INSERT INTO `exam_simulation2` (`id`, `examYear`, `questions`, `parent_que`, `child_que`, `gen_child_que_desc`, `imageDir`, `explanation`, `parent_que_expl`, `child_que_exp`, `gen_child_que_expl`, `package_id`, `subject_id`, `status`) VALUES
(715, '2018', '\n\nQuestion\n\n(a) Using ruler a pair of compasses only, construct:\n(i) a trapezium PQRS such that |PQ| = 6.8 cm, < PQR = 120\\(^o\\), QR||PS, |PS| =10.6 cm, and IPRI = 93 cm;\n(ii) locus \\(l_1\\)of points equidistant from P and R;\n(iii) locus \\(l_2\\) of points equidistant from Q and R\n\n(b) Measure: (i) |QR|;\nii. <PSR\nii. < PSR\niii. |QY|, where Y is the point of intersection h and h.\n\n\n\n\n\n(a) Using ruler a pair of compasses only, construct:\n(i) a trapezium PQRS such that |PQ| = 6.8 cm, < PQR = 120\\(^o\\), QR||PS, |PS| =10.6 cm, and IPRI = 93 cm;\n(ii) locus \\(l_1\\)of points equidistant from P and R;\n(iii) locus \\(l_2\\) of points equidistant from Q and R\n\n(b) Measure: (i) |QR|;\nii. <PSR\nii. < PSR\niii. |QY|, where Y is the point of intersection h and h.\n\n\n', '', '(a) Using ruler a pair of compasses only, construct:\n(i) a trapezium PQRS such that |PQ| = 6.8 cm, < PQR = 120\\(^o\\), QR||PS, |PS| =10.6 cm, and IPRI = 93 cm;\n(ii) locus \\(l_1\\)of points equidistant from P and R;\n(iii) locus \\(l_2\\) of points equidistant from Q and R\n\n(b) Measure: (i) |QR|;\nii. <PSR\nii. < PSR\niii. |QY|, where Y is the point of intersection h and h.\n\n\n\n\n\n(a) Using ruler a pair of compasses only, construct:\n(i) a trapezium PQRS such that |PQ| = 6.8 cm, < PQR = 120\\(^o\\), QR||PS, |PS| =10.6 cm, and IPRI = 93 cm;\n(ii) locus \\(l_1\\)of points equidistant from P and R;\n(iii) locus \\(l_2\\) of points equidistant from Q and R\n\n(b) Measure: (i) |QR|;\nii. <PSR\nii. < PSR\niii. |QY|, where Y is the point of intersection h and h.\n', '(a) Using ruler a pair of compasses only, construct:\n(i) a trapezium PQRS such that |PQ| = 6.8 cm, < PQR = 120\\(^o\\), QR||PS, |PS| =10.6 cm, and IPRI = 93 cm;\n(ii) locus \\(l_1\\)of points equidistant from P and R;\n(iii) locus \\(l_2\\) of points equidistant from Q and R\n\n(b) Measure: (i) |QR|;\nii. <PSR\nii. < PSR\niii. |QY|, where Y is the point of intersection h and h.\n\n\n\n\n\n(a) Using ruler a pair of compasses only, construct:\n(i) a trapezium PQRS such that |PQ| = 6.8 cm, < PQR = 120\\(^o\\), QR||PS, |PS| =10.6 cm, and IPRI = 93 cm;\n(ii) locus \\(l_1\\)of points equidistant from P and R;\n(iii) locus \\(l_2\\) of points equidistant from Q and R\n~(b) Measure: (i) |QR|;\nii. <PSR\nii. < PSR\niii. |QY|, where Y is the point of intersection h and h.\n\n\n\n\n\n(a) Using ruler a pair of compasses only, construct:\n(i) a trapezium PQRS such that |PQ| = 6.8 cm, < PQR = 120\\(^o\\), QR||PS, |PS| =10.6 cm, and IPRI = 93 cm;\n(ii) locus \\(l_1\\)of points equidistant from P and R;\n(iii) locus \\(l_2\\) of points equidistant from Q and R\n\n(b) Measure: (i) |QR|;\nii. <PSR\nii. < PSR\niii. |QY|, where Y is the point of intersection h and h.\n', NULL, '\n\nExplanation\n(a) The trapezium PQRS is as shown\n\n(b)|QR| = (3.9 ± 0.1) cm, < PSR = (60 ± 1)\\(^o\\) and |QY| = (5.2 ± 0.1) cm.\n\n', '', 'Explanation\n(a) The trapezium PQRS is as shown\n\n(b)|QR| = (3.9 ± 0.1) cm, < PSR = (60 ± 1)\\(^o\\) and |QY| = (5.2 ± 0.1) cm.\n\n', '(a) The trapezium PQRS is as shown\n~(b)|QR| = (3.9 ± 0.1) cm, < PSR = (60 ± 1)\\(^o\\) and |QY| = (5.2 ± 0.1) cm.\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(716, '2018', '\n\nQuestion\n\n1. A donkey is tied with a rope to a post which is 15 m from a fence. If the length of the rope between the donkey and the post is 17m, calculate the length of the fence within the reach of the donkey.\n2. The base of a right pyramid with vertex, V, is a square, PQRS, of side 15 cm. If the slant height is 32 cm long:\n3. represent the information in a diagram;\n4. calculate its:\n5. height, correct to one decimal place;\n6. volume, correct to the nearest \\(cm^3\\)\n\n', '1. A donkey is tied with a rope to a post which is 15 m from a fence. If the length of the rope between the donkey and the post is 17m, calculate the length of the fence within the reach of the donkey.\n2. The base of a right pyramid with vertex, V, is a square, PQRS, of side 15 cm. If the slant height is 32 cm long:\n3. represent the information in a diagram;\n4. calculate its:\n5. height, correct to one decimal place;\n6. volume, correct to the nearest \\(cm^3\\)', '', '', NULL, '\n\nExplanation\n(a) first is to sketch the diagram\n\n\nUsing Pythagoras theorem, x\\(^2\\) = 17\\(^2\\) - 15\\(^2\\) = 64 and x = 8 m. Then, multiplying by 2 we have 16m as the length of the fence within the reach of the donkey.\n(b)(i)\n\n\nPR = \\(\\sqrt{15^2 + 15^2}\\) = 21.2132 cm and PO = OR = \\(\\frac{21.2132}{2}\\) = 10.61 cm.\nThen height of the pyramid is 32\\(^2\\) = h\\(^2\\) + (10.6066)\\(^2\\) and h yields h = 30.2 cm.\n\n(b)(ii) Volume = \\(\\frac{1}{3}\\) x 15 x 15 x 30.19106 = 2264 cm\\(^2\\) (correct to the nearest cm\\(^3\\)).\n\n\n', '', 'Explanation\n(a) first is to sketch the diagram\n\n\nUsing Pythagoras theorem, x\\(^2\\) = 17\\(^2\\) - 15\\(^2\\) = 64 and x = 8 m. Then, multiplying by 2 we have 16m as the length of the fence within the reach of the donkey.\n(b)(i)\n\n\nPR = \\(\\sqrt{15^2 + 15^2}\\) = 21.2132 cm and PO = OR = \\(\\frac{21.2132}{2}\\) = 10.61 cm.\nThen height of the pyramid is 32\\(^2\\) = h\\(^2\\) + (10.6066)\\(^2\\) and h yields h = 30.2 cm.\n\n(b)(ii) Volume = \\(\\frac{1}{3}\\) x 15 x 15 x 30.19106 = 2264 cm\\(^2\\) (correct to the nearest cm\\(^3\\)).\n\n\n', '(a) first is to sketch the diagram\n\n\nUsing Pythagoras theorem, x\\(^2\\) = 17\\(^2\\) - 15\\(^2\\) = 64 and x = 8 m. Then, multiplying by 2 we have 16m as the length of the fence within the reach of the donkey.\n(b)(i)\n\n\nPR = \\(\\sqrt{15^2 + 15^2}\\) = 21.2132 cm and PO = OR = \\(\\frac{21.2132}{2}\\) = 10.61 cm.\nThen height of the pyramid is 32\\(^2\\) = h\\(^2\\) + (10.6066)\\(^2\\) and h yields h = 30.2 cm.\n~(b)(i)\n\n\nPR = \\(\\sqrt{15^2 + 15^2}\\) = 21.2132 cm and PO = OR = \\(\\frac{21.2132}{2}\\) = 10.61 cm.\nThen height of the pyramid is 32\\(^2\\) = h\\(^2\\) + (10.6066)\\(^2\\) and h yields h = 30.2 cm.\n\n(b)(ii) Volume = \\(\\frac{1}{3}\\) x 15 x 15 x 30.19106 = 2264 cm\\(^2\\) (correct to the nearest cm\\(^3\\)).\n\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(717, '2018', '\n\nQuestion\n\na) Copy and complete the following table of values for y = 2 cos x – sin x ,\\(0^o \\leq x \\leq 300^o\\)\n\\[\\begin{array}{c|c} x & 0^o & 30^o & 60^o & 90^o & 120^o & 150^o & 180^o & 210^o & 240^o & 270^o& 300^o \\\\ \\hline Y & 2.00 & & 0.13 & & -1.87 & & -2.00 & & -0.13 & & \\end{array}\\]\n(b) Using scales of 2 cm to 30\\(^o\\) on the x-axis and 2cm to 1 unit on the y-axis, draw the graph of y = 2 cos x – sin x for \\(0^o \\leq x \\leq 300^o\\)\n(c) Use the graph to find the value(s) of x for which:\n(i) 2 cos x – sin x = 1;\n(ii) tan x = 2.\n\n', '', 'a) Copy and complete the following table of values for y = 2 cos x – sin x ,\\(0^o \\leq x \\leq 300^o\\)\n\\[\\begin{array}{c|c} x & 0^o & 30^o & 60^o & 90^o & 120^o & 150^o & 180^o & 210^o & 240^o & 270^o& 300^o \\\\ \\hline Y & 2.00 & & 0.13 & & -1.87 & & -2.00 & & -0.13 & & \\end{array}\\]\n(b) Using scales of 2 cm to 30\\(^o\\) on the x-axis and 2cm to 1 unit on the y-axis, draw the graph of y = 2 cos x – sin x for \\(0^o \\leq x \\leq 300^o\\)\n(c) Use the graph to find the value(s) of x for which:\n(i) 2 cos x – sin x = 1;\n(ii) tan x = 2.', 'a) Copy and complete the following table of values for y = 2 cos x – sin x ,\\(0^o \\leq x \\leq 300^o\\)\n\\[\\begin{array}{c|c} x & 0^o & 30^o & 60^o & 90^o & 120^o & 150^o & 180^o & 210^o & 240^o & 270^o& 300^o \\\\ \\hline Y & 2.00 & & 0.13 & & -1.87 & & -2.00 & & -0.13 & & \\end{array}\\]~(b) Using scales of 2 cm to 30\\(^o\\) on the x-axis and 2cm to 1 unit on the y-axis, draw the graph of y = 2 cos x – sin x for \\(0^o \\leq x \\leq 300^o\\)\n(c) Use the graph to find the value(s) of x for which:\n(i) 2 cos x – sin x = 1;\n(ii) tan x = 2.~(c) Use the graph to find the value(s) of x for which:\n(i) 2 cos x – sin x = 1;\n(ii) tan x = 2.', NULL, '\n\nExplanation\na) Table\n\\[\\begin{array}{c|c} x & 0^o & 30^o & 60^o & 90^o & 120^o & 150^o & 180^o & 210^o & 240^o & 270^o& 300^o \\\\ \\hline Y & 2.00 & 1.23 & 0.13 & -1.00 & -1.87 & -2.23 & -2.00 & -1.23 & -0.13 & 1.00 &1.87 \\end{array}\\]\n\n(b)(i) The value of x for which 2 cos x - sinx = 1\nx = \\((36 \\pm 3)^o\\) or \\((270 \\pm 3)^o\\)\n(ii) The value of x for which tan x = 3\nx = \\((64 \\pm 3)^o\\) or \\((244 \\pm 3)^o\\)\n\n\n\n', '', 'Explanation\na) Table\n\\[\\begin{array}{c|c} x & 0^o & 30^o & 60^o & 90^o & 120^o & 150^o & 180^o & 210^o & 240^o & 270^o& 300^o \\\\ \\hline Y & 2.00 & 1.23 & 0.13 & -1.00 & -1.87 & -2.23 & -2.00 & -1.23 & -0.13 & 1.00 &1.87 \\end{array}\\]\n\n(b)(i) The value of x for which 2 cos x - sinx = 1\nx = \\((36 \\pm 3)^o\\) or \\((270 \\pm 3)^o\\)\n(ii) The value of x for which tan x = 3\nx = \\((64 \\pm 3)^o\\) or \\((244 \\pm 3)^o\\)\n\n\n\n', 'a) Table\n\\[\\begin{array}{c|c} x & 0^o & 30^o & 60^o & 90^o & 120^o & 150^o & 180^o & 210^o & 240^o & 270^o& 300^o \\\\ \\hline Y & 2.00 & 1.23 & 0.13 & -1.00 & -1.87 & -2.23 & -2.00 & -1.23 & -0.13 & 1.00 &1.87 \\end{array}\\]\n~(b)(i) The value of x for which 2 cos x - sinx = 1\nx = \\((36 \\pm 3)^o\\) or \\((270 \\pm 3)^o\\)\n(ii) The value of x for which tan x = 3\nx = \\((64 \\pm 3)^o\\) or \\((244 \\pm 3)^o\\)\n\n\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(718, '2018', '\n\nQuestion\n\nIf log\\(_a\\)(y + 2) = 1 + log\\(_a\\) x, find x in terms of y.\n2. The table shows the distribution of timber production in five communities in a certain year\n\n\n\n\nCommunity\n\n\nTimber Production (tonnes)\n\n\n\n\nBibiani\nAmenfi\nOda\nWiawso\nSankore\n\n\n600\n900\n1800\n1500\n2400\n\n\n\n\n\n1. Draw a pie chart to represent the information.\n2. What percentage of timber produced that year was from Amenfi?\n3. If a tonne of timber is sold at $560.00, how much more revenue would Oda community receive than Bibiani?\n\n\nIf log\\(_a\\)(y + 2) = 1 + log\\(_a\\) x, find x in terms of y.\n2. The table shows the distribution of timber production in five communities in a certain year\n\n\n\n\nCommunity\n\n\nTimber Production (tonnes)\n\n\n\n\nBibiani\nAmenfi\nOda\nWiawso\nSankore\n\n\n600\n900\n1800\n1500\n2400\n\n\n\n\n', 'If log\\(_a\\)(y + 2) = 1 + log\\(_a\\) x, find x in terms of y.\n2. The table shows the distribution of timber production in five communities in a certain year\n\n\n\n\nCommunity\n\n\nTimber Production (tonnes)\n\n\n\n\nBibiani\nAmenfi\nOda\nWiawso\nSankore\n\n\n600\n900\n1800\n1500\n2400\n\n\n\n\n\n1. Draw a pie chart to represent the information.\n2. What percentage of timber produced that year was from Amenfi?\n3. If a tonne of timber is sold at $560.00, how much more revenue would Oda community receive than Bibiani?\n\n\nIf log\\(_a\\)(y + 2) = 1 + log\\(_a\\) x, find x in terms of y.\n2. The table shows the distribution of timber production in five communities in a certain year\n\n\n\n\nCommunity\n\n\nTimber Production (tonnes)\n\n\n\n\nBibiani\nAmenfi\nOda\nWiawso\nSankore\n\n\n600\n900\n1800\n1500\n2400\n\n\n', '', '', NULL, '\n\nExplanation\n(a) Applying the laws of logarithm, log(y + 2) = log ax which amplies that y + 2 = ax and finding x to get\nx = \\(\\frac{y + 2}{a}\\)\n(b)(i) The pie is shown\n\n(b)(i) The percentage of timber produced that year that was from Amenfi = \\(\\frac{900}{7200}\\) x 100% = 12.5%\n(ii) Difference in revenue = $560.00(1800 - 600) = $672,000.00\n\n', '', 'Explanation\n(a) Applying the laws of logarithm, log(y + 2) = log ax which amplies that y + 2 = ax and finding x to get\nx = \\(\\frac{y + 2}{a}\\)\n(b)(i) The pie is shown\n\n(b)(i) The percentage of timber produced that year that was from Amenfi = \\(\\frac{900}{7200}\\) x 100% = 12.5%\n(ii) Difference in revenue = $560.00(1800 - 600) = $672,000.00\n\n', '(a) Applying the laws of logarithm, log(y + 2) = log ax which amplies that y + 2 = ax and finding x to get\nx = \\(\\frac{y + 2}{a}\\)\n(b)(i) The pie is shown\n~(b)(i) The pie is shown\n\n(b)(i) The percentage of timber produced that year that was from Amenfi = \\(\\frac{900}{7200}\\) x 100% = 12.5%\n(ii) Difference in revenue = $560.00(1800 - 600) = $672,000.00\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(719, '2018', '\n\nQuestion\n\n(a) Mr John paid N4,800.00 in N1.00 ordinary shares of a company which sold at N2.50 per share. If dividend was declared at 25k per share, how much dividend did he get?