ratio of the mass of the cold water to that of the hot water', '7~3~2~1', '3', 'Q = MC\\(\\theta\\)\n\nM = \\(\\frac{Q}{C\\theta}\\)\n\n\\(\\frac{Q}{20C}\\) ', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(251, '2016', 'The mass of an empty density bottle is 30g. When filled with a liquid, the mass reduces to 38g. Calculate the apparent cubic expansivity of the liquid', '6.25 x 10K-1~6.25 x 10-3K-1~2.50 x 10-3K-1~2.50 x 10-4K-1', '6.25 x 10-3K-1', 'Apparent cubic expansivity = \\(\\frac{\\text{mass of hot liquid expelled}}{\\text{mass of hot liquid left x temp. rise}}\\)\n\n= \\(\\frac{2}{8 \\times 40} = 0.00625\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(252, '2016', 'A car', '0.23hp~0.40hp~4.00hp~4.40hp', '4.00hp', 'P = FV = \\(\\frac{100 \\times 30}{1000} = 3 kW\\)\n\n\\(\\frac{3}{0.75} = 4hp\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(253, '2016', 'The quality of a note depends on its', 'frequency~pitch~overtones~amplitude', 'overtones', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(254, '2016', 'A transverse wave can be distinguished from a longitudinal wave by', 'diffraction~relection~refraction~polarization', 'polarization', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(255, '2016', 'Refraction of lights differs from reflection in that, in refraction i. at least two media are involved ii. there is a change in the direction of the ray iii. the speed of the ray changes. Which of the statements above is', 'i only~i ad ii only~ii and iii only~i and iii only', 'i ad ii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(256, '2016', 'Which of the following relations about the focal length fo of the objective and focal length fe of the eye piece of a compound is correct?', 'fo = fe~fo ~fo ~fe = 2fo', 'fo ', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(257, '2016', 'The functional difference between a lens and a mirror is that a lens', 'reflects a beam of light while a mirror refracts it~refracts a beam of light while a mirror reflects it~absorbs incident rays while a mirror transmit them~transmits incidents ray whle a mirror absorbs them', 'refracts a beam of light while a mirror reflects it', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(258, '2016', 'The diagram above illustrates an electromagnetic wave travelling with speed 3.0 x 108ms-1. Calculate the wave length of the wave', '0.05m~0.15m~0.16m~0.40m', '0.16m', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(259, '2016', 'A fish inside a pond appears to be at a depth of 1.5m when viewed vertically from above. The refractive index of the water in the pound is 1.3. Calculate the apparent displacement of the fish', '2.50m~1.95m~1.50m~0.45m', '0.45m', 'Real depth = n x apparent depth \n\n= 1.3 x 1.5 = 1.95m \n\nApparent displacement = 1.95 - 1.5 = 0.45m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(260, '2016', 'an observer hears an echo 1.26 seconds after blowing a whistle near a cliff. calculate the distance of the observer from the cliff. [speed of sound in air = 330ms-1]', '104.4m~207.9m~415.8m~523.8m', '207.9m', 'S = \\(\\frac{vt}{2} = \\frac{330 \\times 1.26}{2} = 207.9\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(261, '2016', 'An object is placed in front of two plane mirrors inclined at 60o to each other. Determine the number of the images formed', '2~3~5~7', '5', 'n = \\(\\frac{360}{\\theta}\\) - 1\n\n= \\(\\frac{360}{60} -1\\)\n\n= 6 - 1 = 5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(262, '2016', 'An ammeter can be adapted to measure potential difference by using a', 'shunt~multiplier~rheostat~resistance box', 'multiplier', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(263, '2016', 'The region around a magnet in which magnetic force can be expressed is known as', 'declination~flux density~field~flux', 'field', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(264, '2016', 'In an ac circuit when the supply voltage frequency is equal to the resonant frequency, the current', 'leads the supply voltge by 90o~lags behind the supply voltage by 90o~leads the supply voltage by 45o~is in phase with the supply voltage', 'is in phase with the supply voltage', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(265, '2016', 'The energy stored in a simple cell is', 'electrical~nuclear~thermal~chemical', 'chemical', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(266, '2016', 'Which of the following conditions occur at resonance in a series RLC circuit? i. Impedance equal resistance ii. Current is maximum iii. Reactance are maximum iv. Current and voltage are 90o out of phase', 'i and ii only~i and ii only~i, ii and iii only~i, ii, iii and iv', 'i and ii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(267, '2016', 'An electric motor converts', 'electrical energy to mechanical energy~mechanical energy to electrical energy~mechanical energy to chemical energy~electrical energy to thermal energy', 'electrical energy to mechanical energy', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(268, '2016', 'A 15 \\(\\mu F\\) capacitor is connected to a 240V, 50Hz ac. source. Calculate the reactance of the capacitance [\\(\\pi = 3.142\\)]', '16\\(\\Omega\\)~68\\(\\Omega\\)~106\\(\\Omega\\)~212\\(\\Omega\\)', '212\\(\\Omega\\)', '\\(X_c = \\frac{1}{2 \\pi fc}\\)\n\n= 2 x 3.142 x 50 x 15 x 10-6\n\n= 212.179\\(\\Omega\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(269, '2016', 'Two identical charges situated 20cm apart in vacuum repel each other with a force of 1.0N.Calculate the value of each other with a force of 1.0N. Calculate the value of each charge. [(14 \\(\\pi \\varepsilon_o)^{-1}\\) = 9 x 109Nm2C-2]', '21\\(\\mu C\\)~3.6\\(\\mu C\\)~4.0\\(\\mu C\\)~4.4\\(\\mu C\\)', '21\\(\\mu C\\)', 'F = \\(\\frac{Q^2}{4 \\pi \\varepsilon_o r^2}\\)\n\nI = 9 x 109 x \\(\\frac{Q^2}{0.2^2}\\)\n\nQ = \\(\\sqrt{\\frac{0.04}{9 \\times 10^9}}\\)\n\n= 2.11 x 10-6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(270, '2016', 'In the circuit diagram above, E is a battery of negligible internal resistance. If its emf is 9.0V. Calculate the current in the circuit ', '1.8A~1.0A~0.8A~0.3A', '1.0A', '\\(\\frac{1}{r} = \\frac{1}{r_1} + \\frac{1}{r_2}\\)\n\n= \\(\\frac{1}{5} + \\frac{1}{20}\\)\n\n= \\(\\frac{4 + 1}{20} = \\frac{5}{20}\\)\n\nr = \\(\\frac{20}{5}\\)\n\n= 4\\(\\Omega\\)\n\nR = R1 + R2\n\n= 5 + 4 \n\n= 9\\(\\Omega\\)\n\nbut V = IR \n\nI = \\(\\frac{V}{R} = \\frac{9}{9}\\)\n\n= 1A', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(271, '2016', 'A wire of length 100 cm has a resistance of 10\\(\\Omega\\). If its cross-sectional area is 0.005cm2, determine its resistivity', '0.0005\\(\\Omega\\)cm~0.0015\\(\\Omega\\)cm~0.0016\\(\\Omega\\)cm~0.0700\\(\\Omega\\)cm', '0.0005\\(\\Omega\\)cm', 'e = \\(\\frac{RA}{L} = \\frac{10 \\times 0.005}{100} = 0.0005\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(272, '2016', 'A transformer has 400 turns of wire in the primary coil and 40 turns in the secondary col. If the input voltage is 150 volts. Calculate the magnitude of the output voltage', '150V~55V~36V~15V', '15V', '\\(\\frac{ES}{EP} = \\frac{Ns}{Np} = \\frac{Es}{150} = \\frac{40}{400}\\)\n\nEs = \\(\\frac{150 \\times 40}{400}\\)\n\n= 15V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(273, '2016', 'The circuit above illustrates a standard resistor R, voltage source E and a lamp L connected in series. If the temperature of R is increased, the brightness of the lamp will', 'increase sharply~decrease slightly~remains the same~increase gradually', 'decrease slightly', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(274, '2016', 'The energy required to separate the nucleus in an atom completely is known as', 'mass defect of the atom~electron binding energy~excitation energy~nuclear binding energy', 'nuclear binding energy', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(275, '2016', 'Which of the following statements is the major advantage of nuclear fusion over nuclear fission?', 'nuclear fusion releases more energy~more neutrons are released in fusion than in fission~fussion does not release as much dangerous radiation as fission~fusion reactions occur more readily than fission', 'fussion does not release as much dangerous radiation as fission', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(276, '2016', 'An aluminum foil is placed across a beam of radiation from a radioactive source. Which of the following types of radiation will be stopped by it?', 'alpha and beta particles~alpha and gamma particles~beta and gamma particles~gamma particles only', 'alpha and beta particles', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(277, '2016', 'An element of nucleon number P and atomic number Q emits an alpha particle from its nucleus. The resultant numbers of the new element formed are respectively', 'P - 4 and Q + 2~P - 4 and Q - 2~P + 2 and Q + 2~P + 2 and Q - 2', 'P - 4 and Q - 2', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(278, '2016', 'Which of the following statements about mass and weight are correct? i. Weight is the force of gravity on a body. ii. The mass of a body is the quantity of matter in the body. iii. The weight of a body is greatest at the equator. iv. The mass of a body is greatest at the poles', 'i and ii only~i and iii only~ii and iv only~iii and iv only', 'i and ii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(279, '2016', 'Materials that can be stretched and still return to their original forms when the stresses are removed are said be', 'elastic~elastomer~plastic~thermoplastic', 'elastic', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(280, '2016', 'Which of the following units is derived?', 'kg~m~K~N', 'N', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(281, '2016', 'The barometric reading at a place is 73.5m Hg. Calculate the pressure at a point 30m below the surface of water contained in a reservoir at the place. [g = ms-2, density = 1.2 x 104kg m-3, density of water = 1.0 x 103m-3]', '4.0 x 105 Nm-2~3.0 x 10 5 Nm-2~2.0 x 105 Nm-2~1.0 x 105 Nm-2', '3.0 x 10 5 Nm-2', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(282, '2016', 'An object floats in a fluid when it displaces it\'s', 'volume of liquid in which it floats~mass of fluid in which it foats~weith of fluid in which it foats~density of fluid in which it foats', 'weith of fluid in which it foats', 'A floating object displaces a weight of fluid equal to its own weigh', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(283, '2016', 'The resultant force in a couple is', 'zero~infinite~the sum of the forces~thr product of the forces', 'zero', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(284, '2016', 'The slope of a straight-line velocity-time graph represents', 'uniform acceleration~uniform speed~total distance travelled~workdone', 'uniform acceleration', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(285, '2016', 'A body is projected with an initial velocity U at an angle O to the horizontal. The time taken by it to reach its maximum height is given by the expression', '\\(\\frac{2u \\text{sin}\\theta}{g}\\)~\\(\\frac{u^2 \\text{sin}^2\\theta}{2g}\\)~\\(\\frac{u \\text{sin}\\theta}{g}\\)~\\(\\frac{u \\text{sin}\\theta}{2g}\\)', '\\(\\frac{u \\text{sin}\\theta}{g}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(286, '2016', 'Which of the following statements describes a body in a stable equilibrium correctly?', 'a person walking on a tight-rope~ball on a smooth horizontal table~ball resting on an inverted hemisphere bowl~ball in the middle of a nemispherical bowl', 'ball in the middle of a nemispherical bowl', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(287, '2016', 'In a school compound a girl walks 40km due east from the laboratory to the staff room to submit her report. Then she returns and walks 30m due north to her classroom. Determine the magnitude of her displacement from the10m laboratory', '10m~35m~50m~70m', '50m', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(288, '2016', 'Two strings each inclined at an angle 30o to the horizontal are used to hold a bucket of water weighing 20N. Calculate the tension i n each string.', '20\\(sqrt{3}\\)N~20N~10\\(sqrt{3}\\)N~10N', '10\\(sqrt{3}\\)N', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(289, '2016', 'A bullet fired vertically upwards reaches a height of 500m. Neglecting air resistance, calculate the magnitude of the initial velocity of the bullet. [g = 10ms-2]', '500.0ms-1~100.0ms-1~70.0ms-1~50.0ms-1', '100.0ms-1', 'V2 = U2 + 2gs\n\nV2 = 0\n\nV2 = 2gs\n\nh = 500m\n\ng = 10ms-2\n\nV2 2 x 10 x 500\n\nV2 = 10,000 \n\nV = \\(\\sqrt{10000}\\)\n\nV = 100ms-1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(290, '2016', 'A uniform bar AB is balanced on a knife-edge which is 60cm from B by a mass of 22g which hangs at C 10cm from A. Calculate the mass of the bar.', '133.2g~66.0g~60.0g~22.0g', '66.0g', 'clockwise movement = anticlockwise movement \n\nw x 10 = 22 x 30\n\nw = \\(\\frac{22 \\times 30}{10}\\)\n\nw = 66.0g', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(291, '2016', 'A body of mass 1000kg is released from a height of 10m above the ground. Determine its kinetic energy just before it strikes the ground .[g = 10ms-2]', '10J~103J~104J~105J', '105J', 'Ke = mgh\n\nKe = Pe\n\n\\(\\frac{1}{2}\\)MV2 = mgh \n\nKe = 1000 x 10 x 10\n\nKe = 100000J\n\nKe = 105J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(292, '2016', 'The crackling noise produced by aluminum roofing sheets on a house during a hot sunny day is a result of', 'thermal equilibrium of the sheets~conduction of heat by the sheets~contraction of the sheets~expansion of the sheets', 'expansion of the sheets', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(293, '2016', 'Water is unsuitable for use as a thermometric liquid because it', 'expands unevenly between 0oC and 40oC~has narrow temperature range~has a concave meniscus~msintsin s fixed density', 'expands unevenly between 0oC and 40oC', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(294, '2016', 'The diagram above illustrates a block ans tackle pulley system in which an effort E supports a load of 100.0N. If the efficiency of the machine is 75%, calculate the value of E', '22.2N~38.0N~67.0N~75.0N', '22.2N', 'Given', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(295, '2016', 'A quantity of hot water at 100oC is added to 400g of water at 10oC until the temperature of the mixture is 60oC.', '200g~320g~400g~500g', '500g', 'Heat lost by hot water = Heat gained by cold water \n\nM x 4200 x (100 - 60 = 0.4 x 4200 x (60 - 10)\n\n4200m x 40 = 0.4 x 4200 x 50 \n\n40m = 0.4 x 50 \n\nm = \\(\\frac{0.4 \\times 50}{40}\\) = 0.5kg\n\n= 500g', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(296, '2016', 'A battery of emf 24V is connected to three resistor P, Q and R as illustrated in the diagram. Determine the voltage across the resistor Q', '5v~10v~14v~24v', '10v', 'E - V1 + V2\n\n24V = 14V + VQP \n\nVQP = 4 + 14V \n\nVQP =10V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(297, '2016', 'In an experiment in which a molten substance is allowed to cool, the cooling curve above was obtained. The temperature 60oC is known as the', 'vaporization point~cooling temperature~boiling point~melting point', 'melting point', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(298, '2016', 'Which of the following concepts is a method of heat transfer that does not require a material medium?', 'conduction~radiation~diffusion~convection', 'radiation', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(299, '2016', 'Which of the following units is the S.I. unit of heat capacity?', 'Jkg-1~Jkg-1 K-1~JK-1~Jg-1K-1', 'JK-1', 'Heat capacity = \\(\\frac{\\text{Heat energy supplied}}{\\text{Rise in temperature}}\\)\n= JK\\(^{-1}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(300, '2016', 'The pressure applied to an enclosed fluid to one end id transmitted equally throughout the fluid and to the container walls. This statement is', 'Archimede\'s principle~Bernoulli\'s principle~Pascal\'s principle Heisenberg\'s~Heisenberg\'s uncertainty principle', 'Pascal\'s principle Heisenberg\'s', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(301, '2015', 'The diagram given illustrates a wave form. Determine the speed of the wave', '5.4 ms-1~8.4 ms-1~9.6 ms-1~10.0 ms-1', '10.0 ms-1', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(302, '2015', 'What type of wave is emitted by a loud speaker?', 'Transverse~Longitudinal~Gamma~Radio', 'Longitudinal', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(303, '2015', 'An object is placed 15cm from a diverging lens of focal length 12cm. The image of the object formed by the lens in', 'real and 6.67cm from the lens~virtual and 6.67cm from the lens~real and 60.00cm from the lens~virtual and 60.00cm from the lens', 'virtual and 6.67cm from the lens', 'The focal length of a diverging lens is negative.\nf = -12 cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(304, '2015', 'A swimming pool is .1m deep. If it contains water of refractive index 1.3, calculate the apparent depth of pool', '3.4m~2.7m~1.6m~0.8m', '1.6m', 'n = \\(\\frac{\\text{real depth}}{\\text{apparent depth}}\\)\n\n1.3 = \\(\\frac{2.1}{\\text{apparent}}\\)\n\nA.D = \\(\\frac{2.1}{1.3} = 1.6\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(305, '2015', 'When an air column is set into vibrations, the distance between two consecutive nodes of the resultant wave is', 'one quarter of the wavelength~half of the wavelength~the wavelength~twice the wavelength', 'half of the wavelength', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(306, '2015', 'A girl standing some distance from the cliff claps her hands and hears the echo 0.8s later. calculate her distance from the cliff. [speed of sound in air = 320 ms-1]', '23m~128m~288m~298m', '128m', 'V = \\(\\frac{2nx}{E}\\)\n\n= \\(\\frac{2 \\times 1 \\times X}{0.8} = 320\\)\n\n2x = 0.8 x 320\n\nx = \\(\\frac{0.8 \\times 320}{2}\\)\n\n= 128m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(307, '2015', 'Red light travels faster than blue light when both of them pass through a glass prism because the', 'refractive index of red light is grester than that of blue light~refractive index of blue light is greater than that of red light~red light is more intense than the blue light~blue light is more intense than the red light', 'blue light is more intense than the red light', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(308, '2015', 'An object is placed 20cm from a concave mirror of focal length 15cm. Calculate the linear magnification of the image formed', '0.5~1.5~2~3', '3', '\\(\\frac{1}{U} + \\frac{1}{V} = \\frac{1}{F}\\)\n\n\\(\\frac{1}{V} = \\frac{1}{F} - \\frac{1}{U}\\)\n\n\\(\\frac{1}{V} = \\frac{1}{15} - \\frac{1}{20}\\)\n\n\\(\\frac{1}{V} = \\frac{\\text{4 - 3}}{60}\\)\n\n\n\\(\\frac{1}{V} = \\frac{1}{60}\\)\n\nV = 60cm\n\nM = \\(\\frac{V}{U} = \\frac{60}{20}\\)\n\nM = 3.0cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(309, '2015', 'All electromagnetic waves in a vacuum have the same', 'wavelength~frequency~speed~amplitude', 'speed', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(310, '2015', 'The diagram given illustrates two charged particles W and X. The charges on W and x are respectively', 'negative~negative~positive~positive', 'negative', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(311, '2015', 'An alternating current supply is connected to an electric lamp which lights with the same brightness as it does with direct current source emf 6v. The peak potential difference of the a.c supply is', '4.6v~6.0v~8.5v~12.0v', '8.5v', 'Vo = V\\(\\_{rms}\\) x \\(\\sqrt{2}\\)\n\nVo = 6 x 1.414\n\nVo = 8.484\n\n= 8.5v', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(312, '2015', 'An electric generator', '120 w~360 w~720 w~2400 w', '720 w', 'Power - IV\n\nI = \\(\\frac{P}{V}\\)\n\n= \\(\\frac{12000}{2000}\\)\n\nI = 6A\n\nPower loss = I\\(^2\\)R = 6\\(^2\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(313, '2015', 'Which of the following statements is correct? When capacitors of different values are connected in series', 'the same charge flows through them~the same voltage appears across each capacitor~different quantities of charges flow through them in different voltages across them~different quantities of charges flows through them with the same voltage across them', 'the same charge flows through them', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(314, '2015', 'Which of the following statements about a three-pin plug is', 'i only~ii only~i and ii only~i, ii and iii', 'i and ii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(315, '2015', 'The symbol illustrated above is that of a resistor', 'which absorb light~which emits light~which absorbs heat to function properly~whose resistance is light dependent', 'which absorbs heat to function properly', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(316, '2015', 'A wire of cross-sectional area 0.60mm2 has a restivity of 7.2 x 10-7 \\(\\Omega\\). Calculate the length of wire that will have a resistance of 3\\(\\Omega\\).', '0.25m~2.50m~3.60m~36', '2.50m', 'R = \\(\\frac{PL}{A}\\)\n\nC = \\(\\frac{RA}{P}\\)\n\nC = \\(\\frac{0.60 \\times 10^{-6} \\times 3}{7.2 \\times 10^{-7}}\\)\n\nC = 2.50m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(317, '2015', 'A battery of emf 24V is connected to three resistor P, Q and R as illustrated in the given diagram. Determine the voltage across the resistor Q.', '5V~10V~14V~24V', '10V', 'E - V1 + V2\n\n24V = 14V + VQP\n\nVQP = 24 + 14V\n\nVQP = 10V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(318, '2015', 'The mass of the earth is 6.0 x 1024kg and that of the moon is 7.0 x 1022kg. If the distance between them is 4.0 x 108m, calculate the force of attraction between them. [G = 6.7 x 10-11Nm2kg-2]', '1.8 x 105N~1.8 x 1010N~1.8 x 1015N~1.8 x 1020N', '1.8 x 1020N', 'F = \\(\\frac{GM_1M_2}{12^2}\\)\n\nF = 6.7 x 10-11x\n\nF = \\(\\frac{M_1M_2}{R^2}\\)\n\nF = \\(\\frac{6.7 \\times 10^{-11} \\times 6.0 \\times 10^{24} \\times 7.0 \\times 10^{22}}{(4 \\times 10^8)^2}\\) \n\n= 1.8 x 1020N', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(319, '2015', 'The angle which the direction of the earth magnetic field makes with the horizontal at a palace is know as.', 'angle of contact~angle of dip~angle of declination~magnetic meridian', 'angle of dip', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(320, '2015', 'What must be connected between the points P and Q to establish a steady current through the incomplete circuit diagram given?', 'Fuse~ammeter~Cell~voltmeter', 'Cell', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(321, '2015', 'When current flows through a moving-coil galvanometer, the force exerted on the pointer depends on the', 'i only~ii only~i and iii only~i, ii and iii', 'i and iii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(322, '2015', 'in a nuclear fission process, the mass defect was 1.2 x 10-5kg. Calculate the energy released. [speed of the light in vacuum = c = 3.0 x 108ms-1]', '1.08 x 1011J~5.20 x 1011J~1.08 x 1012J~2.50 x 1013J', '1.08 x 1012J', 'E - Mec2\n\nE = 1.2 x 10-5 x (3 x 108)2\n\nE = 1.08 x 1012J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(323, '2015', 'Which of the following statements about diode is correct?', 'reverse bias diodes have low resistance~forward bias diodes have high resistance~forward bias diodes produce high current~forward bias diodes function as a result of heat', 'forward bias diodes have high resistance', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(324, '2015', 'Which of the following radiations constitutes a stream of electrons?', 'Ramma rays~X-rays~Cathode rays~Radio waves', 'Cathode rays', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(325, '2015', '\\(^{226}_{88}Ra\\) emits two alpha particles to produce polonium(po) nuclide. The correct formula for the nuclide?', '\\(^{224}_{86}po\\)~\\(^{222}_{86}po\\)~\\(^{222}_{84}po\\)~\\(^{218}_{84}po\\)', '\\(^{218}_{84}po\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(326, '2015', 'The dimensions of momentum are', 'MLT~ML-1T-1~MLT-1~ML-1T', 'MLT-1', 'Momentum = kgms-1 = MLT-1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(327, '2015', 'A student measures the volume of a liquid using a measuring cylinder. What else needs to be measured by the student in order to determine the density of the liquid?', 'depth of the liquid in the cylinder~mass of the cylinder~mass of the liquid~tempersture of the liquid', 'mass of the liquid', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(328, '2015', 'The diagram given, represents the graph of stress against strain for an elastic wire. The point Q on the graph is the', 'elastic linit~breaking point~yield point~proportional limit', 'breaking point', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(329, '2015', 'A ball is dropped from the top of a tower. Due to air resistance,it reaches terminal velocity. Which of the following statement(s) about its motion is', 'i only~i and ii only~ii and iii only~i, ii and iii', 'i only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(330, '2015', 'Which of the following substances lowers the surface tension of water?', 'metal~sand~detergent~paper', 'detergent', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(331, '2015', 'An object of volume 400cm3 and 2.5gcm-3 is suspended from a spring balance with half its volume immersed in water. Determine the reading on the spring balance. (Density of water = 1gcm-3)', '1200g~1000g~800g~400g', '800g', 'Mass = density x volume \n\n400 x 2.5 = 1000g\n\nLoss in mass = volume x density \n\n= \\(\\frac{400}{2}\\) x 1 = 200g\n\nReading on spring balance = 1000 - 200g = 800g', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(332, '2015', 'The diagram given illustrates a force-distance graph for the motion of a wooden block. Determine the work done on the block when moved through a distance of 5m.', '4J~15J~5J~100J', '100J', 'W = FS = 20 X 5 \n\n= 100J', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(333, '2015', 'The two person of a body undergoing a uniformly accelerated motion are (10s, 10ms-1) and (30s, 50ms-1). On the velocity-time graph pf the body.', '0.5ms-2~2.0ms-2~10.0ms-2~40.0ms-2', '2.0ms-2', 'Slope = a = \\(\\frac{\\deltav}{\\deltat}\\)\n\n= \\(\\frac{50 - 10}{30 - 10}\\) \n\n= 2.0ms-2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(334, '2015', 'At a birthday party, the celebrant pops a corked fruit wine. If the cork shoots out of the bottle at an angle of 40o to the horizontal and travels a horizontal distance of 4.50m in 1.25s. Calculate the initial speed of the cork.', '4.2ms-1~4.7ms-1~5.6ms-1~7.1ms-1', '4.7ms-1', 'R = Ucos\\(\\theta\\) x t \n\nU = \\(\\frac{R}{Cos \\theta \\times t}\\)\n\n= \\(\\frac{4.50}{Cos40N.25}\\)\n\n= 4.699m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(335, '2015', 'A uniform metre rule is balanced on a fulcrum placed at the 35cm mark by suspending a mass of 120g at the 10cm mark. Calculate the mass of the metre rule.', '60g~80g~120g~200g', '200g', 'Clock-wise moment = Anti-clock wise \n\n15 x m = 5 x 10 \n\nm = 200g', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(336, '2015', 'A plank is placed along the path on which a wheel barrow containing sand is pushed at a construction site to prevent it from sticking as illustrated in the diagram given. The large area of the plank prevents the wheel barrow from getting stuck by', 'increasing the reaction on the ground~increasing the pressure on the ground~decreasing the pressure on the ground~decreasing the weight on the ground', 'decreasing the pressure on the ground', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(337, '2015', 'When a body is thrown vertically upwards, its velocity at the maximum height is', 'maximium~zero~double its initial value~half its initial value', 'zero', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(338, '2015', 'Resonance occurs when one vibrating object causes a second object to vibrate at its own natural', 'amplitude~speed~frequency~intensity', 'frequency', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(339, '2015', 'The mouth piece of a telephone handset converts', 'electrical energy to sound energy~sound energy to electrical energy~sound energy to radiowave~radiowave to sound energy', 'sound energy to electrical energy', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(340, '2015', 'In the clinical thermometer, the function of the kink is to i. Prevent the back flow of mercury after use. ii. Ensure the back flow of mercury after use. iii. Maintain the thermometric property of mercury. iv. Allow the temperature attained to be read.', 'i only~i and ii only~i and iv only~iii and iv only', 'i and iv only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(341, '2015', 'Which of the following statements correctly defines the boiling point of a liquid? The temperature at which the', 'saturated vapour pressure equals the atmospheric pressure~molecules leaves the liquid at a rate equal to the rate at which they return~molecules leave the liquid at a rate higher than that at which they return~molecules leave the liquid at a rate lower than the rate at which they return', 'saturated vapour pressure equals the atmospheric pressure', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(342, '2015', 'The diagram given is used to determine the', 'boiling point of water~atmospheric pressure~upper fixed point of a thermometer~amount of water in the atmosphere', 'upper fixed point of a thermometer', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(343, '2015', 'An aluminium rod of length 1.8m at 10', '155oC~160oC~169oC~179oC', '179oC', '\\(\\alpha = \\frac{L_2 - L_1}{L_1(\\theta_2 - \\theta_1)}\\)\n\nL\\(_2\\) - L\\(_1\\) = \\(\\alpha L_1 (\\theta_2 - \\theta_1)\\)\n\n\\(\\theta_2 = \\frac{0.007}{2.3 \\times 10^{-5} \\times 1.8}\\) + 10\n\n= 179', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1);
INSERT INTO `exam_simulation` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`, `status`) VALUES
(344, '2015', 'A mercury-in-glass thermometer read 4cm at ice point and 29cm at steam point. Calculate the temperature when the mercury level is at 9cm', '13oC~20oC~33oC~38oC', '20oC', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(345, '2015', 'The continuous stirring in the method of mixtures to determine the specific thermal capacity of a substance ensures', 'continuous dissipation of heat to the room~uniform distribution of thermal energy to all parts of the mixture~that the thermal energy is confined to the mixture~that there is rapid heat exchange', 'uniform distribution of thermal energy to all parts of the mixture', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(346, '2015', 'Which of the following statements is correct about the effect of dissolved salt on the freezing point of water?', 'the freezing point is lowered~the freezing point is increased~there is no change in the freezing point~the change in the freezing point depends on the temperature of the surrounding', 'the freezing point is lowered', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(347, '2015', 'A pressurized perfume bottle is left on the window pane of a room. What happens to he gas molecules of the perfume on a sunny day? They', 'expand~collide less often~move more rapidly~contract', 'move more rapidly', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(348, '2015', 'Given that v, f and \\(\\lambda\\) are the velocity, frequency and wavelength of a wave respectively. Which of the following equations is correct?', 'v = f2\\(\\lambda\\)~f = \\(\\frac{v}{\\lambda}\\)~f = \\(\\frac{v}{\\lambda^2}\\)~\\(\\lambda = \\frac{f}{v^2}\\)', 'f = \\(\\frac{v}{\\lambda}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(349, '2015', 'The distance between two successive trough of a wave is 0.4m. If the frequency of the source is 825Hz, Calculate the speed of the wave', '165.0 ms-1~330.0ms-1~41.5ms-1~85.0ms-1', '330.0ms-1', 'v = f\\(\\lambda\\) \n\n= 825 x 0.4 \n\n= 330.0ms-1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(350, '2015', 'X-rays and infrared rays are both electromagnetic. Which common property do the waves have? Both waves', 'are longitudinal~have same frequency~have the same wavelength~travel at the same speed in a vacuum', 'travel at the same speed in a vacuum', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(351, '2015', 'The image formed by a concave mirror is real, inverted and magnified, when object is placed', 'at the focus~at the centre of curvature~beyond the centre of curvature~between the centre of curvature and the focus', 'between the centre of curvature and the focus', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(352, '2015', 'Total internal reflection. i. is a phenomenon of refraction of light. ii. occurs when light rays travel into a denser medium. iii. occurs when the critical angle is just exceeded. iv. is a phenomenon of reflection of light. Which of the statements above are correct?', 'i and ii only~i and iii only~i, ii and iii only~i, iii and iv only', 'i and iii only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(353, '2015', 'Complementary colours are those which', 'have the same refractive index~have the same wavelength~add-up to produce black light~add-up to produce white light', 'add-up to produce white light', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(354, '2015', 'The diagram given illustrates the waveform of a note produced by vibrations in an air column of length L. If the speed of sound in air is V, derive an expression for the frequency of the notes', '\\(\\frac{V}{L}\\)~\\(\\frac{5VL}{2}\\)~\\(\\frac{5L}{4V}\\)~\\(\\frac{5V}{4L}\\)', '\\(\\frac{5V}{4L}\\)', 'L = \\(\\frac{5\\lambda}{4}\\)\n\n\\(\\lambda = \\frac{4L}{5}\\)\n\nBut \\(\\lambda = f\\lambda\\)\n\nf = \\(\\frac{v}{\\lambda} = \\frac{v}{\\frac{4L}{5}}\\)\n\n= \\(\\frac{5v}{4L}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(355, '2015', 'The pair of musical instruments that works on the vibration of air in pipes is', 'piano and the organ~guitar and the flute~trumpet and the violin~flute and the trumpet', 'flute and the trumpet', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(356, '2015', 'An astronomical telescope has objectives and eye-piece lenses of focal length 3.5m and 5cm respectively. Determine the magnifying power of the telescope when in normal adjustment', '70~17.5~7~0.7', '70', 'Magnify power = \\(\\frac{f_o}{f_e}\\)\n\n= \\(\\frac{3.5 \\times 100}{5.0}\\)\n\n= 70', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(357, '2015', 'An aluminium cable of diameter 4 x 10-3m and resistivity 3.0 x 10-8\\(\\omega\\)m has a resistance of 21\\(\\Omega\\). Calculate the length of the cable. (\\(\\pi = 3.14\\))', '8.0 x 102m~8.8 x 103m~8.0 x 104m~8.8 x 104m', '8.8 x 103m', 'R = \\(\\frac{4eL}{\\pid^2}\\)\n\nL = \\(\\frac{R\\pid^2}{4e}\\)\n\n= \\(\\frac{21 \\times 3.14(4 \\times 10^{-3})^2}{4 \\times 3.0 x 10^{-8}}\\)\n\n= 8.8 x 103m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(358, '2015', 'The electricity meters in houses measure energy unit consumed in', 'kilowatt-hour~volt~ampere~coulomb', 'kilowatt-hour', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(359, '2015', 'A man and his friend have masses 70kg and 60kg respectively. If they are seated 1.0m apart, calculate the gravitational force of attraction between them. (G = 6.67 x 10-11 Nm2 kg-2)', '1.59 x 10-14 N~2.80 x 10-7 N~1.30 x 10-2 N~6.30 x 1013 N', '2.80 x 10-7 N', 'F = \\(\\frac{GM_1M_}{r^2}\\)\n\n= \\(\\6.67 \\times 10^{-11} \\times 70 \\times 60}{1^2}\\)\n\n= 2.8014 x 10-7 N', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(360, '2015', 'The p.d across a parallel-plate capacitor is 103V. If the distance between the two plates is 10cm. Calculate the magnitude of the electric field strength between the plates.', '1.0 x 104Vm-1~1.0 x 105Vm-1~1.5 x 105Vm-1~2.0 x 105Vm-1', '1.0 x 104Vm-1', 'E = \\(\\frac{v}{d} = \\frac{10^3}{0.1}\\)\n\n= 10000\n\n= 1.0 x 104Vm-1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(361, '2014', 'Two different materials, rubbed against each other acquired opposite charges when separated. This is an example of charging by', 'induction~friction~conduction~convection', 'friction', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(362, '2014', 'Which of the following factors does not affect the e.m.f of a primary cell? Its', 'size~internal resistance~operating temperature~duration of usage', 'size', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(363, '2014', 'Two magnets are used to magnetize a soft iron bar PQ as illustrated in the diagram given. The correct polarity at P and Q respectively', 'S and N~N and N~S and S~N and S', 'N and N', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(364, '2014', 'In storing magnets, keepers are used to', 'reduced self-demagnetization~cancel the effect of the earth\'s magnetic field~protect the magnet from stray electric field~increase the strangth of the magnets', 'reduced self-demagnetization', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(365, '2014', 'A 10\\(\\mu\\)C charge moves with a velocity of 1.0 x 105 ms-1 at right angle to a uniform magnetic field of flux density 5.0 x 10-4T. Calculate the force on the charge', '5.0 x 10-5N~5.0 x 10-4N~5.0 x 105N~5.0 x 106N', '5.0 x 10-4N', 'F = qvB\n\n= 10 x 10-6 x 1.0 x 105 x 10-4\n\n= 5.0 x 10-4N', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(366, '2014', 'Which of the following statements is not correct about steel and soft iron?', 'steel is more magnetized than soft iron~permanent magnets are usually made of steel~soft iron is more readily magnetized than steel~soft iron more readily loses its magnetism than steel', 'steel is more magnetized than soft iron', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(367, '2014', 'What determines the polarity at the ends of an electromagnet? The', 'magnitude of the current passing through the wire~material of the core of the magnet~material of the coil~direction of current in the wire', 'direction of current in the wire', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(368, '2014', 'How many beta particle(s) are emitted in the radioactive decay of \\(^{198}_{79}Au \\leftarrow ^{198}_{80}Hg\\)?', '1~2~3~5', '1', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(369, '2014', 'The phenomenon by which two light atomic nuclear combine to form a heavy nuclide with the release of energy is known as', 'radioactivity~nuclear fusion~nuclear fission~chain reaction', 'nuclear fusion', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(370, '2014', 'In a p-type semiconductor, the', 'number of holes are equal to the number of electrons~electrical resistivity increases~electrons are the majority charge carriers~holes are the majority charge carriers', 'holes are the majority charge carriers', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(371, '2014', 'Let \\(\\Delta\\)x be the uncertainty in the measurements of position and \\(\\Delta\\)p the uncertainty in measurement of momentum. The uncertainty principle relation is given as', '\\(\\Delta\\)x . \\(\\Delta\\)p = h~\\(\\Delta\\)x . \\(\\Delta\\)p \\(\\leq\\) = h~\\(\\Delta\\)x . \\(\\Delta\\)p \\(\\geq\\) = h~\\(\\Delta\\)x . \\(\\Delta\\)p ', '\\(\\Delta\\)x . \\(\\Delta\\)p \\(\\geq\\) = h', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(372, '2014', 'Two angles of a pentagon are in the ratio 2', '72o~100o~120o~144o', '144o', '\n\n\nThe diagram given simple illustrates that a pentagon contains three \\(\\Delta\\)s. \n\nTwo angles which are in the ratio 2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(373, '2014', 'The S.I unit for sound energy is', 'Hz~cd~dB~J', 'J', 'Every form of energy is measured in joules (J).', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(374, '2014', 'The general definition of elastic modulus is', '\\(\\frac{stress}{strain}\\)~\\(\\frac{strain}{stress}\\)~\\(stress \\times strain\\)~\\(\\sqrt{\\frac{stress}{strain}}\\)', '\\(\\frac{stress}{strain}\\)', 'Elastic modulus is the ratio of pressure (stress) applied to a body to the resistance (strain) produced by the body.\n= \\(\\frac{stress}{strain}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(375, '2014', 'The diagram above illustrates a simple barometer. Which distance measures the atmospheric pressure?', 'PQ~QR~RS~QS', 'QR', 'The height of the mercury column in a simple barometer is calculated as the atmospheric pressure.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(376, '2014', 'The property of a body to remain at rest or to continue in uniform motion in a straight line is called', 'momentum~Inertia~impulse~Energy', 'Inertia', 'Inertia is the resistance of the object to any change in its motion, including a change in direction. An object will stay still or keep moving at the same speed and in a straight line, unless it is acted upon by an external unbalanced force.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(377, '2014', 'During a training session, two footballers pass a ball repeatedly between each other. The \'to and fro\' motion of the ball is not simple harmonic because the', 'I and III only~I and II only~II and III only~I, II and III', 'I and III only', 'In SHM, the body must have acceleration in a direction opposite to the displacement and the acceleration must be directly proportional to displacement. Also, the acceleration must be directed towards its mean position. This is not the case with a football on the pitch.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(378, '2014', 'A dam is able to hold a large quantity of water because its wall is', 'thickest at the top~thickest at the middle~thickest at the bottom~of the same thickness throughout', 'thickest at the bottom', 'The pressure of the water is much greater deeper down and the dam needs to be thick at the bottom so that it is strong enough to withstand this larger pressure.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(379, '2014', 'A body of mass m moving around a circle of radius r with a uniform speed v experiences a centripetal force F. The work done by the centripetal force on it is', 'Fv~zero~Fmr~\\(\\frac{Fr}{m}\\)', 'zero', 'The work done by centripetal force in the case of a uniform circular motion is 0 joules.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(380, '2014', 'A block is acted upon by TWO horizontal forces as illustrated in the diagram above. The block accelerates at 1.5\\(ms^{-2}\\). Calculate the mass of the block.', '6kg~9kg~10kg~15kg', '6kg', 'Total force exerted on the block = (10 - 1)N =9N\nForce = mass x acceleration\n9 = m x 1.5\nm = 9', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(381, '2014', 'Which of the following quantities are dimensionally independent?', 'I and II~II, III and IV~I, II, III and IV~I, III and IV', 'I, III and IV', 'The quantities Efficiency, Dielectric constant and Refractive index are dimensionless.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(382, '2014', 'A body is projected with an initial velocity u at angle \\(\\theta\\) to the horizontal. If \\(R_{max}\\) is the maximum range of the projectile, what does the relation \\(\\frac{u^{2}}{R_{max}}\\) represent?', 'The vertical distance covered~Acceleration due to gravity~The horizontal distance covered~The acceleration of the body', 'Acceleration due to gravity', '\\(R_{max} = \\frac{u^{2}}{g}\\)\nHence, \\(g = \\frac{u^{2}}{R_{max}}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(383, '2014', 'An object at rest is said to possess', 'potential energy~kinetic energy~chemical energy~electrical energy', 'potential energy', 'Potential energy is the energy that is stored in an object due to its position relative to some zero position.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(384, '2014', 'According to Newton\'s law of cooling, the heat energy lost per unit area of a body depends on the', 'I and II only~II and IV only~I,II and III~I, II and IV', 'I,II and III', 'The rate of cooling of liduid according to Newton\'s law of cooling depends on', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(385, '2014', 'The graph of density against temperature for water is correctly illustrated by', 'I~II~III~IV', 'III', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(386, '2014', 'A football is kicked at an angle of 45', '0.0\\(ms^{-1}\\)~5.6\\(ms^{-1}\\)~10.6\\(ms^{-1}\\)~15.0\\(ms^{-1}\\)', '10.6\\(ms^{-1}\\)', 'The horizontal component of velocity, \\(V_{x}\\), is unaffected by the acceleration of free fall and remains constant.\n\\(V_{x} = U_{x} = Ucos\\theta\\)\n= \\(15 \\times cos45 = 15\\times 0.7071\\)\n\\(\\approxeq 10.6ms^{-1}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(387, '2014', 'The ice point on the absolute scale of temperature is', '0K~~100K~273K', '0K', 'The absolute zero of the scale of temperature being the ice point of the absolute scale of temperature is 0K, which is -273', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(388, '2014', 'Which of the following factors does not increase the rate of evaporation of water in a lake?', 'Increase in the pressure of the atmosphere~Rise in temperature~Increase in the surface area of the lake~Increase in the speed of the wind', 'Increase in the pressure of the atmosphere', 'The rate of evaporation is increased by the lowering of atmospheric pressure and not its increase. Every other factor stands, for the increase of evaporation process.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(389, '2014', 'The bob of a simple pendulum takes 8.0s to complete 10 oscillations. Determine the frequency of oscillation of the bob.', '0.125Hz~1.25Hz~7.50Hz~8.00Hz', '1.25Hz', '10 complete oscillations = 8.0s\n1 complete oscillation (period) = \\(\\frac{8}{10}\\)s\nFrequency = \\(\\frac{1}{period}\\) = \\(\\frac{1}{0.8} = 1.25Hz\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(390, '2014', 'The diagram above illustrates the mercury-in-glass thermometer used for determining the temperature of a room. Use the data on it to determine the room temperature.', '3.3~7~13~30', '30', 'Let the room temperature be X.\nWe have, \\(\\frac{3-0}{10-0} = \\frac{X-0}{100-0}\\)\n\\(\\frac{3}{10} = \\frac{X}{100}\\)\n\\(X = \\frac{3 \\times 100}{10}\\)\n= 30', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(391, '2014', 'Frequency is measured in', 'meter per second~seconds~hertz~farad', 'hertz', 'The unit of frequency is hertz, abbreviated Hz.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(392, '2014', 'Which of the following electromagnetic waves is most energetic?', 'Radio waves~X-ray~Gamma rays~Ultra-violet rays', 'Gamma rays', 'The gamma rays have the shortest wavelength and therefore, impart the highest photon energy.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(393, '2014', 'Rainbow formation is a natural phenomenon illustrating that white light', 'splits into three components after rainfall~is dispersed by glass prisms~splits into its constituent colours before rainfall~is dispersed into its constituent colours after rainfall', 'is dispersed into its constituent colours after rainfall', 'A rainbow is caused by the dispersion of sunlight by tiny water droplets present in the atmosphere, which can be seen after the rain.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(394, '2014', 'The lens illustrated above can best be described as a', 'converging meniscus~plano-convex~diverging meniscus~bi-convex', 'plano-convex', 'The diagram is that of a plano-convex lens', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(395, '2014', 'Two plane mirrors are inclined to each other such that an object placed between them has 11 images. Determine the angle of inclination', '30~45~60~90', '30', 'Formula for number of images = \\(\\frac{360}{n} - 1\\)\nwhere n is the angle of inclination.\nGiven the number of images = 11, we have\n\\(\\frac{360}{n} - 1 = 11\\)\n\\(\\frac{360}{n} = 12\\)\n\\(n = \\frac{360}{12} =30', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(396, '2014', 'The pitch of a note is not affected by', 'frequency~ tension in a vibrating string~mass of a vibrating string~amplitude of sound wave', 'amplitude of sound wave', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(397, '2014', 'When two flat plate conductors are arranged in such a way that they possess equal and opposite charges seperated by a dielectric, they form a', 'electroscope~electrophorus~capacitor~cell', 'capacitor', 'Most capacitors contain at least two electrical conductors often in the form of metallic plates or surfaces separated by a dielectric medium.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(398, '2014', 'Which electrical device is illustrated above?', 'a.c. generator~a.c. motor~d.c. generator~d.c. motor', 'd.c. generator', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(399, '2014', 'A simple barometer is constructed using a liquid \\(Q_{1}\\) of density 16.2\\(g', '1358mm~957mm~760mm~638mm', '638mm', 'Let \\(h_{Q}\\) and \\(\\rho_{Q}\\) be the least length and the density of \\(Q_{1}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(400, '2014', 'A bar AB is balanced horizontally on two knife edges as illustrated as in the diagram above. Determine the weight of the bar.', '10.0N~20.0N~40.0N~50.0N', '40.0N', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(401, '2014', 'To obtain a virtual, erect and magnified image from a thin converging lens, an object must be placed', 'between the focus and the lens~at the focus~between the focal length and twice the focal length~beyond twice the focal length', 'between the focus and the lens', 'When the object is placed between the optical centre of the lens and the focal length, the image formed is virtual, erect and magnified.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(402, '2014', 'The diagram above represents a transverse travelling wave. Which two points are 180', 'A and E~B and D~C and F~D and H', 'D and H', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(403, '2014', 'Two objects P and Q of masses 100kg and 20kg respectively are 1.2m apart on a horizontal surface. Calculate the net gravitational force acting on Q. ', '\\(1.11\\times 10^{-7} N\\) towards P~\\(1.11\\times 10^{-7} N\\) towards Q~\\(9.26\\times 10^{-8} N\\) towards P~\\(9.26\\times 10^{-8} N\\) towards Q', '\\(9.26\\times 10^{-8} N\\) towards Q', '\\(F= \\frac{Gm_{1}m_{2}}{r^{2}}\\)\n\\(m_{1} = 100kg\\)\n\\(m_{2} = 20kg', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(404, '2014', 'The primary of a transformer has 100 turns and its secondary has 200 turns. If the voltage at the primary is 100V, determine the voltage at the secondary.', '50V~100V~200V~400V', '200V', 'The ideal transformer (either step-up or step-down) works with the equation', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(405, '2014', 'In the diagram illustrated a block of mass M is at rest on a plane inclined at an angle \\(\\theta\\) to the horizontal. As \\(\\theta\\) increases, the velocity ratio of the plane', 'increases~decreases~remain the same~decreases and later increases', 'decreases', 'The velocity ratio and therefore, the mechanical advantage of an inclined plane system increases as \\(\\theta\\) decreases and vice-versa.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(406, '2014', 'When the speed of a car is halved, its kinetic energy is', 'doubled~quartered~halved~quadrupled', 'quartered', 'Given \\(K_{1}\\) = \\(\\frac{mv^{2}}{2}\\).\nWhen v is halved, we have\n\\(K_{2}\\) = \\(\\frac{m\\times (\\frac{v}{2})^{2}}{2}\\)\n= \\(\\frac{K_{1}}{4}\\)\nHence, the initial kinetic energy is quartered.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(407, '2014', 'A wire of length 400cm is stretched between two fixed points. When plucked, its fundamental frequency is 150Hz. Calculate the speed of the wave produced.', '250\\(ms^{-1}\\)~625\\(ms^{-1}\\)~1200\\(ms^{-1}\\)~1500\\(ms^{-1}\\)', '1200\\(ms^{-1}\\)', 'The fundamental frequency \\((f_{0})\\) = \\(\\frac{v}{2l}\\)\n\\(f_{0} = 150Hz', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(408, '2014', 'The diagram above illustrates a waveform. Determine the number of wavelengths in it', '4~3\\(\\frac{1}{2}\\)~2\\(\\frac{1}{2}\\)~2', '2\\(\\frac{1}{2}\\)', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(409, '2014', 'A resistor with fixed resistance value is called a', 'resistance box~standard resistor~shunt resistor~multiplier resistor', 'standard resistor', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(410, '2014', 'Which of the following statements is not an advantage of an alkaline accumulator?', 'The electrolyte does not need attention~It can be recharged~It has low internal resistance~It has a much longer life than lead-acid accumulator', 'The electrolyte does not need attention', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(411, '2014', 'The diagram above illustrates the wire connections to a three-pin plug. The wires P, Q and R respectively are', 'live, neutral and earth~neutral, earth and live~earth, live and neutral~earth, neutral and live', 'neutral, earth and live', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(412, '2014', 'Which of the following statements about parallel plate capacitors is', 'I only~I and II only~II and III only~I, II and III', 'II and III only', 'Capacitors pass AC but block DC signals (when charged up to the applied DC voltage), they are often used to separate the AC and DC components of a signal. Capacitors are also primarily used to store energy.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(413, '2014', 'The circuit contains three ammeters A1, A2 and A3 with readings of A2 and A3 shown as indicated in the diagram. Determine the reading of A1.', '2A~3A~5A~8A', '3A', 'Ammeters are connected in series so,\nA3= A2 + A1\nA1 = A3 - A1\n= 5A - 2A\n= 3A', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(414, '2014', 'Which of the following statements about magnetic lines of force is not correct? They', 'pass through even non-magnetic materials~run from the north pole to the south pole~are in a state of tension and tend to be shorted~intersect one another', 'intersect one another', 'Two magnetic lines of force can not intersect each other.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(415, '2014', 'In which of the following activities is an induction coil not useful?', 'Investigation of high voltages~Study of electric discharge~Operation of X-ray tubes~A.C. power transmission', 'A.C. power transmission', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(416, '2014', 'In a series R-L-C circuit, R = 10\\(\\Omega\\), \\(X_{c}\\)= 4\\(\\Omega\\) and \\(X_{L}\\) = 9\\(\\Omega\\). The impedance of the circuit is', '4.1\\(\\Omega\\)~5.0\\(\\Omega\\)~10.8\\(\\Omega\\)~11.2\\(\\Omega\\)', '11.2\\(\\Omega\\)', 'The impedance for a RLC circuit is\n\\(Z = \\sqrt{R^{2} + (X_{L} - X_{C})^{2}}\\)\n= \\(\\sqrt{10^{2} + (9 - 4)^{2}}\\)\n= \\(\\sqrt{125}\\)\n= 11.18\\(\\Omega\\) \\(\\approxeq\\) 11.2\\(\\Omega\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(417, '2014', 'A student uses two compass needles to investigate the magnetic field around a bar magnet. Which of the following diagrams show the correct directions of the needles?', 'A~B~C~D', 'B', 'By convention, the field direction is taken to be outward from the North pole and in to the South pole of the magnet. Also, they form closed lines.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(418, '2014', 'Which of the following is emitted in a process of natural radioactivity?', '\\(\\alpha\\)- particles and \\(\\beta\\)- particles~\\(\\alpha\\)- particles and X-rays~\\(\\beta\\)- particles and X-rays~\\(\\lambda\\)- rays and X-rays', '\\(\\alpha\\)- particles and \\(\\beta\\)- particles', 'In the course of natural radioactivity, alpha, beta and gamma rays are emitted.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(419, '2014', 'In which of the following situations is photoelectric effect employed?', 'I, II and IV only~I, III and IV only~III and IV only~I and II only', 'I, II and IV only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(420, '2014', 'Which of the following radiations has the longest wavelength?', 'Gamma ray~Radio wave~Infrared ray~X-ray', 'Radio wave', 'Radio wave has the longest wavelength and shortest frequency.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(421, '2013', 'In which of the following fields is radioisotopes not used?', 'Medicine~Oil industry~Agriculture~Weather forecast', 'Weather forecast', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(422, '2013', 'A nuclide is represented by \\(_{32}^{70}B\\). Determine its neutron-proton ratio', '0.5~0.8~1.2~1.5', '1.2', 'The element B has a mass number of 70 with atomic number 32. Hence, B has 32 protons and (70-32) = 38 neutrons.\nThe neutron- proton ratio is 38', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(423, '2013', 'The diagram above is a micrometer screw gauge. Determine its reading.', '2.44mm~2.46mm~2.86mm~2.96mm', '2.46mm', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(424, '2013', 'Which of the following is the dimension for impulse?', 'MLT\\(^{-1}\\)~MLT\\(^{-2}\\)~MLT~ML', 'MLT\\(^{-1}\\)', 'Impulse = Force \\(\\times\\) time\nForce has the dimension \\(\\frac{ML}{T^{2}}\\), hence', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(425, '2013', 'A body accelerates uniformly from rest at 2\\(ms^{-2}\\). Calculate its velocity when it has travelled a distance of 9m.', '3.0\\(ms^{-1}\\)~4.5\\(ms^{-1}\\)~6.0\\(ms^{-1}\\)~18.0\\(ms^{-1}\\)', '6.0\\(ms^{-1}\\)', 'Given that \\(u = 0ms^{-1}, a = 2ms^{-2}, s = 9m\\)\nWe can use the equation, \\(v^{2}=u^{2} +2as\\) so that we have,\n\\(v^{2} = 0^{2} + 2\\times 2\\times 9\\)\n\\(v^{2} = 36', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(426, '2013', 'Which of the following statements about matter is not correct?', 'Molecules of solids move more freely than molecules of liquids and gases~Molecules of solids are more closely packed than those of liquids~Energy is required to break the intermolecular forces of attraction between molecules~Molecules of liquids move about within the liquid and they are in constant motion', 'Molecules of solids move more freely than molecules of liquids and gases', 'All other properties of the different states of matter holds except that the molecules of solids don\'t move freely due to the fact that the particles in the solids are closely packed so it inhibits free motion.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(427, '2013', 'A ball is projected horizontally from the top of a tower. Neglecting air resistance, which of the following statements about its motion is', 'I only~II only~I and II only~II and III only', 'II and III only', 'The body while coming down is acted upon by acceleration due to gravity, hence, the vertical force is constant. Also, at maximum height, the vertical velocity is 0 and then increases as the body comes downward.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(428, '2013', 'Two forces 100N and 60N act on an object of mass 10kg as illustrated in the diagram above. Neglecting friction, calculate the acceleration of the object.', '4.0\\(ms^{-2}\\)~13.1\\(ms^{-2}\\)~16.0\\(ms^{-2}\\)~22.6\\(ms^{-2}\\)', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(429, '2013', 'A body weighing 14N in air is partially immersed in water. If the mass of water displaced in the process is 200g, calculate the upthrust on the body. [g=10\\(m', '2.0N~3.0N~3.5N~7.0N', '2.0N', 'Upthrust = weight of liquid displaced\n= mass of liquid displaced \\(\\times\\) acceleration due to gravity\n= \\(\\frac{200}{1000} \\times 10\\)\n= 2N', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(430, '2013', 'Which of the following processes is not a surface phenomenon?', 'Condensation~Evaporation~Photo Emission~Thermionic Emission', 'Condensation', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(431, '2013', 'A chemical balance is used for measuring', 'volume~mass~thickness~density', 'mass', 'It is a type of beam balance with great precision, and it can pick up the slightest mass placed on it.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(432, '2013', 'A body is whirled round a circular path at constant speed. Which of the following diagrams correctly indicates the direction of the body\'s velocity (v) and its acceleration (a)?', 'I~II~III~IV', 'II', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(433, '2013', 'A motorist travelling at 72\\(kmh^{-1}\\) had his eyes shut for 0.4s during a hard sneeze. Calculate the distance covered by him during this time interval.', '50.0m~28.8m~18.0m~8.0m', '8.0m', 'Convert velocity from', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(434, '2013', 'The angle at which a projectile must be fired to cover maximum range is', '30~45~60~90', '45', 'The formula is \\(\\frac{v^{2}sin2\\theta}{g}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(435, '2013', 'A body can undergo the following types of motion except', 'random~rotational~translational~relative', 'relative', 'Relative motion is the calculation of the motion of an object with regard to some other moving object. Hence, relative motion is not a type of motion.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(436, '2013', 'Which of the following graphs correctly represents the relationship between the kinetic energy (K.E) and the displacement (d) from point of release of a swinging pendulum bob?', 'I~II~III~IV', 'II', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(437, '2013', 'The energy stored in a spring of stiffness constant k = 2000\\(Nm^{-1}\\) when extended 4cm is', '0.16J~1.60J~16.00J~160.00J', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(438, '2013', 'Ice of mass 50g at 0', '2400J~6800J~7251J~24000J', '24000J', 'The quantity of heat needed to melt ice = mL (where m is the mass of ice and L is the specific latent heat of fusion of ice)\nQ = \\(50 \\times 336 = 16800J\\) but this is 70% of the total heat supplied so that we have,\n70% total heat = 16800J\n\\(\\frac{70}{100}\\) of total', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(439, '2013', 'A plane is inclined at an angle \\(\\theta\\) to the horizontal. Its velocity ratio is', '\\(sin\\theta\\)~\\(tan\\theta\\)~\\(\\frac{1}{sin\\theta}\\)~\\(\\frac{1}{tan\\theta}\\)', '\\(\\frac{1}{sin\\theta}\\)', 'Velocity ratio = \\(\\frac{Effort distance}{Load distance}\\)\nOn an inclined plane, it is the inverse of \\(sin\\theta\\) = \\(\\frac{1}{sin\\theta}\\)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(440, '2013', 'The diagram above illustrates a beaker of water being heated. It is observed that as the bubbles rise they get bigger in size.The reason for this observation is', 'water pressure on the bubbles decreases~density of water increases with rise in temperature~volume of water increases with rise in temperature~atmospheric pressure on the bubbles decreases', 'water pressure on the bubbles decreases', 'When a bubble is deep under water, it has both atmospheric pressure and water pressure (giving it depth), acting on it but as it rises, the water pressure decreases. At this point, the basic pressre acting on the bubble is the atmospheric pressure. Recall that pressure is inversely proportional to volume (Boyles\' law), hence, the less the pressure, the more the volume.