\n\n(b) Using the method of completing the square, solve \\(\\frac{1 - x}{x} + \\frac{x}{1 - x} = \\frac{5}{2}\\)\n\n\n\n\n(a) Mr John paid N4,800.00 in N1.00 ordinary shares of a company which sold at N2.50 per share. If dividend was declared at 25k per share, how much dividend did he get?\n\n(b) Using the method of completing the square, solve \\(\\frac{1 - x}{x} + \\frac{x}{1 - x} = \\frac{5}{2}\\)\n\n', '', '(a) Mr John paid N4,800.00 in N1.00 ordinary shares of a company which sold at N2.50 per share. If dividend was declared at 25k per share, how much dividend did he get?\n\n(b) Using the method of completing the square, solve \\(\\frac{1 - x}{x} + \\frac{x}{1 - x} = \\frac{5}{2}\\)\n\n\n\n\n(a) Mr John paid N4,800.00 in N1.00 ordinary shares of a company which sold at N2.50 per share. If dividend was declared at 25k per share, how much dividend did he get?\n\n(b) Using the method of completing the square, solve \\(\\frac{1 - x}{x} + \\frac{x}{1 - x} = \\frac{5}{2}\\)', '(a) Mr John paid N4,800.00 in N1.00 ordinary shares of a company which sold at N2.50 per share. If dividend was declared at 25k per share, how much dividend did he get?\n\n(b) Using the method of completing the square, solve \\(\\frac{1 - x}{x} + \\frac{x}{1 - x} = \\frac{5}{2}\\)\n\n\n\n\n(a) Mr John paid N4,800.00 in N1.00 ordinary shares of a company which sold at N2.50 per share. If dividend was declared at 25k per share, how much dividend did he get?\n~(b) Using the method of completing the square, solve \\(\\frac{1 - x}{x} + \\frac{x}{1 - x} = \\frac{5}{2}\\)\n\n\n\n\n(a) Mr John paid N4,800.00 in N1.00 ordinary shares of a company which sold at N2.50 per share. If dividend was declared at 25k per share, how much dividend did he get?\n\n(b) Using the method of completing the square, solve \\(\\frac{1 - x}{x} + \\frac{x}{1 - x} = \\frac{5}{2}\\)', NULL, '\n\nExplanation\n(a) The quantity of shares bought \\(\\frac{8400}{2.5}\\) = 3360 shares. Therefore, the dividend the man received is 3360 X 0.25 = N840.00.\n\n(b) Clearing fractions and simplifying they got the quadratic equations 9x\\(^2\\) - 9x + 2 = 0. Next, dividing by 9 and adding the square of the coefficient of x to both sides yields (x - \\(\\frac{1}{2}\\))\\(^2\\) = \\(\\frac{1}{4} - \\frac{2}{9}\\).\nThen, taking square root and solving for x\nTo obtain x = \\(\\frac{2}{3}\\) or x = \\(\\frac{1}{3}\\)\n\n', '', 'Explanation\n(a) The quantity of shares bought \\(\\frac{8400}{2.5}\\) = 3360 shares. Therefore, the dividend the man received is 3360 X 0.25 = N840.00.\n\n(b) Clearing fractions and simplifying they got the quadratic equations 9x\\(^2\\) - 9x + 2 = 0. Next, dividing by 9 and adding the square of the coefficient of x to both sides yields (x - \\(\\frac{1}{2}\\))\\(^2\\) = \\(\\frac{1}{4} - \\frac{2}{9}\\).\nThen, taking square root and solving for x\nTo obtain x = \\(\\frac{2}{3}\\) or x = \\(\\frac{1}{3}\\)\n\n', '(a) The quantity of shares bought \\(\\frac{8400}{2.5}\\) = 3360 shares. Therefore, the dividend the man received is 3360 X 0.25 = N840.00.\n~(b) Clearing fractions and simplifying they got the quadratic equations 9x\\(^2\\) - 9x + 2 = 0. Next, dividing by 9 and adding the square of the coefficient of x to both sides yields (x - \\(\\frac{1}{2}\\))\\(^2\\) = \\(\\frac{1}{4} - \\frac{2}{9}\\).\nThen, taking square root and solving for x\nTo obtain x = \\(\\frac{2}{3}\\) or x = \\(\\frac{1}{3}\\)\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(720, '2018', '\n\nQuestion\n\nThe sum of the first ten terms of an Arithmetic Progression (A.P.) is 130. If the fifth term is 3 times the first term, find the:\n\ncommon difference;\nfirst term;\nnumber of terms of the A.P. if the last term is 28.\n\n\n\n\n\n\nThe sum of the first ten terms of an Arithmetic Progression (A.P.) is 130. If the fifth term is 3 times the first term, find the:\n\ncommon difference;\nfirst term;\nnumber of terms of the A.P. if the last term is 28.\n\n\n\n', '', 'The sum of the first ten terms of an Arithmetic Progression (A.P.) is 130. If the fifth term is 3 times the first term, find the:\n\ncommon difference;\nfirst term;\nnumber of terms of the A.P. if the last term is 28.\n\n\n\n\n\n\nThe sum of the first ten terms of an Arithmetic Progression (A.P.) is 130. If the fifth term is 3 times the first term, find the:\n\ncommon difference;\nfirst term;\nnumber of terms of the A.P. if the last term is 28.\n\n', '', NULL, '\n\nExplanation\n(a)it was expected that they substitute into the formula for sum of an Arithmetic Progression to have 130 = 1\\(\\frac{1}{2}\\) [2a+(10 - 1)d] and simplifying will yield 2a + 9d = 26 -------(1).\nAlso, U5 = a + (5 – 1)d = 3a and simplifying will yield a = 2d --------------------------------(2)\nSubstituting for a in equation (1) will yield 2(2d) + 9d = 26 and solving for d, d = 2.\n(b), Substituting for d in equation (2) to get the first term:a = 2(2) = 4\n(c) The number of terms required can be obtained by solving 28 = 4 + (n – 1)2 which resulted to n = 13.\n\n', '', 'Explanation\n(a)it was expected that they substitute into the formula for sum of an Arithmetic Progression to have 130 = 1\\(\\frac{1}{2}\\) [2a+(10 - 1)d] and simplifying will yield 2a + 9d = 26 -------(1).\nAlso, U5 = a + (5 – 1)d = 3a and simplifying will yield a = 2d --------------------------------(2)\nSubstituting for a in equation (1) will yield 2(2d) + 9d = 26 and solving for d, d = 2.\n(b), Substituting for d in equation (2) to get the first term:a = 2(2) = 4\n(c) The number of terms required can be obtained by solving 28 = 4 + (n – 1)2 which resulted to n = 13.\n\n', '(a)it was expected that they substitute into the formula for sum of an Arithmetic Progression to have 130 = 1\\(\\frac{1}{2}\\) [2a+(10 - 1)d] and simplifying will yield 2a + 9d = 26 -------(1).\nAlso, U5 = a + (5 – 1)d = 3a and simplifying will yield a = 2d --------------------------------(2)\nSubstituting for a in equation (1) will yield 2(2d) + 9d = 26 and solving for d, d = 2.~(b), Substituting for d in equation (2) to get the first term:a = 2(2) = 4\n(c) The number of terms required can be obtained by solving 28 = 4 + (n – 1)2 which resulted to n = 13.\n~(c) The number of terms required can be obtained by solving 28 = 4 + (n – 1)2 which resulted to n = 13.\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(721, '2018', '\n\nQuestion\n\n(a) In a right-angled triangle, sin â¡X = \\(\\frac{3}{5}\\). Evaluate, leaving the answer as a fraction, 5 (cosX)\\(^2\\) – 3.\n(b) The base of a pyramid, 12 cm high, is a rectangle with dimensions 42 cm by 11 cm. if the pyramid is filled with water and emptied into a conical container of equal height and volume, calculate, leaving the answer in surd form (radicals), the base radius of the container. [Take π=\\(\\frac{22}{7}\\)]\n\n\n\n\n\n(a) In a right-angled triangle, sin â¡X = \\(\\frac{3}{5}\\). Evaluate, leaving the answer as a fraction, 5 (cosX)\\(^2\\) – 3.\n(b) The base of a pyramid, 12 cm high, is a rectangle with dimensions 42 cm by 11 cm. if the pyramid is filled with water and emptied into a conical container of equal height and volume, calculate, leaving the answer in surd form (radicals), the base radius of the container. [Take π=\\(\\frac{22}{7}\\)]\n\n\n', '', '(a) In a right-angled triangle, sin â¡X = \\(\\frac{3}{5}\\). Evaluate, leaving the answer as a fraction, 5 (cosX)\\(^2\\) – 3.\n(b) The base of a pyramid, 12 cm high, is a rectangle with dimensions 42 cm by 11 cm. if the pyramid is filled with water and emptied into a conical container of equal height and volume, calculate, leaving the answer in surd form (radicals), the base radius of the container. [Take π=\\(\\frac{22}{7}\\)]\n\n\n\n\n\n(a) In a right-angled triangle, sin â¡X = \\(\\frac{3}{5}\\). Evaluate, leaving the answer as a fraction, 5 (cosX)\\(^2\\) – 3.\n(b) The base of a pyramid, 12 cm high, is a rectangle with dimensions 42 cm by 11 cm. if the pyramid is filled with water and emptied into a conical container of equal height and volume, calculate, leaving the answer in surd form (radicals), the base radius of the container. [Take π=\\(\\frac{22}{7}\\)]\n', '(a) In a right-angled triangle, sin â¡X = \\(\\frac{3}{5}\\). Evaluate, leaving the answer as a fraction, 5 (cosX)\\(^2\\) – 3.\n(b) The base of a pyramid, 12 cm high, is a rectangle with dimensions 42 cm by 11 cm. if the pyramid is filled with water and emptied into a conical container of equal height and volume, calculate, leaving the answer in surd form (radicals), the base radius of the container. [Take π=\\(\\frac{22}{7}\\)]\n\n\n\n\n\n(a) In a right-angled triangle, sin â¡X = \\(\\frac{3}{5}\\). Evaluate, leaving the answer as a fraction, 5 (cosX)\\(^2\\) – 3.~(b) The base of a pyramid, 12 cm high, is a rectangle with dimensions 42 cm by 11 cm. if the pyramid is filled with water and emptied into a conical container of equal height and volume, calculate, leaving the answer in surd form (radicals), the base radius of the container. [Take π=\\(\\frac{22}{7}\\)]\n\n\n\n\n\n(a) In a right-angled triangle, sin â¡X = \\(\\frac{3}{5}\\). Evaluate, leaving the answer as a fraction, 5 (cosX)\\(^2\\) – 3.\n(b) The base of a pyramid, 12 cm high, is a rectangle with dimensions 42 cm by 11 cm. if the pyramid is filled with water and emptied into a conical container of equal height and volume, calculate, leaving the answer in surd form (radicals), the base radius of the container. [Take π=\\(\\frac{22}{7}\\)]\n', NULL, '\n\nExplanation\n(a) By the use of Pythagoras theorem, the adjacent side of the right – angled triangle is 4.\nThen, cosâ¡(X = \\(\\frac{4}{5}\\)) and substituting to get 5(cos X)\\(^2\\)– 3\n= 5(\\(\\frac{4}{5}\\))\\(^2\\) - 3\n= \\(\\frac{16}{5}\\) - 3\n= \\(\\frac{(16 - 15)}{5}\\) = \\(\\frac{1}{5}\\)\n(b) find Volume of pyramid = \\(\\frac{1}{3}\\) × 42 × 11 × 12 = 1,848 (cm)\\(^2\\)\nVolume of conical container = \\(\\frac{1}{3}\\) × \\(\\frac{22}{7}\\) x r\\(^2\\) × 12 = 1,848\nand simplifying to get r\\(^2\\) = 147 so that r =7√3 cm as required.\n\n', '', 'Explanation\n(a) By the use of Pythagoras theorem, the adjacent side of the right – angled triangle is 4.\nThen, cosâ¡(X = \\(\\frac{4}{5}\\)) and substituting to get 5(cos X)\\(^2\\)– 3\n= 5(\\(\\frac{4}{5}\\))\\(^2\\) - 3\n= \\(\\frac{16}{5}\\) - 3\n= \\(\\frac{(16 - 15)}{5}\\) = \\(\\frac{1}{5}\\)\n(b) find Volume of pyramid = \\(\\frac{1}{3}\\) × 42 × 11 × 12 = 1,848 (cm)\\(^2\\)\nVolume of conical container = \\(\\frac{1}{3}\\) × \\(\\frac{22}{7}\\) x r\\(^2\\) × 12 = 1,848\nand simplifying to get r\\(^2\\) = 147 so that r =7√3 cm as required.\n\n', '(a) By the use of Pythagoras theorem, the adjacent side of the right – angled triangle is 4.\nThen, cosâ¡(X = \\(\\frac{4}{5}\\)) and substituting to get 5(cos X)\\(^2\\)– 3\n= 5(\\(\\frac{4}{5}\\))\\(^2\\) - 3\n= \\(\\frac{16}{5}\\) - 3\n= \\(\\frac{(16 - 15)}{5}\\) = \\(\\frac{1}{5}\\)~(b) find Volume of pyramid = \\(\\frac{1}{3}\\) × 42 × 11 × 12 = 1,848 (cm)\\(^2\\)\nVolume of conical container = \\(\\frac{1}{3}\\) × \\(\\frac{22}{7}\\) x r\\(^2\\) × 12 = 1,848\nand simplifying to get r\\(^2\\) = 147 so that r =7√3 cm as required.\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(722, '2018', '\n\nQuestion\n\n(a) The frequency distribution shows the range of prices of a brand of a car sold by a dealer and the corresponding quantity demanded.\n\n\n\n\nPrice\n(N1,000,000.00\n\n1.0 - 1.9\n2.0 - 2.9\n3.0 - 3.9\n4.0 - 4.9\n5.0 - 5.9\n\n\nNumber of Vehicles\n23\n48\n107\n90\n32\n\n\n\n\n(b) Represent the information in a histogram and use the histogram to determine the most preferred selling price for the brand of car.\n\n\n(a) The frequency distribution shows the range of prices of a brand of a car sold by a dealer and the corresponding quantity demanded.\n\n\n\n\nPrice\n(N1,000,000.00\n\n1.0 - 1.9\n2.0 - 2.9\n3.0 - 3.9\n4.0 - 4.9\n5.0 - 5.9\n\n\nNumber of Vehicles\n23\n48\n107\n90\n32\n\n\n\n', '', '(a) The frequency distribution shows the range of prices of a brand of a car sold by a dealer and the corresponding quantity demanded.\n\n\n\n\nPrice\n(N1,000,000.00\n\n1.0 - 1.9\n2.0 - 2.9\n3.0 - 3.9\n4.0 - 4.9\n5.0 - 5.9\n\n\nNumber of Vehicles\n23\n48\n107\n90\n32\n\n\n\n\n(b) Represent the information in a histogram and use the histogram to determine the most preferred selling price for the brand of car.\n\n\n(a) The frequency distribution shows the range of prices of a brand of a car sold by a dealer and the corresponding quantity demanded.\n\n\n\n\nPrice\n(N1,000,000.00\n\n1.0 - 1.9\n2.0 - 2.9\n3.0 - 3.9\n4.0 - 4.9\n5.0 - 5.9\n\n\nNumber of Vehicles\n23\n48\n107\n90\n32\n\n', '(a) The frequency distribution shows the range of prices of a brand of a car sold by a dealer and the corresponding quantity demanded.\n\n\n\n\nPrice\n(N1,000,000.00\n\n1.0 - 1.9\n2.0 - 2.9\n3.0 - 3.9\n4.0 - 4.9\n5.0 - 5.9\n\n\nNumber of Vehicles\n23\n48\n107\n90\n32\n\n\n\n~(b) Represent the information in a histogram and use the histogram to determine the most preferred selling price for the brand of car.\n\n\n(a) The frequency distribution shows the range of prices of a brand of a car sold by a dealer and the corresponding quantity demanded.\n\n\n\n\nPrice\n(N1,000,000.00\n\n1.0 - 1.9\n2.0 - 2.9\n3.0 - 3.9\n4.0 - 4.9\n5.0 - 5.9\n\n\nNumber of Vehicles\n23\n48\n107\n90\n32\n\n', NULL, '\n\nExplanation\n(a) The expected table with class boundaries was\n\n\n\n\nPrice\n(N1,000,000.00)\n\n\nClass\nBoundaries\n\nNumber of Vehicles\n\n\n1.0 - 1.9\n0.95 - 1.95\n23\n\n\n2.0 - 2.9\n1.95 - 2.95\n48\n\n\n3.0 - 3.9\n2.95 - 3.95\n107\n\n\n4.0 - 4.9\n3.95 - 4.95\n90\n\n\n5.0 - 5.9\n4.95 - 5.95\n32\n\n\n\n\n(b) From the first graph, the most preffered selling price for the brand of car is 2.95 + 0.75 = 3.70\n= N1,000,000 x 3.70 = N3,700,000.00\n\n', '', 'Explanation\n(a) The expected table with class boundaries was\n\n\n\n\nPrice\n(N1,000,000.00)\n\n\nClass\nBoundaries\n\nNumber of Vehicles\n\n\n1.0 - 1.9\n0.95 - 1.95\n23\n\n\n2.0 - 2.9\n1.95 - 2.95\n48\n\n\n3.0 - 3.9\n2.95 - 3.95\n107\n\n\n4.0 - 4.9\n3.95 - 4.95\n90\n\n\n5.0 - 5.9\n4.95 - 5.95\n32\n\n\n\n\n(b) From the first graph, the most preffered selling price for the brand of car is 2.95 + 0.75 = 3.70\n= N1,000,000 x 3.70 = N3,700,000.00\n\n', '(a) The expected table with class boundaries was\n\n\n\n\nPrice\n(N1,000,000.00)\n\n\nClass\nBoundaries\n\nNumber of Vehicles\n\n\n1.0 - 1.9\n0.95 - 1.95\n23\n\n\n2.0 - 2.9\n1.95 - 2.95\n48\n\n\n3.0 - 3.9\n2.95 - 3.95\n107\n\n\n4.0 - 4.9\n3.95 - 4.95\n90\n\n\n5.0 - 5.9\n4.95 - 5.95\n32\n\n\n\n~(b) From the first graph, the most preffered selling price for the brand of car is 2.95 + 0.75 = 3.70\n= N1,000,000 x 3.70 = N3,700,000.00\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(723, '2018', '\n\nQuestion\n\nIn the diagram. PQR is an isosceles triangle. If the perimeter of the triangle is 28 cm, find the:\na. values of x and y;\nb. lengths of the sides of the triangle.\n\n', '', 'In the diagram. PQR is an isosceles triangle. If the perimeter of the triangle is 28 cm, find the:\na. values of x and y;\nb. lengths of the sides of the triangle.', '', NULL, '\n\nExplanation\n\n(a) By summing 2y + x + 6y - 2x + 1 + 4y = 28 and simplified to arrive at 12y - x = 27 ...............(1).\nSimilarly, IPRI = IRQI, which implied that 4y = 6y - 2x + 1. This simplified to 2y - 2x - 1 ...............(2)\nSolving equations (1) and (2) simultaneously gave 2y - 2(12y - 27) = -1.\nso that y = 2(\\(\\frac{1}{2}\\)). Then, x = 12(\\(\\frac{5}{2}\\)) - 27 = 30 - 27 = 3\n(b) The lengths of the sides of the triangle were also obtained as |PO| = 2y + x = 2(\\(\\frac{5}{2}\\)) + 3 = 8 cm.\n|QR| = 4y = 4(\\(\\frac{5}{2}\\)) = 10 cm and IPRI = 6y - 2x + 1 = 6(\\(\\frac{5}{2}\\)) - 2(3) + 1 = 10 cm\n\n', '', 'Explanation\n\n(a) By summing 2y + x + 6y - 2x + 1 + 4y = 28 and simplified to arrive at 12y - x = 27 ...............(1).\nSimilarly, IPRI = IRQI, which implied that 4y = 6y - 2x + 1. This simplified to 2y - 2x - 1 ...............(2)\nSolving equations (1) and (2) simultaneously gave 2y - 2(12y - 27) = -1.\nso that y = 2(\\(\\frac{1}{2}\\)). Then, x = 12(\\(\\frac{5}{2}\\)) - 27 = 30 - 27 = 3\n(b) The lengths of the sides of the triangle were also obtained as |PO| = 2y + x = 2(\\(\\frac{5}{2}\\)) + 3 = 8 cm.\n|QR| = 4y = 4(\\(\\frac{5}{2}\\)) = 10 cm and IPRI = 6y - 2x + 1 = 6(\\(\\frac{5}{2}\\)) - 2(3) + 1 = 10 cm\n\n', '(a) By summing 2y + x + 6y - 2x + 1 + 4y = 28 and simplified to arrive at 12y - x = 27 ...............(1).\nSimilarly, IPRI = IRQI, which implied that 4y = 6y - 2x + 1. This simplified to 2y - 2x - 1 ...............(2)\nSolving equations (1) and (2) simultaneously gave 2y - 2(12y - 27) = -1.\nso that y = 2(\\(\\frac{1}{2}\\)). Then, x = 12(\\(\\frac{5}{2}\\)) - 27 = 30 - 27 = 3~(b) The lengths of the sides of the triangle were also obtained as |PO| = 2y + x = 2(\\(\\frac{5}{2}\\)) + 3 = 8 cm.\n|QR| = 4y = 4(\\(\\frac{5}{2}\\)) = 10 cm and IPRI = 6y - 2x + 1 = 6(\\(\\frac{5}{2}\\)) - 2(3) + 1 = 10 cm\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(724, '2018', '\n\nQuestion\n\na. Find the range of values of x which satisfy the following inequalities simultaneously: 5 - x > 1 and 9 + x \\(\\geq\\) 8\n\nIn the diagram, Ois the centre of the circle, IPQI = IQRI and < PSR = 56°. Find < QRS.\n\n', 'a. Find the range of values of x which satisfy the following inequalities simultaneously: 5 - x > 1 and 9 + x \\(\\geq\\) 8\n\nIn the diagram, Ois the centre of the circle, IPQI = IQRI and < PSR = 56°. Find < QRS.', '', '', NULL, '\n\nExplanation\n(a) x < 4 or -1 \\(\\geq\\) x. The range of values of x is -1\\(\\geq\\) x < 4.\n(b) First, < PQR + 56°= 180°\nso that < PQR = 180°- 56°= 124° From triangle PQR,\n< PQR + < QRP+ < QPR = 180°. But IRQI = IQPI\nso that < QRP = < QPR.\n124° + 2 < QRP = 180° and < QRP =28°.\nBut < PRS = 90° (angle on a semi-circle), therefore, < QRS = 28°+ 90° = 118°.\n\n', '', 'Explanation\n(a) x < 4 or -1 \\(\\geq\\) x. The range of values of x is -1\\(\\geq\\) x < 4.\n(b) First, < PQR + 56°= 180°\nso that < PQR = 180°- 56°= 124° From triangle PQR,\n< PQR + < QRP+ < QPR = 180°. But IRQI = IQPI\nso that < QRP = < QPR.\n124° + 2 < QRP = 180° and < QRP =28°.\nBut < PRS = 90° (angle on a semi-circle), therefore, < QRS = 28°+ 90° = 118°.\n\n', '(a) x < 4 or -1 \\(\\geq\\) x. The range of values of x is -1\\(\\geq\\) x < 4.~(b) First, < PQR + 56°= 180°\nso that < PQR = 180°- 56°= 124° From triangle PQR,\n< PQR + < QRP+ < QPR = 180°. But IRQI = IQPI\nso that < QRP = < QPR.\n124° + 2 < QRP = 180° and < QRP =28°.\nBut < PRS = 90° (angle on a semi-circle), therefore, < QRS = 28°+ 90° = 118°.\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(725, '2018', '\n\nQuestion\n\na. A textbook company discovered that the profit made from selling its books is given by y = \\(\\frac{x^2}{8}\\) + 5x, where x is the number of textbooks sold (in thousands) and y is the corresponding profit (in Ghana Cedis). If the company made a profit of GH₵ 20,000.00\ni. form a quadratic equation in x;\nii. (using the quadratic formula, find, correct to the nearest whole number, the number of textbooks sold to make the profit.\nb. The angle of elevation of the top T of a tree from a point P on the same ground level as the foot Q of a tree is 28\\(^o\\). A bird perched at a point R, halfway up the tree.\ni. Represent the information in a diagram.\nii. Calculate, correct to the nearest degree, the angle of elevation of R from P.\n\n', '', 'a. A textbook company discovered that the profit made from selling its books is given by y = \\(\\frac{x^2}{8}\\) + 5x, where x is the number of textbooks sold (in thousands) and y is the corresponding profit (in Ghana Cedis). If the company made a profit of GH₵ 20,000.00\ni. form a quadratic equation in x;\nii. (using the quadratic formula, find, correct to the nearest whole number, the number of textbooks sold to make the profit.\nb. The angle of elevation of the top T of a tree from a point P on the same ground level as the foot Q of a tree is 28\\(^o\\). A bird perched at a point R, halfway up the tree.\ni. Represent the information in a diagram.\nii. Calculate, correct to the nearest degree, the angle of elevation of R from P.', '', NULL, '\n\nExplanation\n(a) They were expected to obtain 20,000 = \\(\\frac{x^2}{8} + 5x\\) and thereafter multiply through by 8 and simplify to get \\(x ^2\\) + 40x - 16,000. Using the quadratic formula\nx = \\(\\frac {-b \\pm \\sqrt{b^2 - 4ac} }{2a}\\)\nwhere a = 1, b = 40 and c = - 160,000\nx = \\(\\frac{-40 \\pm \\sqrt{(40)^2 - 4(1) (-160000)}} {2(1)}\\)\n= \\(\\frac{-40 \\pm \\sqrt{(40)^2 - 4(1) (-160000)}} {2}\\)\n= \\(\\frac{-40 \\pm \\sqrt{1600 + 640000}}{2}\\)\n= 38.4997 or -420.4997\nThe number of books required to make the profit approximately 380,500, correct to the nearest whole number.\n(b) The required diagram is\n\nFrom triangle PQR, tan x = \\(\\frac{y}{2}\\)W\ny = 2w tan x..........(1)\nAlso, from \\(\\bigtriangleup\\) PTQ,\ntan 28\\(^o\\) = \\(\\frac{y}{w}\\)\ny = w tan 28\\(^o\\).........(2)\nEquating (1) and (2) yielded 2w tan X = w tan 28\\(^o\\)\nso that tanX = \\(\\frac{\\text{w} tan 28^o}{2w}\\) = \\(\\frac{0.5317}{2}\\) which implies that tan X = 0.2659\nX = tan\\(^{-1}\\)(0.2659) = 15.42\\(^o\\).\nThe angle of elevation of R from P = 15\\(^o\\), correct to the nearest degree.\n\n\n\n\n\n\n\n', '', 'Explanation\n(a) They were expected to obtain 20,000 = \\(\\frac{x^2}{8} + 5x\\) and thereafter multiply through by 8 and simplify to get \\(x ^2\\) + 40x - 16,000. Using the quadratic formula\nx = \\(\\frac {-b \\pm \\sqrt{b^2 - 4ac} }{2a}\\)\nwhere a = 1, b = 40 and c = - 160,000\nx = \\(\\frac{-40 \\pm \\sqrt{(40)^2 - 4(1) (-160000)}} {2(1)}\\)\n= \\(\\frac{-40 \\pm \\sqrt{(40)^2 - 4(1) (-160000)}} {2}\\)\n= \\(\\frac{-40 \\pm \\sqrt{1600 + 640000}}{2}\\)\n= 38.4997 or -420.4997\nThe number of books required to make the profit approximately 380,500, correct to the nearest whole number.\n(b) The required diagram is\n\nFrom triangle PQR, tan x = \\(\\frac{y}{2}\\)W\ny = 2w tan x..........(1)\nAlso, from \\(\\bigtriangleup\\) PTQ,\ntan 28\\(^o\\) = \\(\\frac{y}{w}\\)\ny = w tan 28\\(^o\\).........(2)\nEquating (1) and (2) yielded 2w tan X = w tan 28\\(^o\\)\nso that tanX = \\(\\frac{\\text{w} tan 28^o}{2w}\\) = \\(\\frac{0.5317}{2}\\) which implies that tan X = 0.2659\nX = tan\\(^{-1}\\)(0.2659) = 15.42\\(^o\\).\nThe angle of elevation of R from P = 15\\(^o\\), correct to the nearest degree.\n\n\n\n\n\n\n\n', '(a) They were expected to obtain 20,000 = \\(\\frac{x^2}{8} + 5x\\) and thereafter multiply through by 8 and simplify to get \\(x ^2\\) + 40x - 16,000. Using the quadratic formula\nx = \\(\\frac {-b \\pm \\sqrt{b^2 - 4ac} }{2a}\\)\nwhere a = 1, b = 40 and c = - 160,000\nx = \\(\\frac{-40 \\pm \\sqrt{(40)^2 - 4(1) (-160000)}} {2(1)}\\)\n= \\(\\frac{-40 \\pm \\sqrt{(40)^2 - 4(1) (-160000)}} {2}\\)\n= \\(\\frac{-40 \\pm \\sqrt{1600 + 640000}}{2}\\)\n= 38.4997 or -420.4997\nThe number of books required to make the profit approximately 380,500, correct to the nearest whole number.~(b) The required diagram is\n\nFrom triangle PQR, tan x = \\(\\frac{y}{2}\\)W\ny = 2w tan x..........(1)\nAlso, from \\(\\bigtriangleup\\) PTQ,\ntan 28\\(^o\\) = \\(\\frac{y}{w}\\)\ny = w tan 28\\(^o\\).........(2)\nEquating (1) and (2) yielded 2w tan X = w tan 28\\(^o\\)\nso that tanX = \\(\\frac{\\text{w} tan 28^o}{2w}\\) = \\(\\frac{0.5317}{2}\\) which implies that tan X = 0.2659\nX = tan\\(^{-1}\\)(0.2659) = 15.42\\(^o\\).\nThe angle of elevation of R from P = 15\\(^o\\), correct to the nearest degree.\n\n\n\n\n\n\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(726, '2018', '\n\nQuestion\n\n(a) Evaluate: \\(\\int \\limits_1^2 (2x^3 - 4x + 3) dx\\)\n\n(b) Given that P\\(^{-1}\\) = \\(\\begin{pmatrix} -1 & 1 \\\\ 4 & -3 \\end{pmatrix}\\), find the matrix P.\n\n\n\n\n(a) Evaluate: \\(\\int \\limits_1^2 (2x^3 - 4x + 3) dx\\)\n\n(b) Given that P\\(^{-1}\\) = \\(\\begin{pmatrix} -1 & 1 \\\\ 4 & -3 \\end{pmatrix}\\), find the matrix P.\n\n', '', '(a) Evaluate: \\(\\int \\limits_1^2 (2x^3 - 4x + 3) dx\\)\n\n(b) Given that P\\(^{-1}\\) = \\(\\begin{pmatrix} -1 & 1 \\\\ 4 & -3 \\end{pmatrix}\\), find the matrix P.\n\n\n\n\n(a) Evaluate: \\(\\int \\limits_1^2 (2x^3 - 4x + 3) dx\\)\n\n(b) Given that P\\(^{-1}\\) = \\(\\begin{pmatrix} -1 & 1 \\\\ 4 & -3 \\end{pmatrix}\\), find the matrix P.', '(a) Evaluate: \\(\\int \\limits_1^2 (2x^3 - 4x + 3) dx\\)\n\n(b) Given that P\\(^{-1}\\) = \\(\\begin{pmatrix} -1 & 1 \\\\ 4 & -3 \\end{pmatrix}\\), find the matrix P.\n\n\n\n\n(a) Evaluate: \\(\\int \\limits_1^2 (2x^3 - 4x + 3) dx\\)\n~(b) Given that P\\(^{-1}\\) = \\(\\begin{pmatrix} -1 & 1 \\\\ 4 & -3 \\end{pmatrix}\\), find the matrix P.\n\n\n\n\n(a) Evaluate: \\(\\int \\limits_1^2 (2x^3 - 4x + 3) dx\\)\n\n(b) Given that P\\(^{-1}\\) = \\(\\begin{pmatrix} -1 & 1 \\\\ 4 & -3 \\end{pmatrix}\\), find the matrix P.', NULL, '\n\nExplanation\n(a). They integrated the given function correctly to obtain (\\(\\frac{x^4}{2} - 2x^2 + 6x\\)). Substituting the limits 2 and 1 for x and simplifying yielded 12 - \\(\\frac{9}{2}\\) = 7\\(\\frac{1}{2}\\)\n(b). Find the determinant of which was P(\\(^{-1}\\))\\(^{-1}\\) = |P=\\(^{-1}\\)| (-3 x -1) - (4 x 1) = -1.\nUsing the concept of P(\\(^{-1}\\))\\(^{-1}\\) = P, then, P = -1 \\(\\begin{pmatrix} -3 & -1 \\\\ 4 & -3 \\end{pmatrix}\\) = \\(\\begin{pmatrix} 3 & 1 \\\\ 4 & 1 \\end{pmatrix}\\)\n\n', '', 'Explanation\n(a). They integrated the given function correctly to obtain (\\(\\frac{x^4}{2} - 2x^2 + 6x\\)). Substituting the limits 2 and 1 for x and simplifying yielded 12 - \\(\\frac{9}{2}\\) = 7\\(\\frac{1}{2}\\)\n(b). Find the determinant of which was P(\\(^{-1}\\))\\(^{-1}\\) = |P=\\(^{-1}\\)| (-3 x -1) - (4 x 1) = -1.