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(441, '2013', 'Which of the following devices converts light energy to electrical energy?', 'Bulb~Television~Solar cell~Light emitting diode (LED)', 'Solar cell', 'The solar cell converts light from the sun to electricity.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(442, '2013', 'A motor of a corn mill machine operates on electrical energy of \\(1.44 \\times 10^{5}\\)J. If one-quarter of the energy is wasted on sound and heat, determine the efficiency of the machine.', '0.25~0.36~0.64~0.75', '0.75', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(443, '2013', 'Thermal energy added or removed from a substance that changes the state of the substance is called', 'latent heat~heat of reaction~calorimetry~specific heat', 'latent heat', 'Latent heat is thermal energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(444, '2013', 'The maximum density of water occurs at a temperature of', '0~4~37~273', '4', 'This is as a result of the Hydrogen bonding in water. Due to the high Kinetic Energy of water, the hydrogen bonds can\'t hold for too long but from 4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(445, '2013', 'A vapour whose molecules are in dynamic equilibrium with those of its own liquid is said to be', 'unsaturated~gaseous~saturated~diffused', 'saturated', 'A saturated vapour is one which is in a dynamic equilibrium with its own liquid.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(446, '2013', 'The diagram above illustrates two waves of equal amplitudes A and frequencies approaching each other. When the two waves meet at a point I midway between them, the vertical displacement of the resulting wave will be', '0~\\(\\frac{A}{2}\\)~\\(\\frac{A}{4}\\)~\\(2A\\)', '\\(2A\\)', 'This is a type of constructive interference. When', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(447, '2013', 'A rainbow is formed when sunlight is incident on water droplets suspended in the air due to', 'interference~refraction~dispersion~diffraction', 'dispersion', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(448, '2013', 'Which of the following statements about the 3rd overtone of a vibrating air column of an open pipe is correct? It has', '4 nodes~5 nodes~3 antinodes~4 antinodes', '4 nodes', 'The 3rd overtone for an open pipe has 5 antinodes and 4 nodes.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(449, '2013', 'Consider the wave equation', 'Acceleration~Speed~Amplitude~Wavelength', 'Amplitude', 'Comparing the given equation with the wave equation', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(450, '2013', 'Plane waves through a narrow gap emerge as circular waves. This phenomenon is known as', 'interference~dispersion~refraction~diffraction', 'diffraction', 'Diffraction refers to the various things that occur when a wave encounters an obstacle. This bending of the wave after it passes a small gap is an example of diffraction.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(451, '2013', 'A ray of light incident at an angle \\(\\theta\\) in a rectangular prism grazes the surface of the prism on emerging from the prism. Determine the value of the angle. [Absolute refractive index of the material of the prism is 1.5]', '41.8~48.2~60.8~90', '41.8', '\\(\\eta = \\frac{1}{sin\\theta}\\)\n\\(1.5 = \\frac{1}{sin\\theta}\\)\n\\(sin\\theta = \\frac{1}{1.5} = 0.667\\)\n\\(\\theta = sin^{-1}(0.667) = 41.835', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(452, '2013', 'The diagram above illustrates a wave setup between two fixed ends 4.0m apart. If the speed of the wave is 1.0\\(ms^{-1}\\), its wavelength and frequency respectively are', '1m~2m~2m~4m', '2m', 'For the 4th harmonic, \\(L = 2\\lambda\\)\n\\(4m = 2\\lambda \\implies \\lambda = \\frac{4m}{2}\\)\n=\\(2m\\)\nRecall, \\(v = f\\lambda\\)\n\\(1 = f \\times 2 \\implies f = \\frac{1}{2}\\)\n= 0.50Hz', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(453, '2013', 'Two plane mirrors are inclined at an angle 20', '17~18~19~20', '17', 'The number of images formed = \\(\\frac{360}{n}\\) where the value gotten is odd\nelse, = \\(\\frac{360}{n} -1\\).\nSolving, we have that \\(\\frac{360}{20} = 18\\)\nHence, the no of images formed is 18 - 1 = 17.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(454, '2013', 'A converging lens of focal length 10cm forms an erect image three times the size of the real object. Calculate the distance between the image and the object.', '6.6cm~11.1cm~13.3cm~20.0cm', '13.3cm', 'Given, image size = 3U\nobject size = U\nfocal length = 10cm\nlens to object distance = \\(\\frac{focal length \\times object size}{image size}\\)\n= \\(\\frac{10 \\times u}{3u} = 3.33\\)\ndistance between image and object = 10 + 3.33 = 13.33cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(455, '2013', 'The inverse of the time required for a wave to complete one full cycle is called', 'wavelength~period~frequency~amplitude', 'frequency', 'The time required to complete one full cycle is the period', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(456, '2013', 'Two bar magnets are placed near each other. Which of the following diagrams correctly illustrates the magnetic field pattern formed by the pair?', 'I~II~III~IV', 'II', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(457, '2013', 'The force per unit charge experienced at a point in a field is the', 'gravitational field strength~electric potential~electric field intensity~magnetic field strength', 'electric field intensity', 'Electric intensity at a point is defined as the force experienced per unit positive charge at a point placed in the electric field.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(458, '2013', 'Which of the following objects is not a conductor of electricity?', 'The Earth~Human body~Iron rod~Dry wood', 'Dry wood', 'Dry wood is rather an insulator and not a conductor.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(459, '2013', 'A circuit is set up as shown in the diagram above. When the key is closed, the ammeter reading will be', '6A~4A~2A~1A', '2A', 'The resistors are connected both in parallel and series. To calculate the total resistance, we have', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(460, '2013', 'Which of the following statements is', 'I, II and III~III only~II only~I only', 'I only', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(461, '2013', 'The diagrams above illustrate electrical connections to the element of an electric pressing iron.In which of the connections is the fuse correctly fixed?', 'I~II~III~IV', 'II', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(462, '2013', 'A transformer connected to a 240\\(V_{r.m.s}\\) has 3000 turns in its primary coil and 500 turns in its secondary coil. Calculate the output voltage.', '4000V~400V~40V~4V', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(463, '2013', 'A lamp rated 100W, 240V is lit for 5hours. Calculate the cost of lighting the lamp if 1kWh of electrical energy cost N5.', 'N2.50~N3.20~N6.50~N9.60', 'N2.50', 'Power = 100W', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(464, '2013', 'A battery of e.m.f 3.0V is connected across a potentiometer wire AB of length 10\\(\\Omega m^{-1}\\) as illustrated in the diagram above. If the jockey J makes contact at the 30cm mark, determine the resistance of length AJ and voltage across AJ.', '3.0\\(\\Omega\\)~3.0\\(\\Omega\\)~3.3\\(\\Omega\\)~3.3\\(\\Omega\\)', '3.0\\(\\Omega\\)', 'E = 3.0V', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(465, '2013', 'The main reason why a.c. is transmitted at very high voltage and low current is that', 'flows faster through the conductor~can be stepped down~is cheaper to generate~reduces heat loss', 'reduces heat loss', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(466, '2013', 'The diagram above illustrates two charged bodies, X and Y seperated by a distance r. Each body has charge q and mass m. Which of the following statements about the electrostatic force \\(F_{e}\\) and fravitational force \\(F_{g}\\) acting between the bodies is correct?', '\\(F_{e}\\) is attraction while \\(F_{g}\\) is repulsion~Both \\(F_{e}\\) and \\(F_{g}\\) are that of repulsion~Both \\(F_{e}\\) and \\(F_{g}\\) is that of attraction~\\(F_{e}\\) is repulsion while \\(F_{g}\\) is attraction', '\\(F_{e}\\) is repulsion while \\(F_{g}\\) is attraction', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1);
INSERT INTO `exam_simulation` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`, `status`) VALUES
(467, '2013', 'The opposition offered to an alternating current in a C-R series circuit is known as', 'impedance~resistance~reactance~friction', 'impedance', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(468, '2013', 'Which of the following pairs of concepts constitutes complementary variables as expressess by the Heinsberg uncertainty principle?', 'Momentum and time~Energy and acceleration~Position and momentum~Velocity and Momentum', 'Position and momentum', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(469, '2013', 'The nucleon number of an atom is the total number of', 'electrons and protons~electrons and neutrons~neutrons minus electrons~protons and neutrons', 'protons and neutrons', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(470, '2013', 'n = \\(\\alpha\\)', '+21.2eV~+10.4eV~-10.4eV~-21.2eV', '+10.4eV', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(471, '2013', 'Which of the following statements about Gamma radiation is correct? Gamma radiation can', 'be seen by the naked eye~not pass through an aluminium foil~be present naturally in our surroundings~be used as a tracer', 'be used as a tracer', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(472, '2013', 'Radio wave', 'Visible, ultraviolet, X-ray~X-ray, visible, ultraviolet~Ultraviolet, visible, X-ray~X-ray, ultraviolet, visible', 'Visible, ultraviolet, X-ray', 'No official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here', 'None', '', 'WAEC-PK-1', 'WAEC-PHY', 1),
(473, '1989', 'In the diagram, P, Q and R are three points in a plane such that the bearing of R from Q is 110o and the bearing of Q from P is 050o. Find angle PQR.', ' 60o~ 70o~ 120o~ 160o~', ' 120o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(474, '1989', 'If 3loga + 5loga - 6loga = log64, what is a?', '4~6~8~16~32', '8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(475, '1989', 'If the second and fourth term of a G.P are 8 and 32 respectively,what is the sum of the first four terms?', '28~40~48~60~68', '60', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(476, '1989', 'IN the diagram above, TPS is a straight line, PQRS is a parallelogram with base QR and height 8cm. |QR| = 6cm and the area of triangle QST is 52cm2. Find the area of ΔQPT.', ' 39cm2~ 28cm2~ 24cm2~ 21cm2~ 19cm2', ' 28cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(477, '1989', 'In the diagram O is the center of the circle, if ', ' 14o~ 28o~ 31o~ 45o~ 90o', ' 28o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(478, '1989', 'Evaluate, using logarithm tables5.34 x 67.4/2.7', '1.332~13.32~133.2~1332~13.32', '133.2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(479, '1989', 'Factorize 35 - 2b - b2', ' (35-2b)(b-1)~ (7+b)(5-b)~ (3+7b)(5-b)~ (35-b)(3b+7)~ (7+b)(5+b)', ' (7+b)(5-b)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(480, '1989', 'Evaluate 0.009 / 0.012, leaving your answer in standard form', ' 7.5 x 102~ 7.5 x 101~ 7.5 x 10-1~ 7.5 x 10-2~ 7.5 x 10-3', ' 7.5 x 10-1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(481, '1989', 'The graph above is that of a quadratic function y = 2x2 - x - 6.The roots of the equation are', ' 1.5, 2~ -1.5, 2~ 1, -6~ 1, 6~ -1, 6', ' -1.5, 2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(482, '1989', 'Factorize the following expression; 2x2 + x - 15', ' (2x+5)(x-3)~ (2x-5)(x+3)~ (2x-5)(x-3)~ (2x-3)(x+5)~ (2x+5)(x+3)', ' (2x-5)(x+3)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(483, '1989', 'The angle of elevation of X from Y is 30o. If XY = 40m, how high is X above the level of Y?', ' 10m~ 20m~ 20√3m~ 40m~ 50m', ' 20m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(484, '1989', 'Instead of recording the number 1.23cm of the radius of a tube, a student recorded 1.32cm. Find the percentage of error, correct to one decimal place.', '0.068~0.073~0.096~0.144~0.154', '0.073', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(485, '1989', 'In the diagram above, ', ' x = p + 2~ x = p - 2~ x = p2~ x = p/2~ x = 2p', ' x = p/2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(486, '1989', 'In the diagram above ABDE and FCDE are parallelograms. If |FC| = 12.2cm and the height |PC| = 4.0cm, calculate the area of the parallelogram ABDE.', ' 3.05cm2~ 8.20cm2~ 16.20cm2~ 24.40cm2~ 48.8cm2', ' 48.8cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(487, '1989', 'Using the above graph, if 10o < x < 60o, what is the value of x for which sin x = cos x?', ' 0o~ 20o~ 30o~ 45o~ 50o', ' 45o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(488, '1989', 'The venn diagram below shows the number of students who studied Physics, Chemistry, and Mathematics in a certain school. How many students took at least two of the three subjects?', '165~160~155~135~85', '160', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(489, '1989', 'An arc of a circle radius 7cm is 14cm long. What angle does the arc subtend at the center of circle?', ' 25.7o~ 44o~ 51.43o~ 98o~ 114.55o', ' 114.55o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(490, '1989', 'If 5 times a certain integer is subtracted from twice the integer, the result is 63. Find the integer.', '21~9~7~4~3', '21', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(491, '1989', 'If 3 y = 243, find the value of y', '2~3~4~5~6', '5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(492, '1989', 'Points X and Y are respectively 20km North and 9km East of a point O. What is the bearing of Y from X? Correct to the nearest degree', ' 024o~ 114o~ 156o~ 204o~ 336o', ' 156o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(493, '1989', 'In the diagram above, O is the center of the circle. Calculate the length of the chord AB if |OA| = 5cm, |OD| = 3cm and ', ' 3cm~ 4cm~ 5cm~ 8cm~ 15cm', ' 8cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(494, '1989', 'Calculate the surface area of a hallow cylinder which is closed at one end, if the base radius is 3.5cm and the height 8cm.', ' 126.5cm2~ 165cm2~ 176cm2~ 214.5cm2~ 253.5cm2', ' 214.5cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(495, '1989', 'Solve the following equation: 6x2 - 7x - 5 = 0', ' x = 1/2 or x = -21/2~ x = 1/3 or x = 21/2~ x = 1 2/3 or x = -1/2~ x = 12/3 or x = 1/2~ x = 5/6 or x = -1', ' x = 1 2/3 or x = -1/2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(496, '1989', 'What angle represents grown up girls ? Correct to one decimal place', ' 37.5o~ 26.7o~ 25.7o~ 20o~ 3.75o', ' 26.7o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(497, '1989', 'What percentage of the population are married? correct to one decimal place', '0.148~0.204~0.305~0.352~0.365', '0.352', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(498, '1989', 'If A = (a,b,c), B = (a,b,c,d,e) and C = (a,b,c,d,e,f). Find (A', ' (a,b,c,d)~ (a,b,c,d,e)~ (a,b,c,d,e,f)~ (a,b,c)~ ', ' (a,b,c,d,e)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(499, '1989', 'For a class of 30 students, the scores in a Mathematics test out of 10 marks were as follows;4,5,7,2,3,6,5,5,8,9,5,4,2,3,7,9,8,7,7,7,3,4,5,5,2,3,6,7,7,2 What is the mode of the score', '3~4~5~6~7', '7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(500, '1989', 'For a class of 30 students, the scores in a Mathematics test out of 10 marks were as follows;4,5,7,2,3,6,5,5,8,9,5,4,2,3,7,9,8,7,7,7,3,4,5,5,2,3,6,7,7,2 What is the median score?', '2~7~8~9~10', '8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(501, '1989', 'For a class of 30 students, the scores in a Mathematics test out of 10 marks were as follows;4,5,7,2,3,6,5,5,8,9,5,4,2,3,7,9,8,7,7,7,3,4,5,5,2,3,6,7,7,2 What is the range of the distribution?', '2~7~8~9~10', '7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(502, '1989', 'In the diagram above O is the center of the circle, if ', ' 15o~ 75o~ 105o~ 150o~ 210o', ' 105o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(503, '1989', 'Simplify 91/2/272/3', '1~ 1/3~ 1/9~ 1/18~ 1/27', ' 1/3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(504, '1989', 'In the diagram above, what is the size of angle ACB.', ' 40o~ 50o~ 60o~ 80o~ 100o', ' 60o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(505, '1989', 'With reference to the graph above, which f the following solution sets is represented by ΔOPQ?', ' y ≥ x, y ≤ 0, y + x ≥ 7~ y ≤ x, y ≥ 0, y + x ≤ 7~ y ≥ x, y ≥ 0, y + x ≤ 7~ y ≤ x, y ≤ 0, y + x ≤ 7~ y ≤ x, y ≥ 0, y + x ≥ 7', ' y ≤ x, y ≤ 0, y + x ≤ 7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(506, '1989', 'Find the volume of a cone of radius 3.5cm and vertical height 12cm ', ' 3.4cm2~ 15.5cm2~ 21.0cm2~ 42.0cm2~ 154.0cm2', ' 154.0cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(507, '1989', 'The table above gives the scores of a group of students in an English Language test.If a student is chosen at random from the group, what is the probability that the scored at least 6 marks?', ' 3/20~ 1/5~ 1/4~ 3/10~ 3/4', ' 1/4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(508, '1989', 'The angle of a sector of a circle of diameter 8cm ', ' 93/7cm2~ 124/7cm2~ 185/7cm2~ 251/7cm2~ 313/7cm2', ' 185/7cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(509, '1989', 'In the diagram above, O is the center of the circle QRT and PT is a tangent to the circle at T. Calculate the angle x.', ' 55o~ 40o~ 35o~ 25o~ 20o', ' 20o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(510, '1989', 'Which of the following gives the point of intersection of the graph y = x2 and y = x + 6 shown above?', ' (0,6), (3,9)~ (-3, 0)(2,4)~ (-2,4)(3,9)~ (-2,3)(-3,2)~ (-2,2)(3,6)', ' (-2,4)(3,9)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(511, '1989', 'A sector is cut off from a circle radius 8.2cm to form a cone, if the radius of the resulting cone is 3.5cm, calculate the curved surface area of the cone. ', ' 11.25cm2~ 12.83cm2~ 22.0cm2~ 67.2cm2~ 90.2cm2', ' 90.2cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(512, '1989', 'If logax = p, express x in terms  of a and p', ' x = u + p~ x = a/p~ x = p~ x = ap~ x = ap', ' x = ap', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(513, '1989', 'Calculate and correct to three significant figures, the length of an arc subtends an angle of 70o at the center of the circle radius 4cm. ', ' 2.44cm~ 4.89cm~ 9.78cm~ 25.1cm~ 50.3cm', ' 4.89cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(514, '1989', 'In the diagram above, O is the center of the circle. If ', ' 123o~ 118.5o~ 117o~ 114o~ 54o', ' 123o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(515, '1989', 'The angle of depression of a point on the ground from the top of a building is 20.3o. If the foot of the building is 40m, calculate the height of the building, correct to one decimal place', ' 37.5m~ 28.1m~ 27.8m~ 14.8m~ 13.9m', ' 14.8m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(516, '1989', 'Solve for x: (x2 + 2x + 1) = 25', ' -6, -4~ 6, -4~ 6, 4~ -6, 4~ 5, 5', ' -6, 4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(517, '1989', 'Given that logp = 2 logx + 3logq, which of the following expresses p in terms of x and q?', ' p = 5xq~ p = 6xq~ p = x2 + q3~ p = 2x + 3q~ p = x2q3', ' p = x2q3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(518, '1989', 'sinθ = 1/2 and cosθ = -√3/2, what is the value of  θ?', ' 30 0~ 60 0~ 90 o~ 120 o~ 150 o', ' 150 o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(519, '1989', 'What is the probability that 3 customers waiting in a bank will be served in the sequence of their arrival at the bank', ' 1/6~ 1/3~ 1/2~ 2/3~ 5/6', ' 1/3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(520, '1989', 'In the diagram, O is the center of the circle, If ', ' 4o~ 8o~ 16o~ 20o~ 32o', ' 8o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(521, '1989', 'In an A.p the first term is 2, and the sum of the 1st and the 6th term is 161/2. What is the 4th term', '12~ 91/2~8~7~ 51/2', ' 91/2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(522, '1990', 'What must be added to 4x2 - 4 to make it a perfect square?', ' −1x2−1x2\\frac{-1}{x^2}~ 1x21x2\\frac{1}{x^2}~1~-1~', ' 1x21x2\\frac{1}{x^2}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(523, '1990', 'Each of the interior angles of a regular polygon is 140o. How many sides has the polygon?', '9~8~7~5~', '9', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(524, '1990', 'If sin x = cos 50o, then x equals', ' 40o~ 45o~ 50o~ 90o~ 130o', ' 40o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(525, '1990', 'Simplify 125-1/3 x 49-1/2 x 100', '350~35~ 1/35~ 1/350~', ' 1/35', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(526, '1990', 'If 32x = 27, what is x?', '1~1.5~4.5~18~40.5', '1.5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(527, '1990', 'Express 0.00562 in standard form', ' 5.62 x 10-3~ 5.62 x 10-2~ 562 x 10-2~ 5.62 x 102~ 5.62 x 103', ' 5.62 x 10-3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(528, '1990', 'Given that 1/3log10 P = 1, find the value of P', ' 1/10~3~10~100~1000', '1000', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(529, '1990', 'Simplifylog√8/log8', ' 1/3~ 1/2~ 1/3log√2~ 1/3log√8~ 1/2log√2', ' 1/2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(530, '1990', 'Evaluate using the logarithm table, log(0.65)2', '1.6258~0.6272~0.6258~3.6258~1.6272', '3.6258', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(531, '1990', 'If log x = 2.3675 an log y = 0.9750, what is the value of x + y? Correct to three significant figures', '1.18~1.31~9.03~9.44~9.46', '9.46', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(532, '1990', 'While doing his physics practical, Idowu recorded a reading as 1.12cm instead of 1.21cm. Calculate his percentage error', '0.0117~0.0638~0.0744~0.0804~0.09', '0.0804', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(533, '1990', 'Find the 4th term of an A.P, whose first term is 2 and the common difference is 0.5', '0.5~2.5~3.5~4~4.5', '3.5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(534, '1990', 'From the graph determine the roots of the equation y = 2x2 + x - 6', ' -3, 4~ -2, -6~ -2, 1.5~ -1, 1~ 2, 1.5', ' -2, 1.5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(535, '1990', 'Find the values of x for which y = 5', ' -2.5, 2.0~ -2.6, 2.1~ -2.0, 1.5~ -2.0, 2.0~ 0, 0', ' 0, 0', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(536, '1990', 'An arc of length 22cm subtends an angle of θ at the center of the circle. What is the value of θ if the radius of the circle is 15cm?', ' 70o~ 84o~ 96o~ 156o~ 168o', ' 84o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(537, '1990', 'Find the sum of the first five terms of the G.P 2.6 18 ....', '484~243~242~130~121', '242', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(538, '1990', 'In a class of 80 students, every students had to study economics or geography, or both economics and geography, if 65 students studied economics and 50 studied geography, how many studied both subjects?', '15~30~35~45~50', '35', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(539, '1990', 'The area shaded with horizontal lines is the solution set of the inequalities:', ' y ≥ x, y + 3 ≥ 2x, x ≤ 3~ y ≤ x, y + 2x ≥ -3, x ≤ 3~ y ≤ -x, y + 2x ≤ 3, x ≥ -3~ y ≥ -x, y + 3 ≤ 2x, x ≥ -3~ y ≤ x, y ≤ 2x - 3, x ≥ 3', ' y ≤ x, y + 2x ≥ -3, x ≤ 3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(540, '1990', 'The area shaded with vertical lines is the solution set of the inequalities:', ' y ≤ x, y + 2x ≤ -3~ y ≥ x, y + 2x ≥ - 3~ y ≤ x, y < 2x - 3, x ≤ 3~ y ≤ -x, y ≤ 2x - 3, x ≤ 3~ y ≥ x, y + 2x ≥ 3, x ≤ 3', ' y ≤ x, y < 2x - 3, x ≤ 3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(541, '1990', 'In the diagram above, O is the center of the circle with radius 10cm, and ', ' 5.2cm~ 10.5cm~ 13.2cm~ 20.6cm~ 31.4cm', ' 10.5cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(542, '1990', 'Factorize x2 + 4x - 192', ' (x-4) (x+48)~ (x-48) (x+4)~ (x-12) (x+16)~ (x-12) (x-16)~ (x+12) (x+16)', ' (x-12) (x+16)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(543, '1990', 'Factorize 2e2 - 3e + 1', ' (2e-1) (e-1)~ (e+1) (2e+1)~ (2e+3) (e+2)~ (2e-3) (e-1)~ (e2-3(2e-1)', ' (2e-1) (e-1)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(544, '1990', 'Solve the equation 7y2 = 3y', ' y = 3 or 7~ y = 0 or 7~ y = 0 or 3/7~ y = 0 or 9~ y = 0 or 10', ' y = 0 or 3/7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(545, '1990', 'Find the value of m which makes x2 + 8 + m a perfect square', '2~4~8~12~16', '16', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(546, '1990', 'Solve the equation 2a2 - 3a - 27 = 0', ' 3/2, 9~ -2/3, 9~ 3, 9/2~ -3, -9/2~ -3, 9/2', ' -3, 9/2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(547, '1990', 'A sector of a circle of radius 7cm has an area of 44cm2. Calculate the angle of the sector correct to the nearest degree  ', ' 6o~ 26o~ 52o~ 103o~ 206o', ' 103o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(548, '1990', 'calculate the surface area of a sphere of radius 7cm ', ' 86cm2~ 154cm2~ 616cm2~ 1434cm2~ 4312cm2', ' 616cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(549, '1990', 'If the radius of the parallel of latitude 30oN is equal to the radius of the parallel of latitude θoS, what is the value of θ?', ' 75o~ 60o~ 45o~ 30o~ 0o', ' 30o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(550, '1990', 'A cylindrical container closed at both ends, has a radius of 7cm and height 5cm ', ' 35cm3~ 154cm3~ 220cm3~ 528cm3~ 770cm3', ' 528cm3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(551, '1990', 'In the diagram above, |PQ| = |PR| = |RS| and ', ' 72o~ 64o~ 52o~ 32o~ 26o', ' 52o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(552, '1990', 'In the diagram above, WXYZ is a rhombus and ', ' 20o~ 30o~ 45o~ 60o~ 70o', ' 70o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(553, '1990', 'In the diagram above PS||RQ, |RQ| = 6.4cm and perpendicular PH = 3.2cm. Find the area of SQR.', ' 5.12cm2~ 9.60cm2~ 10.24cm2~ 20.48cm2~ 40.96cm2', ' 10.24cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(554, '1990', 'Which angle is equal to ', ' ~~~~', ' ', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(555, '1990', 'Which triangle is equal in area to ΔVWZ', ' ΔVXZ~ ΔVYZ~ ΔXYV~ ΔWYV~ ΔWYZ', ' ΔVYZ', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(556, '1990', 'In the diagram above, PQRS s a cyclic quadrilateral, ', ' 58o~ 53o~ 48o~ 43o~ 38o', ' 48o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(557, '1990', 'In the diagram below, O is the center of the circle if ', ' 110o~ 70o~ 55o~ 35o~ 20o', ' 35o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(558, '1990', 'In the diagram above, PQ is a tangent at T to the circle ABT. ABC is a straight line and TC bisects ', ' 20o~ 30o~ 35o~ 40o~ 50o', ' 50o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(559, '1990', 'Which of the sketches above gives a correct method for constructed an angle of 120o at the point P?', ' I only~ II only~ III only~ I and II only~ I, II and III', ' I and II only', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(560, '1990', 'Use mathematical table to evaluate (cos40o - sin30o)', '-0.266~-0.0266~0.0266~0.266~1.532', '0.266', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(561, '1990', 'If the shadow of a pole 7m high is 1/2 its length what is the angle of elevation of the sun, correct to the nearest degree?', ' 90o~ 63o~ 60o~ 26o~ 0o', ' 63o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(562, '1990', 'From the top of a building 10m high, the angle of depression of a stone lying on the horizontal ground is 69o. Calculate ,correct to one decimal place, the distance of the stone from the foot of the building', ' 3.6m~ 3.8m~ 6.0m~ 9.3m~ 26.1m', ' 3.8m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(563, '1990', 'The bearing of a point x from a point y is 074o. What is the bearing of y from x?', ' 106o~ 146o~ 164o~ 254o~ 286o', ' 254o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(564, '1990', 'The annual salary of Mr. Johnson Mohammed for 1989 was N12,000.00. He spent this on agriculture projects, education of his children, food items, saving , maintenance and miscellaneous items as shown in the pie chartHow much did he spend on food items?', ' N9,700.00~ N6,700.00~ N4,000.00~ N3,700.00~ N2,300.00', ' N2,300.00', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(565, '1990', 'The annual salary of Mr. Johnson Mohammed for 1989 was N12,000.00. He spent this on agriculture projects, education of his children, food items, saving , maintenance and miscellaneous items as shown in the pie chartHow much money did he invest in agriculture', ' N1,200.00~ N1,440.00~ N2,000.00~ N2,910.00~ N4,000.00', ' N4,000.00', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(566, '1990', 'The table shows that the amount of money (in naira) collected through voluntary donations in a secondary school.What is the mode?', ' N3~ N6~ N9~ N12~ N15', ' N12', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(567, '1990', 'The table shows that the amount of money (in naira) collected through voluntary donations in a secondary school.What is the median of distribution?', ' N3.00~ N9.00~ N12.00~ N15.00~ N18.00', ' N12.00', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(568, '1990', 'If a student in favour of the proposal is selected for a post, what is the probability that he is from group A?', ' 8/19~ 16/35~ 10/19~ 4/7~ 4/5', ' 4/5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(569, '1990', 'If a student is chosen at random, what is probability that he is against the proposal?', ' 3/19~ 4/19~ 5/19~ 9/19~ 10/19', ' 5/19', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(570, '1991', 'Simplify 11+√511+√5\\frac{1}{1 + \\sqrt{5}} - 11−√511−√5\\frac{1}{1 - \\sqrt{5}}', ' - 12√512√5\\frac{1}{2}\\sqrt{5}~ 12√512√5\\frac{1}{2}\\sqrt{5}~ -- 14√514√5\\frac{1}{4}\\sqrt{5}~5~', ' - 12√512√5\\frac{1}{2}\\sqrt{5}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(571, '1991', 'The population of a village is 6538. Express this number to three significant figures.', '6540~6538~6530~654~', '6540', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(572, '1991', 'A cylinder of base radius 4cm is open at one end. If the radio of the area of its base to that of its curved surface is 1:4, calculate the height of the cylinder.', ' 1cm~ 2cm~ 4cm~ 8cm~', ' 8cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(573, '1991', 'A headmaster contributes 7% of his income into a fund and his wife contributes 