\nUsing the concept of P(\\(^{-1}\\))\\(^{-1}\\) = P, then, P = -1 \\(\\begin{pmatrix} -3 & -1 \\\\ 4 & -3 \\end{pmatrix}\\) = \\(\\begin{pmatrix} 3 & 1 \\\\ 4 & 1 \\end{pmatrix}\\)\n\n', '(a). They integrated the given function correctly to obtain (\\(\\frac{x^4}{2} - 2x^2 + 6x\\)). Substituting the limits 2 and 1 for x and simplifying yielded 12 - \\(\\frac{9}{2}\\) = 7\\(\\frac{1}{2}\\)~(b). Find the determinant of which was P(\\(^{-1}\\))\\(^{-1}\\) = |P=\\(^{-1}\\)| (-3 x -1) - (4 x 1) = -1.\nUsing the concept of P(\\(^{-1}\\))\\(^{-1}\\) = P, then, P = -1 \\(\\begin{pmatrix} -3 & -1 \\\\ 4 & -3 \\end{pmatrix}\\) = \\(\\begin{pmatrix} 3 & 1 \\\\ 4 & 1 \\end{pmatrix}\\)\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(727, '2018', '\n\nQuestion\n\n(a)\n(i) Copy and complete the addition \\(\\oplus\\) and multiplication\\(\\otimes\\) tables in modulo 5 on the set {2, 3, 4}.\n\n\n\n\\(\\oplus\\)\n2\n3\n4\n\n\n2\n\n\n\n\n\n3\n\n\n\n\n\n4\n\n\n\n\n\n\n\n\n\n\n\\(\\otimes\\)\n2\n3\n4\n\n\n2\n\n\n\n\n\n3\n\n\n\n\n\n4\n\n\n\n\n\n\n\n(ii) Use the tables to:\n(a) solve the equation 4 \\(\\otimes\\)e\\(\\oplus\\) 2 \\(\\equiv\\) 1 (mod 5):\n(b) find the value of n, if 4 \\(\\oplus\\)n\\(\\otimes\\) 2\\(\\equiv\\) (mod 5).\n\n(b) Consider the following statements:\np: Landi has cholera,\nq: Landi is in the hospital.\nIf p = q, state whether or not the following statements are valid:\n(i) If Landi is in the hospital, then he has cholera.\n(ii) If Landi is not in the hospital, then he does not have cholera.\n(iii) If Landi does not have cholera, then he is not in the hospital.\n\n\n\n(a)\n(i) Copy and complete the addition \\(\\oplus\\) and multiplication\\(\\otimes\\) tables in modulo 5 on the set {2, 3, 4}.\n\n\n\n\\(\\oplus\\)\n2\n3\n4\n\n\n2\n\n\n\n\n\n3\n\n\n\n\n\n4\n\n\n\n\n\n\n\n\n\n\n\\(\\otimes\\)\n2\n3\n4\n\n\n2\n\n\n\n\n\n3\n\n\n\n\n\n4\n\n\n\n\n\n\n', '', '(a)\n(i) Copy and complete the addition \\(\\oplus\\) and multiplication\\(\\otimes\\) tables in modulo 5 on the set {2, 3, 4}.\n\n\n\n\\(\\oplus\\)\n2\n3\n4\n\n\n2\n\n\n\n\n\n3\n\n\n\n\n\n4\n\n\n\n\n\n\n\n\n\n\n\\(\\otimes\\)\n2\n3\n4\n\n\n2\n\n\n\n\n\n3\n\n\n\n\n\n4\n\n\n\n\n\n\n\n(ii) Use the tables to:\n(a) solve the equation 4 \\(\\otimes\\)e\\(\\oplus\\) 2 \\(\\equiv\\) 1 (mod 5):\n(b) find the value of n, if 4 \\(\\oplus\\)n\\(\\otimes\\) 2\\(\\equiv\\) (mod 5).\n\n(b) Consider the following statements:\np: Landi has cholera,\nq: Landi is in the hospital.\nIf p = q, state whether or not the following statements are valid:\n(i) If Landi is in the hospital, then he has cholera.\n(ii) If Landi is not in the hospital, then he does not have cholera.\n(iii) If Landi does not have cholera, then he is not in the hospital.\n\n\n\n(a)\n(i) Copy and complete the addition \\(\\oplus\\) and multiplication\\(\\otimes\\) tables in modulo 5 on the set {2, 3, 4}.\n\n\n\n\\(\\oplus\\)\n2\n3\n4\n\n\n2\n\n\n\n\n\n3\n\n\n\n\n\n4\n\n\n\n\n\n\n\n\n\n\n\\(\\otimes\\)\n2\n3\n4\n\n\n2\n\n\n\n\n\n3\n\n\n\n\n\n4\n\n\n\n\n', '(a)\n(i) Copy and complete the addition \\(\\oplus\\) and multiplication\\(\\otimes\\) tables in modulo 5 on the set {2, 3, 4}.\n\n\n\n\\(\\oplus\\)\n2\n3\n4\n\n\n2\n\n\n\n\n\n3\n\n\n\n\n\n4\n\n\n\n\n\n\n\n\n\n\n\\(\\otimes\\)\n2\n3\n4\n\n\n2\n\n\n\n\n\n3\n\n\n\n\n\n4\n\n\n\n\n\n\n\n(ii) Use the tables to:\n(a) solve the equation 4 \\(\\otimes\\)e\\(\\oplus\\) 2 \\(\\equiv\\) 1 (mod 5):\n(b) find the value of n, if 4 \\(\\oplus\\)n\\(\\otimes\\) 2\\(\\equiv\\) (mod 5).\n~(b) find the value of n, if 4 \\(\\oplus\\)n\\(\\otimes\\) 2\\(\\equiv\\) (mod 5).\n\n(b) Consider the following statements:\np: Landi has cholera,\nq: Landi is in the hospital.\nIf p = q, state whether or not the following statements are valid:\n(i) If Landi is in the hospital, then he has cholera.\n(ii) If Landi is not in the hospital, then he does not have cholera.\n(iii) If Landi does not have cholera, then he is not in the hospital.\n\n\n\n(a)\n(i) Copy and complete the addition \\(\\oplus\\) and multiplication\\(\\otimes\\) tables in modulo 5 on the set {2, 3, 4}.\n\n\n\n\\(\\oplus\\)\n2\n3\n4\n\n\n2\n\n\n\n\n\n3\n\n\n\n\n\n4\n\n\n\n\n\n\n\n\n\n\n\\(\\otimes\\)\n2\n3\n4\n\n\n2\n\n\n\n\n\n3\n\n\n\n\n\n4\n\n\n\n\n', NULL, '\n\nExplanation\n(a). Completing the table as follows\n\n\n\n\\(\\oplus\\)\n2\n3\n4\n\n\n2\n4\n0\n1\n\n\n3\n0\n1\n2\n\n\n4\n1\n2\n3\n\n\n\n\n\n\n\n\\(\\otimes\\)\n2\n3\n4\n\n\n2\n4\n1\n3\n\n\n3\n1\n4\n2\n\n\n4\n3\n2\n1\n\n\n\n(a) (ii) (a), they obtained the value of e as 1.\n(a) (ii) (b), the value of n was 2.\n\n(b), they couldn\'t answer this question correctly. If p = q, then:\n(i) q \\(\\Rightarrow\\) p, this is invalid\n(ii) \\(sin\\) q \\(\\Rightarrow\\) \\(sin\\) p, this is valid\n(iii) \\(sin\\) p \\(\\Rightarrow\\) \\(sin\\) q, this is invalid\n\n\n', '', 'Explanation\n(a). Completing the table as follows\n\n\n\n\\(\\oplus\\)\n2\n3\n4\n\n\n2\n4\n0\n1\n\n\n3\n0\n1\n2\n\n\n4\n1\n2\n3\n\n\n\n\n\n\n\n\\(\\otimes\\)\n2\n3\n4\n\n\n2\n4\n1\n3\n\n\n3\n1\n4\n2\n\n\n4\n3\n2\n1\n\n\n\n(a) (ii) (a), they obtained the value of e as 1.\n(a) (ii) (b), the value of n was 2.\n\n(b), they couldn\'t answer this question correctly. If p = q, then:\n(i) q \\(\\Rightarrow\\) p, this is invalid\n(ii) \\(sin\\) q \\(\\Rightarrow\\) \\(sin\\) p, this is valid\n(iii) \\(sin\\) p \\(\\Rightarrow\\) \\(sin\\) q, this is invalid\n\n\n', '(a). Completing the table as follows\n\n\n\n\\(\\oplus\\)\n2\n3\n4\n\n\n2\n4\n0\n1\n\n\n3\n0\n1\n2\n\n\n4\n1\n2\n3\n\n\n\n\n\n\n\n\\(\\otimes\\)\n2\n3\n4\n\n\n2\n4\n1\n3\n\n\n3\n1\n4\n2\n\n\n4\n3\n2\n1\n\n\n\n(a) (ii) (a), they obtained the value of e as 1.\n(a) (ii) (b), the value of n was 2.\n~(b), the value of n was 2.\n\n(b), they couldn\'t answer this question correctly. If p = q, then:\n(i) q \\(\\Rightarrow\\) p, this is invalid\n(ii) \\(sin\\) q \\(\\Rightarrow\\) \\(sin\\) p, this is valid\n(iii) \\(sin\\) p \\(\\Rightarrow\\) \\(sin\\) q, this is invalid\n\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(728, '2018', '\n\nQuestion\n\nUsing ruler and a pair of compasses only, construct:\n(a) (i) quadrilateral PQRS with |PQ| = 6 cm, |PS| = 8 cm, < PSR = 90\\(^o\\), |SR| = 12 cm and |QR| = 11 cm;\n(ii) perpendicular from Q to cut \\(\\over{SR}\\) at K.\n\n(b) Measure:\n(i) IQRI;\n(ii) < QRS.\n\n\n', '', 'Using ruler and a pair of compasses only, construct:\n(a) (i) quadrilateral PQRS with |PQ| = 6 cm, |PS| = 8 cm, < PSR = 90\\(^o\\), |SR| = 12 cm and |QR| = 11 cm;\n(ii) perpendicular from Q to cut \\(\\over{SR}\\) at K.\n\n(b) Measure:\n(i) IQRI;\n(ii) < QRS.\n', 'Using ruler and a pair of compasses only, construct:\n(a) (i) quadrilateral PQRS with |PQ| = 6 cm, |PS| = 8 cm, < PSR = 90\\(^o\\), |SR| = 12 cm and |QR| = 11 cm;\n(ii) perpendicular from Q to cut \\(\\over{SR}\\) at K.\n~(b) Measure:\n(i) IQRI;\n(ii) < QRS.\n', NULL, '\n\nExplanation\n(a) The following solution was expected from the candidates\n\n\n(b) (i) |QK| = 9.3cm\n(ii) < QRS = 55\\(^o\\)\n\n', '', 'Explanation\n(a) The following solution was expected from the candidates\n\n\n(b) (i) |QK| = 9.3cm\n(ii) < QRS = 55\\(^o\\)\n\n', '(a) The following solution was expected from the candidates\n\n~(b) (i) |QK| = 9.3cm\n(ii) < QRS = 55\\(^o\\)\n', 'WAEC-PK-1', 'WAEC-MATH', 1);
INSERT INTO `exam_simulation2` (`id`, `examYear`, `questions`, `parent_que`, `child_que`, `gen_child_que_desc`, `imageDir`, `explanation`, `parent_que_expl`, `child_que_exp`, `gen_child_que_expl`, `package_id`, `subject_id`, `status`) VALUES
(729, '2018', '\n\nQuestion\n\nThe table shows the distribution of marks scored by students in a test.\n\n\n\n\nMark\n(%)\n\n10 - 19\n20 - 29\n30 - 39\n40 - 49\n50 - 59\n60 - 69\n70 - 79\n80 - 89\n90 - 99\n\n\nFrequency\n4\n7\n12\n18\n20\n14\n9\n4\n2\n\n\n\n\n(a) Construct a cumulative frequency table for the distribution.\n\n(b) Draw a cumulative frequency curve for the distribution.\n\n(c) Use the curve to estimate the:\n(i) median;\n(ii) probability that a student selected at random obtained distinction, if the lowest mark for distinction is 75%.\n\n\n\n\n\nThe table shows the distribution of marks scored by students in a test.\n\n\n\n\nMark\n(%)\n\n10 - 19\n20 - 29\n30 - 39\n40 - 49\n50 - 59\n60 - 69\n70 - 79\n80 - 89\n90 - 99\n\n\nFrequency\n4\n7\n12\n18\n20\n14\n9\n4\n2\n\n\n\n\n(a) Construct a cumulative frequency table for the distribution.\n\n(b) Draw a cumulative frequency curve for the distribution.\n\n(c) Use the curve to estimate the:\n(i) median;\n(ii) probability that a student selected at random obtained distinction, if the lowest mark for distinction is 75%.\n\n\n', '', 'The table shows the distribution of marks scored by students in a test.\n\n\n\n\nMark\n(%)\n\n10 - 19\n20 - 29\n30 - 39\n40 - 49\n50 - 59\n60 - 69\n70 - 79\n80 - 89\n90 - 99\n\n\nFrequency\n4\n7\n12\n18\n20\n14\n9\n4\n2\n\n\n\n\n(a) Construct a cumulative frequency table for the distribution.\n\n(b) Draw a cumulative frequency curve for the distribution.\n\n(c) Use the curve to estimate the:\n(i) median;\n(ii) probability that a student selected at random obtained distinction, if the lowest mark for distinction is 75%.\n\n\n\n\n\nThe table shows the distribution of marks scored by students in a test.\n\n\n\n\nMark\n(%)\n\n10 - 19\n20 - 29\n30 - 39\n40 - 49\n50 - 59\n60 - 69\n70 - 79\n80 - 89\n90 - 99\n\n\nFrequency\n4\n7\n12\n18\n20\n14\n9\n4\n2\n\n\n\n\n(a) Construct a cumulative frequency table for the distribution.\n\n(b) Draw a cumulative frequency curve for the distribution.\n\n(c) Use the curve to estimate the:\n(i) median;\n(ii) probability that a student selected at random obtained distinction, if the lowest mark for distinction is 75%.\n', 'The table shows the distribution of marks scored by students in a test.\n\n\n\n\nMark\n(%)\n\n10 - 19\n20 - 29\n30 - 39\n40 - 49\n50 - 59\n60 - 69\n70 - 79\n80 - 89\n90 - 99\n\n\nFrequency\n4\n7\n12\n18\n20\n14\n9\n4\n2\n\n\n\n\n(a) Construct a cumulative frequency table for the distribution.\n\n(b) Draw a cumulative frequency curve for the distribution.\n\n(c) Use the curve to estimate the:\n(i) median;\n(ii) probability that a student selected at random obtained distinction, if the lowest mark for distinction is 75%.\n\n\n\n\n\nThe table shows the distribution of marks scored by students in a test.\n\n\n\n\nMark\n(%)\n\n10 - 19\n20 - 29\n30 - 39\n40 - 49\n50 - 59\n60 - 69\n70 - 79\n80 - 89\n90 - 99\n\n\nFrequency\n4\n7\n12\n18\n20\n14\n9\n4\n2\n\n\n\n\n(a) Construct a cumulative frequency table for the distribution.\n~(b) Draw a cumulative frequency curve for the distribution.\n\n(c) Use the curve to estimate the:\n(i) median;\n(ii) probability that a student selected at random obtained distinction, if the lowest mark for distinction is 75%.\n\n\n\n\n\nThe table shows the distribution of marks scored by students in a test.\n\n\n\n\nMark\n(%)\n\n10 - 19\n20 - 29\n30 - 39\n40 - 49\n50 - 59\n60 - 69\n70 - 79\n80 - 89\n90 - 99\n\n\nFrequency\n4\n7\n12\n18\n20\n14\n9\n4\n2\n\n\n\n\n(a) Construct a cumulative frequency table for the distribution.\n\n(b) Draw a cumulative frequency curve for the distribution.\n\n(c) Use the curve to estimate the:\n(i) median;\n(ii) probability that a student selected at random obtained distinction, if the lowest mark for distinction is 75%.\n~(c) Use the curve to estimate the:\n(i) median;\n(ii) probability that a student selected at random obtained distinction, if the lowest mark for distinction is 75%.\n\n\n\n\n\nThe table shows the distribution of marks scored by students in a test.\n\n\n\n\nMark\n(%)\n\n10 - 19\n20 - 29\n30 - 39\n40 - 49\n50 - 59\n60 - 69\n70 - 79\n80 - 89\n90 - 99\n\n\nFrequency\n4\n7\n12\n18\n20\n14\n9\n4\n2\n\n\n\n\n(a) Construct a cumulative frequency table for the distribution.\n\n(b) Draw a cumulative frequency curve for the distribution.\n\n(c) Use the curve to estimate the:\n(i) median;\n(ii) probability that a student selected at random obtained distinction, if the lowest mark for distinction is 75%.\n', NULL, '\n\nExplanation\n(a)\n\n\n\nMarks \n\nClass\nBoundaries\n\nFrequency\n\nCumulative\nFrequency\n\n\n\n10 - 19\n9.5 - 19.5\n4\n4\n\n\n20 - 29\n19.5 - 29.5\n7\n11\n\n\n30 - 39\n29.5 - 39.5\n12\n23\n\n\n40 - 49\n39.5 - 49.5\n18\n41\n\n\n50 - 59\n49.5 - 59.5\n20\n61\n\n\n60 - 69\n59.5 - 69.5\n14\n75\n\n\n70 - 79\n69.5 - 79.5\n9\n84\n\n\n80 - 89\n79.5 - 89.5\n4\n88\n\n\n90 - 99\n89.5 - 99.5\n2\n90\n\n\n\n\n(b) The cumulative frequency curve\n\n(c)(i) using the curve, the median was 51.5.\n(ii) Using the curve, the estimate of tbe number of students who scored at least 75% was 90 - 80 = 10\nTherefore, Prob(that a student selected at random obtained distinction) = \\(\\frac{10}{90} = \\frac{1}{9}\\)\n\n\n\n', '', 'Explanation\n(a)\n\n\n\nMarks \n\nClass\nBoundaries\n\nFrequency\n\nCumulative\nFrequency\n\n\n\n10 - 19\n9.5 - 19.5\n4\n4\n\n\n20 - 29\n19.5 - 29.5\n7\n11\n\n\n30 - 39\n29.5 - 39.5\n12\n23\n\n\n40 - 49\n39.5 - 49.5\n18\n41\n\n\n50 - 59\n49.5 - 59.5\n20\n61\n\n\n60 - 69\n59.5 - 69.5\n14\n75\n\n\n70 - 79\n69.5 - 79.5\n9\n84\n\n\n80 - 89\n79.5 - 89.5\n4\n88\n\n\n90 - 99\n89.5 - 99.5\n2\n90\n\n\n\n\n(b) The cumulative frequency curve\n\n(c)(i) using the curve, the median was 51.5.\n(ii) Using the curve, the estimate of tbe number of students who scored at least 75% was 90 - 80 = 10\nTherefore, Prob(that a student selected at random obtained distinction) = \\(\\frac{10}{90} = \\frac{1}{9}\\)\n\n\n\n', '(a)\n\n\n\nMarks \n\nClass\nBoundaries\n\nFrequency\n\nCumulative\nFrequency\n\n\n\n10 - 19\n9.5 - 19.5\n4\n4\n\n\n20 - 29\n19.5 - 29.5\n7\n11\n\n\n30 - 39\n29.5 - 39.5\n12\n23\n\n\n40 - 49\n39.5 - 49.5\n18\n41\n\n\n50 - 59\n49.5 - 59.5\n20\n61\n\n\n60 - 69\n59.5 - 69.5\n14\n75\n\n\n70 - 79\n69.5 - 79.5\n9\n84\n\n\n80 - 89\n79.5 - 89.5\n4\n88\n\n\n90 - 99\n89.5 - 99.5\n2\n90\n\n\n\n~(b) The cumulative frequency curve\n\n(c)(i) using the curve, the median was 51.5.\n(ii) Using the curve, the estimate of tbe number of students who scored at least 75% was 90 - 80 = 10\nTherefore, Prob(that a student selected at random obtained distinction) = \\(\\frac{10}{90} = \\frac{1}{9}\\)\n\n\n~(c)(i) using the curve, the median was 51.5.\n(ii) Using the curve, the estimate of tbe number of students who scored at least 75% was 90 - 80 = 10\nTherefore, Prob(that a student selected at random obtained distinction) = \\(\\frac{10}{90} = \\frac{1}{9}\\)\n\n\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(730, '2018', '\n\nQuestion\n\nA container, in the form of a cone resting on its vertex, is full when 4.158 litres of water is poured into it.\n(a) If the radius of its base is 21 cm,\n(i) represent the information in a diagram;\n(ii) calculate the height of the container.\n\n(b) A certain amount of water is drawn out of the container such that the surface diameter of the water drops to 28 cm. Calculate the volume of the water drawn out. (Take \\(\\pi\\) = \\(\\frac{22}{7}\\))\n\n\n\n\n\n\nA container, in the form of a cone resting on its vertex, is full when 4.158 litres of water is poured into it.\n(a) If the radius of its base is 21 cm,\n(i) represent the information in a diagram;\n(ii) calculate the height of the container.\n\n(b) A certain amount of water is drawn out of the container such that the surface diameter of the water drops to 28 cm. Calculate the volume of the water drawn out. (Take \\(\\pi\\) = \\(\\frac{22}{7}\\))\n\n\n\n', '', 'A container, in the form of a cone resting on its vertex, is full when 4.158 litres of water is poured into it.\n(a) If the radius of its base is 21 cm,\n(i) represent the information in a diagram;\n(ii) calculate the height of the container.\n\n(b) A certain amount of water is drawn out of the container such that the surface diameter of the water drops to 28 cm. Calculate the volume of the water drawn out. (Take \\(\\pi\\) = \\(\\frac{22}{7}\\))\n\n\n\n\n\n\nA container, in the form of a cone resting on its vertex, is full when 4.158 litres of water is poured into it.\n(a) If the radius of its base is 21 cm,\n(i) represent the information in a diagram;\n(ii) calculate the height of the container.\n\n(b) A certain amount of water is drawn out of the container such that the surface diameter of the water drops to 28 cm. Calculate the volume of the water drawn out. (Take \\(\\pi\\) = \\(\\frac{22}{7}\\))\n\n', 'A container, in the form of a cone resting on its vertex, is full when 4.158 litres of water is poured into it.\n(a) If the radius of its base is 21 cm,\n(i) represent the information in a diagram;\n(ii) calculate the height of the container.\n\n(b) A certain amount of water is drawn out of the container such that the surface diameter of the water drops to 28 cm. Calculate the volume of the water drawn out. (Take \\(\\pi\\) = \\(\\frac{22}{7}\\))\n\n\n\n\n\n\nA container, in the form of a cone resting on its vertex, is full when 4.158 litres of water is poured into it.\n(a) If the radius of its base is 21 cm,\n(i) represent the information in a diagram;\n(ii) calculate the height of the container.\n~(b) A certain amount of water is drawn out of the container such that the surface diameter of the water drops to 28 cm. Calculate the volume of the water drawn out. (Take \\(\\pi\\) = \\(\\frac{22}{7}\\))\n\n\n\n\n\n\nA container, in the form of a cone resting on its vertex, is full when 4.158 litres of water is poured into it.\n(a) If the radius of its base is 21 cm,\n(i) represent the information in a diagram;\n(ii) calculate the height of the container.\n\n(b) A certain amount of water is drawn out of the container such that the surface diameter of the water drops to 28 cm. Calculate the volume of the water drawn out. (Take \\(\\pi\\) = \\(\\frac{22}{7}\\))\n\n', NULL, '\n\nExplanation\n(a) (i) The diagram can be represented as:\n\n\n(ii) first they were expected to convert from litres to cm\\(^3 \\) by using the fact that 1000 cm\\(^3\\) = 1 litre, then 4.158 litres = 4158 cm\\(^3\\).\nIf the volume and height of the container were V\\(_1\\) and h\\(_1\\) respectively, then, V\\(_1\\) = \\(\\frac{1}{3}\\) x \\(\\frac{22}{7}\\) x 21 x 21 x h\\(_1\\) = 4,158 which simplified to 462h\\(_1\\) = 4,158. Therefore, h\\(_1\\) = 9cm.\n(b) let h\\(_2\\) be the height of the water remaining in the container.\nThen by similar triangles, \\(\\frac{h_2}{9}\\) = \\(\\frac{14}{21}\\), h\\(_2\\) = 6 cm.\nIf we let V\\(_2\\) be the volume of water remaining in the container, V\\(_2\\) = \\(\\frac{1}{3} \\times \\frac{22}{7}\\) x 14 x 14 x 6 = 1,232 cm\\(^2\\).\nVolume of water drawn out = (4,158 — 1,232) cm\\(^3\\) = 2,926 cm\\(^3\\)\n\n', '', 'Explanation\n(a) (i) The diagram can be represented as:\n\n\n(ii) first they were expected to convert from litres to cm\\(^3 \\) by using the fact that 1000 cm\\(^3\\) = 1 litre, then 4.158 litres = 4158 cm\\(^3\\).\nIf the volume and height of the container were V\\(_1\\) and h\\(_1\\) respectively, then, V\\(_1\\) = \\(\\frac{1}{3}\\) x \\(\\frac{22}{7}\\) x 21 x 21 x h\\(_1\\) = 4,158 which simplified to 462h\\(_1\\) = 4,158. Therefore, h\\(_1\\) = 9cm.\n(b) let h\\(_2\\) be the height of the water remaining in the container.\nThen by similar triangles, \\(\\frac{h_2}{9}\\) = \\(\\frac{14}{21}\\), h\\(_2\\) = 6 cm.\nIf we let V\\(_2\\) be the volume of water remaining in the container, V\\(_2\\) = \\(\\frac{1}{3} \\times \\frac{22}{7}\\) x 14 x 14 x 6 = 1,232 cm\\(^2\\).\nVolume of water drawn out = (4,158 — 1,232) cm\\(^3\\) = 2,926 cm\\(^3\\)\n\n', '(a) (i) The diagram can be represented as:\n\n\n(ii) first they were expected to convert from litres to cm\\(^3 \\) by using the fact that 1000 cm\\(^3\\) = 1 litre, then 4.158 litres = 4158 cm\\(^3\\).\nIf the volume and height of the container were V\\(_1\\) and h\\(_1\\) respectively, then, V\\(_1\\) = \\(\\frac{1}{3}\\) x \\(\\frac{22}{7}\\) x 21 x 21 x h\\(_1\\) = 4,158 which simplified to 462h\\(_1\\) = 4,158. Therefore, h\\(_1\\) = 9cm.~(b) let h\\(_2\\) be the height of the water remaining in the container.\nThen by similar triangles, \\(\\frac{h_2}{9}\\) = \\(\\frac{14}{21}\\), h\\(_2\\) = 6 cm.\nIf we let V\\(_2\\) be the volume of water remaining in the container, V\\(_2\\) = \\(\\frac{1}{3} \\times \\frac{22}{7}\\) x 14 x 14 x 6 = 1,232 cm\\(^2\\).\nVolume of water drawn out = (4,158 — 1,232) cm\\(^3\\) = 2,926 cm\\(^3\\)\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(731, '2018', '\n\nQuestion\n\nA man starts from a point X and walk 285 m to Y on a bearing of 078\\(^o\\). He then walks due South to a point Z which is 307 m from X.\n(a) Illustrate the information on a diagram.\n(b) Find, correct to the nearest whole number, the:\n(i) bearing of X from Z;\n(ii) distance between Y and Z.\n\n\n', '', 'A man starts from a point X and walk 285 m to Y on a bearing of 078\\(^o\\). He then walks due South to a point Z which is 307 m from X.\n(a) Illustrate the information on a diagram.\n(b) Find, correct to the nearest whole number, the:\n(i) bearing of X from Z;\n(ii) distance between Y and Z.\n', 'A man starts from a point X and walk 285 m to Y on a bearing of 078\\(^o\\). He then walks due South to a point Z which is 307 m from X.\n(a) Illustrate the information on a diagram.~(b) Find, correct to the nearest whole number, the:\n(i) bearing of X from Z;\n(ii) distance between Y and Z.\n', NULL, '\n\nExplanation\n(a) They sketched the required diagram as follows:\n\n\n(b) (i), using sine rule \\(\\frac{285}{\\sin z} = \\frac{307}{\\sin 307}\\)\nThen sin z \\(\\frac{285 \\times \\sin 78^o}{307} = \\frac{285 \\times 0.9781}{307}\\) = 0.9080\nZ = \\(\\sin^{-1}(0.9080)\\) = 65.23\\(^o\\)\nThe bearing of X from Z = 360\\(^o\\) - 65.23\\(^o\\) = 294.77\\(^o\\) \\(\\approx\\) 295\\(^o\\) or N65\\(^o\\)W correct to the nearest whole number.\n\n(b)(ii) They obtained < YXZ = 180\\(^o\\) - 143.23\\(^o\\) = 36.77\\(^o\\)\nThen, using sine rule, \\(\\frac{\\text{|YZ|}}{\\sin 36.77^o} = \\frac{307}{\\sin 78^o}\\) and computing for |YZ|,\n|YZ| = \\(\\frac{307 \\times 0.5986}{0.9781}\\) = 187.88m\n and Therefore, the distance between Y and Z \\(\\approx\\) 188 m correct to the nearest whole number\n\n', '', 'Explanation\n(a) They sketched the required diagram as follows:\n\n\n(b) (i), using sine rule \\(\\frac{285}{\\sin z} = \\frac{307}{\\sin 307}\\)\nThen sin z \\(\\frac{285 \\times \\sin 78^o}{307} = \\frac{285 \\times 0.9781}{307}\\) = 0.9080\nZ = \\(\\sin^{-1}(0.9080)\\) = 65.23\\(^o\\)\nThe bearing of X from Z = 360\\(^o\\) - 65.23\\(^o\\) = 294.77\\(^o\\) \\(\\approx\\) 295\\(^o\\) or N65\\(^o\\)W correct to the nearest whole number.\n\n(b)(ii) They obtained < YXZ = 180\\(^o\\) - 143.23\\(^o\\) = 36.77\\(^o\\)\nThen, using sine rule, \\(\\frac{\\text{|YZ|}}{\\sin 36.77^o} = \\frac{307}{\\sin 78^o}\\) and computing for |YZ|,\n|YZ| = \\(\\frac{307 \\times 0.5986}{0.9781}\\) = 187.88m\n and Therefore, the distance between Y and Z \\(\\approx\\) 188 m correct to the nearest whole number\n\n', '(a) They sketched the required diagram as follows:\n\n\n(b) (i), using sine rule \\(\\frac{285}{\\sin z} = \\frac{307}{\\sin 307}\\)\nThen sin z \\(\\frac{285 \\times \\sin 78^o}{307} = \\frac{285 \\times 0.9781}{307}\\) = 0.9080\nZ = \\(\\sin^{-1}(0.9080)\\) = 65.23\\(^o\\)\nThe bearing of X from Z = 360\\(^o\\) - 65.23\\(^o\\) = 294.77\\(^o\\) \\(\\approx\\) 295\\(^o\\) or N65\\(^o\\)W correct to the nearest whole number.\n~(b) (i), using sine rule \\(\\frac{285}{\\sin z} = \\frac{307}{\\sin 307}\\)\nThen sin z \\(\\frac{285 \\times \\sin 78^o}{307} = \\frac{285 \\times 0.9781}{307}\\) = 0.9080\nZ = \\(\\sin^{-1}(0.9080)\\) = 65.23\\(^o\\)\nThe bearing of X from Z = 360\\(^o\\) - 65.23\\(^o\\) = 294.77\\(^o\\) \\(\\approx\\) 295\\(^o\\) or N65\\(^o\\)W correct to the nearest whole number.\n\n(b)(ii) They obtained < YXZ = 180\\(^o\\) - 143.23\\(^o\\) = 36.77\\(^o\\)\nThen, using sine rule, \\(\\frac{\\text{|YZ|}}{\\sin 36.77^o} = \\frac{307}{\\sin 78^o}\\) and computing for |YZ|,\n|YZ| = \\(\\frac{307 \\times 0.5986}{0.9781}\\) = 187.88m\n and Therefore, the distance between Y and Z \\(\\approx\\) 188 m correct to the nearest whole number\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(732, '2018', '\n\nQuestion\n\n(a) Using a scale of 2cm to 2units on both axes, draw on a sheet of graph paper two perpendicular axes 0x and 0y for - 10 \\(\\leq\\) x\\(\\leq\\) 10 and -10 \\(\\leq\\) y \\(\\leq\\)10\n\n(b) Given the points P(3, 2). Q(-1. 5). R(0. 8) and S(3, 7). draw on the same graph, indicating clearly the vertices and their coordinates, the:\n(i) quadrilateral PQRS;\n(ii) image P\\(_1\\)Q\\(_1\\)R\\(_1\\)S\\(_1\\) of PQRS under an anticlockwise rotation of 90\\(^o\\) about the origin where P \\(\\to\\) P\\(_1\\), Q\\(\\to\\) Q\\(_{1}\\), R\\(\\to\\) R\\(_{1}\\) and S\\(\\to\\) S\\(_{1}\\)\n(iii) image P\\(_2\\)Q\\(_2\\)R\\(_2\\)S\\(_2\\) of P\\(_1\\)Q\\(_1\\)R\\(_1\\)S\\(_1\\) under a reflection in the line y - x = 0 where P\\(_1\\) \\(\\to\\) P\\(_2\\), Q\\(_1\\) \\(\\to\\) Q\\(_{2}\\), R\\(_1\\) \\(\\to\\) R\\(_{2}\\) and S\\(_1\\) \\(\\to\\) S\\(_{2}\\)\n\n(c) Describe precisely the single transformation T for which T : PQRS \\(\\to\\) P\\(_2\\)Q\\(_2\\)R\\(_2\\)S\\(_2\\)\n(d) The side P\\(_1\\)Q\\(_1\\) of the quadrilateral P\\(_1\\)Q\\(_1\\)R\\(_1\\)S\\(_1\\) cuts the x-axis at the point W. What type of quadrilateral is P\\(_1\\)S\\(_1\\)R\\(_1\\)W?\n\n\n', '', '(a) Using a scale of 2cm to 2units on both axes, draw on a sheet of graph paper two perpendicular axes 0x and 0y for - 10 \\(\\leq\\) x\\(\\leq\\) 10 and -10 \\(\\leq\\) y \\(\\leq\\)10\n\n(b) Given the points P(3, 2). Q(-1. 