4% of her income. If the husband earns ', ' ~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(574, '1991', 'Given that 1/2 log10 P = 1, find the value Of P', '104~103~102~101~ 10-1', '102', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(575, '1991', 'In the diagram above, |PQ| = |QR|, |PS| = |RS|, ', ' 15o~ 25o~ 40o~ 50o~ 55o', ' 25o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(576, '1991', 'Express 0.0462 in standard form', ' 0.462 x 10-1~ 0.462 x 10-2~ 4.62 x 10-1~ 4.62 x 10-2~ 4.62 x 103', ' 4.62 x 10-2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(577, '1991', 'Simplify: log6 + log2 --  log12', '-4~-1~ o~1~4', ' o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(578, '1991', 'Find the number whose logarithm to base 10 is 2.6025', '400.4~0.4004~0.04004~0.004004~0.0004004', '400.4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(579, '1991', 'Simplify: (1)-11/2/4', ' 1/8~ 1/4~2~4~8', ' 1/4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(580, '1991', 'For what value of y is the expression (y + 2)/y2 - 3y- 10 undefined?', ' y = 0~ y = 2~ y = 3~ y = 5~ y = 10', ' y = 5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(581, '1991', 'Factorize 3a2 - 11a + 6', ' (3a - 2)(a - 3)~ (2a -2)(a - 3)~ (3a - 2)(a + 3)~ (3a + 2)(a - 3)~ (2a-3)(a + 2)', ' (3a - 2)(a - 3)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(582, '1991', 'Solve the equation: 3a + 10 = a2', ' a = 5 or a = 2~ a = -5 or a = 2~ a = 10 or a = 0~ a = 5 or a = 0~ a = 5 or a = -2', ' a = 5 or a = -2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(583, '1991', 'Simplify 3x+152y+6xy3x+152y+6xy\\frac{3}{x} + \\frac{15}{2y} + \\frac{6}{xy}', ' 2y−5x42y−5x4\\frac{2y - 5x}{4}~ 9(2x−5x)x2y29(2x−5x)x2y2\\frac{9(2x - 5x)}{x^2y^2}~ 5x−2y25x−2y2\\frac{5x - 2y}{2}~ c2y218y−45xc2y218y−45x\\frac{c^2y^2}{18y - 45x}~ 42y−5x42y−5x\\frac{4}{2y - 5x}', ' 2y−5x42y−5x4\\frac{2y - 5x}{4}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(584, '1991', 'Simplify: 1/4(2n - 2n+2)', ' 2n2 - 2n~ 2n-2(1-2n)~ 2n + 22n + 2~ 22n~', ' 2n2 - 2n', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(585, '1991', 'Find the equation whose roots are -2/3 and -1/4', ' 12x2 + 11x + 2 = 0~ 12x2 - 11x + 2 = 0~ x2 - 11/12x + 2 = 0~ 12x2 - 11x - 2 = 0~ x2 - 11/12x - 2 = 0', ' 12x2 + 11x + 2 = 0', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(586, '1991', 'Solve: 6(x - 4) + 3(x + 7) = 3', ' 3/2~ 2/3~ 1/2~ 1/3~ o', ' 2/3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(587, '1991', 'If 2x + y = 7 and 3x - 2y = 3, by how much is 7x greater than 10?', '1~3~7~10~17', '7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(588, '1991', 'A car is travelling at an average speed of 80km/hr. Its speed in meters per second (m/s) is', ' 13.3m/s~ 22.2m/s~ 133.3m/s~ 222.2m/s~ 1333.3m/s', ' 22.2m/s', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(589, '1991', 'Mrs. Kofi sold an article for C7.50 instead of C12.75. Calculate her percentage of error, correct to one decimal place.', '0.412~0.183~0.053~0.017~0.014', '0.412', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(590, '1991', 'Find the area of the enclosed region, PXROY correct to the nearest whole number.', ' 96cm2~ 116cm2~ 154cm2~ 192cm2~ 385cm2', ' 96cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(591, '1991', 'Find the perimeter of the region.', ' 22cm~ 33cm~ 40cm~ 47cm~ 66cm', ' 40cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(592, '1991', 'The shaded portion shows the outer boundary of the half plane defined by the inequality', ' 4x + 3y ≥≥\\geq 6~ 4x + 3y = 6~ 4x + 3y < 6~ 3y >6~ 4x < 6', ' 4x + 3y ≥≥\\geq 6', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(593, '1991', 'Find the coordinates of point B.', ' (0,11/2)~ (O,2)~ (2,0)~ (11/2, 2)~ (11/2, 0)', ' (11/2, 2)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(594, '1991', 'The first term a of an A.P is equal to twice theCommon difference d. Find, in terms of d, the 5thTerm of the A.P.', ' 4d~ 5d~ 6d~ a + 5d~ 2a + 4d', ' 6d', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(595, '1991', 'The common ratio of a G.P. is 2. If the 5th term isGreater than the 1st term by 45, find the 5th term,', '3~6~45~48~90', '48', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(596, '1991', 'Two towns, P and Q, are on (4oN 40oW) and (4oN 20oE) respectively. What is the distance between them, along their line of latitude? (Give your answer in teems of ', '2~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(597, '1991', 'The graph above is a sketch of', ' y = sin 2x~ y=sinx~ y=cos2x~ y=2sinx~ y = 2cos x', ' y=2sinx', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(598, '1991', 'Given that sin 9 = -0.9063, where O ≤≤\\leq θθ\\theta o ≤≤\\leq 270o.Find θθ\\theta.', ' 65o~ 115o~ 145o~ 245o~ 265o', ' 245o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(599, '1991', 'From the top of a cliff, the angle of depression of a boat on the sea is 60o, if the top of the cliff is 25 m above the sea level, calculate the horizontal distance from the bottom of the cliff to the boat.', ' 50√3 m~ 25√3 m~ 25√3/3 m~ 25/3 m~ √3/25 m', ' 25√3/3 m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(600, '1991', 'The angle of elevation of the top of a tree 39m away from a point on the ground is 30o. Find the height of the tree.', ' 39√3m~ 13√3m~ 13/√3√3\\sqrt{3}m~ 13/3√3√3\\sqrt{3}m~ √3√3\\sqrt{3}/13m', ' 13√3m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(601, '1991', 'In the diagram above, ATR is a tangent at the point T; to the circle centre O, if ', ' 20o~ 35o~ 45o~ 55o~ 65o', ' 55o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(602, '1991', 'P=(2, 1,3, 9, 1/2)Q=(1,21/2,3, 7)and R=(5, 4, 21/2)Find P', ' (21/2)~ (1, 9)~ (1, 2, 3, 4, 5, 6, 7)~ (5, 4, 21/2)~ (1/2, 1, 2, 21/2, 3, 4, 5, 7, 9)', ' (1/2, 1, 2, 21/2, 3, 4, 5, 7, 9)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(603, '1991', 'P=(2, 1,3, 9, 1/2)Q=(1,21/2,3, 7)andR=(5, 4, 21/2)Find P∩Q∩R', ' (21/2)~~ (1, 3, 7)~-4~ (5,7,9)', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(604, '1991', 'In a class of 80 students, every student had toStudy Economics or Geography or bothEconomics and Geography. lf 65 students studiedEconomics and 50 studied Geography, how manyStudied both subjects?', '15~30~35~45~50', '35', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(605, '1991', 'Which of the following is not a measure ofDispersion?', ' Mode~ Mean deviation~ Range~ interquartile range~ Standard deviation', ' Mode', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(606, '1991', 'The mean of 30 observations recorded in anExperiment is 5. lf the observed largest value of34 is deleted, find the mean of the remainingObservations', '5~4~3.9~3.4~3', '4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(607, '1991', 'Find the mean of the distribution.', '3.5~4~4.4~5~5', '4.4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(608, '1991', 'Find the mode of the distribution.', '40~9~7~5~2', '5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(609, '1991', 'Find the median of the distribution.', '9~6.5~5~4.5~4', '5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(610, '1991', 'If events X and Y are mutually exclusive, .P(X) = 1/3 and P(Y) = 2/5,P(X∩Y) is', ' o~ 2/15~ 11/15~ 4/15~1', ' 2/15', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(611, '1991', 'If events X and Y are mutually exclusive, .P(X) = 1/3 and P(Y) = 2/5,P(X', ' o~ 2/15~ 4/14~ 11/15~1', ' 11/15', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(612, '1991', 'A box contains 2 white and 3 blue identicalMarbles. If two marbles are picked at random,One after the other without replacement, what isThe probability of picking two marbles of differentColours?', ' 2/3~ 3/5~ 2/5~ 7/20~ 3/10', ' 3/5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(613, '1991', 'Mrs. Jones is expecting a baby. The probabilityThat it will be a boy is 1/2 and probability that theBaby will have blue eyes is 1/4. What is theProbability that she will have a blue-eyed boy?', ' 1/8~ 1/4~ 3/8~ 1/2~ 3/4', ' 1/8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(614, '1991', 'Which of the following about a rhombus may notBe true?', ' The diagonals are equal~ The diagonals bisect the angles through which they pass~ the diagonals bisect each other~ The adjacent sides are equal~ Opposite angles are equal', ' The diagonals are equal', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(615, '1991', 'The angles of a pentagon are xo, 2xo (x + 6O) o,(X + 10) o, (x -1O) o. Find the value of x', '40~60~75~80~90', '80', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(616, '1991', 'In a given regular polygon, the ratio of the exterior angle to the interior angles is 1:3. How many side has the polygon?', '40~5~6~8~12', '8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(617, '1991', 'In the diagram above, O is the center of the circle, |SQ| = |QR| and ', ' 34o~ 45o~ 56o~ 62o~ 68o', ' 34o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(618, '1991', 'Find the area of an equivalent triangle of side 16cm', ' 64√3cm2~ 72√3cm2~ 96cm2~ 128√3cm2~ 128cm2', ' 64√3cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(619, '1991', 'In the diagram above, PQ and XY are two concentric arc; center O, the ratio of the length of the two arc is 1:3, find the ratio of the areas of the two sectors OPQ and OXY.', ' 1:3~ 1:6~ 1:9~ 2:3~ 4:9', ' 1:9', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(620, '1991', 'In the diagram above , |AD| = 10cm, |DC| = 8cm and |CF| = 15cmIf the area of triangle DCF = 24cm2, find the area of the quadrilateral ABCD.', ' 24cm2~ 48cm2~ 80cm2~ 96cm2~ 120cm2', ' 48cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(621, '1991', 'In the diagram above , |AD| = 10cm, |DC| = 8cm and |CF| = 15cm.Which of the following is correct?', ' Area BCF = Area DCF~ Area ADE = Area ADF~ Area ADE = Area DCFE~ Area CBF = Area DABC~ Area DABO = Area CFEO', ' Area DABO = Area CFEO', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(622, '1992', 'A cliff on the bank of a river is 300 meter high. if the angle of depression  of a point on the opposite side of the river is 60', ' 100m~ 75√3 m~ 100√3m~ 200√3m~', ' 100√3m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(623, '1992', 'What must be added to expression x2−18xx2−18xx^2 - 18x to make a perfect square?', '9~36~72~81~', '81', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(624, '1992', 'The area of a parallelogram is 513cm22^2 and the height is 19cm, calculate the base.', ' 13.5cm~ 25cm~ 27cm~ 54cm~', ' 27cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(625, '1992', 'A bricklayer measured the length of a wall to be 4.10m. if the actual length of the wall is 4.25m, find his percentage error.', '0.0366~0.0353~0.15~0.17~', '0.0353', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(626, '1992', 'A town P is on bearing 315° from town Q while town R is South of town P and West of town Q. If town R is 60km away from Q, how far is R from P?', ' 30km~ 42km~ 45km~ 60km~', ' 60km', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(627, '1992', 'Let U = (1, 2, 3, 4), P = (2, 3) and Q = (2, 4). What is (P∩Q)\'?', ' (1, 2, 3)~ (1, 3, 4)~ (2, 3)~ (1, 3)~ (1, 4)', ' (1, 3, 4)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(628, '1992', 'Simplify (3/4 + 1/3) x 41/3 + 31/4', ' 1/2~ 13/12~ 10/9~ 17/12~ 13/9', ' 13/9', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(629, '1992', 'If x varies over the set of real numbers, which of', ' -3 -3≤x<2 -3 -3≤x≤2 x≥2~ -3≤x<2~ -3 -3≤x≤2 x≥2~ -3≤x≤2~ x≥2', ' -3≤x<2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(630, '1992', 'Convert 77 to a number in base two', ' 1001 101~111001~100110~10101~10011', ' 1001 101', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(631, '1992', 'The nth term of a sequence is given by 3.2n+2Write down the first three terms of the sequence.', ' 2/3, 0, 6~ 3/2, 3, 6,~ 2/3, 3, 8/3~ 2/3, 3/4,  6~ 2/3, 3, 1/3', ' 3/2, 3, 6,', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(632, '1992', 'Simplify: (16/81) 1/4', ' 8/27~ 1/3~ 4/9~ 2/3~ -4/3', ' 2/3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(633, '1992', 'Evaluate log1025 + log1032 - log108', '0.2~2~100~409~490', '2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(634, '1992', 'Factorize the expression 2y2 + xy - 3x2', ' 2y (y + x) - 3x2~ (2y - x)(2y + X)~ (3x - 2y(x - y)~ (2y + 3) x (y - X)~ (X ', ' (2y + 3) x (y - X)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(635, '1992', 'Construct a quadratic equation whose roots are-1/2 and 2.', ' 3x2-3x+2=0~ 3x2+3x-2=0~ 2x2+3x-2=0~ 2x2-3x+2=0~ 2x2-3x-2=0', ' 2x2-3x-2=0', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(636, '1992', 'Write a single fraction1/1 - x +2/1 + x', '~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(637, '1992', 'Solve the equationm/3 +1/2 =3/4 +m/4', '-3~-2~2~3~4', '3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(638, '1992', 'The angle of a sector of a circle of radius Bam is240o. This sector is bent to form a cone. Find theRadius of the base of the cone.', ' 16/3cm~ 15/3cm~ 16/5cm~ 8/3cm~ 16/10cm', ' 16/3cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(639, '1992', 'The curved surface area of a cylindrical tin is704cm2. Calculate the height when the radius is8cm. ', ' 3.5cm~ 7cm~ 14cm~ 28cm~ 32cm', ' 14cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(640, '1992', 'The volume of a cone of height 9cm is 1848cm', ' 7cm~ 14cm~ 28cm~ 98cm~ 196cm', ' 14cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(641, '1992', 'The diagram above shows the shaded segment of a circle of radius 7cm. If the area of the triangle OXY is 121/2cm2, calculate the area of the segment. ', ' 5/12cm2~ 7/12cm2~ 11/6cm2~ 2 1/3cm2~ 6 1/6cm2', ' 7/12cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(642, '1992', 'In the diagram above PQT is a tangent to the circle QRS at Q. Angle QTR = 48o and ', ' 48o~ 45o~ 37o~ 32o~ 30o', ' 37o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(643, '1992', 'In the diagram above, O is the center of the circle and ', ' 234o~ 117o~ 72o~ 63o~ 54o', ' 117o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(644, '1992', 'In the diagram above, TR = TS and ', '30~45~60~120~150', '60', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(645, '1992', 'In the diagram above, O is the center of the circle PQRS and ', ' 36o~ 72o~ 108o~ 144o~ 288o', ' 72o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(646, '1992', 'In the diagram above, O is the center of the circle QOR is a diameter and ', ' 37o~ 53o~ 65o~ 127o~ 147o', ' 53o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(647, '1992', 'In the diagram above, ML//PQ and NP//QR, if ', ' 15o~ 25o~ 35o~ 40o~ 55o', ' 15o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(648, '1992', 'The angles marked in the diagram above are measured in degrees. Find x.', ' 15o~ 24o~ 30o~ 36o~ 48o', ' 24o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(649, '1992', 'Find the value of t in the diagram above.', ' 5.6cm~ 6.5cm~ 6.6cm~ 6.8cm~ 7.0cm', ' 5.6cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(650, '1992', 'A regular polygon has each of its exterior angles as 18o. How many sides has the polygon', '10~11~12~20~24', '20', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(651, '1992', 'In the diagram above, PQT is an isosceles triangle.|PQ| = |QT|, ', ' 20o~ 50o~ 55o~ 70o~ 75o', ' 55o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(652, '1992', 'Sin 60o has the same value as I. Sin 120o II. cos 240o III. -sin 150o IV. cos 210o V. sin 240o', ' I only~ II only~ IV only~ III only~ IV and V only', ' I only', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(653, '1992', 'The value of sin 210o is', ' -1/2~ -√3/2~ 1/2~ √2/2~ √3/2', ' -1/2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(654, '1992', 'A ladder leans against a vertical wall at an angle60° to the wall, if the foot of the ladder is 5 metresAway from the wall, calculate the length of theLadder.', '~ 5m~~~ 10m', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(655, '1992', 'Points X and Y are respectively 12m Nonh and5m of point Z. Calculate XY', ' 7m~ 12m~ 13m~ 17m~ 18m', ' 13m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(656, '1992', 'Find the median of the following set of scores:65, 72, 55, 48, 78', '55~60~63.5~65~72', '65', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(657, '1992', 'The data above shows the frequency distribution of marks scored by a group of students in a class test.How many students took the test?', '13~14~15~18~20', '15', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(658, '1992', 'The data below shows the frequency distribution of marks scored by a group of students in a class test.What is the modal score', '2~3~4~5~6', '4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(659, '1992', 'The data below shows the frequency distribution of marks scored by a group of students in a class test.Find the mean mark.', '1~1.3~2~3~3.8', '3.8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(660, '1992', 'A group of students measured a certain angle (to the nearest degree) and obtained the following results: 75o, 76o, 72o, 73o, 74o, 79o, 72o, 72o, 77o, 72o, 71o, 70o, 78o, 73o. Find the mode.', ' 79o~ 78o~ 74o~ 73o~ 72o', ' 72o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(661, '1992', 'The table above shows the scores of 15 students in a Physics test.How many students scored at least 5?', '1~6~8~9~14', '9', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(662, '1992', 'A number is chosen at random from the set (1 ,2,3....,9, 10). What is the probability that the numberIs greater than or equal to 7?', ' 1/10~ 3/10~ 2/5~ 3/5~ 7/10', ' 2/5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(663, '1992', 'What is the probability of throwing a number greater than 2 with a single fair die', ' 1/6~ 1/3~ 1/2~ 2/3~ 5/6', ' 2/3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(664, '1992', 'A fair die is rolled once. What is the probability ofObtaining 4 or 6?', ' 1/12~ 1/6~ 1/3~ 1/2~ 2/3', ' 1/3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(665, '1992', 'Three balls are drawn one after the other with replacement, from a bag containing 5 red, 9white and 4 blue identical balls, What is the probability that they are one red, one white and one blue?', ' 5/102~ 5/136~ 5/162~ 5/204~ 5/243', ' 5/162', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(666, '1992', 'The data below shows the number of worker?Employed in the various sections of a constructionCompany in Lagos.Carpenters 24 Labourers 27Plumbers 12 Plasterers 15Painters 9 Messengers 3Bricklayers 18If one of the workers is absent on a certain day,What is the probability that he is a bricklayer?', ' 1/12~ 1/9~ 2/9~ 1/6~ 1/4', ' 1/6', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(667, '1992', 'The data below shows the number of worker?Employed in the various sections of a constructionCompany in Lagos.Carpenters 24 Labourers 27Plumbers 12 Plasterers 15Painters 9 Messengers 3Bricklayers 18If a worker is retrenched, what is the probability that he is a plumber or plasterer.', ' 1/27~ 1/9~ 5/36~ 1/4~ 3/4', ' 1/4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(668, '1993', 'Simplify 1p1p\\frac{1}{p} - 1q1q\\frac{1}{q} + pqpq\\frac{p}{q} - qpqp\\frac{q}{p}', ' 1p−q1p−q\\frac{1}{p - q}~ −1p+q−1p+q\\frac{-1}{p + q}~ 1pq1pq\\frac{1}{pq}~ 1pq(p−q)1pq(p−q)\\frac{1}{pq(p - q)}~', ' −1p+q−1p+q\\frac{-1}{p + q}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(669, '1993', 'The nth term of a sequence is given by (−1)n−22n−1(−1)n−22n−1(-1)^{n-2}2^{n-1}, find the sum of the second and third terms.', '-2~1~2~6~-1', '-2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(670, '1993', 'S = (1, 2, 3, 4, 5, 6), T = (2,4,5,7) and R = (1,4, 5), and (S∩T) ', ' (1, 4, 5)~ (2, 4, 5)~ (1, 2, 4, 5)~ (2, 3, 4, 5)~ (1, 2, 3, 4, 5)', ' (1, 2, 4, 5)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(671, '1993', 'Simplify: 3/4 + 11/4 x (11/2-2/3)', ' 7/30~ 7/24~ 9/25~ 1/2~ 18/25', ' 1/2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(672, '1993', 'Solve the inequality: 3m + 3 > 9', ' m > 2~ m > 3~ m>4~ m>6~ m>12', ' m > 2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(673, '1993', 'Convert 89ten to a number in base two.', '1101001~1011001~1001101~101101~11001', '1011001', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(674, '1993', 'A stick of length 1.75m was measured by a boy as 1.80m. Find the percentage error in his measurement', ' 27/9%~ 26/7%~0.05~ 277/9%~ 284/7%.', ' 26/7%', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(675, '1993', 'Simplify:4-1/2 x 163/4/41/2', ' 1/4~ o~1~2~4', '2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(676, '1993', 'Simplify:log√27/log81', ' 1/6~ 3/8~ 1/2~ 3/4~6', ' 3/8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(677, '1993', 'Factorize the expression 2s2 - 3st - 2t2.', ' (2s - t)(s + 2t)~ (2s + t)(s - 2t)~ (S + t)(2s - 1)~ (25 + t)(s -t)~ (2s + t)(s + 2t)', ' (2s + t)(s - 2t)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(678, '1993', 'Solve the equation x2 - 2x - 3 = 0', ' (-3, 1)~ (-1, -3)~ (3,1)~ (43, 0)~ (-1, 3).', ' (-1, 3).', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(679, '1993', 'Write as a single fraction5/6r -3/4r', '~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(680, '1993', 'Factorize 2x2 - 21x + 45', ' (2x - 9)(x - 5)~ (2x-15)(x + 3)~ (2x +15)(x - 3)~ (2x -15(x - 3)~ (2x - 9)(x + 5)', ' (2x -15(x - 3)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(681, '1993', 'Solve the simultaneous equations y = 3x; 4y - 5x =14', ' .-2,-6~ 2,6~ 2,-6~ -2,6~ -1,-3', ' 2,6', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(682, '1993', 'A sector of a circle of radius 9cm subtends angle 120o at the centre of the circle. Find the area of the sector to the nearest cm2 ', ' 75cm2~ 84cm2~ 85cm2~ 86cm2~ 95cm2', ' 85cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0);
INSERT INTO `exam_simulation` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`, `status`) VALUES
(683, '1993', 'Calculate the total surface area of a cone of height 12cm and base radius 5cm. ', ' 180 5/7cm2~ 240 2/7cm2~ 235 5/7cm2~ 282 6/7cm2~ 361 3/7cm2', ' 282 6/7cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(684, '1993', 'A cone is 14cm deep and the base radius is 41/2cm. Calculate the volume of water that is exactly half the volume of the cone.', ' 49.5cm3~ 99cm3~ 148.5cm3~ 297cm3~ 445.5cm3', ' 148.5cm3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(685, '1993', 'The area and a diagonal of a rhombus are 60cm and 12cm respectively. Calculate the length of the other diagonal.', ' 5cm~ 6cm~ 10cm~ 12cm~ 15cm', ' 5cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(686, '1993', 'The angle of a sector of a circle radius 10.5cm is 120o. Find the perimeter of the sector ', ' 22cm~ 33.5cm~ 43cm~ 66cm~ 115.5cm', ' 43cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(687, '1993', 'In the diagram, PQR is a tangent to the circle QST at Q. If |QT| = |ST| and ', ' 34o~ 48o~ 56o~ 68o~ 73o', ' 56o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(688, '1993', 'The sum of an interior angles of a regular polygon is 30 right angles. How many sides has the polygon?', ' 34 sides~ 30 sides~ 26 sides~ 17 sides~ 15 sides', ' 17 sides', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(689, '1993', 'In the diagram above, |QR| = 12cm and |QS| = 10cm. If ', ' 3.3cm~ 4.4cm~ 5cm~ 5.5cm~ 6.6cm', ' 4.4cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(690, '1993', 'Two chords PQ and RS of a circle when produced meet at K. If ', ' 11o~ 73o~ 107o~ 138o~ 149o', ' 107o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(691, '1993', 'In the diagram above, QRS is a straight line, QP//RT, PRQ = 56o, ', '28~40~44~84~124', '40', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(692, '1993', 'Simplify2.25/0.015 leaving your answer in standard form', ' 1.5 x 10-4~ 1.5 x 10-2~ 1.5 x 10-3~ 1.5 x 101~ 1.5 x 102', ' 1.5 x 102', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(693, '1993', 'State the fifth and seventh terms of the sequence -2, -3, -41/2 ...........', ' -81/8, -729/32~ 8/81, 72/39~ -27/729, -718/39~ -27/16, -79/81~ -21/8, 32/618', ' -81/8, -729/32', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(694, '1993', 'If x is a rational number, which of the following is represented on the number line?', ' (x: - 5 < x ≤ 3)~ (x: - 5 ≤ x ≤ 3)~~~', ' (x: - 5 < x ≤ 3)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(695, '1993', 'A plane tiles 90km on a bearing 030° and then flies 150km due east. How far east of the starting point is the plane?', ' 120km~ 165km~ 195km~ (150 + 45√3)km~ 240km', ' 195km', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(696, '1993', 'From a point on the edge of the sea, one ship is 24km away on a bearing S 50oE and another ship is 7km away on a bearing S40oW. How far apart are the ships?', ' 20km~ 24km~ 25km~ 31km~ 84km', ' 25km', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(697, '1993', 'Given that tan x = 5/12, what is the value of sin x + cos x ?', ' 5/13~ 7/13~ 12/13~ 17/13~ 5/12', ' 17/13', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(698, '1993', 'Cos 75o has the same value as', ' cos 115o~ cos 255o~ cos 285o~ -sin165o~ -sin 255o', ' cos 285o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(699, '1993', 'If sin x = 12/13, where 0o< x < 90o, find the value of 1-cos2x', ' 25/169~ 64/169~ 105/169~ 144/169~ 8/13', ' 144/169', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(700, '1993', 'The angle of elevation of the top of a tower from a point on the horizontal ground, 40m away from the foot of the tower is 30o. Find the height of the tower.', ' 20m~~ 20√3m~ 40√3m~ 60cm', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(701, '1993', 'At a point 500m from the base of a water tank the angle of elevation of the top of the tank is 45o. Find the height of the tank,', ' 250m~ 353m~ 354m~ 433m~ 500m', ' 500m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(702, '1993', 'Find the median of the following set of numbers: 28, 29, 39, 38, 33, 37, 26, 20, 15, 25', '33~29.5~29~28.5~28', '28.5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(703, '1993', 'What is A∩B in the diagram above?', ' (2,3)~ (2,3,4)~ (1,2,3)~ (2,3,8)~ (6,4,7)', ' (2,3,4)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(704, '1993', 'The table above shows the scores of a group of 40 students in a physics test.If the mode is m and the median is n, then (m,n) is', ' (5,5)~ (5,6)~ (6,5)~ (9,4)~ (9,5)', ' (5,5)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(705, '1993', 'The table above shows the scores of a group of 40 students in a physics test.What is the mean of the distribution?', '4.2~4.5~4.8~5~5.2', '4.8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(706, '1993', 'Find the median of the set of numbers 12, 15, 13, 14, 12, 12.', '12~12.5~13~13.5~14', '12.5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(707, '1993', 'The distribution by state of 840 students in the Faculty of Science of a Nigerian University in a certain session is as follows:Bendel45kwara410Ogun105Ondo126Oyo154In a pie chart drawn to represent this distribution, the angle subtended by Ondo\'s', ' 36o~ 42o~ 45o~ 48o~ 54o', ' 54o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(708, '1993', 'How many students took the examination?', '18~20~21~23~24', '24', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(709, '1993', 'How many students scored less than 7 marks?', '9~15~18~21~25', '15', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(710, '1993', 'What is the probability that an integer selected from the set of integers (20, 21, ...., 30) is a prime number', ' 2/11~ 5/11~ 6/11~ 9/11~ 2/3', ' 2/11', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(711, '1993', 'A fair die is rolled once. What is the probability of obtaining a number less than 3?', ' 1/6~ 1/3~ 2/3~ 1/2~ 5/6', ' 1/3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(712, '1993', 'What is the probability of having an even number in a single toss of a fair die?', ' 1/6~ 1/3~ 1/2~ 2/3~ 5/6', ' 1/2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(713, '1993', 'What is the probability that the total sum of seven would appear in toss of a fair die?', ' 5/36~ 1/6~ 7/36~ 5/6~1', ' 1/6', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(714, '1993', 'A die is rolled 200 times the outcomes obtained are shown in the table below. Find the probability of obtaining 2.', '0.002~0.015~0.15~16~0.2', '0.15', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(715, '1993', 'A die  rolled 200 times. The outcome obtained are shown in the table above.What is the probability of obtaining a number less than 3 ?', '0.125~0.15~0.275~0.5~0.725', '0.275', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(716, '1994', 'In the diagram P, Q, R, S are points on the circle RQS = 30o. PRS = 50o and PSQ = 20o. What is the value of xo + yo?', ' 260o~ 130o~ 100o~ 80o~', ' 130o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(717, '1994', 'If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find the sum of the first for term', '-45~-15~15~33~45', '-15', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(718, '1994', 'If sinθθ \\theta  = K find tanθθ \\theta , 0o ≤≤ \\leq  θθ \\theta  ≤≤ \\leq  90o', ' 1-K~ kk−1kk−1 \\frac{k}{k - 1} ~ k√1−k2k1−k2 \\frac{k}{\\sqrt{1 - k^2}} ~ k1−kk1−k \\frac{k}{1 - k} ~ k√k2−1kk2−1 \\frac{k}{\\sqrt{ k^2 - 1}} ', ' k√1−k2k1−k2 \\frac{k}{\\sqrt{1 - k^2}} ', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(719, '1994', 'Simplify: (21/3) / (22/3) x (11/7)', ' o~1~2~3~4', '1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(720, '1994', 'Which of the following is equal to 7212572125 \\frac{72}{125} ', ' 23×325323×3253 \\frac{2^3 \\times 3^2}{5^3} ~ 24×35324×353 \\frac{2^4 \\times 3}{5^3} ~ 23×35323×353 \\frac{2^3 \\times 3}{5^3} ~ 24×35524×355 \\frac{2^4 \\times 3}{5^5} ~ 22×32×425222×32×4252 \\frac{2^2 \\times 3^2 \\times 4^2}{5^2} ', ' 23×325323×3253 \\frac{2^3 \\times 3^2}{5^3} ', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(721, '1994', 'Express in 8.750.0258.750.025 \\frac{8.75}{0.025} standard form', ' 3.5 x 10-3~ 3.5 x 10-2~ 3.5 x 101~ 3.5 x 102~ 3.5 x 103', ' 3.5 x 102', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(722, '1994', 'Evaluate 271316−14271316−14 \\frac{27^{\\frac{1}{3}}}{16^{-\\frac{1}{4}}} ', '6~5~4~3~2', '6', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(723, '1994', 'Simplify: 165/4 x 2-3 x 30', ' o~2~4~10~20', '4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(724, '1994', 'simplify; 2log36 + log312 - log316', '2~3~ 2 - 2log32~ 3 - log32~ 4 - log32', '3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(725, '1994', 'What is the number whose logarithm to base 10Is 3.4771?', '3~0.3~0.03~0.003~0.0003', '0.003', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(726, '1994', 'A house bought for N100,000 was later auctioned for N80.000. Find the loss percent.', '0.2~0.3~0.4~0.5~0.6', '0.2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(727, '1994', 'A string is 4.8m. A boy measured it to be 4.95m. Find the percentage error.', ' 516516 \\frac{5}{16} %~ 151615161\\frac{5}{16} %~ 31333133 3\\frac{1}{33} %~ 318318 3\\frac{1}{8} %~0.25', ' 318318 3\\frac{1}{8} %', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(728, '1994', 'The sum of the 1st and 2nd terms of an A.P. is 