5). R(0. 8) and S(3, 7). draw on the same graph, indicating clearly the vertices and their coordinates, the:\n(i) quadrilateral PQRS;\n(ii) image P\\(_1\\)Q\\(_1\\)R\\(_1\\)S\\(_1\\) of PQRS under an anticlockwise rotation of 90\\(^o\\) about the origin where P \\(\\to\\) P\\(_1\\), Q\\(\\to\\) Q\\(_{1}\\), R\\(\\to\\) R\\(_{1}\\) and S\\(\\to\\) S\\(_{1}\\)\n(iii) image P\\(_2\\)Q\\(_2\\)R\\(_2\\)S\\(_2\\) of P\\(_1\\)Q\\(_1\\)R\\(_1\\)S\\(_1\\) under a reflection in the line y - x = 0 where P\\(_1\\) \\(\\to\\) P\\(_2\\), Q\\(_1\\) \\(\\to\\) Q\\(_{2}\\), R\\(_1\\) \\(\\to\\) R\\(_{2}\\) and S\\(_1\\) \\(\\to\\) S\\(_{2}\\)\n\n(c) Describe precisely the single transformation T for which T : PQRS \\(\\to\\) P\\(_2\\)Q\\(_2\\)R\\(_2\\)S\\(_2\\)\n(d) The side P\\(_1\\)Q\\(_1\\) of the quadrilateral P\\(_1\\)Q\\(_1\\)R\\(_1\\)S\\(_1\\) cuts the x-axis at the point W. What type of quadrilateral is P\\(_1\\)S\\(_1\\)R\\(_1\\)W?\n', '(a) Using a scale of 2cm to 2units on both axes, draw on a sheet of graph paper two perpendicular axes 0x and 0y for - 10 \\(\\leq\\) x\\(\\leq\\) 10 and -10 \\(\\leq\\) y \\(\\leq\\)10\n~(b) Given the points P(3, 2). Q(-1. 5). R(0. 8) and S(3, 7). draw on the same graph, indicating clearly the vertices and their coordinates, the:\n(i) quadrilateral PQRS;\n(ii) image P\\(_1\\)Q\\(_1\\)R\\(_1\\)S\\(_1\\) of PQRS under an anticlockwise rotation of 90\\(^o\\) about the origin where P \\(\\to\\) P\\(_1\\), Q\\(\\to\\) Q\\(_{1}\\), R\\(\\to\\) R\\(_{1}\\) and S\\(\\to\\) S\\(_{1}\\)\n(iii) image P\\(_2\\)Q\\(_2\\)R\\(_2\\)S\\(_2\\) of P\\(_1\\)Q\\(_1\\)R\\(_1\\)S\\(_1\\) under a reflection in the line y - x = 0 where P\\(_1\\) \\(\\to\\) P\\(_2\\), Q\\(_1\\) \\(\\to\\) Q\\(_{2}\\), R\\(_1\\) \\(\\to\\) R\\(_{2}\\) and S\\(_1\\) \\(\\to\\) S\\(_{2}\\)\n\n(c) Describe precisely the single transformation T for which T : PQRS \\(\\to\\) P\\(_2\\)Q\\(_2\\)R\\(_2\\)S\\(_2\\)\n(d) The side P\\(_1\\)Q\\(_1\\) of the quadrilateral P\\(_1\\)Q\\(_1\\)R\\(_1\\)S\\(_1\\) cuts the x-axis at the point W. What type of quadrilateral is P\\(_1\\)S\\(_1\\)R\\(_1\\)W?\n~(c) Describe precisely the single transformation T for which T : PQRS \\(\\to\\) P\\(_2\\)Q\\(_2\\)R\\(_2\\)S\\(_2\\)\n(d) The side P\\(_1\\)Q\\(_1\\) of the quadrilateral P\\(_1\\)Q\\(_1\\)R\\(_1\\)S\\(_1\\) cuts the x-axis at the point W. What type of quadrilateral is P\\(_1\\)S\\(_1\\)R\\(_1\\)W?\n~(d) The side P\\(_1\\)Q\\(_1\\) of the quadrilateral P\\(_1\\)Q\\(_1\\)R\\(_1\\)S\\(_1\\) cuts the x-axis at the point W. What type of quadrilateral is P\\(_1\\)S\\(_1\\)R\\(_1\\)W?\n', NULL, '\n\nExplanation\nNo official explanation is available for this question at this time. Please check contributions posted by others below. If you can provide an explanation to help other student learn, please click here\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\n\n', '', '', 'WAEC-PK-1', 'WAEC-MATH', 1),
(733, '2018', '\n\nQuestion\n\n(a) Solve the inequality: \\(\\frac{1 + 4x}{2}\\) -\\(\\frac{5 + 2x}{7}\\) < x -2\n\n(b) If x: y = 3: 5, find the value of \\(\\frac{2x^2 - y^2}{y^2 - x^2}\\)\n\n', '', '(a) Solve the inequality: \\(\\frac{1 + 4x}{2}\\) -\\(\\frac{5 + 2x}{7}\\) < x -2\n\n(b) If x: y = 3: 5, find the value of \\(\\frac{2x^2 - y^2}{y^2 - x^2}\\)', '(a) Solve the inequality: \\(\\frac{1 + 4x}{2}\\) -\\(\\frac{5 + 2x}{7}\\) < x -2\n~(b) If x: y = 3: 5, find the value of \\(\\frac{2x^2 - y^2}{y^2 - x^2}\\)', NULL, '\n\nExplanation\n(a) majority of the candidates multiplied through by the L.C.M which is 14 to arrive at 7(1+4x) - 2(5+2x) < 14(x - 2) and when simplified yielded 10x < -25 x -2\\(\\frac{1}{2}\\)\n(b) it was expected that they express x = \\(\\frac{3y}{5}\\) or y = \\(\\frac{5x}{3}\\) and thereafter, substitute into the given expression to have \\(\\frac{2x^2 - y^2}{y^2 - x^2} = \\frac{2x^2 - (\\frac{5x}{3})^2}{(\\frac{5x}{3})^2 - x^2} = \\frac{x^(2 - \\frac{25}{9})}{x^2(\\frac{25}{9} - 1)} = \\frac{-7}{16}\\)\n\n', '', 'Explanation\n(a) majority of the candidates multiplied through by the L.C.M which is 14 to arrive at 7(1+4x) - 2(5+2x) < 14(x - 2) and when simplified yielded 10x < -25 x -2\\(\\frac{1}{2}\\)\n(b) it was expected that they express x = \\(\\frac{3y}{5}\\) or y = \\(\\frac{5x}{3}\\) and thereafter, substitute into the given expression to have \\(\\frac{2x^2 - y^2}{y^2 - x^2} = \\frac{2x^2 - (\\frac{5x}{3})^2}{(\\frac{5x}{3})^2 - x^2} = \\frac{x^(2 - \\frac{25}{9})}{x^2(\\frac{25}{9} - 1)} = \\frac{-7}{16}\\)\n\n', '(a) majority of the candidates multiplied through by the L.C.M which is 14 to arrive at 7(1+4x) - 2(5+2x) < 14(x - 2) and when simplified yielded 10x < -25 x -2\\(\\frac{1}{2}\\)~(b) it was expected that they express x = \\(\\frac{3y}{5}\\) or y = \\(\\frac{5x}{3}\\) and thereafter, substitute into the given expression to have \\(\\frac{2x^2 - y^2}{y^2 - x^2} = \\frac{2x^2 - (\\frac{5x}{3})^2}{(\\frac{5x}{3})^2 - x^2} = \\frac{x^(2 - \\frac{25}{9})}{x^2(\\frac{25}{9} - 1)} = \\frac{-7}{16}\\)\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(734, '2018', '\n\nQuestion\n\nThe second, fourth and sixth terms of an Arithmetic Progression (AP.) are x - 1, x + 1 and 7 respectively. Find the:\n(a) common difference;\n(b) first term;\n(c) value of x.\n\n\n\n\nThe second, fourth and sixth terms of an Arithmetic Progression (AP.) are x - 1, x + 1 and 7 respectively. Find the:\n(a) common difference;\n(b) first term;\n(c) value of x.\n\n', '', 'The second, fourth and sixth terms of an Arithmetic Progression (AP.) are x - 1, x + 1 and 7 respectively. Find the:\n(a) common difference;\n(b) first term;\n(c) value of x.\n\n\n\n\nThe second, fourth and sixth terms of an Arithmetic Progression (AP.) are x - 1, x + 1 and 7 respectively. Find the:\n(a) common difference;\n(b) first term;\n(c) value of x.', 'The second, fourth and sixth terms of an Arithmetic Progression (AP.) are x - 1, x + 1 and 7 respectively. Find the:\n(a) common difference;\n(b) first term;\n(c) value of x.\n\n\n\n\nThe second, fourth and sixth terms of an Arithmetic Progression (AP.) are x - 1, x + 1 and 7 respectively. Find the:\n(a) common difference;~(b) first term;\n(c) value of x.\n\n\n\n\nThe second, fourth and sixth terms of an Arithmetic Progression (AP.) are x - 1, x + 1 and 7 respectively. Find the:\n(a) common difference;\n(b) first term;\n(c) value of x.~(c) value of x.\n\n\n\n\nThe second, fourth and sixth terms of an Arithmetic Progression (AP.) are x - 1, x + 1 and 7 respectively. Find the:\n(a) common difference;\n(b) first term;\n(c) value of x.', NULL, '\n\nExplanation\n(a) The second term is a d= x - 1 while the fourth term is a + 3d = x + 1. Subtracting the second tam from the fourth term yielded 2d = 2 so that d = 1.\n(b). Substituting for d in the expression for the sixth term to get a + 5 = 7 and solving for a to obtain a = 2.\n(c). Substituted for a and d in the expression for the second term and found x = 2 + 1 + 1 = 4.\n\n', '', 'Explanation\n(a) The second term is a d= x - 1 while the fourth term is a + 3d = x + 1. Subtracting the second tam from the fourth term yielded 2d = 2 so that d = 1.\n(b). Substituting for d in the expression for the sixth term to get a + 5 = 7 and solving for a to obtain a = 2.\n(c). Substituted for a and d in the expression for the second term and found x = 2 + 1 + 1 = 4.\n\n', '(a) The second term is a d= x - 1 while the fourth term is a + 3d = x + 1. Subtracting the second tam from the fourth term yielded 2d = 2 so that d = 1.~(b). Substituting for d in the expression for the sixth term to get a + 5 = 7 and solving for a to obtain a = 2.\n(c). Substituted for a and d in the expression for the second term and found x = 2 + 1 + 1 = 4.\n~(c). Substituted for a and d in the expression for the second term and found x = 2 + 1 + 1 = 4.\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(735, '2018', '\n\nQuestion\n\n(a) If logo a = 1.3010 and log\\(_{10}\\)b - 1.4771. find the value of ab\n\n(b)\n\n\nIn the diagram. O is the centre of the circle,< ACB = 39\\(^o\\) and < CBE = 62\\(^o\\). Find: (i) the interior angle AOC;\n(ii) angle BAC.\n\n\n(a) If logo a = 1.3010 and log\\(_{10}\\)b - 1.4771. find the value of ab\n\n(b)\n\n', '', '(a) If logo a = 1.3010 and log\\(_{10}\\)b - 1.4771. find the value of ab\n\n(b)\n\n\nIn the diagram. O is the centre of the circle,< ACB = 39\\(^o\\) and < CBE = 62\\(^o\\). Find: (i) the interior angle AOC;\n(ii) angle BAC.\n\n\n(a) If logo a = 1.3010 and log\\(_{10}\\)b - 1.4771. find the value of ab\n\n(b)', '(a) If logo a = 1.3010 and log\\(_{10}\\)b - 1.4771. find the value of ab\n\n(b)\n\n\nIn the diagram. O is the centre of the circle,< ACB = 39\\(^o\\) and < CBE = 62\\(^o\\). Find: (i) the interior angle AOC;\n(ii) angle BAC.\n\n\n(a) If logo a = 1.3010 and log\\(_{10}\\)b - 1.4771. find the value of ab\n~(b)\n\n\nIn the diagram. O is the centre of the circle,< ACB = 39\\(^o\\) and < CBE = 62\\(^o\\). Find: (i) the interior angle AOC;\n(ii) angle BAC.\n\n\n(a) If logo a = 1.3010 and log\\(_{10}\\)b - 1.4771. find the value of ab\n\n(b)', NULL, '\n\nExplanation\n(a) finding a = 10\\(^{1.3010}\\) and b = 10\\(^{1.4771}\\)\nThen, ab = 10\\(^{1.3010}\\) x 10\\(^{1.4771}\\) = 10\\(^{2.4771}\\) = 599.9\n(b)(i) they were expected to find < ABC = 180° - 62° = 118°\nExterior < AOC a 2 x 118° - 236° (< at centre is twice angle at the circumference)\nInterior < AOC = 360° - 236° = 124°(angle at a point) as required.\n(b)(ii) < BAC in 180° - 39° - 118° = 23° (sum of angles of a triangle)\n\n', '', 'Explanation\n(a) finding a = 10\\(^{1.3010}\\) and b = 10\\(^{1.4771}\\)\nThen, ab = 10\\(^{1.3010}\\) x 10\\(^{1.4771}\\) = 10\\(^{2.4771}\\) = 599.9\n(b)(i) they were expected to find < ABC = 180° - 62° = 118°\nExterior < AOC a 2 x 118° - 236° (< at centre is twice angle at the circumference)\nInterior < AOC = 360° - 236° = 124°(angle at a point) as required.\n(b)(ii) < BAC in 180° - 39° - 118° = 23° (sum of angles of a triangle)\n\n', '(a) finding a = 10\\(^{1.3010}\\) and b = 10\\(^{1.4771}\\)\nThen, ab = 10\\(^{1.3010}\\) x 10\\(^{1.4771}\\) = 10\\(^{2.4771}\\) = 599.9\n(b)(i) they were expected to find < ABC = 180° - 62° = 118°\nExterior < AOC a 2 x 118° - 236° (< at centre is twice angle at the circumference)\nInterior < AOC = 360° - 236° = 124°(angle at a point) as required.~(b)(i) they were expected to find < ABC = 180° - 62° = 118°\nExterior < AOC a 2 x 118° - 236° (< at centre is twice angle at the circumference)\nInterior < AOC = 360° - 236° = 124°(angle at a point) as required.\n(b)(ii) < BAC in 180° - 39° - 118° = 23° (sum of angles of a triangle)\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(736, '2018', '\n\nQuestion\n\n(a) Without using mathematical tables or calculator, simplify: \\(\\frac{log_28 + \\log_216 - 4 \\log_22}{\\log_416}\\)\n\n(b) If 1342\\(_{five}\\) - 241\\(_{five}\\) = x\\(_{ten}\\), find the value of x.\n\n\n', '', '(a) Without using mathematical tables or calculator, simplify: \\(\\frac{log_28 + \\log_216 - 4 \\log_22}{\\log_416}\\)\n\n(b) If 1342\\(_{five}\\) - 241\\(_{five}\\) = x\\(_{ten}\\), find the value of x.\n', '(a) Without using mathematical tables or calculator, simplify: \\(\\frac{log_28 + \\log_216 - 4 \\log_22}{\\log_416}\\)\n~(b) If 1342\\(_{five}\\) - 241\\(_{five}\\) = x\\(_{ten}\\), find the value of x.\n', NULL, '\n\nExplanation\n(a) \\(\\frac{\\log_28 + \\log_216 - 4\\log_22}{\\log_416}\\) = \\(\\frac{\\log_22^3 + \\log_2 2^4 - 4\\log_22}{\\log_44^2}\\)\n= \\(\\frac{3 \\log_2 2 + 4\\log_22 - 4 \\log_2^2}{2 \\log 4^4}\\)\nBut log\\(_2\\) 2 = \\(\\log_44 = 1\\)\nThen, \\(\\frac{\\log_28+\\log_216 - 4 \\log_2^2}{\\log_416}\\) = \\(\\frac{3 + 4 - 4}{2}\\) = 1\\(\\frac{1}{2}\\)\n(b) Subtract 241\\(_{five}\\) to get 1101\\(_{five}\\). Thereafter, converting to base ten to find the value of x = (5\\(^3\\) x 1) + (5\\(^2\\) x 1 + (5\\(^1\\) x 0) + (5\\(^o\\) x 1) = 125 + 25 + 0 + 1 = 151\n(b) They subtracted 241\\(_{five}\\) from 1342\\(_{five}\\) to get 1101\\(_{five}\\). Thereafter, converting to base ten to find the value of x = (5\\(^3\\) x 1) + (5\\(^2\\) x 1) + (5\\(^1\\) x 0) + (5°x 1) = 125 + 25 + + 1 = 151.\n\n', '', 'Explanation\n(a) \\(\\frac{\\log_28 + \\log_216 - 4\\log_22}{\\log_416}\\) = \\(\\frac{\\log_22^3 + \\log_2 2^4 - 4\\log_22}{\\log_44^2}\\)\n= \\(\\frac{3 \\log_2 2 + 4\\log_22 - 4 \\log_2^2}{2 \\log 4^4}\\)\nBut log\\(_2\\) 2 = \\(\\log_44 = 1\\)\nThen, \\(\\frac{\\log_28+\\log_216 - 4 \\log_2^2}{\\log_416}\\) = \\(\\frac{3 + 4 - 4}{2}\\) = 1\\(\\frac{1}{2}\\)\n(b) Subtract 241\\(_{five}\\) to get 1101\\(_{five}\\). Thereafter, converting to base ten to find the value of x = (5\\(^3\\) x 1) + (5\\(^2\\) x 1 + (5\\(^1\\) x 0) + (5\\(^o\\) x 1) = 125 + 25 + 0 + 1 = 151\n(b) They subtracted 241\\(_{five}\\) from 1342\\(_{five}\\) to get 1101\\(_{five}\\). Thereafter, converting to base ten to find the value of x = (5\\(^3\\) x 1) + (5\\(^2\\) x 1) + (5\\(^1\\) x 0) + (5°x 1) = 125 + 25 + + 1 = 151.