4 and the 10th term is 19. Find the sum of the 5th and 6th terms.', '11~20~21~22~24', '20', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(729, '1994', 'E = (integers 20), P = (multiples of 3), Q = (multiples of 4), what are the elements of P\'∩Q?', '-12~ (4, 8, 16, 20)~ (3, 6, 9, 15, 18)~ (1,2,5,7,10,11,13,17,19)~ (3, 4, 6, 8, 9, 12, 15, 16, 18, 20)', ' (4, 8, 16, 20)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(730, '1994', 'Given that 2p - m = 6 and 2p + 4m = 1, find the value of (4p + 3m).', '1~3~5~7~9', '7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(731, '1994', 'Which of the following is a point on the curve y = x2 -4x + 7?', ' (0,6)~ (1,4)~ (2,0)~ (7,0)~ (3,2)', ' (1,4)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(732, '1994', 'If 8x- 4 = 6x- 10, find the value of 5x,', '-35~-15~-3~3~7', '-15', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(733, '1994', 'For what value of x is the expressionx2 + 15x + 50/x - 5 not defined ?', '-10~-5~ o~5~10', '5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(734, '1994', 'In the graph above, the gradient of the curve at the point P is', '-113~-34~ 3/7~ 3/4~113', '-113', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(735, '1994', 'What is the equation of the line PQ?', ' y = x - 5~ y = x + 3~ y = x + 5~ y = 2x + 3~ y = 2x - 3', ' y = x + 5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(736, '1994', 'Which of the following equations can be solved by the points of intersection P and Q of the curve and the line PQ?', ' x2 - 2 = 0~ x2 - 4 = 0~ x2 + 6 = 0~ X2 - X ~', ' x2 - 4 = 0', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(737, '1994', 'Which of the following is not a factors of 2p2 - 2?', '2~ p - 1~ p + 1~ 2p - 2~ 2p + 1', ' 2p + 1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(738, '1994', 'Find the quadratic equation whose roots are 3 and 2/3.', ' x2 - 11 / 3x + 6 = 0~ x2 - 11x + 6 = O~ 3x2 - 11x + 2 = O~ 3X2 - 11x ~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(739, '1994', 'Which of the following is a root of the equation x2 +6x = 0?', ' o~1~2~3~ It does not have any root.', ' o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(740, '1994', 'Factorise: 6x2 + 7xy - 5y2', ' (6x + 5y)(x - y)~ (2x + 5y)(3x - y)~ (3x + y)(2x - 5y)~ (3x + 5y)(2x - y)~ (2x + y)(3x - 5y)', ' (3x + 5y)(2x - y)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(741, '1994', 'Solve the equation log8x - 4log8x = 2', ' 1/4~ 1/2~1~2~4', ' 1/4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(742, '1994', 'The angle subtended at the centre by a chord of a circle radius 6cm is 120°', ' 3cm~ 6cm~ 4√l2cm~ 3√l3cm~ 6√l3cm', ' 6√l3cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(743, '1994', 'A cuboid of base 12.5cm by 20cm holds exactly 1 litre of water. What is the height of the cuboid? (1 litre =1000cm3)', ' 2cm~ 4cm~ 5cm~ 8cm~ 10cm', ' 4cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(744, '1994', 'Two ships on the equator are on longitudes 45oW and 45oE respectively. How far are they apart along the equator, correct to 2 significant figures? (Take the radius of earth = 6400km and ', ' 15,000km~ 10,000km~ 6,400km~ 5,000km~ 3,200km', ' 10,000km', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(745, '1994', 'Calculate, correct to 2 significant figures, the length of the arc of a circle of radius 3.5cm which subtends an angle of 75° at the centre of the circle. ', ' 2.3cm~ 4.6cm~ 8cm~ 16cm~ 110cm', ' 4.6cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(746, '1995', 'Find (1012)2, expressing the answer in base 2.', '10101~11001~10010~11101~10110', '11001', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(747, '1995', 'If three children shares N10.50 among themselves in ratio 6:7:8, how much is the largest share?', ' N3.00~ N3.50~ N4.00~ N4.50~ N5.00', ' N4.00', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(748, '1995', 'Express 0.000834 in standard form', ' 8.34 x 10-4~ 8.34 x 10-3~ 8.34 x 103~ 8.34 x 104~ 8.34 x 106', ' 8.34 x 10-4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(749, '1995', 'Given that log2a = log84, find a', ' 21/3~ 42/3~ 42/3~ 22/3~23', ' 22/3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(750, '1995', 'By selling some crates of soft drinks for N600.00, a dealer makes a profit of 50%. How much did the dealer pay for the drinks?', ' N1,200.00~ N900.00~ N450.00~ N400.00~ N200.00', ' N400.00', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(751, '1995', 'Find the nth term Un of the A.P., 11, 4, -3,....... .', ' Un=19+7n~ Un=19-7n~ Un=18+7n~ Un= 18-7n~ Un= 17-7n', ' Un= 18-7n', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(752, '1995', 'lf 16/9 , x, 1, y are in Geometric Progression (GP), find the product of x and y.', ' 9/16~ 3/4~1~ 4/3~ 16/6', '1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(753, '1995', 'If R = ', ' [1,2,4,6,7,8~~~~', ' [1,2,4,6,7,8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(754, '1995', 'Find the values of x for which the expression is underlined;6x - 1/x2 + 4x - 5', ' +4 or+1~ -5 or+1~ -5 or -1~ +5 or -1~ +4 -1', ' -5 or+1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(755, '1995', 'Which of the following could be the inequality illustrated in the sketch graph above?', ' y≥2x+3~ y≤3x+3~ y < 3x+2~ y≤x +3~ y≥3x+2.', ' y≤3x+3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(756, '1995', 'Solve the inequality: 1/3(2x - 1) 5', ' x < - 5~ X~ X<7~ x <8~ x < 16', ' x <8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(757, '1995', 'What is the smaller value  of x for which x2 - 3x + 2=O?', '1~2~3~4~5', '1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(758, '1995', 'Factorize the expression x(a - c) + y(c - a)', ' (a - c)(y - x)~ (a - c)(x - y)~ (a + c)(x - y)~ (a + c)(x + y)~ (a - c)(x + y)', ' (a - c)(x - y)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(759, '1995', 'If y = 1/x and x= 3 when y=4, find y when x=2', '1~3~9~18~21', '9', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(760, '1995', 'Solve the equation 3x2 + 25x -18 = 0', ' -3,2~ -2,3~ -2,9~ -9,2/3~ 2/3, 9.', ' -9,2/3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(761, '1995', 'Solve the equation (x +2)(x - 7) = 0', ' x = 1 or8~ x = 2or7~ x = -4or5~ x = -3 or6~ x= -5or -2', ' x = 2or7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(762, '1995', 'Solve the following Simultaneous equations: x+ y = 3/2; x - y = 5/2 and use your result to find the value of 2y + x', '-2~-1~ 1/2~1~ 31/2', '1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(763, '1995', 'Use the graph of y = 3x2 + x - 7 above to answer the question.What is the minimum value of y?', '-10~-7~-4~-1~2', '-7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(764, '1995', 'Use the graph of y = 3x2 + x - 7 above to answer the question.Find the roots of the equation y=3x2 + x - 7', ' 1.0 and -1.2~ 1.1 and-1.3~ 1.4 and-1.7~ 2.0 and -1.9~ 2.4 and -2.0', ' 1.4 and-1.7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(765, '1995', 'In the diagram above. |AB| = 12cm, |AE| = 8cm, |DCl = 9cm and AB||DC. Calculate |EC|.', ' 10cm~ 9cm~ 8cm~ 7cm~ 6cm', ' 6cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(766, '1995', 'The diagonals AC and BD of a rhombus ABCD are 16cm and 12cm long respectively. Calculate the area of the rhombus.', ' 24cm2~ 36cm2~ 48cm2~ 60cm2~ 96cm2', ' 96cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(767, '1995', 'A water tank of height 1/2 m has a square base of side 11/2 m. lf it is filled with water from a water tanker holding 1500 litres, how many litres of water are left in the water tanker? ', ' 37.5litres~ 375 litres~ 3750 litres~ 37500 litres~ 375000 litres', ' 375 litres', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(768, '1995', 'A cylindrical container, closed at both ends, has a radius of 7cm and height 5cm ', ' 35cm3~ 154cm3~ 220cm2~ 528cm2~ 770cm2', ' 528cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(769, '1995', 'Find the total surface area of solid circular cone with base radius 3cm and slant height 4cm. ', ' 37 5/7cm2~ 66cm2~ 75 3/7cm2~ 78 2/7cm2~ 88cm2', ' 66cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(770, '1995', 'A hollow sphere has a volume of kcm3 and a surface area of kcm2. Calculate the diameter of the sphere.', ' 3cm~ 6cm~ 9cm~ 12cm~ More information is needed', ' 6cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(771, '1995', 'The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone.', ' 12cm~ 15cm~ 18cm~ 24cm~ 30cm', ' 24cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(772, '1995', 'The positions of two countries P and Q are (15oN, 12oE) and (65oN, 12oE) respectively. What is the difference in latitude?', ' 104o~ 100o~ 80o~ 50o~ 24o', ' 50o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(773, '1995', 'The angle of a sector of a circle is 108o. If the radius of the circle is 31/2cm, find the perimeter of the sector', ' 6 3/5cm~ 6 4/5cm~ 7 1/10cm~ 10 2/5cm~ 13 3/5cm,', ' 13 3/5cm,', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(774, '1995', 'In the diagram above; O is the centre of the circle and |BD| = |DC|. If ', ' 20o~ 25o~ 30o~ 35o~ 40o', ' 20o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(775, '1995', 'In the in diagram above, AO is perpendicular to OB. Find x.', ' 7.5o~ 15o~ 22.5o~ 30o~ 38.6o', ' 30o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(776, '1995', 'In the diagram above, PQ is parallel to TU, ', ' 136o~ 120o~ 108o~ 100o~ 96o', ' 100o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(777, '1995', 'In the diagram above, AB//CD, the bisector of ', ' 30o~ 45o~ 60o~ 75o~ 90o', ' 90o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(778, '1995', 'In the diagram above, AB//CD. What is the size of the angle marked x?', ' 103o~ 93o~ 77o~ 62o~ 52o', ' 93o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(779, '1995', 'The locus of a point which is equidistant from two given fixed points is the', ' perpendicular bisector of the straight line joining them~ angle bisector of the straight lines joining the points to the origin~ perpendiculars to the straight line joining them~ parallel-line to the straight line joining them~ a line making an acute angle with the line joining the two points', ' perpendicular bisector of the straight line joining them', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(780, '1995', 'In the diagram above, the value of angles b + c is', ' 180o~ 90o~ 45o~ ao~ do', ' 180o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(781, '1995', 'Which of the following angles is an exterior angle of a regular polygon?', ' 95o~ 85o~ 78o~ 75o~ 72o', ' 72o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(782, '1995', 'In ΔABC above, BC is produced to D, /AB/ = /AC/ and ', ' 50o~ 60o~ 65o~ 100o~ 115o', ' 115o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(783, '1995', 'Without using tables, find the value of sin20', '2~1~0~-1~-2', '2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(784, '1995', 'The bearing of two points Q and R from a point P are 030o and 120o respectively, lf /PQ/ = 12m and /PR/ = 5m, find the distance QR.', ' 13m~ 11m~ 9m~ 7m~ 5m', ' 13m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(785, '1995', 'What is the mode of the numbers 8, 10, 9, 9, 10, 8, 11, B, 10, 9, 8 and 14?', '8~9~10~11~14', '8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(786, '1995', 'The mean of 20 observations in an experiment is 4, lf the observed largest value is 23, find the mean of the remaining observations.', '4~3~2.85~2.6~2.56', '3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(787, '1995', 'Find the median of the following numbers 2.64, 2.50, 2.72, 2.91 and 2.35.', '2.91~2.72~2.64~2.5~2.35', '2.64', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(788, '1995', 'Two fair dice are tossed together once. Find the probability that the sum of the outcome is at least 10.', ' 1/12~ 5/ 36~ 1/ 6~ 1/4~ 5/18', ' 1/ 6', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(789, '1995', 'From a box containing 2 red, 6 white and 5 black balls, a ball is randomly selected. What is the probability that the selected ball is black?', ' 2/13~ 5/13~ 5/11~ 5/6~ 11/13', ' 5/13', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(790, '1996', 'Two points X and Y both on latitude 60oS have longitude 147oE and 153oW respectively. Find to the nearest kilometer the distance between X and Y measured along the parallel of latitude (Take 2', ' 16667km~ 28850km~ 8333km~ 2233km~', ' 16667km', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(791, '1996', 'Find the 9th term of the arithmetic progression 18, 12, 6, 0, -6, ...', '-54~-30~30~42~54', '-30', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(792, '1996', 'The 6th term of a G.P is -2 and its first term is 18. What is the common ratio?', ' -1/2~ -1/3~ 1/4~2~3', ' -1/3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(793, '1996', 'Convert the decimal number 89 to a binary number', '101101~111001~1001001~1001101~1011001', '1011001', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(794, '1996', 'simplify  (21/6 -  12/3) / 22/3', ' 3/16~ 7/16~1.5416666666667~2.4583333333333~10.4', ' 3/16', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(795, '1996', 'Simplify 56x-4 / 14x-8', ' 2x-12~ 3x-3~ 3x-4~ 4x-3~ 4x-4', ' 4x-4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(796, '1996', 'Simplufy Log104 + Log1025', '1~2~3~4~5', '2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(797, '1996', 'A boy measured the length and breath of a rectangular lawn as 59.6m and 40.3m respectively instead of 60m and 40m. What is the percentage error in his calculation of the perimeter of the lawn?', '0.1~0.014~0.07~0.002~0.001', '0.001', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(798, '1996', 'Expand (2x - 5)(x - 3)', ' x2 - 1x -15~ 2x2 - 11x + 15~ 22 - 5x - 8~ x2 - 5x - 15~ 2x2 - 6x + 15', ' 2x2 - 11x + 15', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(799, '1996', 'Simplify5/x - y -4/y - x', '~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(800, '1996', 'If 3p - q = 6 and 2p + 3q = 4, find q', ' o~ 1/2~ 2/3~1~ 33/7', ' o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(801, '1996', 'M varies directly as an inversely as the square of p. If M = 3, when n = 2 and p = 1, find M in terms of n and p.', ' M = 2n/3p~ M = 3n2/2p2~ M = n2/2p~ M = 3n/2p2~ M = 2n/3p2', ' M = 3n/2p2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(802, '1996', 'If x is a real number which of the following is more illustrated on the number line?', ' x < 4~ x > -2~ -2 < x ≤ 4~ -3 ≤ x < 4~ -2 ≤ x < 4', ' -2 ≤ x < 4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(803, '1996', 'Solve the equation4/a +1/5a = 3', ' 21/5~ 12/5~ 11/3~ 14/15~ 1/3', ' 12/5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(804, '1996', 'Make p the subject if formula y =a + p/a - p', '~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(805, '1996', 'Factorize 32x3 - 8xy2', ' 4(4x + y)(2x - y)~ (16x - y)(2x + y)~ 8x(2x - y)~ 8x(2x + y)(2x - y)~ 4(2x + y)(4x - y)', ' 8x(2x + y)(2x - y)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(806, '1996', 'The roots of a quadratic equation are -1/4 and 3. The quadratic equation is', ' 4x2 - 13x - 3 = 0~ 4x2 - 11x - 3 = 0~ 4x2 + 11x - 3 = 0~ 3x2 - 11x - 3 = 0~ 3x2 - 11x + 3 = 0', ' 4x2 - 11x - 3 = 0', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(807, '1996', 'The graph of 2y = 5x2 - 3x2 - 2 cuts the y axis at the point', ' (1,0)~ (-2/5, 0)~ (0, -1)~ (0, -2)~ (0, 1)', ' (0, -1)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(808, '1996', 'In the diagram above, O is the center of the circle of radius 3.5cm, ', ' 22cm~ 181/3cm~ 11cm~ 91/6cm~ 71/3cm', ' 11cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(809, '1996', 'If the hypotenuse of a right-angle isosceles triangle is 2, what is the length of each of the other side?', ' 1/√2~ √2 - 1~1~ √2~ √3', ' √2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(810, '1996', 'Find, correct to 1 decimal place, the volume of cylinder of height 8cm and base radius 3cm. ', ' 503.0cm3~ 300.0cm3~ 250.0cm3~ 226.2cm3~ 150.9cm3', ' 226.2cm3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(811, '1996', 'One side of a rectangle is 8cm and the diagonal is 10cm. What is the area of the rectangle?', ' 80cm2~ 48cm2~ 40cm2~ 36cm2~ 24cm2', ' 48cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(812, '1996', 'The angle of a sector of a circle of radius 35cm is 288o. Find the perimeter of the sector. ', ' 246cm~ 211cm~ 141cm~ 114cm~ 44cm', ' 246cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(813, '1996', 'How many sides has a polygon if the sum of its interior angle is 1440o?', '6~7~8~9~10', '10', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(814, '1996', 'Each interior angle of a regular nonagon(nine sided polygon) is equal to', ' 160o~ 144o~ 140o~ 132o~ 36o', ' 140o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(815, '1996', 'In the diagram above, find x correct to the nearest degree.', ' 15o~ 25o~ 26o~ 36o~ 72o', ' 26o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(816, '1996', 'In the diagram above, TRQ is a straight line. Find p, if p = 1/3(a + b + c).', ' 45o~ 60o~ 90o~ 120sup>o~ 150o', ' 45o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(817, '1996', 'Which of the following is not true? You may construct a', ' triangle given all the three sides~ triangle given one side and two angles~ triangle given two sides and the included angle~ quatrilateral given all the four sides~ parallelogram given two adjacent sides and the diagonal joining them', ' quatrilateral given all the four sides', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(818, '1996', 'In the diagram above, PQ is parallel to RST. /RS/ = /SQ/ = /TQ/ and ', ' 30o~ 35o~ 40o~ 70o~ 110o', ' 40o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(819, '1996', 'In the diagram above, /PQ/ = /PS/ and /QR/ = /SR/. Which of the following is/are true?  i. the line PR bisects ', ' I only~ III only~ I and II only~ I and III only~ I, II and III', ' I, II and III', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(820, '1996', 'In the diagram, ', ' 1cm~ 3cm~ 31/2~ 5cm~ 6cm', ' 1cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(821, '1996', 'In the diagram above, PQ is a tangent to the circle MTN at T. What is the size of ', ' 52o~ 54o~ 66o~ 72o~ 128o', ' 66o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(822, '1996', 'In the diagram above, KLMN is a cyclic quadrilateral. /KL/ = /KN/, ', ' 35o~ 40o~ 45o~ 50o~ 55o', ' 45o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(823, '1996', 'Two angles (a + 31) and (b - 49o) are adjacent angles on a straight line. Which of the following is true', ' a + b = 198o~ a + b = 180o~ a + b = 162o~ a + b = 100o~ a + b = 80o', ' a + b = 198o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(824, '1996', 'The trapezium PQRS parallel to SR, ', ' 58o~ 68o~ 78o~ 90o~ 112o', ' 90o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(825, '1996', 'In the diagram above, AB, CD and XY are straight lines intersecting at W. Find ', ' 20o~ 80o~ 100o~ 120o~ 140o', ' 80o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(826, '1996', 'If sinθθ\\theta cosθθ\\theta, for 0o ≤≤\\leq θ ≤≤\\leq 360o, find the value of θθ\\theta', ' 45o, 225o~ 135o, 315o~ 45o, 315o~ 135o, 225o~ 45o, 135o', ' 45o, 225o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(827, '1996', 'If tan x = 2252252\\frac{2}{5}, find the value of sin x; 0 ≤≤\\leq x ≤≤\\leq 90o', ' 5/13~ 5/12~ 144/169~ 12/13~ 13/12', ' 12/13', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(828, '1996', 'A town P is 150km from a town Q in the direction 050o. What is the bearing of Q from P?', ' 050o~ 130o~ 230o~ 270o~ 310o', ' 230o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(829, '1996', 'The angle of elevation of the top X of a vertical pole from a point P on a level ground is 60o. The distance from P to the foot of the pole is 55m. Without using tables, find the height of the pole.', ' 50/3m~ 50m~ 55√3m~ 60m~ 65m', ' 55√3m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(830, '1996', 'The number of goals scored by a football team in 20 matches is shown in the table above.What is the mean goal scored?', '0.75~1.75~1.9~2~2.15', '1.75', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(831, '1996', 'The number of goals scored by a football team in 20 matches is shown in the table above.What is the modal goal scored?', ' o~1~2~5~7', '2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(832, '1996', 'The cumulative frequency curve may be used to find the', ' variance~ standard deviation~ mode~ median~ mean', ' median', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(833, '1996', 'The marks obtained by pupils of class are grouped as shown below; 0 - 4, 5 - 9,10 -14, 15 -19. Which of the following is/are not true? l. The mid values of the grouped marks are 2, 7, 12 and 17. II The class interval is 4. III The class boundaries are 0.5, 4.5, 9.5, 14.5 and 19.5', ' I only~ II only~ III only~ I and II only~ II and III only', ' II only', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(834, '1996', 'What percentage of observation lie outside interquartile range of any distribution?', ' 121/2%~0.25~0.5~ 621/2 %~0.75', '0.5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(835, '1996', 'A bag contains 3 red, 4 black and 5 green identical balls. Two balls are picked at random, one after the other without replacement. Find the probability that one is red and the other is green', ' 2/3~ 5/11~ 5/22~ 5/24~ 5/48', ' 5/22', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(836, '1996', 'The table gives the distribution of outcomes obtained when a die was rolled 100 times.What is the experimental probability that it shows at most 4 when rolled again?', ' 8/25~ 12/25~ 13/25~ 2/3~ 17/25', ' 17/25', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(837, '1997', 'The table above shows that the scores of a group of students in a test. If the average score is 3.5, find the value of x', '1~2~3~4~', '2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(838, '1997', 'Express (0.0425 / 2.5)   as a fraction', '~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(839, '1997', 'If P = {3, 5, 6} and Q = {4, 5, 6} then P∩Q equals', ' {3, 4}~ {4, 5}~ {4, 6}~ {5, 6}~ {3, 5}', ' {5, 6}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(840, '1997', 'A and B are two sets. The number of elements in A', '105~27~15~12~7', '7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(841, '1997', 'A student found the approximate value of 0.02548 correct to two places of decimal instead of two significant figures. Find the percentage error.', '0~ 131/3%~0.1538~ 2/3%~0.2', '0.2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(842, '1997', 'Simplify log39 + log315 - log35', ' log319~ log3~3~1~ o', '3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(843, '1997', 'Solve me equation: 2/3 (x + 5) = 1/4(5x - 3)', ' 11/7~ 18/23~3~ 43/7~7', '7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(844, '1997', 'Which of the following equations has its roots as 4and 5?', ' x2 + 4x - 20 = 0~ x2 + x + 20 = 0~ x2 - x + 20 = 0~ x2 + x - 20 = 0~ x2 - x - 20 = 0', ' x2 + x - 20 = 0', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(845, '1997', 'Solve the equations: 4x -y = 11 5x + 2y = 4', ' x = 6, y = 13~ x = -2, y = -3~ x = -2, y = 3~ x = 2, y = -3~ x = 2, y = 3.', ' x = 2, y = -3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(846, '1997', 'Make q the subject of the relation t = √pq/r ', '~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(847, '1997', 'P varies inversely as the square of W. When W = 4, P = 9. Find the value of P when W = 9', ' 729/16~6~4~ 16/9~ 4/3', ' 16/9', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(848, '1997', 'If x varies over the set of real numbers, which of the following is illustrated in the diagram above?', ' -2 ≤ x < 3~ -2 < x ≤ 3~ -2 < x < 3~ -2 ≤ x ≤ 3~ x ≥ 3', ' -2 < x ≤ 3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(849, '1997', 'In the triangle XYZ , XM is the altitude from X to YZ.XY = 13cm, XZ = 15cm and YM = 5cm. Find the length of YZ.', ' 9cm~ 12cm~ 14cm~ 19.85cm~ 23cm', ' 14cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(850, '1997', 'Two points P and Q are on longitude 67oW. Their latitudes differ by 90o. Calculate their distance apart in terms of ', '6400~~~~ 3200km/', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(851, '1997', 'The length of the two parallel sides of trapezium are 6cm and 10cm and the perpendicular distance between them is 5cm. Find the area of the trapezium', ' 21cm2~ 4Ocm2~ 8Ocm2~ 150cm2~ 300cm2', ' 4Ocm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(852, '1997', 'Calculate the total surface area of a solid cone of slant height 15cm and base radius 8cm in terms of ', '64~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(853, '1997', 'The cross-section of a prism is a right-angled triangle 3cm by 4cm by 5cm. The height of the prism is 8cm. Calculate its volume', ' 48cm3~ 6Ocm3~ 96cm3~ 120cm3~ 24Ocm3', ' 48cm3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(854, '1997', 'Find the radius of a circle in which an arc of length 44cm subtends angle 200° at the centre of the circle. ', ' 3.9cm~ 12.6cm~ 25.2cm~ 38.4cm~ 124.5cm', ' 12.6cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(855, '1997', 'The diagram above is a triangle XYZ whose area is 23.5cm2. XY =1Ocm and YZ = 8cm, calculate θ correct to the nearest degree.', ' 34o~ 35o~ 36o~ 37o~ 40o', ' 36o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(856, '1997', 'Which of the following is not necessarily sufficient for the construction of a Q triangle?', ' Three sides~ Two sides and an included angle~ Two sides and a right angle~ Two sides and an angle~ Two angles and a side.', ' Two sides and a right angle', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(857, '1997', 'In the diagram, EF//QR, PE = 2cm, EQ = 4cm and FR = 6cm. Find x.', ' 2cm~ 3cm~ 4cm~ 5cm~ 6cm', ' 3cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(858, '1997', 'Which of the following statements is/are true when two straight lines intersect?I. Adjacent angles are equal II. Vertically opposite angles are equal III. Adjacent angles are supplementary', ' II  only~ I and III only~ II and III only~ I, II and III~ I and II', ' I, II and III', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(859, '1997', 'PQRS and GHRS are parallelograms on the same base SR and between the same parallel straight line PH and SR. Which of the following is true?', ' Δ PGS = Δ QHR~ Parallelogram PQRS = Δ QHR~ Trapezium PQXS = Δ QHR~ Δ PGS = Parallelogram GHRS~ Parallelogram PQRS = Parallelogram GHRS', ' Parallelogram PQRS = Parallelogram GHRS', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(860, '1997', 'From the diagram above, which of the following is true?', ' a +b + x =180~ a = b + x~~~ a ', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(861, '1997', 'The interior angles of a pentagon are 126o, 114o, y, 92o and 83o. Find the value of y.', ' 85o~ 95o~ 105o~ 115o~ 125o', ' 125o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(862, '1997', 'Solve the inequality 3x - 8 ≥ 5x', ' x ≤ 4~ x ≥ 1~ x ≤ -4~ x ≤ -1~ x < 2', ' x ≤ -4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(863, '1997', 'Divide 3.6721 by 4', '0.918~1.418~ 1.168O~1.168~1.918', '0.918', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(864, '1997', 'The eleventh term of an AP, is 25 and its first term is -3. Find its common difference.', ' 19/10~ 21/5~ 23/11~ 21/2~ 24/5', ' 24/5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(865, '1997', 'Find the common ratio in the GP: log 3, log 9, log 81 ..........', '1~2~3~6~9', '2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(866, '1997', 'Find the value oft for which 64/27 = (3/4)t-1', '-4~-2~ 11/3~2~4', '-2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(867, '1997', 'O is the centre of the circle PQRS. PR and QS intersect at T POR is a diameter, ', ' 68o~ 64o~ 42o~ 32o~ 22o.', ' 68o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(868, '1997', 'TR is the tangent to the circle PQR with centre O. Find the size of ', ' 44o~ 46o~ 60o~ 74o~ 118o', ' 60o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(869, '1997', 'If two triangles are similar, which of the following is true? Their', ' corresponding sides are equal~ corresponding angles are equal~ corresponding altitudes are equal~ areas are equal~ perimeters are equal', ' corresponding angles are equal', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(870, '1997', 'Which of the following is not necessarily true of aRectangle?', ' The diagonals are equal~ The diagonals bisect each other~ The diagonals are perpendicular~ Each diagonal divides the area of the rectangle equally~ Each diagonal divides the rectangle into two congruent triangles', ' The diagonals are perpendicular', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(871, '1997', 'A chord is 5cm from the centre of a circle of diameter 26cm. Find the length of the chord', ' 16cm~ 18cm~ 24cm~ 25.51cm~ 51.1cm', ' 24cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(872, '1997', 'The angle of elevation of a point T on a tower from a point U on the horizontal ground is 30o. If TU = 54m, how high is T above the horizontal ground?', ' 108m~ 72m~ 46.3m~ 31.2m~ 27m', ' 27m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(873, '1997', 'Express the true bearing of 250o as a compass bearing', ' N2OoE~ S20oE~ N20oW~ S7OoW~ S70oE', ' S7OoW', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(874, '1997', 'Cos 65o has the same value as', ' Sin 65o~ Cos 25o~ Cos 115o~ Cos 205o~ Cos 295o', ' Cos 295o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(875, '1997', 'Two sides of a triangle are perpendicular. If the two sides are 8cm and 6cm, calculate correct to the nearest degree, the smallest angle of the triangle.', ' 35o~ 36o~ 37o~ 38o~ 53o.', ' 37o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(876, '1997', 'The graph is the cumulative frequency curve for the weight distribution of 100 workers in a factory. Which of the points P, Q, R, S and T indicates the median weight?', ' T~ S~ R~ Q~ P', ' Q', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(877, '1997', 'A bag contains red, black and green identical balls. A ball is picked and replaced. The table shows the result of 100 trials. Find the experimental probability of picking a green ball.', '16~ 21/25~ 1/3~ 4/21~ 4/25', ' 4/25', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(878, '1997', 'What is the probability of having an odd number in a single throw of a fair die with the faces numbered 1,2,3,4,5,6?', ' 5/6~ 2/3~ 1/2~ 1/3~ 1/6', ' 1/2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(879, '1997', 'A bag contains 3 white, 6 red, 5 blue identical balls. A ball is picked at random from bag. What is the probability that is either white or blue?', ' 9/14~ 4/7~ 3/7~ 5/14~ 3/14', ' 4/7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(880, '1998', 'In the venn diagram, the shaded region is', ' (P ∩\\cap Q) ~ (P ∩\\cap Q) ∩\\cap R~ (P ∩\\cap Q1) ∩\\cap R~ (P ∩\\cap Q1) ~', ' (P ∩\\cap Q1) ∩\\cap R', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(881, '1998', 'A chord of circle radius 26cm is 10cm from the centre of the circle. Calculate the length of the chord.', ' 1cm~ 27.86cm~ 32cm~ 40cm~ 48cm', ' 27.86cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(882, '1998', 'Find the value of x in the diagram.', ' 50o~ 60o~ 70o~ 80o~', ' 70o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(883, '1998', 'Find the root of the equation 2x2 - 3x - 2 = 0', ' x = -2 or 1/2~ x = -2 or1~ x = -2 or 2~ x = -1 or 2~ x = -1/2 or 2', ' x = -1/2 or 2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(884, '1998', 'What value of k makes the given expression a perfect square ? m2 - 8m + k = 0', '2~4~8~16~64', '16', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(885, '1998', 'If log10q = 2.7078, what is q?', '5102~849.9~510.2~84.99~51.02', '510.2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(886, '1998', 'Simplify 0.663954 + 0.003 giving your answer correct to two signifiicant figures', '213.18~213~213~210~21', '210', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(887, '1998', 'If log10a = 4; what is a?', '0.4~40~400~1000~10000', '10000', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(888, '1998', 'A student measured the length of a room and obtained the  measurement of 3.99. If the percentage error of is measurement was 5% and his own measurement was smaller than the length , what is the length of the room?', ' 3.78m~ 3.80m~ 4.18m~4.2~ 4.788m', '4.2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(889, '1998', 'When an aeroplane is 800m above the ground, its angle of elevation from a point P on the ground is 30o. How far is the plane from P by line of sight?', ' 400m~ 800m~ 1500m~ 1600m~ 1700m', ' 1600m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(890, '1998', 'Convert 35 to a number in base two', ' 1011two~ 10011two~ 100011two~ 110010two~ 110001two', ' 100011two', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(891, '1998', 'The nth term of a sequence is represented by 3 x 2(2-n). Write down the first three terms of the sequence', ' 3/2, 3, 6~ 6, 3, 3/2~ 3/2, 3, 1/3~ 2/3, 3, 8/3~ 3/2, 0, 6', ' 6, 3, 3/2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(892, '1998', 'A piece of cloth was measured as 6.10m. If the actual length of the cloth is 6.35, find the percentage error, correct to 2 decimal places', '0.0305~0.0395~0.15~0.25~0.393', '0.0395', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(893, '1998', 'Simplify 823', '-3~ 1919\\frac{1}{9}~ 1313\\frac{1}{3}~ 278278\\frac{27}{8}~4', ' 1313\\frac{1}{3}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(894, '1998', 'Solve the equation 5x2 - 4x - 1 = 0', ' -1, 1/5~ -1, -1/5~ 1, 1/5~ 1, -1/5~ -1, 5', ' 1, -1/5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(895, '1998', 'p and q are two positive numbers such that p > 2q. Which one of the following statements is not true?', ' -p < -2q~ -p > -2q~~~', ' -p > -2q', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(896, '1998', 'For what value of x is the expressionx - 5/x2 - 2x - 3 not defined?', ' 3, 1~ -1, -3~ -1, 3~ 3, -2~ 1, -3', ' -1, 3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(897, '1998', 'Make S the subject of the formula: V=K√T−SV=K√T−SV = \\frac{K}{\\sqrt{T-S}}', ' T−K2V2=ST-\\frac{K^2}{V^2} = S~ T+K2V2=ST+\\frac{K^2}{V^2} = S~ T−K2V=ST-\\frac{K^2}{V} = S~ T−KV=ST-\\frac{K}{V} = S~ T−KV2=ST-\\frac{K}{V^2} = S', ' T−K2V2=ST-\\frac{K^2}{V^2} = S', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(898, '1998', 'Find the equation whose roots are 23and−14\\frac{2}{3}and \\frac{-1}{4}', ' 12x2+11x+2=012x^2+11x+2=0~ 12x2−11x+2=012x^2-11x+2=0~ x2−1112x+2=0x^2-\\frac{11}{12}x+2=0~ x2+1112x−2=0x^2+\\frac{11}{12}x-2=0~ 12x2+11x+2=012x^2+11x+2=0', ' 12x2+11x+2=012x^2+11x+2=0', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(899, '1998', 'Find (X-Y) if 4x - 3y = 7 and 3x - 2y = 5', '4~3~2~-2~-3', '2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(900, '1998', 'Solve the inequality: (y−3)<y3(y−3)<y3(y−3)<\\frac{y}{3}.', ' y > -9~ y < 3~ y > 4~ y < 9~ y > 0', ' y > 4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(901, '1998', 'If h(m+n) = m(h+r) find h in terms of m, n and r', ' h=mr2m+nh=mr2m+nh=\\frac{mr}{2m+n}~ h=mrn+mh=mrn+mh=\\frac{mr}{n+m}~ h=m+nnh=m+nnh=\\frac{m+n}{n}~ h=m+nmh=m+nmh=\\frac{m+n}{m}~ h=mrnh=mrnh=\\frac{mr}{n}', ' h=mrnh=mrnh=\\frac{mr}{n}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0);
INSERT INTO `exam_simulation` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`, `status`) VALUES
(902, '1998', 'Given that 6x−yx+2y=26x−yx+2y=2\\frac{6x-y}{x+2y}=2, find the value of xyxy\\frac{x}{y}', ' 3838\\frac{3}{8}~ 5858\\frac{5}{8}~ 4545\\frac{4}{5}~ 5454\\frac{5}{4}~ 8585\\frac{8}{5}', ' 5454\\frac{5}{4}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(903, '1998', 'The radius of a geographical globe is 60cm. Find the length of the parallel of latitude 60oN', '66~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(904, '1998', 'In the diagram above, O is the center if the two concentric circle of radii 13cm and 10cm respectively. Find the area of the shaded portion in the sector with angle 1200 at the center.', '13~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(905, '1998', 'Express as a single fraction: xx−2−x+2x+3xx−2−x+2x+3\\frac{x}{x-2}-\\frac{x+2}{x+3}', ' 2x2−3x−4(x−2)(x+3)2x2−3x−4(x−2)(x+3)\\frac{2x^2 - 3x - 4}{(x-2)(x+3)}~ 2x2+3x−4(x−2)(x+3)2x2+3x−4(x−2)(x+3)\\frac{2x^2 + 3x - 4}{(x-2)(x+3)}~ 2(x−2)(x+3)2(x−2)(x+3)\\frac{2}{(x-2)(x+3)}~ 3x+4(x−2)(x+3)3x+4(x−2)(x+3)\\frac{ 3x + 4}{(x-2)(x+3)}~ 3x−4(x−2)(x+3)3x−4(x−2)(x+3)\\frac{3x - 4}{(x-2)(x+3)}', ' 3x+4(x−2)(x+3)3x+4(x−2)(x+3)\\frac{ 3x + 4}{(x-2)(x+3)}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(906, '1998', 'The following numbers represent at a set of scores for a class of 32 students, where the maximum score possible was 12, 6, 5, 9, 4, 4, 8, 7, 5, 6, 3, 2, 5, 4, 6, 9, 10, 4, 3, 2, 3, 4, 6, 8, 7, 4, 2, 1, 8, 7, 7, 6, 11. What is the percentage of the class, correct to the nearest whole number, scored above 6?', '0.34~0.35~0.37~0.38~0.5', '0.34', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(907, '1998', 'A die with faces numbered 1 to 6 is rolled once. What is the probability of obtaining  4?', ' 136136\\frac{1}{36}~ 1616\\frac{1}{6}~ 1313\\frac{1}{3}~ 1212\\frac{1}{2}~ 2323\\frac{2}{3}', ' 1313\\frac{1}{3}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(908, '1998', 'In the diagram above, the area of triangle ABC is 35cm2, find the value of y.', ' 5cm~ 10cm~ 17.5cm~ 28cm~ 70cm', ' 10cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(909, '1998', 'The graph of the quadratic expression', ' y=x2+x−2y=x2+x−2y=x^2 + x - 2~ y=x2−x+2y=x2−x+2y=x^2 - x + 2~ y=x2−x−2y=x2−x−2y=x^2 - x - 2~ y=x+x+2y=x+x+2y=x + x + 2~ y=x2−2x−2y=x2−2x−2y=x^2 - 2 x - 2', ' y=x2−x−2y=x2−x−2y=x^2 - x - 2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(910, '1998', 'The values of x when y = -1 are approximately', ' -10 and 2.0~ -1.3 and 2.3~ -0.6 and 2.6~ -0.6 and 1.6~ 1.6 and 1.6', ' -0.6 and 1.6', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(911, '1998', 'A box contain 2 white and 3 blue identical balls. If two balls are picked at random, one after the other, without replacement, what is the probability of picking two balls of different colours?', ' 525525\\frac{5}{25}~ 720720\\frac{7}{20}~ 3535\\frac{3}{5}~ 2323\\frac{2}{3}~ 5656\\frac{5}{6}', ' 3535\\frac{3}{5}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(912, '1998', 'In ', ' 4√3cm~ 4cm~ 2√3cm~ 43cm43cm\\frac{4}{3}cm~ 1cm', ' 4cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(913, '1998', 'In the diagram, PQ||SR. Find the value of Z.', ' 30o~ 40o~ 45o~ 90o~ 120o', ' 90o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(914, '1998', 'In sin(X+30)o=cos40osin(X+30)o=cos40osin(X+30)^o=cos40^o,find X', ' 10o~ 20o~ 50o~ 60o~ 90o', ' 20o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(915, '1998', 'Find the value of X if cosx=58for0o≤X≤180ocosx=58for0o≤X≤180ocos x = \\frac{5}{8}for 0^o\\le X\\le 180^o', ' 141.3o~ 128.7o~ 51.3o~ 48.7o~ 38.7o', ' 51.3o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(916, '1998', 'A ladder 5cm long long rest against a wall such that its foot makes an angle 30o with the horizontal. How far is the foot of the ladder from the wall?', ' 5√23m5√23m\\frac{5\\sqrt{2}}{3}m~ 212m212m2\\frac{1}{2}m~ 5√32m5√32m\\frac{5\\sqrt{3}}{2}m~ 10√33m10√33m\\frac{10\\sqrt{3}}{3}m~ 10√3m10√3m10\\sqrt{3}m', ' 212m212m2\\frac{1}{2}m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(917, '1998', 'Two chords PQ and RS of a circle intersected at right angles at a point inside the circle. If ', ' 35o~ 45o~ 55o~ 70o~ 90o', ' 55o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(918, '1998', 'In the diagram, O is the center of the circle and the reflex angle ROS is 264o. Find ', ' 48o~ 53o~ 66o~ 132o~ 192o', ' 48o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(919, '1998', 'If the exterior angles of quadrilateral are yo, (y + 5)o, (y + 10)o and (y + 25)o, find y', ' 10o~ 20o~ 40o~ 60o~ 80o', ' 80o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(920, '1998', 'In the diagram PQ is a diameter of circle PMQN center O, if ', ' 58.5o~ 44o~ 35o~ 31.5o~ 27o', ' 27o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(921, '1998', 'In the diagram O is the center of circle PRQ. The radius is 3.5cm and ', ' 175.0cm~ 157.1cm~ 37.7cm~ 11.0cm~ 3.1cm', ' 3.1cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(922, '1998', 'Calculate the perimeter of the trapezium PQRS.', ' 24cm~ 36cm~ 44cm~ 72cm~ 520cm', ' 44cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(923, '1998', 'The length of an arc of a circle of radius 5cm is 4cm. Find the area of the sector', ' 135cm2135cm21\\frac{3}{5}cm^2~ 2cm2~ 8cm2~ 10cm2~ 20cm2', ' 10cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(924, '1998', 'The pie chart above show the distribution of how students travelled to a certain school on a particular day. Use this information to answer the question below.If a hundred students travelled by bus, find the total number of students in the school', '300~400~500~600~750', '400', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(925, '1998', 'The pie chart above show the distribution of how students travelled to a certain school on a particular day. Use this information to answer the question below.What percentage, to the nearest whole number, of tghe students travelled to school on foot?', '0.24~0.23~0.2~0.15~0.14', '0.24', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(926, '1998', 'The diagram above is a rectangle. If the perimeter is 36m, find the area of the rectangle.', ' 64m264m264m^2~ 65m265m265m^2~ 84m284m284m^2~ 124m2124m2124m^2~ 275m2275m2275m^2', ' 65m265m265m^2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(927, '1998', 'Find the value of x in the diagram above', ' 8.0cm~ 6.8cm~ 6.6cm~ 6.5cm~ 5.6cm', ' 5.6cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(928, '1998', 'Find the angle x in the diagram above.', ' 310o~ 230o~ 190o~ 130o~ 100o', ' 100o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(929, '1998', 'The diagonal and one side of a square are x and y units respectively. Find an expression for y in terms of x', ' y=x2y=\\frac{x}{2}~ yx√2y\\frac{x}{\\sqrt{2}}~ y=√xy=\\sqrt{x}~ y=√x2y=\\sqrt{\\frac{x}{2}}~', ' yx√2y\\frac{x}{\\sqrt{2}}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(930, '1998', 'Find the curved surface area of a cone of radius 3cm and slant height 7cm (take', ' 22cm222cm^2~ 44cm244cm^2~ 66cm266cm^2~ 132cm2132cm^2~ 198cm2198cm^2', ' 66cm266cm^2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(931, '1998', 'P varies inversely as Q. The table above shows the value of Q for some selected values of P.What is the missing value of Q in the table?', '4~9~15~16~144', '16', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(932, '1998', 'Three of the angles of a hexagon are each Xo. The others are each 3Xo. Find X', ' 30o~ 40o~ 60o~ 80o~ 120o', ' 60o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(933, '1998', 'Evaluate √20×(√5)3\\sqrt{20}\\times (\\sqrt{5})^3', '10~20~25~50~', '50', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(934, '1998', 'If P = {3, 7, 11, 13} and Q = {2, 4, 8, 16}, which of the following is correct', ' (P∩Q)l=2,3,4,13(P\\cap Q)^l={2, 3, 4, 13}~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(935, '1998', 'It is observed that 1+3=22,1+3+5=32,1+3+5+7=42.If1+3+5+7+9+11+13+15=P2findP1 + 3 = 2^2, 1 + 3 + 5 = 3^2, 1 + 3 + 5 + 7 = 4^2. \\\\If \\hspace{1mm}1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = P^2 find\\hspace{1mm}P', '6~7~8~9~', '8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(936, '1998', 'Evaluate 3.0×101−2.8×10−13.0×101−2.8×10−13.0\\times 10^1 - 2.8\\times 10^{-1}leaving  the answer in standard form', ' 2×10−12×10−12\\times 10^{-1}~ 2×1022×1022\\times 10^{2}~ 2.972×1012.972×1012.972 \\times 10^{1}~ 2.972×1022.972×1022.972 \\times 10^{2}~', ' 2.972×1012.972×1012.972 \\times 10^{1}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(937, '1998', 'A trader makes a loss of 15% when selling an article. Find the ratio, selling price : cost price', ' 3:20~ 3:17~ 17:20~ 20:23~', ' 17:20', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(938, '1998', 'The side of a square is increased from 20cm to 21cm. Calculate the percentage increase in its area', '0.025~0.093~0.1~0.1025~', '0.1025', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(939, '1998', 'Arrange in ascending order of magnitude 268,367,and259268,367,and25926', '2.59E+19~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(940, '1999', 'An interior angle of a regular polygon is 5 times each exterior angle. How many sides has the polygon?', '15~12~9~6~', '12', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(941, '1999', 'if y=√ax−by=√ax−by = \\sqrt{ax-b} express x in terms of y and b', ' x=y2−bax=y2−bax = \\frac{y^2-b}{a}~ x=y−bax=y−bax = \\frac{y-b}{a}~ x=y+bax=y+bax = \\frac{y+b}{a}~ x=y2+bax=y2+bax = \\frac{y^2+b}{a}~', ' x=y2+bax=y2+bax = \\frac{y^2+b}{a}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(942, '1999', 'The side of a rhombus is 10cm long, correct to the nearest whole number. Between what limits should the perimeter P lie?', ' 39cm ≤ P ≤41cm~~ 38.5 ≤ P ≤ 41.5cm~ 38.5 ≤ P ≤ 40cm~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(943, '1999', 'Simplify log82−log72+log74log82−log72+log74log', ' zero~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(944, '1999', 'If K√28+√63−√7=0,findKK√28+√63−√7=0,findKK\\sqrt{28}+\\sqrt{63}-\\sqrt{7}=0, find \\hspace{1mm} K', '-2~-1~1~2~', '-1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(945, '1999', 'From a set A=', ' 1515\\frac{1}{5}~ 2525\\frac{2}{5}~ 3535\\frac{3}{5}~ 4545\\frac{4}{5}~', ' 2525\\frac{2}{5}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(946, '1999', 'The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below.Find the value of K', ' 15o~ 30o~ 60o~ 90o~', ' 30o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(947, '1999', 'The pie chart illustrate the amount of private time a student spends in a week studying various subjects. Use it to answer the question below.If he sends 2122122\\frac{1}{2} hours week on science, find the total number of hours he studies in a week', ' 3133133\\frac{1}{3} hours~ 5 hours~ 8 hours~ 12 hours~', ' 12 hours', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(948, '1999', 'A group of 11 people can speak either English or French or Both. Seven can speak English and six can speak French. What is the probability that a person chosen at random can speak both English and french', ' 211211\\frac{2}{11}~ 411411\\frac{4}{11}~ 511511\\frac{5}{11}~ 11131113\\frac{11}{13}~', ' 211211\\frac{2}{11}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(949, '1999', 'Which of the following figures have one line of symmetry only? I. Isosceles triangle II. Rhombus III. Kite', ' I and II only~ II and III only~ I and III only~ I, II, and III~', ' I and III only', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(950, '1999', 'In the diagram above, |XR| = |RY| = |YZ| and ', ' 50o~ 62o~ 112o~ 115o~', ' 115o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(951, '1999', 'In the diagram above, RST is a tangent to circle VSU center O ', ' 90o~ 50o~ 45o~ 40o~', ' 40o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(952, '1999', 'Calculate the value of Y in the diagram.', ' 18o~ 42o~ 48o~ 132o~', ' 48o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(953, '1999', 'In the diagram, POR is a circle with center O. ', ' 20o~ 25o~ 30o~ 50o~', ' 20o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(954, '1999', 'Given that m = -3 and n = 2 find the value of 3n2−2m3m3n2−2m3m\\frac{3n^2 - 2m^3}{m}', '-22~-14~14~22~', '-22', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(955, '1999', 'Simplify 2−18m21+3m\\frac{2-18m^2}{1+3m}', ' 2(1+3m)2(1+3m)~ 2(1+3m2)2(1+3m^2)~ 2(1−3m)2(1-3m)~ 2(1−3m2)2(1-3m^2)~', ' 2(1−3m)2(1-3m)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(956, '1999', 'If y=√ax−by = \\sqrt{ax-b} express x in terms of y, a and b', ' x=y2−bax = \\frac{y^2-b}{a}~ x=y+bax = \\frac{y+b}{a}~ x=y−bax = \\frac{y-b}{a}~ x=y2−bax = \\frac{y^2 - b}{a}~', ' x=y2−bax = \\frac{y^2 - b}{a}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(957, '1999', 'Given that 81×22n−2=K,find√K81\\times 2^{2n-2} = K, find \\sqrt{K}', ' 4.5×2n4.5\\times 2^{n}~ 4.5×22n4.5\\times 2^{2n}~ 9×2n−19\\times 2^{n-1}~ 9×22n9\\times 2^{2n}~', ' 9×2n−19\\times 2^{n-1}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(958, '1999', 'Simplify 4x+1−3x−1\\frac{4}{x+1}-\\frac{3}{x-1}', ' x+7x2−1\\frac{x+7}{x^2 - 1}~ x−7x2+1\\frac{x-7}{x^2 + 1}~ x−7x2−1\\frac{x-7}{x^2 - 1}~ x−11x2−1\\frac{x-11}{x^2 - 1}~', ' x−7x2−1\\frac{x-7}{x^2 - 1}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(959, '1999', 'If y varies inversely as x2, how does x vary with y?', ' x varies inversely as y2~ x varies inversely as y~ x varies directly as y2~ x varies directly as y~', ' x varies inversely as y', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(960, '1999', 'If tanx=1√3,findcosx−sinxtanx=1√3,findcosx−sinxtan x = \\frac{1}{\\sqrt{3}}, find cos x - sin xsuch that 0o≤x≥90o0o≤x≥90o0^o \\le x \\ge 90^o', ' √3+12√3+12\\frac{\\sqrt{3}+1}{2}~ 2√3+12√3+1\\frac{2}{\\sqrt{3}+1}~ √3−12√3−12\\frac{\\sqrt{3}-1}{2}~ 2√3−12√3−1\\frac{2}{\\sqrt{3}-1}~', ' √3−12√3−12\\frac{\\sqrt{3}-1}{2}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(961, '1999', 'The diagram shows the position of three ships A, B and C at sea. B is due north of C such that |AB| = |BC| and the bearing of B from A = 040o. What is the bearing of A from C?', ' 040o~ 070o~ 110o~ 290o~', ' 290o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(962, '1999', 'A pole of length L leans against a vertical wall so that it makes an angle of 60o with the horizontal ground. If the top of the pole is 8m above the ground, calculate L.', ' 16√3m16√3m16\\sqrt{3}m~ 4√3m4√3m4\\sqrt{3}m~ √316√316\\frac{\\sqrt{3}}{16}~ 16√3316√33\\frac{16\\sqrt{3}}{3}~', ' 16√3316√33\\frac{16\\sqrt{3}}{3}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(963, '1999', 'In the diagram, PQST and QRST are parallelograms. Calculate the area of the trapezium PRST.', ' 60cm2~ 50cm2~ 40cm2~ 30cm2~', ' 30cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(964, '1999', 'The height of a pyramid on square base is 15cm. If the volume is 80cm3, find the length of the side of the base', ' 3.3cm~ 5.3cm~ 4.0cm~ 8.0cm~', ' 4.0cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(965, '1999', 'Simplify 3.72 x 0.025 and express your answer in the standard form', ' 9.3×1039.3×1039.3\\times 10^3~ 9.3×1029.3×1029.3\\times 10^2~ 9.3×10−29.3×10−29.3\\times 10^{-2}~ 9.3×10−39.3×10−39.3\\times 10^{-3}~', ' 9.3×10−29.3×10−29.3\\times 10^{-2}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(966, '1999', 'Two numbers 24 and 31 are equal in value when converted to base ten. Find the equation connecting x and y', ' 2x = 3(y - 1)~ 4x - y = 1~ 3y + 2x = 3~ 3y = 2 (x + 3)~', ' 2x = 3(y - 1)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(967, '1999', 'A car travel at x km per hour for 1 hour and at y k per hour for 2 hours. Find its average speed', ' 2x+2y3kmh−12x+2y3kmh−1\\frac{2x + 2y}{3}kmh^{-1}~ x+y3kmh−1x+y3kmh−1\\frac{x + y}{3}kmh^{-1}~ x+2y3kmh−1x+2y3kmh−1\\frac{x + 2y}{3}kmh^{-1}~ 2x+y3kmh−12x+y3kmh−1\\frac{2x + y}{3}kmh^{-1}~', ' x+2y3kmh−1x+2y3kmh−1\\frac{x + 2y}{3}kmh^{-1}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(968, '1999', 'The height and base if a triangle are in ratio 1:3 respectively. If the area of the triangle is 216cm2, find the length of the base.', ' 24cm~ 36cm~ 72cm~ 144cm~', ' 36cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(969, '1999', 'Water flows from a tap into cylindrical container at the rate 5', ' 2cm~ 5cm~ 8cm~ 15cm~', ' 5cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(970, '1999', 'Amina had m mangoes. she ate 3 and shared the remainder equally with her brother Uche. Each had at least 10. Which of the following inequalities represents the statements above.', ' m2−3≤10m2−3≤10\\frac{m}{2}-3\\le 10~ m2−3≥10m2−3≥10\\frac{m}{2}-3\\ge 10~ m−32≥10m−32≥10\\frac{m-3}{2}\\ge10~ m−32≤10m−32≤10\\frac{m-3}{2}\\le10~', ' m−32≥10m−32≥10\\frac{m-3}{2}\\ge10', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(971, '1999', 'Which of the following pairs of inequalities is represented on the number line?', ' \\(x~ x≥−2andx>1x≥−2andx>1x\\ge -2 and x>1~ x≤−2andx≥1x≤−2andx≥1x\\le -2 and x\\ge1~ x<−2andx>1x<−2andx>1x< -2 and x>1~', ' x≤−2andx≥1x≤−2andx≥1x\\le -2 and x\\ge1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(972, '1999', 'If x2+15x+50=ax2+bx+c=0x2+15x+50=ax2+bx+c=0x^2 +15x + 50 = ax^2 + bx + c = 0. Which of the following statement is not true?', ' x = -5~ x = 10~ x + 10 = 0~ bc = 750~', ' x = 10', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(973, '1999', 'The root of a quadratic equation in x, are -m and 2n. Find the equation', ' x2+x(m−2n)−2mn=0x2+x(m−2n)−2mn=0x^2 + x(m - 2n)-2mn=0~ x2−x(m−2n)−2mn=0x2−x(m−2n)−2mn=0x^2 - x(m - 2n)-2mn=0~ x2−x(m−2n)+2mn=0x2−x(m−2n)+2mn=0x^2 - x(m - 2n)+2mn=0~ x2+x(m−2n)+2mn=0x2+x(m−2n)+2mn=0x^2 + x(m - 2n)+2mn=0~', ' x2−x(m−2n)−2mn=0x2−x(m−2n)−2mn=0x^2 - x(m - 2n)-2mn=0', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(974, '1999', 'A survey shows that 28% of all the men in a village wear a size 9 shoes. What i the probability that a man selected t random in the village wears size 9 shoes?', ' 725725\\frac{7}{25}~ 41504150\\frac{41}{50}~ 1212\\frac{1}{2}~1~', ' 725725\\frac{7}{25}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(975, '1999', 'In the diagram, DE||BC, |AD| = x cm and |DB| = |AE| = ycm. Find |CE| in terms of x and y.', ' x~ x2yx2y\\frac{x^2}{y}~ yx2yx2\\frac{y}{x^2}~ y2xy2x\\frac{y^2}{x}~', ' y2xy2x\\frac{y^2}{x}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(976, '1999', 'Describe the locus L shown in the diagram below.', ' Locus of points equidistant from X and Y~ Locus of points equidistant from X and Z~ Locus of points equidistant from ¯ZXZX¯\\bar{ZX} and ¯ZYZY¯\\bar{ZY}~ Locus of points equidistant from ¯XYXY¯\\bar{XY} and ¯ZYZY¯\\bar{ZY}~', ' Locus of points equidistant from ¯ZXZX¯\\bar{ZX} and ¯ZYZY¯\\bar{ZY}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(977, '1999', 'Which of the following statements is true from the diagram above?', ' m + n = 90o~ m = n~ n > 45o~ m < 45o~', ' m + n = 90o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(978, '1999', 'In the diagram, O is the centre of the circle ', '15~30~45~75~', '30', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(979, '1999', 'The sides of a right angle triangle in ascending order of magnitude are 8cm, (x-2)cm and x cm. Find x', '16~17~34~90~', '17', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(980, '1999', 'In the diagram, CDE is a triangle, ABEF is cyclic quadrilateral, AB||CD, ', ' 20o~ 30o~ 50o~ 65o~', ' 30o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(981, '2000', 'Express 398753 correct to three significant figures', '398000~398700~398800~399000~', '399000', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(982, '2000', 'Express 719719\\frac{7}{19} as a percentage, correct to 1 decimal place.', '0.027~0.037~0.271~0.368~0.422', '0.368', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(983, '2000', 'Find the missing number in the addition of the following numbers, in base seven.43211234', '3453~5556~6016~13453~', '3453', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(984, '2000', 'What fraction must be subtracted from the sum of 2162162\\frac{1}{6} and 3143143\\frac{1}{4}?', ' 1313\\frac{1}{3}~ 1212\\frac{1}{2}~ 1161161\\frac{1}{6}~ 1121121\\frac{1}{2}~', ' 1121121\\frac{1}{2}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(985, '2000', 'Simplify (1681)−34×√10081(1681)−34×√10081\\left(\\frac{16}{81}\\right)^{-\\frac{3}{4}}\\times \\sqrt{\\frac{100}{81}}', ' 8024380243\\frac{80}{243}~ 164164\\frac{1}{64}~ 256256\\frac{25}{6}~ 154154\\frac{15}{4}~', ' 154154\\frac{15}{4}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(986, '2000', 'Which of the following numbers is perfect cube?', '350~504~950~1728~', '1728', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(987, '2000', 'If 104x=68104x=68104', '5~7~8~9~', '8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(988, '2000', 'The ages of three men are in the ratio 3:4:5. If the difference between the ages of the oldest and youngest is 18 years, find the sum of the ages of the three men', ' 45 years~ 72 years~ 108 years~ 216 years~', ' 108 years', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(989, '2000', 'Given that log4X=−3,log4X=−3,log', ' 181181\\frac{1}{81}~ 164164\\frac{1}{64}~64~81~', ' 164164\\frac{1}{64}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(990, '2000', 'Given that the logarithm of a number is 1.8732, find, correct to 2 significant figures the square root of the mumber', '0.29~0.75~0.86~0.93~', '0.86', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(991, '2000', 'A car moves at an average speed of 30kmh-1 how long does it take to cover 200 meters?', ' 2.4 sec~ 24 sec~ 144 sec~ 240 sec~', ' 24 sec', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(992, '2000', 'A man bought a television set on hire purchase for N25,000, out of which he paid N10,000, if he is allowed to pay the balance in eight equal installments, find the value of each installment.', ' N1250~ N1578~ N1875~ N3125~', ' N1875', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(993, '2000', 'A tree is 8km due south of a building. Kofi is standing 8km west of the tree. Use this information to answer the question below How far is kofi from the building?', ' 4√2km~ 8km~ 8√2km~ 16km~', ' 8√2km', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(994, '2000', 'A tree is 8km due south of a building. Kofi is standing 8km west of the tree. Use this information to answer the question below Find the bearing of kofi from the building', ' 315o~ 270o~ 225o~ 135o~', ' 225o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(995, '2000', 'Which of the following bearings is equivalent to S50oW?', ' 040o~ 130o~ 220o~ 230o~', ' 230o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(996, '2000', 'In the diagram, AB is a vertical pole and BC is horizontal. If |AC| = 10m and |BC| = 5m, calculate the angle of depression of C from A.', ' 63o~ 60o~ 45o~ 27o~', ' 60o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(997, '2000', 'The bar chart shows the distribution of marks scored by a group of students in a test. Use the chart to answer the question below.How many students scored 4 marks and above?', '15~11~10~17~', '17', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(998, '2000', 'The bar chart shows the distribution of marks scored by a group of students in a test. Use the chart to answer the question below.How many students took the test?', '38~22~15~11~', '22', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(999, '2000', 'Calculate the standard deviation of the following marks; 2, 3, 6, 2, 5, 0, 4, 2', '1.5~1.7~1.8~1.9~', '1.8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1000, '2000', 'The probabilities that Kodjo and Adoga pass an examination are frac34and35frac34and35frac{3}{4} \\hspace{1mm} and \\hspace{1mm}\\frac{3}{5} respectively. Find the probability of both boys failing the examination\\)', ' 110110\\frac{1}{10}~ 310310\\frac{3}{10}~ 920920\\frac{9}{20}~ 2323\\frac{2}{3}~', ' 110110\\frac{1}{10}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1001, '2000', 'Which of the following statement is not true about triangle? I.Each diagonal cuts the rectangle into two congruent triangles. II. A rectangle has four lines of symmetry III. A The diagonals intersect at right angles', ' I and II only~ III only~ II only~ II and III only~', ' III only', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1002, '2000', 'In the diagram, PQRS is a circle center O. PQR is a diameter and ', ' 30o~ 40o~ 45o~ 50o~', ' 50o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1003, '2000', 'Each side of a regular convex polygon subtends an angle of 30o at its center. Calculate each interior angle', ' 75o~ 150o~ 160o~ 68o~', ' 150o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1004, '2000', 'If the interior angles of hexagon are 107', '5712~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1005, '2000', 'In the diagram, POS and ROT are straight lines, OPQR is a parallelogram. |OS| = |OT| and ', ' 160o~ 140o~ 120o~ 100o~', ' 100o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1006, '2000', 'Given that x=12andy=4evaluate3x2y+xy2x=12andy=4evaluate3x2y+xy2x = \\frac{1}{2}and \\hspace{1mm} y = 4 \\hspace{1mm} evaluate \\hspace{1mm} 3x^2y+xy^2', '-5~-1~4~11~', '-5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1007, '2000', 'Given that \\(27^{(1+x)}=9,)\\ find x', '-3~ −13−13\\frac{-1}{3}~ 5353\\frac{5}{3}~2~', ' −13−13\\frac{-1}{3}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1008, '2000', 'If x varies inversely as y and x=23x=23x = \\frac{2}{3} when y = 9, find the value of y when x=34x=34x=\\frac{3}{4}', ' 118118\\frac{1}{18}~ 881881\\frac{8}{81}~ 9292\\frac{9}{2}~8~', '8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1009, '2000', 'Given that (2x + 7) is a factor of 2x2+3x−142x2+3x−142x^2 + 3x - 14, find the other factor', ' x + 2~ 2 - x~ x - 2~ x + 1~', ' x - 2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1010, '2000', 'Simplify 1x−3−3(x−1)x2−91x−3−3(x−1)x2−9\\frac{1}{x-3}-\\frac{3(x-1)}{x^2 - 9}', ' x−1x−3x−1x−3\\frac{x-1}{x-3}~ −2x+3−2x+3\\frac{-2}{x+3}~ x−1x+3x−1x+3\\frac{x-1}{x+3}~ 4xx2−94xx2−9\\frac{4x}{x^2-9}~', ' −2x+3−2x+3\\frac{-2}{x+3}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1011, '2000', 'For an inequality for a distance of meters which is more than 18m, but not more than 23m', ' 18 ≤ d ≤ 23~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1012, '2000', 'Find the equation whose roots are -8 and 5', ' X2+13X+40=0X2+13X+40=0X^2 + 13X + 40=0~ X2−13X−40=0X2−13X−40=0X^2 - 13X - 40=0~ X2−13X+40=0X2−13X+40=0X^2 - 13X +40=0~ X2+13X−40=0X2+13X−40=0X^2 + 13X - 40=0~', ' X2+13X−40=0X2+13X−40=0X^2 + 13X - 40=0', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1013, '2000', 'Make t the subject of formula k=m√t−prk=mt−prk = m\\sqrt{\\frac{t-p}{r}}', ' rk2+pm2rk2+pm2\\frac{rk^2 + p}{m^2}~ rk2+pm2m2rk2+pm2m2\\frac{rk^2+pm^2}{m^2}~ rk2−pm2rk2−pm2\\frac{rk^2-p}{m^2}~ rk2−p2m2rk2−p2m2\\frac{rk^2-p^2}{m^2}~', ' rk2+pm2m2rk2+pm2m2\\frac{rk^2+pm^2}{m^2}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1014, '2000', 