\n\n', '(a) \\(\\frac{\\log_28 + \\log_216 - 4\\log_22}{\\log_416}\\) = \\(\\frac{\\log_22^3 + \\log_2 2^4 - 4\\log_22}{\\log_44^2}\\)\n= \\(\\frac{3 \\log_2 2 + 4\\log_22 - 4 \\log_2^2}{2 \\log 4^4}\\)\nBut log\\(_2\\) 2 = \\(\\log_44 = 1\\)\nThen, \\(\\frac{\\log_28+\\log_216 - 4 \\log_2^2}{\\log_416}\\) = \\(\\frac{3 + 4 - 4}{2}\\) = 1\\(\\frac{1}{2}\\)\n(b) Subtract 241\\(_{five}\\) to get 1101\\(_{five}\\). Thereafter, converting to base ten to find the value of x = (5\\(^3\\) x 1) + (5\\(^2\\) x 1 + (5\\(^1\\) x 0) + (5\\(^o\\) x 1) = 125 + 25 + 0 + 1 = 151~(b) Subtract 241\\(_{five}\\) to get 1101\\(_{five}\\). Thereafter, converting to base ten to find the value of x = (5\\(^3\\) x 1) + (5\\(^2\\) x 1 + (5\\(^1\\) x 0) + (5\\(^o\\) x 1) = 125 + 25 + 0 + 1 = 151\n(b) They subtracted 241\\(_{five}\\) from 1342\\(_{five}\\) to get 1101\\(_{five}\\). Thereafter, converting to base ten to find the value of x = (5\\(^3\\) x 1) + (5\\(^2\\) x 1) + (5\\(^1\\) x 0) + (5°x 1) = 125 + 25 + + 1 = 151.\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(737, '2018', '\n\nQuestion\n\nThe cost of dinner for a group of tourist is partly constant and partly varies as the number of tourists present. It costs $740.00 when 20 tourists were present and $960.00 when the number of tourists increased by 10. Find the cost of the dinner when only 15 tourists were present.\n\n\n', 'The cost of dinner for a group of tourist is partly constant and partly varies as the number of tourists present. It costs $740.00 when 20 tourists were present and $960.00 when the number of tourists increased by 10. Find the cost of the dinner when only 15 tourists were present.\n', '', '', NULL, '\n\nExplanation\nLet C be the cost and n the number of tourists. then C = x + ny. Where x and y are constants\n740 = x + 20y...........(1)\n960 = x + 30y.............(2)\nSolving (1) and (2) simultaneously will yield x = 300 and y = 22.\nThen, C = 300 + 22n.\nIf we substitute 15 for n this implies that C = 300 + (22 x 15)= $630.00\n\n', 'Let C be the cost and n the number of tourists. then C = x + ny. Where x and y are constants\n740 = x + 20y...........(1)\n960 = x + 30y.............(2)\nSolving (1) and (2) simultaneously will yield x = 300 and y = 22.\nThen, C = 300 + 22n.\nIf we substitute 15 for n this implies that C = 300 + (22 x 15)= $630.00\n\n', '', '', 'WAEC-PK-1', 'WAEC-MATH', 1),
(738, '2019', '\n\nQuestion\n\n(a) Fred bought a car for $5,600.00 and later sold it at 90% of the cost price. He spent $1,310.00 out of the amount received and invested the rest at 6% per annum simple interest. Calculate the interest earned in 3 years.\n(b) Solve the equations 2\\(^x\\)(4\\(^{-7}\\)) = 2 and 3\\(^{-x}\\)(9\\(^{2y}\\)) = 3 simultaneously.\n\n\n', '', '(a) Fred bought a car for $5,600.00 and later sold it at 90% of the cost price. He spent $1,310.00 out of the amount received and invested the rest at 6% per annum simple interest. Calculate the interest earned in 3 years.\n(b) Solve the equations 2\\(^x\\)(4\\(^{-7}\\)) = 2 and 3\\(^{-x}\\)(9\\(^{2y}\\)) = 3 simultaneously.\n', '(a) Fred bought a car for $5,600.00 and later sold it at 90% of the cost price. He spent $1,310.00 out of the amount received and invested the rest at 6% per annum simple interest. Calculate the interest earned in 3 years.~(b) Solve the equations 2\\(^x\\)(4\\(^{-7}\\)) = 2 and 3\\(^{-x}\\)(9\\(^{2y}\\)) = 3 simultaneously.\n', NULL, '\n\nExplanation\n(a) Selling price = \\(\\frac{90 \\times 5600}{100}\\) = $5,040.00. Thereafter, to obtain the amount invested = 5,040 - 1310 = $3,730.00\nThe interest amount invested is \\(\\frac{3730 \\times 6 \\times 3}{100}\\) = $671.40\n\n(b) 2\\(^x\\)(2\\(^{-14}\\)) = 2. This will be simplified and solved for x to get x = 15.\nSimilarly, 3\\(^{-x}\\)(3\\(^{4y}\\)) = 3 and this will yield -x + 4y = 1.\nSubstituting for x and solving for y yielded y = 4.\n\n', '', 'Explanation\n(a) Selling price = \\(\\frac{90 \\times 5600}{100}\\) = $5,040.00. Thereafter, to obtain the amount invested = 5,040 - 1310 = $3,730.00\nThe interest amount invested is \\(\\frac{3730 \\times 6 \\times 3}{100}\\) = $671.40\n\n(b) 2\\(^x\\)(2\\(^{-14}\\)) = 2. This will be simplified and solved for x to get x = 15.\nSimilarly, 3\\(^{-x}\\)(3\\(^{4y}\\)) = 3 and this will yield -x + 4y = 1.\nSubstituting for x and solving for y yielded y = 4.\n\n', '(a) Selling price = \\(\\frac{90 \\times 5600}{100}\\) = $5,040.00. Thereafter, to obtain the amount invested = 5,040 - 1310 = $3,730.00\nThe interest amount invested is \\(\\frac{3730 \\times 6 \\times 3}{100}\\) = $671.40\n~(b) 2\\(^x\\)(2\\(^{-14}\\)) = 2. This will be simplified and solved for x to get x = 15.\nSimilarly, 3\\(^{-x}\\)(3\\(^{4y}\\)) = 3 and this will yield -x + 4y = 1.\nSubstituting for x and solving for y yielded y = 4.\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(739, '2019', '\n\nQuestion\n\n\nNOT DRAWN TO SCALE\nIn the diagram, is a chord of a circle with centre 0. 22.42 cm and the perimeter of triangle MON is 55.6 cm. Calculate, correct to the nearest degree. < MON.\n(b) T is equidistant from P and Q. The bearing of P from T is 60\\(^o\\) and the bearing of Q from T is 130\\(^o\\).\n(i) Illustrate the information on a diagram.\n(ii) Find the bearing of Q from P.\n\n\n\n', '', 'NOT DRAWN TO SCALE\nIn the diagram, is a chord of a circle with centre 0. 22.42 cm and the perimeter of triangle MON is 55.6 cm. Calculate, correct to the nearest degree. < MON.\n(b) T is equidistant from P and Q. The bearing of P from T is 60\\(^o\\) and the bearing of Q from T is 130\\(^o\\).\n(i) Illustrate the information on a diagram.\n(ii) Find the bearing of Q from P.\n\n', 'NOT DRAWN TO SCALE\nIn the diagram, is a chord of a circle with centre 0. 22.42 cm and the perimeter of triangle MON is 55.6 cm. Calculate, correct to the nearest degree. < MON.~(b) T is equidistant from P and Q. The bearing of P from T is 60\\(^o\\) and the bearing of Q from T is 130\\(^o\\).\n(i) Illustrate the information on a diagram.\n(ii) Find the bearing of Q from P.\n\n', NULL, '\n\nExplanation\n(a) Using length of chord = 2r sin (\\(\\frac{\\theta}{2}\\)) = 22.42 and simplifying sin(\\(\\frac{\\theta}{2}\\)) = \\(\\frac{22.42}{33.18}\\) = 0.6757\nTaking the sine inverse of 0.6757 to obtain \\(\\frac{\\theta}{2}\\) = 42.51\\(^o\\) and multiplying through to get \\(\\theta\\) = 58.02\\(^o\\) = 885\\(^o\\)\n(b(i), the expected diagram is\n\n(b)(ii) since T is equidistant from P and Q, then ITPI = ITQI. Using sum of the angles in a triangle. 70° + x + x = 180° and solving for x.\nx = 55°. Therefore. the bearing of Q from P = 270° — 30° — 55° = 185°.\n\n', '', 'Explanation\n(a) Using length of chord = 2r sin (\\(\\frac{\\theta}{2}\\)) = 22.42 and simplifying sin(\\(\\frac{\\theta}{2}\\)) = \\(\\frac{22.42}{33.18}\\) = 0.6757\nTaking the sine inverse of 0.6757 to obtain \\(\\frac{\\theta}{2}\\) = 42.51\\(^o\\) and multiplying through to get \\(\\theta\\) = 58.02\\(^o\\) = 885\\(^o\\)\n(b(i), the expected diagram is\n\n(b)(ii) since T is equidistant from P and Q, then ITPI = ITQI. Using sum of the angles in a triangle. 70° + x + x = 180° and solving for x.\nx = 55°. Therefore. the bearing of Q from P = 270° — 30° — 55° = 185°.\n\n', '(a) Using length of chord = 2r sin (\\(\\frac{\\theta}{2}\\)) = 22.42 and simplifying sin(\\(\\frac{\\theta}{2}\\)) = \\(\\frac{22.42}{33.18}\\) = 0.6757\nTaking the sine inverse of 0.6757 to obtain \\(\\frac{\\theta}{2}\\) = 42.51\\(^o\\) and multiplying through to get \\(\\theta\\) = 58.02\\(^o\\) = 885\\(^o\\)\n(b(i), the expected diagram is\n~(b)(ii) since T is equidistant from P and Q, then ITPI = ITQI. Using sum of the angles in a triangle. 70° + x + x = 180° and solving for x.\nx = 55°. Therefore. the bearing of Q from P = 270° — 30° — 55° = 185°.\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(740, '2019', '\n\nQuestion\n\nThe ages of a group of athletes are as follows: 18, 16. 18,20, 17, 16, 19, 17, 18, 17 and 13. (a) Find the range of the distribution.\n(b) Draw a frequency distribution table for the data.\n(c) What is the median age?\n(d) Calculate, correct to two decimal places, the;\n(i) mean age:\n(ii) standard deviation.\n\n\n', '', 'The ages of a group of athletes are as follows: 18, 16. 18,20, 17, 16, 19, 17, 18, 17 and 13. (a) Find the range of the distribution.\n(b) Draw a frequency distribution table for the data.\n(c) What is the median age?\n(d) Calculate, correct to two decimal places, the;\n(i) mean age:\n(ii) standard deviation.\n', 'The ages of a group of athletes are as follows: 18, 16. 18,20, 17, 16, 19, 17, 18, 17 and 13. (a) Find the range of the distribution.~(b) Draw a frequency distribution table for the data.\n(c) What is the median age?\n(d) Calculate, correct to two decimal places, the;\n(i) mean age:\n(ii) standard deviation.\n~(c) What is the median age?\n(d) Calculate, correct to two decimal places, the;\n(i) mean age:\n(ii) standard deviation.\n~(d) Calculate, correct to two decimal places, the;\n(i) mean age:\n(ii) standard deviation.\n', NULL, '\n\nExplanation\n(a) The range; 20 - 15 = 5.\n(b) They drew the frequency distribution table as\n\\(\\sum\\) f = 11\\(\\sum\\) fx = 191 \\(\\sum\\)f\\(^2\\) = 3337\n\n\n\nAge(x)\nTally\n\nFreq\n(f)\n\n\n\n Com.\nFreq\n\nfx\nfx\\(^2\\)\n\n\n\n15\n16\n17\n18\n19\n20\n\n\nI\nII\nIII\nIII\nI\nI\n\n\n1\n2\n3\n3\n1\n1\n\n\n\n1\n3\n6\n9\n10\n11\n\n\n15\n32\n51\n54\n19\n20\n\n\n225\n512\n867\n972\n361\n400\n\n\n\n\n\n(c) Median age as 17.\n(d)(i) Mean = \\(\\frac{\\sum fx}{\\sum f}\\) = \\(\\frac{191}{11}\\) = 17.3636\n\n(d)(ii). The standard deviation was \\(\\sqrt{\\frac{2227}{11} - (\\frac{191}{11})^2}\\)\n= \\(\\sqrt{1.8677}\\) = 1.37(correct to two decimal places)\n\n\n', '', 'Explanation\n(a) The range; 20 - 15 = 5.\n(b) They drew the frequency distribution table as\n\\(\\sum\\) f = 11\\(\\sum\\) fx = 191 \\(\\sum\\)f\\(^2\\) = 3337\n\n\n\nAge(x)\nTally\n\nFreq\n(f)\n\n\n\n Com.\nFreq\n\nfx\nfx\\(^2\\)\n\n\n\n15\n16\n17\n18\n19\n20\n\n\nI\nII\nIII\nIII\nI\nI\n\n\n1\n2\n3\n3\n1\n1\n\n\n\n1\n3\n6\n9\n10\n11\n\n\n15\n32\n51\n54\n19\n20\n\n\n225\n512\n867\n972\n361\n400\n\n\n\n\n\n(c) Median age as 17.\n(d)(i) Mean = \\(\\frac{\\sum fx}{\\sum f}\\) = \\(\\frac{191}{11}\\) = 17.3636\n\n(d)(ii). The standard deviation was \\(\\sqrt{\\frac{2227}{11} - (\\frac{191}{11})^2}\\)\n= \\(\\sqrt{1.8677}\\) = 1.37(correct to two decimal places)\n\n\n', '(a) The range; 20 - 15 = 5.~(b) They drew the frequency distribution table as\n\\(\\sum\\) f = 11\\(\\sum\\) fx = 191 \\(\\sum\\)f\\(^2\\) = 3337\n\n\n\nAge(x)\nTally\n\nFreq\n(f)\n\n\n\n Com.\nFreq\n\nfx\nfx\\(^2\\)\n\n\n\n15\n16\n17\n18\n19\n20\n\n\nI\nII\nIII\nIII\nI\nI\n\n\n1\n2\n3\n3\n1\n1\n\n\n\n1\n3\n6\n9\n10\n11\n\n\n15\n32\n51\n54\n19\n20\n\n\n225\n512\n867\n972\n361\n400\n\n\n\n\n\n(c) Median age as 17.\n(d)(i) Mean = \\(\\frac{\\sum fx}{\\sum f}\\) = \\(\\frac{191}{11}\\) = 17.3636\n\n(d)(ii). The standard deviation was \\(\\sqrt{\\frac{2227}{11} - (\\frac{191}{11})^2}\\)\n= \\(\\sqrt{1.8677}\\) = 1.37(correct to two decimal places)\n\n~(c) Median age as 17.\n(d)(i) Mean = \\(\\frac{\\sum fx}{\\sum f}\\) = \\(\\frac{191}{11}\\) = 17.3636\n\n(d)(ii). The standard deviation was \\(\\sqrt{\\frac{2227}{11} - (\\frac{191}{11})^2}\\)\n= \\(\\sqrt{1.8677}\\) = 1.37(correct to two decimal places)\n\n~(d)(i) Mean = \\(\\frac{\\sum fx}{\\sum f}\\) = \\(\\frac{191}{11}\\) = 17.3636\n\n(d)(ii). The standard deviation was \\(\\sqrt{\\frac{2227}{11} - (\\frac{191}{11})^2}\\)\n= \\(\\sqrt{1.8677}\\) = 1.37(correct to two decimal places)\n\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(741, '2019', '\n\nQuestion\n\nA survey of 40 students showed that 23 students study Mathematics, 5 study Mathematics and Physics, 8 study Chemistry and Mathematics, 5 study Physics and Chemistry and 3 study all the three subjects. The number of students who study Physics only is twice the number who study Chemistry only.\n(a) Find the number of students who study:\n(i) only Physics.\n(ii) only one subject\nb) What is the probability that a student selected at random studies exactly 2 subjects?\n\n\n', '', 'A survey of 40 students showed that 23 students study Mathematics, 5 study Mathematics and Physics, 8 study Chemistry and Mathematics, 5 study Physics and Chemistry and 3 study all the three subjects. The number of students who study Physics only is twice the number who study Chemistry only.\n(a) Find the number of students who study:\n(i) only Physics.\n(ii) only one subject\nb) What is the probability that a student selected at random studies exactly 2 subjects?