'Solve the equation 3y2=27y3y2=27y3y^2 = 27y', ' y = o or 3~ y = 0 or 9~ y = -3 or 3~ y = 3 or 9~', ' y = 0 or 9', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1015, '2000', 'Find the value of X such that the expression 1x+43x−56x+11x+43x−56x+1\\frac{1}{x}+\\frac{4}{3x}-\\frac{5}{6x}+1 equals zero', ' 1616\\frac{1}{6}~ 1414\\frac{1}{4}~ −32−32\\frac{-3}{2}~ −76−76\\frac{-7}{6}~', ' −32−32\\frac{-3}{2}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1016, '2000', 'Given that p varies directly as q while q varies inversely as r, which of the following statements is true?', ' r varies directly as p~ p varies inversely as r~ p varies directly as r~ q varies inversely as p~', ' p varies inversely as r', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1017, '2000', 'In the diagram, PQS is a circle with center O. RST is a tangent at S and ', ' 42o~ 48o~ 60o~ 66o~', ' 48o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1018, '2000', 'A bicycle wheel of radius 42cm is rolled over a distance 66 meters. How many revolutions does it make?', '2.5~5~25~50~', '25', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1019, '2000', 'The height for a pyramid on  square base is 15cm. if the volume is 80cm^3, find the area of the square base.', ' 8cm2~ 9.6cm2~ 16cm2~ 25cm2~', ' 16cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1020, '2000', 'A tap leaks at the rate of 2cm3 per seconds. How long will it take the tap to fill a container of 45 liters capacity? (1 liters = 1000cm3)', ' 8 hours~ 16hr 15min~ 4hr 25min~ 3hr~', ' 16hr 15min', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1021, '2000', 'The length of the parallel sides of a trapezium are 5cm and 7cm. If its area is 120cm2, find the perpendicular distance between the parallel sides', ' 5.0cm~ 6.9cm~ 10.0cm~ 20.0cm~', ' 20.0cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1022, '2000', 'The arc of a circle 50 cm long, subtends angle of 75o at the center of the circle. Find correct to 3 significant figures, the radius of the circle. Take ', ' 8.74cm~ 38.2cm~ 61.2cm~ 76.4cm~', ' 38.2cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1023, '2000', 'In the diagram, |PQ| = |PS|, which of the following statements is true?', ' ~ |PO| = |RO|~ QR||PS~ ~', ' ', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1024, '2000', 'The area of a circle is 38.5cm2. Find its diameter ', ' 22cm~ 14cm~ 7cm~ 6cm~', ' 7cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1025, '2000', 'Find the volume (in cm3) of the solid shown above.', ' 100cm3~ 150cm3~ 175cm3~ 250cm3~', ' 175cm3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1026, '2000', 'Solve the equation 3 + 5x - 2x2 = 0', ' −12,−3-\\frac{1}{2},-3~ 2, 3~ -2, 3~ −12,3-\\frac{1}{2},3~', ' −12,3-\\frac{1}{2},3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1027, '2000', 'If the simple interest on N2000 after 9 months is N60, at what rate per annum is the interest charged?', ' 214%2\\frac{1}{4}\\%~ 4%4\\%~ 5%5\\%~ 6%6\\%~', ' 4%4\\%', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1028, '2001', 'Given that y = px + q and y = 5 when x = 3, while y = 4 when x = 2, find the values of p and q.', ' p = 1, q = 3~ p = 1, q = 2~ p = -2, q = 3~ p = 3, q = -2~', ' p = 1, q = 2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1029, '2001', 'A boy estimated his transport fare for a journey as ', '0.05~0.475~0.0526~0.95~', '0.05', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1030, '2001', 'In a bag of oranges, the ratio of good ones to bad ones is 5:4. If the number of bad oranges in the bag is 36, how many oranges are there altogether?', '72~81~54~45~', '81', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1031, '2001', 'A man is four times as old as his son. The difference between their ages is 36. Find the sum of their ages', ' 45 years~ 48 years~ 60 years~ 74 years~', ' 60 years', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1032, '2001', 'The variance of a given distribution is 25. What is the standard deviation?', '125~75~25~5~3', '5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1033, '2001', 'Which of the following correctly expresses 48 as a product of prime factors?', ' 3 x 4 x 4~ 2 x 3 x 8~ 2 x 2 x 2 x 3 x 4~ 2 x 2 x 2 x 2 x 3~', ' 2 x 2 x 2 x 2 x 3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1034, '2001', 'Evaluate (20three)2−(11three)2(20three)2−(11three)2(20', '101~121~202~2020~', '202', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1035, '2001', 'Evaluate log105+log1020log105+log1020log', '2~3~4~5~', '2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1036, '2001', 'In a class of 80 students, every students studies Economics pr geography or both. If 65 students study Economics and 50 study Geography, how many study both subjects?', '15~30~35~45~', '35', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1037, '2001', 'If N varies directly as M and N = 8 when M = 20 find M when N = 7', '13~15~ 1712171217\\frac{1}{2}~ 1812181218\\frac{1}{2}~', ' 1712171217\\frac{1}{2}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1038, '2001', 'Evaluate 525×(23)2', ' 825\\frac{8}{25}~ 1225\\frac{12}{25}~ 3353\\frac{3}{5}~ 4184\\frac{1}{8}~', ' 3353\\frac{3}{5}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1039, '2001', 'The nth term of a sequence is 22n−12^{2n-1}. Which term of the sequence is 29?2^9?', ' 3rd~ 4th~ 5th~ 6th~', ' 5th', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1040, '2001', 'Evaluate 12+34of25', ' 1516\\frac{15}{16}~ 1116\\frac{11}{16}~ 4950\\frac{49}{50}~ 3153\\frac{1}{5}~', ' 1116\\frac{11}{16}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1041, '2001', 'Evaluate x2+x−22x2+x−3\\frac{x^2 + x - 2}{2x^2 + x -3} when x = -1', '-2~-1~ −12-\\frac{1}{2}~1~', '1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1042, '2001', 'Factorize 6x2+7x−206x^2 + 7x - 20', ' (6x - 5)(x + 4)~ 2(3x-5)(x+2)~ (3x+4)(2x-5)~ (3x-4)(2x+5)~', ' (3x-4)(2x+5)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1043, '2001', 'Simplify 2x−13−x+32\\frac{2x-1}{3}-\\frac{x+3}{2}', ' x+36\\frac{x+3}{6}~ x+86\\frac{x+8}{6}~ x−116\\frac{x-11}{6}~ x−46\\frac{x-4}{6}~', ' x−116\\frac{x-11}{6}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1044, '2001', 'If y−32<2y−13\\frac{y-3}{2} <', ' y > 7~ y < -7~ y > -7~ y < 7~', ' y > -7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1045, '2001', 'if 4m+3n4m−3n=52\\frac{4m+3n}{4m-3n}=\\frac{5}{2}, find the ratio m:n', ' 7:4~ 4:3~ 3:4~ 4:7~', ' 4:7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1046, '2001', 'The number line represents', ' 0>x≥−70>x\\ge -7~ −7≤x<−1-7 \\le x < -1~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1047, '2001', 'If 2x2+kx−14=(x+2)(2x−7)2x^2 + kx - 14 = (x+2)(2x-7), find the value of K', '-3~5~9~11~', '-3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1048, '2001', 'which of the following is not quadratic expression?', ' y=2x2−5xy = 2x^2 - 5x~ y=x(x−5)y=x(x-5)~ y=x2−5y = x^2 - 5~ y = 5(x-1)~', ' y = 5(x-1)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1049, '2001', 'The graph of the curve y=2x2−5x−1y = 2x^2 - 5x - 1 and a straight line PQ were drawn to solve the equation 2x2−5x+2=02x^2 - 5x + 2 = 0What is the equation of the straight line pQ?', ' y = -1~ y = 1~ y = 3~ y = -3~', ' y = -3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1050, '2001', 'Subtract (-y + 3x + 5z) from (4y - x - 2z)', ' 5y - 4x - 7z~ 3y + 2x + 3z~ -5y + 4x + 7z~ 2x - 5y + 3z~', ' 5y - 4x - 7z', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1051, '2001', 'If y', ' 19\\frac{1}{9}~ 16\\frac{1}{6}~ 13\\frac{1}{3}~ 23\\frac{2}{3}~', ' 13\\frac{1}{3}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1052, '2001', 'If 2x : (x +1) = 3:2, what is the value of x?', ' 12\\frac{1}{2}~1~ 1121\\frac{1}{2}~3~', '3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1053, '2001', 'The bearing S40oE is the same as', ' 040o~ 050o~ 130o~ 140o~', ' 140o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1054, '2001', 'Given that sin P=513P = \\frac{5}{13}, where p is acute, find the value of cos p - tan p', ' 79156\\frac{79}{156}~ 85156\\frac{85}{156}~ 713\\frac{7}{13}~ 81\\frac{8}{1}~', ' 79156\\frac{79}{156}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1055, '2001', 'Three observation posts P,Q and R are such that Q is due east of P and R is due north of Q. If |PQ| = 5km and |PR| = 10km, find |QR|', ' 5.0km~ 7.5km~ 7.6km~ 8.7km~', ' 8.7km', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1056, '2001', 'Express 25o 45l in decimal (Hint 1o = 60l)', ' 25.75o~ 25.55o~ 25.45o~ 25.15o~', ' 25.75o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1057, '2001', 'A box contains 5 red, 3 green and 4 blue balls. A boy is allowed to take away two balls from the box. Use this information to answer the question below.What is the probability that the two balls are red?', ' 533533\\frac{5}{33}~ 536536\\frac{5}{36}~ 103132103132\\frac{103}{132}~ 31363136\\frac{31}{36}~', ' 533533\\frac{5}{33}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1058, '2001', 'A box contains 5 red, 3 green and 4 blue balls. A boy is allowed to take away two balls from the box. Use this information to answer the question below. What is the probability that one is green and the other is blue?', ' 211211\\frac{2}{11}~ 512512\\frac{5}{12}~ 812812\\frac{8}{12}~ 711711\\frac{7}{11}~', ' 211211\\frac{2}{11}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1059, '2001', 'If the probability that an event will occur is p and the probability that it will not occur is q, which of the following is true?', ' p-q=1~ q-p=0~ p+q=1~ p+q=0~', ' p+q=1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1060, '2001', 'What is the range of their age?', ' 14 years~ 20 years~ 30.5 years~ 31 years~', ' 20 years', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1061, '2001', 'What is the mode?', ' 22.5 years~ 23.0 years~ 24.0 years~ 27.5 years~', ' 23.0 years', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1062, '2001', 'How many students are there in the group?', '25~30~52~55~', '52', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1063, '2001', 'Which of the following is not the the size of an exterior angle of a regular polygon?', ' 15o~ 18o~ 20o~ 21o~', ' 21o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1064, '2001', 'In the diagram, PQR is a triangle.|PQ| = |PR|, |PS| = |SQ| and PRS = 50o. What is the size of ', ' 75o~ 80o~ 85o~ 95o~', ' 80o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1065, '2001', 'PQRS is a rhombus of side 16cm. The diagonal |QS| = 20cm. Calculate, correct to the nearest degree, ', ' 51o~ 64o~ 77o~ 103o~', ' 103o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1066, '2001', 'In the diagram, PQ is a diameter of the circle and ', ' 29o~ 32o~ 42o~ 53o~', ' 32o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1067, '2001', 'A chord of length 30cm is 8cm away fro the center of the circle. What is the radius of the circle. What is the perimeter of the sector? Take ', ' 16cm~ 17cm~ 18cm~ 20cm~', ' 17cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1068, '2001', 'A sector of a circle radius 14cm subtends an  angle 135o at the center of the circle. What is the perimeter of the sector? Take ', ' 47cm~ 81cm~ 88cm~ 231cm~', ' 81cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1069, '2001', 'In the diagram, MN||PQ, |LM| = 3cm and |LP| = 4cm. If the area of ', ' 3cm2~ 6cm2~ 14cm2~ 24cm2~', ' 6cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1070, '2001', 'The diagram shows a triangular prism of length 7cm. The right - angled triangle PQR is a cross section of the prism |PR| = 5cm and |RQ| = 3cm. Use the information to answer the question below.What is the area of the cross-section?', ' 4 cm2~ 6cm2~ 15cm2~ 20cm2~', ' 6cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1071, '2001', 'The diagram shows a triangular prism of length 7cm. The right - angled triangle PQR is a cross section of the prism |PR| = 5cm and |RQ| = 3cm. Use the information to answer the question below.What is the volume of the prism?', ' 28cm2~ 42cm2~ 70cm2~ 84cm2~', ' 42cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1072, '2001', 'A solid cylinder of radius 7cm is 10cm long. Find its total surface area', '70~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1073, '2001', 'PQRS is a trapezium in which |PS| = 9cm, |QR| = 15m, |PQ| = 2√32√32\\sqrt{3}, ', ' 24√324√324\\sqrt{3} cm22^2~ 36√336√336\\sqrt{3} cm22^2~ 42√342√342\\sqrt{3} cm22^2~ 72√372√372\\sqrt{3} cm22^2~', ' 24√324√324\\sqrt{3} cm22^2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1074, '2001', 'Given that P = {b, d, e, f} and Q = {a, c, f, g} are subsets of the universal set U = {a,b, c, d, e, f, g}. Find PI ∩ Q', ' {a,c}~ {a, c, d, g}~ {c, d, g}~ {a, c, g}~', ' {a, c, g}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1075, '2001', 'What is the length of ¯RP¯RP\\bar{RP}?', '6~5~3~2~', '5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1076, '2002', 'Simplify 35', ' 4545\\frac{4}{5}~ 710710\\frac{7}{10}~ 6666\\frac{6}{6}~ 216216\\frac{21}{6}~', ' 710710\\frac{7}{10}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1077, '2002', 'In the diagram O is the center of the circle. Reflex angle XOY = 210o and the length of the minor arc is 5.5m. Find, correct to the nearest meter, the length of the major arc.', ' 8m~ 9m~ 10m~ 13m~', ' 8m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1078, '2002', 'A right pyramid is on a square base of side 4cm. The slanting side of the pyramid is 2√32√32\\sqrt{3}. Calculate the volume of the pyramid', ' 513cm3513cm35\\frac{1}{3}cm^3~ 1023cm31023cm310\\frac{2}{3}cm^3~ 16cm316cm316cm^3~ 32cm332cm332cm^3~', ' 1023cm31023cm310\\frac{2}{3}cm^3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1079, '2002', 'The height of a night circular cone is 4cm. The radius of its base is 3cm. Find the curve surface area', '9~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1080, '2002', 'Find the value of x in 0.5x + 2.6 = 5x + 0.35', '0.5~2~2.6~5~', '0.5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1081, '2002', 'If M5ten=1001011twoM5ten=1001011twoM5', '5~6~7~8~', '7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1082, '2002', 'What is the value of y at Q?', ' 6136136\\frac{1}{3}~6~3~ zero~', ' 6136136\\frac{1}{3}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1083, '2002', 'When y=312y=312y = 3\\frac{1}{2}, what is the positive value of x?', ' 212212 2\\frac{1}{2}~ 215215 2\\frac{1}{5}~ 115115 1\\frac{1}{5}~ zero~', ' 215215 2\\frac{1}{5}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1084, '2002', 'The length, in cm, of the sides of a right angled triangle are x, (x+2) and (x+1) where x > 0. Find , in cm, the length  of its hypotenuse', '4~5~13~17~', '5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1085, '2002', 'If log2 = 0.3010 and log2y = 1.8062, find; correct to the nearest whole number, the value of y', '6~5~4~-5~', '6', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1086, '2002', 'Points X, Y and Z are located in the same horizontal plane such that Y is 12 km north of X and Z is on a bearing of 270° from X. If |XZ| = 6km, calculate, correct to one decimal place, lYZl', ' 18km~ 13.4km~ 13km~ 10.4km~', ' 13.4km', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1087, '2002', 'The ratio of the number of men to the number of women in a 20 member committee is 3:1. How many women must be added to the 20-member committee so as to make the ratio of men to women 3:2?', '2~5~7~9~', '5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1088, '2002', 'If (x + 3) varies directly as y and x = 3 when y = 12, what is the value of x when y = 8?', '1~ 1212\\frac{1}{2}~ −−-\\frac{}{}~-1~', '1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1089, '2002', 'From the diagram, find the bearing of Q from P.', ' 236o~ 214o~ 146o~ 124o~', ' 236o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1090, '2002', 'Find the nth term of the sequence 4, 10, 16 ,...', ' 2(3n- 1)~ 2(2 + 3 n-1)~ 2 n + 2~ 2(3n+2)~', ' 2(3n- 1)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1091, '2002', 'If (-3, -4) is a point on the line y = mx + 2 find the value of m.', '-2~ 7474\\frac{7}{4}~2~ 8383\\frac{8}{3}~', '2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1092, '2002', 'Which of the following is represented by the above sketch?', ' y = x2 + x - 6~ y = x2 - x - 6~ y = x2 - x + 6~ y = x2 + x + 6~', ' y = x2 - x - 6', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1093, '2002', 'In the diagram, SQ is a tangent to the circle at P, XP||YQ, ', ' 24o~ 13.36o~ 44o~ 46o~', ' 24o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1094, '2002', 'For what values of x is the expression 3x−24x2+9x−93x−24x2+9x−9\\frac{3x-2}{4x^2+9x-9} undefined?', ' −34or3−34or3\\frac{-3}{4} \\hspace{1mm}or \\hspace{1mm}3~ −23or−3−23or−3\\frac{-2}{3} \\hspace{1mm}or \\hspace{1mm}-3~ 23or323or3\\frac{2}{3} \\hspace{1mm}or \\hspace{1mm}3~ 34or−334or−3\\frac{3}{4} \\hspace{1mm}or \\hspace{1mm}-3~', ' 34or−334or−3\\frac{3}{4} \\hspace{1mm}or \\hspace{1mm}-3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1095, '2002', 'Simplify 11−x+21+x11−x+21+x\\frac{1}{1-x} + \\frac{2}{1+x}', ' x+31−x2x+31−x2\\frac{x+3}{1-x^2}~ x−31+x2x−31+x2\\frac{x-3}{1+x^2}~ 3−x1−x23−x1−x2\\frac{3-x}{1-x^2}~ 3−x1+x23−x1+x2\\frac{3-x}{1+x^2}~', ' 3−x1−x23−x1−x2\\frac{3-x}{1-x^2}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1096, '2002', 'The lengths of the parallel sides of a trapezium are 9 cm and 12 cm. lf the area of the trapezium is 105 cm2, find the perpendicular distance between the parallel sides.', ' 5cm~ 7cm~ 10cm~ 15cm~', ' 10cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1097, '2002', 'The base diameter of a cone is 14cm, and its volume is 462 cm3. Find its height. ', ' 3.5cm~ 5cm~ 7cm~ 9cm~', ' 9cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0);
INSERT INTO `exam_simulation` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`, `status`) VALUES
(1098, '2002', 'A number is selected at random from the set Y = {18, 19, 2O, . . . 28, 29). Find the probability that the number is prime', ' 1414\\frac{1}{4}~ 311311\\frac{3}{11}~ 1212\\frac{1}{2}~ 3434\\frac{3}{4}~', ' 1414\\frac{1}{4}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1099, '2002', 'The median of the distribution is', '25~17.5~15~12.5~', '15', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1100, '2002', 'The range of the distribution is', '50~30~25~15~', '25', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1101, '2002', 'The upper quartile of the distribution is', '30~27.5~25~17.75~', '17.75', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1102, '2002', 'In the diagram O and OI are the centres of the circles radii 15cm and 8cm respectively. If PQ = 12cm, find |OOI|.', ' 8.46cm~ 19.04cm~ 20.81cm~ 26.16cm~ no option', ' no option', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1103, '2002', 'In the diagram O is the centre of the circle. Which of the following is/are not true? I. a = b  II. b + c = 180o', ' I and II only~ II and III only~ II only~ III only~', ' I and II only', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1104, '2002', 'Simplify 212×8124212×8124\\frac{2^{\\frac{1}{2}}\\times 8^{\\frac{1}{2}}}{4}', '1~2~4~16~', '1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1105, '2002', 'In the diagram, |SR| = |RQ| and ', ' 42o~ 39o~ 38o~ 30o~', ' 42o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1106, '2002', 'The angle of depression of a point Q from a vertical tower PR, 30m high, is 40o. If the foot P of the tower is on the same horizontal level as Q, find, correct to 2 decimal places, |PQ|.', ' 35.75m~ 25.00m~ 22.98m~19.28~', ' 35.75m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1107, '2002', 'The volume of a cylinder of radius 14cm is 210cm3. What is the curved surface area of the cylinder?', ' 15cm2~ 30cm2~ 616cm2~ 1262cm2~', ' 30cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1108, '2002', 'Simplify 2√3+10√3−6−323+103−6−32\\sqrt{3} + 10\\sqrt{3} - \\frac{6}{-3}', ' 7√3737\\sqrt{3}~ 10√310310\\sqrt{3}~ 14√314314\\sqrt{3}~ 18√318318\\sqrt{3}~', ' 14√314314\\sqrt{3}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1109, '2002', 'Factorize m(2a-b)-2n(b-2a)', ' (2a-b)(2n-m)~ (2a+b)(m-2n)~ (2a-b)(m+2n)~ (2a-b)(m-2n)~', ' (2a-b)(m+2n)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1110, '2002', 'If q oranges are sold for t Naira, how many oranges can be bought for p naira?', ' p2tp2t\\frac{p}{2}t~ qtpqtp\\frac{qt}{p}~ qptqpt\\frac{q}{pt}~ pqtpqt\\frac{pq}{t}~', ' pqtpqt\\frac{pq}{t}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1111, '2002', 'In the diagram, QRT is a straight line. If angle PTR = 90o, angle PRT = 60o, angle PQR = 30o and |PQ| = 6√3cm63cm6\\sqrt{3}cm, calculate |RT|.', ' 0.3cm~ √3232\\frac{\\sqrt{3}}{2}cm~ 3cm~ 3√3333\\sqrt{3}cm~', ' 3cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1112, '2002', 'In the diagram, calculate the value of x.', ' 35o~ 80o~ 100o~ 115o~', ' 100o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1113, '2002', 'In the diagram, ¯PSand¯QTPS¯andQT¯\\bar{PS}\\hspace{1mm} and \\hspace{1mm}\\bar{QT} are two altitudes of ', ' ~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1114, '2002', 'In the diagram, |QR| = 10cm, PR', ' 10(1+√3)10(1+√3)10(1+\\sqrt{3})~ 20√320√320\\sqrt{3}~ 10√310√310\\sqrt{3}~ (10+√3)(10+√3)(10+\\sqrt{3})~', ' 10(1+√3)10(1+√3)10(1+\\sqrt{3})', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1115, '2002', 'Calculate and correct to two significant figures, the percentage error in approximating 0.375 to 0.4', '2~2.5~6.6~6.7~', '6.7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1116, '2002', 'To arrive on schedule, a train is to cover a distance of 60km at 72km/hr. If it starts 10 minutes late, at what speed must it move to arrive on schedule?', ' 60km/hr~ 80km/hr~ 90km/hr~ 108km/hr~', ' 90km/hr', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1117, '2002', 'In the diagram, QR||TPQR||TPQR||TP and W', ' 92o~ 68o~ 67o~ 23o~', ' 67o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1118, '2002', 'In the diagram O is the center of the circle, ', ' 100o~ 96o~ 94o~ 86o~', ' 86o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1119, '2002', 'Given that p=x−1xandq=x2+1x2p=x−1xandq=x2+1x2p = x-\\frac{1}{x} and\\hspace{1mm}q = x^2 +  \\frac{1}{x^2} express q in terms of p.', ' (p2 + 2)~ (p - 2) 2~ (p + 2) 2~ (p2 - 2)~', ' (p2 + 2)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1120, '2002', 'The number of goals scored by a school team in 10 netball matches are as follows: 3, 5, 7, 7, 8, 8, 5, 11, 11, 12. Find the probability that in a match, the school team will score at most 8 goals.', ' 710710\\frac{7}{10}~ 2525\\frac{2}{5}~ 3535\\frac{3}{5}~ 1515\\frac{1}{5}~', ' 3535\\frac{3}{5}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1121, '2002', 'Which of the following is not a rational number?', '-5~ √4√4\\sqrt{4}~ 3343343\\frac{3}{4}~ √90√90\\sqrt{90}~', ' √90√90\\sqrt{90}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1122, '2002', 'In the diagram, LMT is a straight line. lf O is the centre of circle LMN, OMN = 20o, LTN = 32o and |NM| = |MT|, find LNM.', ' 44o~ 46o~ 52o~ 70o~', ' 46o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1123, '2003', 'In the diagram, STUV is a straight line. < TSY = < UXY = 40o and < VUW = 110o. Calculate < TYW', ' 150o~ 140o~ 130o~ 120o~', ' 150o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1124, '2003', 'Simplify (34−13)×413', ' 5959\\frac{5}{9}~ 516516\\frac{5}{16}~ 813813\\frac{8}{13}~ 165165\\frac{16}{5}~', ' 5959\\frac{5}{9}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1125, '2003', 'The table below gives the distribution of marks obtained by a number of pupils in a class test. Use the information to answer the question below.The mode of the distribution is', '3~5~8~18~', '3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1126, '2003', 'The table below gives the distribution of marks obtained by a number of pupils in a class test. Use the information to answer the question below.Find the median of the distribution.', '1~2~3~4~', '3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1127, '2003', 'The table below gives the distribution of marks obtained by a number of pupils in a class test. Use the information to answer the question below.How many pupils scored at least 2 marks?', '12~23~37~49~', '49', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1128, '2003', 'Interpret the inequality represented on the number line.', ' -4 < x ≤ 5~ -4 ≤ x < 5~ -4 ≤ x ≤ 5~ -4 ≤ x ≤ 5~', ' -4 < x ≤ 5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1129, '2003', 'A student bought 3 notebooks and 1 pen for N35. After misplacing these items, she again bought 2 notebooks and 2 pens, all of the same type forN30. What is the cost of a pen?', ' N5.00~ N7.50~ N10.00~ N15.00~', ' N5.00', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1130, '2003', 'Simplify 4a−3−1a+34a−3−1a+3\\frac{4}{a-3}-\\frac{1}{a+3}', ' 3a+11(a−3)(a−2)3a+11(a−3)(a−2)\\frac{3a+11}{(a-3)(a-2)}~ 3a+11(a+3)(a−2)3a+11(a+3)(a−2)\\frac{3a+11}{(a+3)(a-2)}~ 3a+11(a+3)(a+2)3a+11(a+3)(a+2)\\frac{3a+11}{(a+3)(a+2)}~ 3a+11(a−3)(a+2)3a+11(a−3)(a+2)\\frac{3a+11}{(a-3)(a+2)}~', ' 3a+11(a−3)(a+2)3a+11(a−3)(a+2)\\frac{3a+11}{(a-3)(a+2)}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1131, '2003', 'Simplify 4√18√84188\\frac{4\\sqrt{18}}{\\sqrt{8}}', '2~3~6~12~', '6', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1132, '2003', 'In the diagram, PQ/RT /RS/ =/QS/, ', ' 235o~ 290o~ 305o~ 325o~', ' 235o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1133, '2003', 'Three men, Bedu, Bakre and Kofi shared\' N500 in the ratio 3:2: x respectively. If Bedu', '1~4~5~6~', '5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1134, '2003', 'Simplify (123)2(23)2(123)2(23)2\\left(1\\frac{2}{3}\\right)^2\\left(\\frac{2}{3}\\right)^2', ' 2132132\\frac{1}{3}~ 1131131\\frac{1}{3}~1~ 3737\\frac{3}{7}~', ' 2132132\\frac{1}{3}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1135, '2003', 'Find the value of x which satisfies the equation5(x-7)=7-2x', ' x =2~ x=4~ x=6~ x = 14~', ' x=6', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1136, '2003', 'Evaluate log8log(14)log8log(14)\\frac{log8}{log\\left(\\frac{1}{4}\\right)}', '-2~ −32−32\\frac{-3}{2}~ 1212\\frac{1}{2}~4~', ' −32−32\\frac{-3}{2}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1137, '2003', 'A pyramid of volume 120cm3 has a rectangular base which measures 5cm by 6cm. Calculate the height of the pyramid', ' 5cm~ 9cm~ 12cm~ 15cm~', ' 12cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1138, '2003', 'PQRS is a cyclic quadrilateral. If ', ' 180o~ 150o~ 105o~ 75o~', ' 105o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1139, '2003', 'In the diagram, ZM is a straight line. Calculate the value of x.', ' 27o~ 30o~ 35o~ 37o~', ' 35o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1140, '2003', 'Find the value of x in the equation 3x2 - 8x - 3 = 0', ' 13,−313,−3\\frac{1}{3},-3~ −13,−3−13,−3-\\frac{1}{3},-3~ −13,3−13,3-\\frac{1}{3},3~ 13,313,3\\frac{1}{3},3~', ' −13,3−13,3-\\frac{1}{3},3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1141, '2003', 'In', '3.4~4.3~5.9~6.2~', '4.3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1142, '2003', 'Given, that 4P45=119104P45=119104P4', '3.4~4.3~5.9~6.2~', '5.9', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1143, '2003', 'A ladder, 6m long, leans against a vertical wall at an angle 53o to the horizontal. How high up the wall does the ladder reach?', ' 3.611m~ 4.521m~ 4.792m~ 7.962m~', ' 4.792m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1144, '2003', 'What is the size of angle x in the diagram?', ' 15o~ 30o~ 45o~ 60o~', ' 30o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1145, '2003', 'The four interior angles of a quadrilateral are (x + 20) o, (x+ 10) o (2x - 45) o and (x - 25) o. Find the value of x', '60~80~100~360~', '80', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1146, '2003', 'Calculate the value of y in the diagram.', '17~34~44~45~', '17', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1147, '2003', 'Out of 60 members of an Association, 15 are Doctors and 9 are Lawyers. If a member is selected at random from the Association, what is the probability that the member is neither a Doctor Nor a Lawyer', ' 35\\frac{3}{5}~ 910\\frac{9}{10}~ 320\\frac{3}{20}~ 14\\frac{1}{4}~', ' 35\\frac{3}{5}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1148, '2003', 'Find the values of x for which 12x2−13x+15 \\frac{1}{2x^2 - 13x +15}  is not defined,', ' 5 or 32 \\frac{3}{2} ~ 1 or 1513 \\frac{15}{13} ~ 2 or 15~ 13 or 15~', ' 5 or 32 \\frac{3}{2} ', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1149, '2003', 'In the diagram, P', ' 85o~ 60o~ 55o~ 45o~', ' 55o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1150, '2003', 'Evaluate (111two)2=−(101two)2(111', ' 10two~ 100two~ 1100two~ 11000two~', ' 11000two', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1151, '2003', 'Given that x ', '0.01014~0.01021~0.01015~0.01016~', '0.01014', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1152, '2003', 'If 3(1−n)9−2n=19\\frac{3^{(1-n)}}{9^{-2n}}=\\frac{1}{9} find n', ' −32-\\frac{3}{2}~ 13\\frac{1}{3}~-1~-3~', '-1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1153, '2003', 'Which of the following is/are not the interior angle(s) of a regular polygon? I.108o II. 116o III. 120o', ' I only~ II only~ III only~ I and III only~', ' II only', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1154, '2003', 'In a ', ' 2√3~ 4√3~ 6√3~ 12√3~', ' 4√3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1155, '2003', 'If P=√QR(1+3tR)P=QR(1+3tR)P = \\sqrt{QR\\left(1+\\frac{3t}{R}\\right)} make R the subject of the formula', ' R=3QTP2−QR=3QTP2−QR = \\frac{3QT}{P^2 - Q}~~ R=P2−3tQ−1R=P2−3tQ−1R = \\frac{P^2-3t}{Q-1}~ R=P2−3QTP2−QR=P2−3QTP2−QR = \\frac{P^2-3QT}{P^2-Q}~', ' R=P2−3QTP2−QR=P2−3QTP2−QR = \\frac{P^2-3QT}{P^2-Q}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1156, '2003', 'Use the Venn diagram to answer the question below.How many elements are in P∩Q?', '1~2~4~6~', '2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1157, '2003', 'Use the Venn diagram to answer Question belowFind Ql∩R', ' (e)~ (c, h)~ (c, g, h)~ (c, e, g, h)~', ' (c, g, h)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1158, '2003', 'The square root of a number is 2k. What is half of the number', ' √k2k2\\sqrt{\\frac{k}{2}}~ √kk\\sqrt{k}~ 12k212k2\\frac{1}{2}k^2~ 2k2~', ' 2k2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1159, '2003', 'Given that p varies as the square of q and q varies inversely as the square root of r. How does p vary with r?', ' p varies as the square of r~ p varies as the square root of r~ p varies inversely as the square of r~ p varies inversely as r~', ' p varies inversely as r', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1160, '2003', 'The probabilities of a boy passing English and Mathematics test are x and y respectively. Find the probability of the boy failing both tests', ' 1-(x-y)+xy~ 1-(x+y)-xy~ 1-(x+y)+xy~ 1 - (x - y) + x~', ' 1-(x+y)+xy', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1161, '2003', 'The locus of points equidistant from two intersecting straight lines PQ and PR is', ' a circle centre P radius Q.~ a circle centre P radius PR~ the point of intersection of the perpendicular bisectors of PQ and PR~ the bisector of angle QPR~', ' the point of intersection of the perpendicular bisectors of PQ and PR', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1162, '2003', 'In the diagram, PR is a tangent at T to the circle O. Find the value of x.', ' 9o~ 20o~ 26o~ 60o~', ' 26o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1163, '2003', 'Find the equation whose roots are −23−23-\\frac{2}{3} and 3', ' 3x2+11x-6=0~ 3x2+7x+6=0~ 3x2-11x-6=0~ 3x2-7x-6=0~', ' 3x2-7x-6=0', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1164, '2003', 'Evaluate Cos 45o Cos 30o - Sin 45o Sin 30o leaving the answer in surd form', ' √2−12√2−12\\frac{\\sqrt{2}-1}{2}~ √3−√24√3−√24\\frac{\\sqrt{3}-\\sqrt{2}}{4}~ √6−√22√6−√22\\frac{\\sqrt{6}-\\sqrt{2}}{2}~ √6−√24√6−√24\\frac{\\sqrt{6}-\\sqrt{2}}{4}~', ' √6−√24√6−√24\\frac{\\sqrt{6}-\\sqrt{2}}{4}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1165, '2003', 'In constructing an angle, Olu draws line OX. With centre O and a convenient radius, he draws an arc intersecting OX at P. With centres P and the same radius, he draws an arc intersecting the first arc at Q and finally joins OQ. What is the size of angle POQ so constructed?', ' 90o~ 75o~ 60o~ 45o~', ' 60o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1166, '2003', 'In the diagram /PS/ = 9 cm, /OR/ = 5cm, P', ' 55cm2~ 25cm2~ 22cm2~ 13cm2~', ' 55cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1167, '2003', 'A right circular cone is such that its radius r is twice its height h. Find its volume in terms of h', '23~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1168, '2003', 'A man made a loss of 15% by selling an article for N595. Find the cost price of the article', ' N600.00~ N684.25~ N700.00~ N892.50~', ' N700.00', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1169, '2003', 'The bearing of P from Q is x, where 270o< x < 360o. Find the bearing of Q from P.', ' (x - 90)o~ (x-270)o~ (x - 135)o~ (x - 180)o~', ' (x - 180)o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1170, '2003', 'Which of the following is not a measure of dispersion?', ' Range~ Mean deviation~ Mean~ Standard deviation~', ' Mean', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1171, '2004', 'Find the average of the first four prime numbers greater than 10.', '20~19~17~15~13', '15', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1172, '2004', 'Find the mean deviation of 6, 7, 8, 9, 10.', '1.2~1.5~2~8~10', '8', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1173, '2004', '1. Evaluate 2022three−1122three2022three−1122three 202^2', '21120~21121~21112~21011~', '21120', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1174, '2004', 'If y=23five+101threey = 23', '1110~10111~11101~111100~', '10111', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1175, '2004', 'Solve for t in the equation 34t+13(21−t)\\frac{3}{4}t+\\frac{1}{3}(21-t) = 11,', ' 913\\frac{9}{13}~ 95\\frac{9}{5}~5~ 9359\\frac{3}{5}~', ' 9359\\frac{3}{5}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1176, '2004', 'A school girl spends 14\\frac{1}{4} of her pocket money on books and 13\\frac{1}{3} on dress. What fraction remains?', ' 56\\frac{5}{6}~ 712\\frac{7}{12}~ 512\\frac{5}{12}~ 16\\frac{1}{6}~', ' 512\\frac{5}{12}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1177, '2004', 'In the diagram, R', ' 2.0cm~ 2.5cm~ 6.4cm~ 10.0cm~', ' 6.4cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1178, '2004', 'There are m boys and 12 girls in a class. What is the probability of selecting at random a girl from the class?', ' m12\\frac{m}{12}~ 12m\\frac{12}{m}~ 12m+12\\frac{12}{m+12}~ 12m−12\\frac{12}{m-12}~', ' 12m+12\\frac{12}{m+12}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1179, '2004', 'Simplify 712−(212+3)', '33~8~7~ o~', ' o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1180, '2004', 'The angle of elevation of the top of a tower from a point on the ground which is 36m away from the foot of the tower is 30o. Calculate the height of the tower.', ' 62.35m~ 20.78m~ 18.00m~ 10.39m~', ' 20.78m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1181, '2004', 'Find the area of a rectangle of length 4cm and whose diagonal is 6cm, (Leave your answer in surd form)', ' 8√3cm2~ 12√3cm2~ 16√2cm2~ 16√3cm2~', ' 16√3cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1182, '2004', 'Given that x + y = 7 and 3x-y = 5, evaluate y2−3\\frac{y}{2}-3.', '-1~1~3~4~', '-1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1183, '2004', 'In the diagram, PDQ is the diameter of the circle centre O. Calculate ', ' 35o~ 70o~ 100o~ 125o~', ' 35o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1184, '2004', 'If (14)(2−y)\\left(\\frac{1}{4}\\right)^{(2-y)}, find y.', '-2~ −12-\\frac{1}{2}.~ 12\\frac{1}{2}~2~', '2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1185, '2004', 'Calculate the total surface area of a cupboard which measures 12cm by 10cm by 8cm', ' 1920cm2~ 592cm2~ 296cm2~ 148cm2~', ' 296cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1186, '2004', 'If xa+1+yb\\frac{x}{a+1}+\\frac{y}{b} 1. Make y the subject of the relation', ' b(a−x+1)a+1\\frac{b(a-x+1)}{a+1}~ a+1b(a−x+1)\\frac{a+1}{b(a-x+1)}~ a(b−x+1)b+1\\frac{a(b-x+1)}{b+1}~ ba(b−x+1)\\frac{b}{a(b-x+1)}~', ' b(a−x+1)a+1\\frac{b(a-x+1)}{a+1}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1187, '2004', 'lf logpp=rlog^p', ' p =qr~ p =rq~ p=rqp = \\frac{r}{q}~ p=qr~', ' p=qr', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1188, '2004', 'Find the next two terms of the sequence1, 5, 14, 30, 50 ....,. ,', '61110~67116~81140~ 91, 140~', ' 91, 140', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1189, '2004', 'Each interior angle of a regular polygon is 108o. How many sides has it?', '5~7~9~14~', '5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1190, '2004', 'Solve the equation 10-3x-x2 = 0', ' x=2 or-5~ x= -2 or 5~ x = 1 or 10~ x = 2 or 5~', ' x=2 or-5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1191, '2004', 'Find, correct to two decimal places, the mean of9, 13, 16, 17, 19, 23, 24.', '23~17.29~16.5~16.33~', '17.29', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1192, '2004', 'Factorise 27p2x2 - 48y2.', ' 9(3px - 4y)2~ 3(3px - 4y)(3px - 4y)~ 9(px - 4y)(3p x + 4y)~ 3(3px -4y)(3px +4y)~', ' 3(3px -4y)(3px +4y)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1193, '2004', 'What is the volume of a solid cylinder of diameter 7cm and height 7cm? (Take ', ' 38.5cm3~ 77cm3~ 269.5cm3~ 1078cm3~', ' 269.5cm3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1194, '2004', 'Find the sum of the roots of the equation 2x2 + 3x - 9 = 0', '-18~-6~ −92-\\frac{9}{2}~ −32-\\frac{3}{2}~', ' −32-\\frac{3}{2}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1195, '2004', 'Given that ', ' {2}~ {1,9}~ {315.7}~ {4, 6, 8, 10}~', ' {1,9}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1196, '2004', 'In the diagram, KS is a tangent to the circle centre O at R and ', ' 90o~ 80o~ 50o~ 40o~', ' 50o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1197, '2004', 'A point X is on the bearing 342o from a point Y. What is the bearing of Y from X?', ' 342o~ 252o~ 198o~ 162o~', ' 162o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1198, '2004', 'In the diagram, O is the centre of the circle where OS//QR and ', ' 35o~ 45o~ 55o~ 70o~', ' 55o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1199, '2004', 'Given that √128+√18−√k√128+√18−√k\\sqrt{128}+\\sqrt{18}-\\sqrt{k}, find K,', '8~16~32~48~', '32', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1200, '2004', 'In the diagram, PQRW is a circle. Line P, V and QR are produced to meet at M, where ', ' 10o~ 25o~ 35o~ 60o~', ' 25o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1201, '2004', 'The table above gives the marks scored by a group of students in a test Use the table to answer the question below.What is the median mark?', '1~2~3~4~', '3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1202, '2004', 'The table above gives the marks scored by a group of students in a test Use the table to answer the question below.What is the probability of selecting a student from the group that scored 2 or 3?', ' 111111\\frac{1}{11}~ 522522\\frac{5}{22}~ 722722\\frac{7}{22}~ 611611\\frac{6}{11}~', ' 611611\\frac{6}{11}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1203, '2004', 'Find the range of values of x for whichx+24−x+13>12\\frac{x+2}{4}-\\frac{x+1}{3}>\\frac{1}{2}', ' x > 4~ x > -4~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1204, '2004', 'A boy walks 800m in 20 minutes. Calculate his average speed in km per hour', '2.4~4~16~24~', '2.4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1205, '2004', 'Simplify 2a+b−1a−b\\frac{2}{a+b}-\\frac{1}{a-b}', ' 3a+b\\frac{3}{a+b}~ a−3ba2−b2\\frac{a-3b}{a^2-b^2}~~~', ' a−3ba2−b2\\frac{a-3b}{a^2-b^2}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1206, '2004', 'The diagram is a circle centre O. Find the value of x.', ' 30o~ 50o~ 61o~ 78o~', ' 61o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1207, '2004', 'Use the graph to answer the question below.What are the roots of the equation x2 + 3x - 4 = 0?', ' 1, 4~ -1, -4~ -1, 4~ -4, 1~', ' -4, 1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1208, '2004', 'The values of x when y = 3 are approximately', ' -4.7 and 1.4~ -4.6 and 1.5~ -3.6 and 0.4~ -3.6 and 1.5~', ' -4.6 and 1.5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1209, '2004', 'Which of the following quadratic equations has −12−12-\\frac{1}{2} and 3434\\frac{3}{4}  as its roots?', ' 8x2 + 11x - 3 = 0~~ 8x2 + 2x -3 = 0~ 8x2 - 2x ~', ' 8x2 - 2x ', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1210, '2004', 'The locus of a point which moves in a plane such that it is equidistant from two fixed points X and Y is', ' the perpendicular bisector of the line segment X Y~ a line parallel to the line segment XY~ a circle with XY as diameter~ the line perpendicular to the line segment XY~', ' the perpendicular bisector of the line segment X Y', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1211, '2004', 'Given that P', '48~64~72~324~', '64', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1212, '2004', 'Which of the following is/are true?  In a plane, the locus of points I. Equidistant from a straight line is a circle radius d where d is the distance between the point and the straight line.II Equidistant from two given points P and Q is a circle of radius |PQ|. III Equidistant from two points is the perpendicular bisector of the line joining the two points.', ' I only~ II only~ III only~ I, II and III~', ' III only', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1213, '2004', 'The sides of two cubes are in the ratio 215. What is the ratio of their volumes?', ' 4:5~ 8: 15~ 6:125~ 8:125~', ' 8:125', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1214, '2004', 'Given that p = 2, q = -5 and r = - 4, evaluate 3p2 - q2 - r3', '101~77~51~-27~', '51', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1215, '2004', 'A Cooperative Society, charges an interest of 51/2% per annum on any amount borrowed by its members. If a member borrows N125,000, how much does he pay back after one year?', ' N136875~ N131,875~ N126750~ N126250~', ' N131,875', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1216, '2004', 'A bag contains 3 red and 2 white identical balls. lf 2 balls are picked at random from the bag, one after the other and with replacement, find the probability that they are of different colours', ' 36625\\frac{36}{625}~ 16625\\frac{16}{625}~ 1225\\frac{12}{25}~ 1325\\frac{13}{25}~', ' 1225\\frac{12}{25}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1217, '2004', 'A point on the ground is 5m away from the foot of a vertical wall 7 m high, Calculate, correct to the nearest degree, the angle of depression of the point from the top of the wall', ' 36o~ 44o~ 46o~ 54o~', ' 54o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1218, '2005', 'If (x - a) is a factor of bx - ax + x2, find the other factor.', ' (x + b)~ (x - b)~ (a + b)~ (a - b)~', ' (x + b)', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1219, '2005', 'Each of the interior angles of a regular polygon is 140o. Calculate the sum of all the interior angles of the polygon', ' 1080o~ 1260o~ 1800o~ 2160o~', ' 1260o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1220, '2005', 'In the diagram, find the size of the angle marked ao', ' 60o~ 80o~ 120o~ 160o~', ' 80o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1221, '2005', 'Correct 0.04945 to two significant figures', '0.04~0.049~0.05~0.49~', '0.049', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1222, '2005', 'Simplify 5√3−3√25√3−3√2\\frac{5}{\\sqrt{3}}-\\frac{3}{\\sqrt{2}}', ' 16(5√3−3√216(5√3−3√2\\frac{1}{6}(5\\sqrt{3}-3\\sqrt{2}~ 16(15√3−6√216(15√3−6√2\\frac{1}{6}(15\\sqrt{3}-6\\sqrt{2}~ 16(3√2−√316(3√2−√3\\frac{1}{6}(3\\sqrt{2}-\\sqrt{3}~ 16(10√3−9√216(10√3−9√2\\frac{1}{6}(10\\sqrt{3}-9\\sqrt{2}~', ' 16(10√3−9√216(10√3−9√2\\frac{1}{6}(10\\sqrt{3}-9\\sqrt{2}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1223, '2005', 'Evaluate, correct to the nearest whole number 712−(212+3)', '33~8~7~ o~', '7', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1224, '2005', 'Simplify the expression log1018−log102.88+log1016log1018−log102.88+log1016log', '31.12~3.112~2~1~', '2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1225, '2005', 'Find the equation whose roots are 2 and −312-3\\frac{1}{2}', ' 2x2 + 3x + 14 = 0~ 2x2 + 5x + 7 = 0~ 2x2 + 5x - 7 = 0~ 2x2 + 3x - 14 = 0~', ' 2x2 + 3x - 14 = 0', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1226, '2005', 'A man bought 220 mangoes at N5x. He sold each for 3x kobo and made a gain of N8. Find the value of x', '2~5~6~10~', '5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1227, '2005', 'From a point P, R is 5km due west and 12km due south. Find the distance between P and R', ' 5km~ 12km~ 13km~ 17km~', ' 13km', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1228, '2005', 'A fair die is tossed once, what is the probability of obtaining neither 5 or 2', ' 56\\frac{5}{6}~ 23\\frac{2}{3}~ 12\\frac{1}{2}~ 16\\frac{1}{6}~', ' 23\\frac{2}{3}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1229, '2005', 'In the diagram, KL//MN, ', ' 285o~ 255o~ 225o~ 210o~', ' 285o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1230, '2005', 'In the diagram, PR is a diameter, ', ' x=75−2y3x=\\frac{75-2y}{3}~ x=105−3y2x=\\frac{105-3y}{2}~ x=105−2y3x=\\frac{105-2y}{3}~ x=75−3y2x=\\frac{75-3y}{2}~', ' x=105−2y3x=\\frac{105-2y}{3}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1231, '2005', 'Convert 101101two to a number in base ten', '61~46~45~44~', '45', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1232, '2005', 'Solve the equation 27=85−x2^7 = 8^{5-x}', ' 58\\frac{5}{8}~ 83\\frac{8}{3}~ 32\\frac{3}{2}~ 154\\frac{15}{4}~', ' 83\\frac{8}{3}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1233, '2005', 'expand (2x-3y)(x-5y)', ' 2x2+13xy−15y22x^2 + 13xy - 15y^2~ 2x2−13xy−15y22x^2 - 13xy - 15y^2~ 2x2+13xy+15y22x^2 + 13xy + 15y^2~ 2x2−13xy+15y22x^2 - 13xy + 15y^2~', ' 2x2−13xy+15y22x^2 - 13xy + 15y^2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1234, '2005', 'Make f the subject of the relation v=u+ftv = u + ft', ' v−ut\\frac{v-u}{t}~ u−vt\\frac{u-v}{t}~ t(v+ut(v+u~ vu−t\\frac{v}{u}-t~', ' v−ut\\frac{v-u}{t}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1235, '2005', 'The lengths of the adjacent sides of a right - angled triangle are xcm, (x-1)cm. If the length of the hypotenuse is √13cm\\sqrt{13}cm, find the value of x', '2~3~4~5~', '3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1236, '2005', 'The probability that John and James pass an examination are 3/4 and 3/5 respectively, find the probability f both boys failing the examination', ' 110\\frac{1}{10}~ 310\\frac{3}{10}~ 920\\frac{9}{20}~ 1120\\frac{11}{20}~', ' 110\\frac{1}{10}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1237, '2005', 'In the diagram PQ and MN are straight lines. Find the value of x.', ' 13o~ 17o~ 28o~ 30o~', ' 17o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1238, '2005', 'In the diagram, PQRS is a parallelogram and ', ' 95o~ 100o~ 120o~ 150o~', ' 150o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1239, '2005', 'From a point R, 300m north of P, man walks eastward to a place Q which is 600m from P. Find the bearing of P from Q, correct to the nearest degreeee', ' 026o~ 045o~ 210o~ 240o~', ' 240o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1240, '2005', 'What is the diameter of a circle of area 77cm2 ', ' √27cm√27cm\\frac{\\sqrt{2}}{7}cm~ 312cm312cm3\\frac{1}{2}cm~ 7cm~ 7√2cm7\\sqrt{2}cm~', ' 7√2cm7\\sqrt{2}cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1241, '2005', 'Solve the equation 2x - 3y = 22; 3x + 2y = 7', '-5~-4~4~5~', '-4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1242, '2005', 'Solve the equation 2y−13−3y−14=1\\frac{2y-1}{3} - \\frac{3y-1}{4} = 1', '-8~-13~13~19~', '-13', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1243, '2005', 'If log9x=1.5log', '36~27~24.5~13.5~', '27', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1244, '2005', 'A sequence is given by 212,5,712,.....2\\frac{1}{2}, 5, 7\\frac{1}{2}, ..... if the nth term is 25, find n', '9~10~12~15~', '10', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1245, '2005', 'Given that the root of an the equation 2x2+(k+2)x+k=02x^2 + (k+2)x+k=0 is 2, find the value of k', '-4~-2~-1~ −14-\\frac{1}{4}~', '-4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1246, '2005', 'Find the mean of the numbers 1, 3, 4, 8, 8, 4 and 7', '4~5~6~7~', '5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1247, '2005', 'What is the total surface area of a closed cylinder of height 10cm and diameter 7cm? ', ' 77cm2~ 227cm2~ 297cm2~ 374cm2~', ' 297cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1248, '2005', 'An arc of a circle of radius 14cm subtends angle 300o at the center. Find the perimeter of the sector formed by the arc', ' 14.67cm~ 42.67cm~ 101.33cm~ 543.33cm~', ' 101.33cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1249, '2005', 'which of the following statements describes the locus of a point R which moves in a plane such that its equidistant from two intersecting lines?', ' the bisector of the angle formed by the lines~ the point of intersection of the two lines~ A cone, with two intersecting lines as slant height~ A circle, with the point of intersection of the two lines as the center~', ' the bisector of the angle formed by the lines', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1250, '2005', 'P = {3, 9, 11, 13} and Q = {3, 7, 9, 15} are subset of the universal set ', ' {3, 9}~ {5, 7, 9}~ {1}~ {1, 11}~', ' {1}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1251, '2005', 'A train moving at a uniform speed covers 36km in 21 minutes. How long does it take to cover 60km?', ' 35 mins~ 40 mins~ 45 mins~ 90 mins~', ' 35 mins', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1252, '2005', 'The salary of a man was increased in the ratio 40:47. calculate the percentage increase in the salary', '0.851~0.585~0.175~0.149~', '0.175', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1253, '2005', 'A regular polygon has 9 sides. What is the size of one of its exterior angles?', ' 20o~ 40o~ 90o~ 140o~', ' 40o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1254, '2005', 'Simplify: 23xy−3yz\\frac{2}{3xy} - \\frac{3}{yz}', ' 2−x12xyz\\frac{2-x}{12xyz}~ 2z−3x12xyz\\frac{2z-3x}{12xyz}~ 4z−3x12xyz\\frac{4z-3x}{12xyz}~ 8z−9x12xyz\\frac{8z-9x}{12xyz}~', ' 8z−9x12xyz\\frac{8z-9x}{12xyz}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1255, '2005', 'The total surface area of the walls of a room 7m long, 5m wide and xm high is 96m2. Find the value of x', ' 23\\frac{2}{3}~2~4~8~', '2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1256, '2005', 'For what values of y is the expression 6y−1y2−y−6\\frac{6y-1}{y^2 - y-6}', ' 16,14\\frac{1}{6}, \\frac{1}{4}~ 3, -2~ -3, 2~ 0,1~', ' 3, -2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1257, '2005', 'What are the roots of the equation?', ' -1 and 1~ 4 and 1~ 1 and 4~ 4 and 4~', ' 1 and 4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1258, '2005', 'What is the equation of the curve?', ' y=x2+6x+4y=x2+6x+4y=x^2+6x+4~ y=x2−5x−4y=x2−5x−4y=x^2-5x-4~ y=x2−5x+4y=x2−5x+4y=x^2-5x+4~ y=x2+5x−4y=x2+5x−4y=x^2+5x-4~', ' y=x2−5x+4y=x2−5x+4y=x^2-5x+4', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1259, '2005', 'In the diagram PQRS is a circle, |PT| = |QT| and ', ' 40o~ 70o~ 80o~ 140o~', ' 70o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1260, '2005', 'The angle of elevation of the top of a cliff 15 meters high from a landmark is 60o. How far is the landmark from the foot of the cliff? Leave your answer in surd form', ' 15√3m15√3m15\\sqrt{3}m~ 15√2m15√2m15\\sqrt{2}m~ 10√3m10\\sqrt{3}m~ 5√3m5\\sqrt{3}m~', ' 5√3m5\\sqrt{3}m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1261, '2005', 'XOY is a real sector of a circle center O of radius 3.5cm which subtends an angle of 144o at the center. Calculate, in term of ', '1.4~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1262, '2005', 'A rectangular packet has inner dimension 16cm by 12cm by 6cm. How many cubes of sugar of side 2cm can be neatly packed into the packet?', '90~144~150~288~', '144', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1263, '2005', 'Ladi sold  a car for N84,000 at a loss of 4%. How much did ladi buy the car', '80500~80640~87360~87500~', '87500', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1264, '2005', 'The monthly salary of a man increased from N2,700 to N3,200. Find the percentage increase', '0.1~0.15~0.156~0.185~', '0.185', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1265, '2005', 'In the diagram, O is the center of the circle, ', ' 40o~ 50o~ 55o~ 75o~', ' 55o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1266, '2005', 'The figure shows a quadrilateral PQRS having equal sides and opposite sides parallel. The diagonals PR and QS intersect perpendicularly at O. Which of the following statements cannot be correct?', ' |PO|=|RO|~ PQR is an equilateral triangle~ PQRX is a parallelogram~ There are two lines of symmetry~', ' PQR is an equilateral triangle', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1267, '2006', 'A machine valued at ', ' ~~~~', ' ', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1268, '2006', 'In the diagram, the tangent MN makes an angle of 55o with the chord PS. IF O is the centre of the circle, find ', ' 55o~ 45o~ 35o~ 25o~', ' 35o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1269, '2006', 'Evaluate (0.13)33^3correct to three significant figures', '0.00219~0.0022~0.003~0.0039~', '0.0022', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1270, '2006', 'Simplify: 1101122', '10100022~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1271, '2006', 'Simplify 2523', '25~ 1515\\frac{1}{5}~1~ 125125\\frac{1}{25}~', '1', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1272, '2006', 'Simplify x−44−x−36x−44−x−36\\frac{x - 4}{4} - \\frac{x - 3}{6}', ' x−1812x−1812\\frac{x - 18}{12}~ x−612x−612\\frac{x - 6}{12}~ x−1824x−1824\\frac{x - 18}{24}~ x−624x−624\\frac{x - 6}{24}~', ' x−612x−612\\frac{x - 6}{12}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1273, '2006', 'Given that y = 1 - 2x4x−3\\frac{2x}{4x - 3}, find the value of x for which y is undefined', '3~ 34\\frac{3}{4}~ −34\\frac{-3}{4}~-3~', ' 34\\frac{3}{4}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1274, '2006', 'P is a point on the same plane with a fixed point A. If P moves such that it is always equidistant from A, the locus of P is', ' a straight line joining A and P~ the perpendicular bisector of AP~ a circle with centre A~ the triangle with centre P~', ' a circle with centre A', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1275, '2006', 'A fair coin is tossed three times. Find the probability of getting two heads and one tail.', ' 12\\frac{1}{2}~ 38\\frac{3}{8}~ 14\\frac{1}{4}~ 18\\frac{1}{8}~', ' 38\\frac{3}{8}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1276, '2006', 'If 30% of y is equal to x, what in terms of x, is 30% of 3y?', ' x9x9\\frac{x}{9}~ x3x3\\frac{x}{3}~ x~ 3x~', ' 3x', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1277, '2006', 'A baker used 40% of a 50kg bag of flour. If 1818\\frac{1}{8} of the amount used was for the cake, how many kilogram of flour was used for the cake?', ' 21212\\frac{1}{2}~ 61212\\frac{1}{2}~ 153838\\frac{3}{8}~ 171212\\frac{1}{2}~', ' 21212\\frac{1}{2}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1278, '2006', 'If tan y = 0.404, where y is acute, find cos 2y', '0.035~0.719~0.808~0.927~', '0.719', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1279, '2006', 'The ratio of boys to girls in a class is 5:3. Find the probability of selecting at random, a girl from the class', ' 1818\\frac{1}{8}~ 1313\\frac{1}{3}~ 3838\\frac{3}{8}~ 3535\\frac{3}{5}~', ' 3838\\frac{3}{8}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1280, '2006', 'x14py0.512.5x14py0.512.5\\begin{array}{c|c} x ', '0.5~1~1.5~2~', '0.5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1281, '2006', 'Given that (2x - 1)(x + 5) = 2x2 - mx - 5, what is the value of m', '11~5~-9~-10~', '-9', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1282, '2006', 'What is the place value of 9 in the number 3.0492?', ' 910000910000\\frac{9}{10000}~ 9100091000\\frac{9}{1000}~ 91009100\\frac{9}{100}~ 910910\\frac{9}{10}~', ' 9100091000\\frac{9}{1000}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1283, '2006', 'If the simple interest on a sum of money invested at 3% per annum for 21212\\frac{1}{2} years is N123, find the principal.', ' N676.50~ N820~ N1,640~ N4,920~', ' N1,640', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1284, '2006', 'If 2x + y = 10, and y ', '4~5~8~10~', '5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1285, '2006', 'If x + y = 12 and 3x - y = 20, find the value of 2x - y', '8~10~12~15~', '12', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1286, '2006', 'Which of these equations best describes the points of intersection of the curve and the line?', ' x2 + 5x - 6 = 0~ x2 - 5x - 6 = 0~ x2 + x - 6 = 0~ x2 - x - 6 = 0~', ' x2 + x - 6 = 0', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1287, '2006', 'If loga270 - loga10 + loga 1313\\frac{1}{3} = 2, what is the value of a?', '3~4~5~6~', '3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1288, '2006', 'a conical water-jug is 7cm in diameter and 6cm deep. find the volume of water it can hold. ', ' 22cm2~ 44cm3~ 77cm3~3082~', ' 77cm3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1289, '2006', 'If p = ', ' T = R + P315QP315Q\\frac{P^3}{15Q}~ T = R - 15P3Q15P3Q\\frac{15P^3}{Q}~ T = R + P315QP315Q\\frac{P^3}{15Q}~ T = 15R - QP3QP3\\frac{Q}{P^3}~', ' T = R - 15P3Q15P3Q\\frac{15P^3}{Q}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1290, '2006', 'A seller allows 20% discount for cash payment on the marked price of his goods. What is the ratio of the cash payment to the marked price', ' 1:4~ 1:5~ 3:4~ 4:5~', ' 4:5', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1291, '2006', 'The wheel of a tractor has a diameter 1.4m. What distance does it cover in 100 complete revolutions? ', ' 140m~ 220m~ 280m~ 440m~', ' 440m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1292, '2006', 'If p = {1, 3, 5, 7, 9} and Q = {2, 4, 6, 8, 10} are subsets of a universal set. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. What are the elements of P1 ∩∩\\cap Q1?', ' {1, 3, 5, 7, 9}~ [2, 4, 6, 8, 10}~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1293, '2006', 'The values of three angles at a point are 3y - 45o, y + 25o and yo . Find the value of y.', ' 40o~ 58o~ 68o~ 76o~', ' 76o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1294, '2006', 'A rectangular carpet 2.5m long and 2.4m wide covers 5% of a rectangular floor. Calculate the area of the floor', ' 30m2~ 57m2~ 120m2~ 225m2~', ' 120m2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1295, '2006', 'Which of the following is not a measure of centre tendency?', ' mean~ mode~ range~ median~', ' range', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1296, '2006', 'The temperature in a chemical plant was -5oC at 2.00 am. The temperature fell by 6oC and then rose again by 7oC. What was the final temperature?', ' -6oC~ -4oC~ 4oC~ 8oC~', ' -4oC', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1297, '2006', 'Simplify 205√28−2√6320528−263\\frac{20}{5\\sqrt{28} - 2 \\sqrt{63}}', ' 5√77577\\frac{5\\sqrt{7}}{7}~ 5√57557\\frac{5\\sqrt{5}}{7}~ 7√57757\\frac{7\\sqrt{5}}{7}~ 7√75775\\frac{7\\sqrt{7}}{5}~', ' 5√77577\\frac{5\\sqrt{7}}{7}', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1298, '2006', 'A ladder 16m long leans against an electric pole. If the ladder makes an angle of 65o with the ground, how far up the electric pole does its top reach', ' 6.8m~ 14.5m~ 17.7m~ 34.3m~', ' 14.5m', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1299, '2006', 'In the diagram, PQUV, PQTU, QRTU and QRST are parallelograms. |UV| = 4.8cm and the perpendicular distance between PR and VS is 5cm. Calculate the area of quadrilateral PRSV.', ' 96cm2~ 72cm2~ 60cm2~ 24cm2~', ' 60cm2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1300, '2006', 'In the diagram, |QR| = 5cm, PQR = 60o and PSR = 45o. Find |PS|, leaving your answer in surd form.', ' 4√55\\sqrt{5}cm~ 3√77\\sqrt{7}cm~ 4√66\\sqrt{6}cm~ 5√66\\sqrt{6}cm~', ' 5√66\\sqrt{6}cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1301, '2006', 'In the diagram, PQRSPQRS\\frac{PQ}{RS}, find xo + yo.', ' 360o~ 300o~ 270o~ 180o~', ' 180o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1302, '2006', 'In the diagram, PR is a diameter of the circle centre O. RS is a tangent at R and QPR = 58o. Find < QRS.', ' 112o~ 116o~ 122o~ 148o~', ' 122o', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1303, '2006', 'In the diagram, the two circles have a common centre O. If the area of the larger circle is 100', '2~3~4~6~', '3', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1304, '2006', 'In the diagram, PQR is a straight line, QRST is a parallelogram, < TPQ = 72o and < RST = 126o. What type of triangle is ', ' An equilateral triangle~ A right-angled triangle~ An isosceles triangle~ A scalene triangle~', ' An isosceles triangle', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1305, '2006', 'How many pupils took the test?', '36~38~39~40~', '40', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1306, '2006', 'If the pass mark was 4. What percentage of the pupils failed the test?', '0.2~0.37~0.625~0.8~', '0.2', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1307, '2006', 'The diagram shows an arc MN of a circle, centre O, with 10cm. If < MON = 72o. Calculate the length of the arc, correct to three significant figures. ', ' 6.28cm~ 12.6cm~ 22.6cm~ 62.8cm~', ' 12.6cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1308, '2006', 'In the diagram what is x + y in terms of z?', ' 180o - z~ 180o + z~ z - 180o~ z~', ' 180o - z', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1309, '2006', 'In the diagram |XY| = 12cm, |XZ| = 9cm, |ZN| = 3cm and ZY||NM, calculate |MY|.', ' 3cm~ 4cm~ 5cm~ 6cm~', ' 4cm', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0),
(1310, '2007', 'Evaluate (111two)2(111', ' 111001two111001~~~~', '', 'No Official Explaination!', 'None', '', 'WAEC-PK-1', 'WAEC-MATH', 0);