\n', '', NULL, '\n\nExplanation\nLet \\(\\mu\\) = 40 n(M) = 23, n(M \\(\\cup\\) P) = 5, n(M \\(\\cup\\) C) = 8, n(P \\(\\cup\\) C) = 5, n(M \\(\\cup\\) P \\(\\cup\\) C) = 3, n(C) only = x and n(P) only = 2x\n\n\n(a)(i) We have 13 + 2 + 3 + 5 + x + 2 + 2x = 40 and solving for x will yield x = 5, so that the number of students that studied only Physics = 2(5) = 10\n(a)(ii) The number of students that studied only one subject is 13 + 10 + 5 = 28\n\n(b) The probability that a student selected at random studies exactly two subjects = \\(\\frac{5 + 2 + 2}{40} = \\frac{9}{48}\\) or 0.225\n\n\n', '', 'Explanation\nLet \\(\\mu\\) = 40 n(M) = 23, n(M \\(\\cup\\) P) = 5, n(M \\(\\cup\\) C) = 8, n(P \\(\\cup\\) C) = 5, n(M \\(\\cup\\) P \\(\\cup\\) C) = 3, n(C) only = x and n(P) only = 2x\n\n\n(a)(i) We have 13 + 2 + 3 + 5 + x + 2 + 2x = 40 and solving for x will yield x = 5, so that the number of students that studied only Physics = 2(5) = 10\n(a)(ii) The number of students that studied only one subject is 13 + 10 + 5 = 28\n\n(b) The probability that a student selected at random studies exactly two subjects = \\(\\frac{5 + 2 + 2}{40} = \\frac{9}{48}\\) or 0.225\n\n\n', '(a)(i) We have 13 + 2 + 3 + 5 + x + 2 + 2x = 40 and solving for x will yield x = 5, so that the number of students that studied only Physics = 2(5) = 10\n(a)(ii) The number of students that studied only one subject is 13 + 10 + 5 = 28\n~(b) The probability that a student selected at random studies exactly two subjects = \\(\\frac{5 + 2 + 2}{40} = \\frac{9}{48}\\) or 0.225\n\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(742, '2019', '\n\nQuestion\n\na) A twenty - kilogram bag of rice is consumed by m number of boys in 10 days. When four more boys joined them, the same quantity of rice lasted only 8 days. If the rate of consumption is the same, find the value of m.\n(b) If \\(\\frac{5}{6}\\) of a number is 10 greater than \\(\\frac{1}{3}\\) of it. find the number\n(c) Find the equation of the line which passes through the points (2, \\(\\frac{1}{2}\\)) and (-1, -\\(\\frac{1}{2}\\)\n\n\n', '', 'a) A twenty - kilogram bag of rice is consumed by m number of boys in 10 days. When four more boys joined them, the same quantity of rice lasted only 8 days. If the rate of consumption is the same, find the value of m.\n(b) If \\(\\frac{5}{6}\\) of a number is 10 greater than \\(\\frac{1}{3}\\) of it. find the number\n(c) Find the equation of the line which passes through the points (2, \\(\\frac{1}{2}\\)) and (-1, -\\(\\frac{1}{2}\\)\n', 'a) A twenty - kilogram bag of rice is consumed by m number of boys in 10 days. When four more boys joined them, the same quantity of rice lasted only 8 days. If the rate of consumption is the same, find the value of m.~(b) If \\(\\frac{5}{6}\\) of a number is 10 greater than \\(\\frac{1}{3}\\) of it. find the number\n(c) Find the equation of the line which passes through the points (2, \\(\\frac{1}{2}\\)) and (-1, -\\(\\frac{1}{2}\\)\n~(c) Find the equation of the line which passes through the points (2, \\(\\frac{1}{2}\\)) and (-1, -\\(\\frac{1}{2}\\)\n', NULL, '\n\nExplanation\n(a) it will take 1 boy 10m days and when 4 more boys are added, it will take 8(m + 4) days. Since the rate of consumption was the same, then 10m = 8m + 32 and when solves, m = 16\n(b) Let x be the number. so that \\(\\frac{5}{6}\\)x = 10 + \\(\\frac{1}{2}\\)x and multiplying through by 6 to get 5x = 60 + 2x. This was solved to get x = 20\n(c) Let the gradient be m = \\(\\frac{\\frac{1}{2} - (\\frac{1}{2})}{2 - (-1)} = \\frac{2}{3}\\). The equation of the lines is y - y\\(_1\\) = m(x - x\\(_1\\)). Sunstituting for x\\(_1\\) and y\\(_1\\)\ny - (\\(\\frac{-1}{2}\\)) = \\(\\frac{1}{2}\\)(x - (-1)) and this can be simplified to y = \\(\\frac{1}{3}x - \\frac{1}{6}\\) or 2x - 6y - 1 = 0\n\n', '', 'Explanation\n(a) it will take 1 boy 10m days and when 4 more boys are added, it will take 8(m + 4) days. Since the rate of consumption was the same, then 10m = 8m + 32 and when solves, m = 16\n(b) Let x be the number. so that \\(\\frac{5}{6}\\)x = 10 + \\(\\frac{1}{2}\\)x and multiplying through by 6 to get 5x = 60 + 2x. This was solved to get x = 20\n(c) Let the gradient be m = \\(\\frac{\\frac{1}{2} - (\\frac{1}{2})}{2 - (-1)} = \\frac{2}{3}\\). The equation of the lines is y - y\\(_1\\) = m(x - x\\(_1\\)). Sunstituting for x\\(_1\\) and y\\(_1\\)\ny - (\\(\\frac{-1}{2}\\)) = \\(\\frac{1}{2}\\)(x - (-1)) and this can be simplified to y = \\(\\frac{1}{3}x - \\frac{1}{6}\\) or 2x - 6y - 1 = 0\n\n', '(a) it will take 1 boy 10m days and when 4 more boys are added, it will take 8(m + 4) days. Since the rate of consumption was the same, then 10m = 8m + 32 and when solves, m = 16~(b) Let x be the number. so that \\(\\frac{5}{6}\\)x = 10 + \\(\\frac{1}{2}\\)x and multiplying through by 6 to get 5x = 60 + 2x. This was solved to get x = 20\n(c) Let the gradient be m = \\(\\frac{\\frac{1}{2} - (\\frac{1}{2})}{2 - (-1)} = \\frac{2}{3}\\). The equation of the lines is y - y\\(_1\\) = m(x - x\\(_1\\)). Sunstituting for x\\(_1\\) and y\\(_1\\)\ny - (\\(\\frac{-1}{2}\\)) = \\(\\frac{1}{2}\\)(x - (-1)) and this can be simplified to y = \\(\\frac{1}{3}x - \\frac{1}{6}\\) or 2x - 6y - 1 = 0\n~(c) Let the gradient be m = \\(\\frac{\\frac{1}{2} - (\\frac{1}{2})}{2 - (-1)} = \\frac{2}{3}\\). The equation of the lines is y - y\\(_1\\) = m(x - x\\(_1\\)). Sunstituting for x\\(_1\\) and y\\(_1\\)\ny - (\\(\\frac{-1}{2}\\)) = \\(\\frac{1}{2}\\)(x - (-1)) and this can be simplified to y = \\(\\frac{1}{3}x - \\frac{1}{6}\\) or 2x - 6y - 1 = 0\n', 'WAEC-PK-1', 'WAEC-MATH', 1);
INSERT INTO `exam_simulation2` (`id`, `examYear`, `questions`, `parent_que`, `child_que`, `gen_child_que_desc`, `imageDir`, `explanation`, `parent_que_expl`, `child_que_exp`, `gen_child_que_expl`, `package_id`, `subject_id`, `status`) VALUES
(743, '2019', '\n\nQuestion\n\nA ladder 11mlong leans against a vertical wall at an angle of 75\\(^o\\) to the ground. The ladder is the pushed 0.2 m up the wall.\n(a) Illustrate the information in a diagram.\n(b) Find correct to the nearest whole number, the:\n(i) new angle which the ladder makes with the ground:\n(ii) distance the foot of the ladder has moved from its original position.\n\n', '', 'A ladder 11mlong leans against a vertical wall at an angle of 75\\(^o\\) to the ground. The ladder is the pushed 0.2 m up the wall.\n(a) Illustrate the information in a diagram.\n(b) Find correct to the nearest whole number, the:\n(i) new angle which the ladder makes with the ground:\n(ii) distance the foot of the ladder has moved from its original position.', 'A ladder 11mlong leans against a vertical wall at an angle of 75\\(^o\\) to the ground. The ladder is the pushed 0.2 m up the wall.\n(a) Illustrate the information in a diagram.~(b) Find correct to the nearest whole number, the:\n(i) new angle which the ladder makes with the ground:\n(ii) distance the foot of the ladder has moved from its original position.', NULL, '\n\nExplanation\n(a)The required diagram was\n\n(b)(i) we have sin 75\\(^o\\) = \\(\\frac{x}{11}\\) and this will give x = 10.625m. Since the ladder has moved up by 0.2 , the new point where the ladder touches the wall is 0.2 + 10.625 = 10.825m.\nThen sin\\(\\theta\\) = \\(\\frac{10.825}{11}\\)\nSin\\(\\theta\\) = 0.9841 and \\(\\theta\\) = sin\\(^{-1}\\)(0.9841) = 79.77\\(^o\\) = 80\\(^o\\)\n\n(b)(ii) Cos 75\\(^o\\) = \\(\\frac{y}{11}\\) so that y = 2.2847m\nSimilarity, cos 79.77 = \\(\\frac{q}{11}\\) and q = 1.9536m. Therefore, the distance the ladder was dragged = 2.8470 - 1.9536 = 0.8934m = 1m\n\n', '', 'Explanation\n(a)The required diagram was\n\n(b)(i) we have sin 75\\(^o\\) = \\(\\frac{x}{11}\\) and this will give x = 10.625m. Since the ladder has moved up by 0.2 , the new point where the ladder touches the wall is 0.2 + 10.625 = 10.825m.\nThen sin\\(\\theta\\) = \\(\\frac{10.825}{11}\\)\nSin\\(\\theta\\) = 0.9841 and \\(\\theta\\) = sin\\(^{-1}\\)(0.9841) = 79.77\\(^o\\) = 80\\(^o\\)\n\n(b)(ii) Cos 75\\(^o\\) = \\(\\frac{y}{11}\\) so that y = 2.2847m\nSimilarity, cos 79.77 = \\(\\frac{q}{11}\\) and q = 1.9536m. Therefore, the distance the ladder was dragged = 2.8470 - 1.9536 = 0.8934m = 1m\n\n', '(a)The required diagram was\n\n(b)(i) we have sin 75\\(^o\\) = \\(\\frac{x}{11}\\) and this will give x = 10.625m. Since the ladder has moved up by 0.2 , the new point where the ladder touches the wall is 0.2 + 10.625 = 10.825m.\nThen sin\\(\\theta\\) = \\(\\frac{10.825}{11}\\)\nSin\\(\\theta\\) = 0.9841 and \\(\\theta\\) = sin\\(^{-1}\\)(0.9841) = 79.77\\(^o\\) = 80\\(^o\\)\n~(b)(i) we have sin 75\\(^o\\) = \\(\\frac{x}{11}\\) and this will give x = 10.625m. Since the ladder has moved up by 0.2 , the new point where the ladder touches the wall is 0.2 + 10.625 = 10.825m.\nThen sin\\(\\theta\\) = \\(\\frac{10.825}{11}\\)\nSin\\(\\theta\\) = 0.9841 and \\(\\theta\\) = sin\\(^{-1}\\)(0.9841) = 79.77\\(^o\\) = 80\\(^o\\)\n\n(b)(ii) Cos 75\\(^o\\) = \\(\\frac{y}{11}\\) so that y = 2.2847m\nSimilarity, cos 79.77 = \\(\\frac{q}{11}\\) and q = 1.9536m. Therefore, the distance the ladder was dragged = 2.8470 - 1.9536 = 0.8934m = 1m\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(744, '2019', '\n\nQuestion\n\n(a) Copy and complete the table of values for the relation y = 4x\\(^2\\) - 8x - 21, for -2.0 \\(\\leq\\) x \\(\\leq\\) 4.0\n\n\n\nx\n-2.0\n-1.5\n-1.0\n0.5\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\n3.0\n3.5\n4.0\n\n\ny\n11\n\n-9\n\n-21\n-24\n\n\n-21\n\n-9\n0\n\n\n\n\n\n(b) Using a scale of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the graph for the relation y = 4x\\(^2\\) - 8x - 21\n(ii) Use the graph to find the solution set of\n(\\(\\alpha\\)) 4x\\(^2\\) - 8x = 3;\n(\\(\\beta\\)) 4x\\(^2\\) - 7x - 21 = 0\n\n\n(a) Copy and complete the table of values for the relation y = 4x\\(^2\\) - 8x - 21, for -2.0 \\(\\leq\\) x \\(\\leq\\) 4.0\n\n\n\nx\n-2.0\n-1.5\n-1.0\n0.5\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\n3.0\n3.5\n4.0\n\n\ny\n11\n\n-9\n\n-21\n-24\n\n\n-21\n\n-9\n0\n\n\n\n\n', '', '(a) Copy and complete the table of values for the relation y = 4x\\(^2\\) - 8x - 21, for -2.0 \\(\\leq\\) x \\(\\leq\\) 4.0\n\n\n\nx\n-2.0\n-1.5\n-1.0\n0.5\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\n3.0\n3.5\n4.0\n\n\ny\n11\n\n-9\n\n-21\n-24\n\n\n-21\n\n-9\n0\n\n\n\n\n\n(b) Using a scale of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the graph for the relation y = 4x\\(^2\\) - 8x - 21\n(ii) Use the graph to find the solution set of\n(\\(\\alpha\\)) 4x\\(^2\\) - 8x = 3;\n(\\(\\beta\\)) 4x\\(^2\\) - 7x - 21 = 0\n\n\n(a) Copy and complete the table of values for the relation y = 4x\\(^2\\) - 8x - 21, for -2.0 \\(\\leq\\) x \\(\\leq\\) 4.0\n\n\n\nx\n-2.0\n-1.5\n-1.0\n0.5\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\n3.0\n3.5\n4.0\n\n\ny\n11\n\n-9\n\n-21\n-24\n\n\n-21\n\n-9\n0\n\n\n', '(a) Copy and complete the table of values for the relation y = 4x\\(^2\\) - 8x - 21, for -2.0 \\(\\leq\\) x \\(\\leq\\) 4.0\n\n\n\nx\n-2.0\n-1.5\n-1.0\n0.5\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\n3.0\n3.5\n4.0\n\n\ny\n11\n\n-9\n\n-21\n-24\n\n\n-21\n\n-9\n0\n\n\n\n\n~(b) Using a scale of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the graph for the relation y = 4x\\(^2\\) - 8x - 21\n(ii) Use the graph to find the solution set of\n(\\(\\alpha\\)) 4x\\(^2\\) - 8x = 3;\n(\\(\\beta\\)) 4x\\(^2\\) - 7x - 21 = 0\n\n\n(a) Copy and complete the table of values for the relation y = 4x\\(^2\\) - 8x - 21, for -2.0 \\(\\leq\\) x \\(\\leq\\) 4.0\n\n\n\nx\n-2.0\n-1.5\n-1.0\n0.5\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\n3.0\n3.5\n4.0\n\n\ny\n11\n\n-9\n\n-21\n-24\n\n\n-21\n\n-9\n0\n\n\n', NULL, '\n\nExplanation\n(a) They completed the table of values as shown\n\n\n\nx\n-2.0\n-1.5\n-1.0\n0.5\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\n3.0\n3.5\n4.0\n\n\ny\n11\n0\n-9\n-16\n-21\n-24\n-25\n-24\n-21\n-16\n-9\n0\n11\n\n\n\n\n(b)(i) The graph\n(b)(ii)(\\(\\alpha\\), deduce that 4x\\(^2\\) - 8x - 21 = 3 - 21 so that y = -18. From the graph, the point of intersection of y = -18 and y = 4x\\(^2\\) - 8x - 21 was atx = {-0.35 \\(\\pm\\) 0.1, 2.3 \\(\\pm\\) 0.1}\n\n(b)(ii)(\\(\\beta\\)), the equation4x\\(^2\\) - 8x - 21 = 0 which can be written as4x\\(^2\\) - x - 7x - 21 = -x. This implies that4x\\(^2\\) - 8x - 21 = -x.\nBut, y =4x\\(^2\\) - 8x - 21 so that y = -x, Next was to draw the line y = -x and from the graph, the point of intersection with the curve y =4x\\(^2\\) - 8x - 21 was at x = {3.3 \\(\\pm\\) 0.1, -1.6 \\(\\pm\\) 0.1}\n\n\n\n', '', 'Explanation\n(a) They completed the table of values as shown\n\n\n\nx\n-2.0\n-1.5\n-1.0\n0.5\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\n3.0\n3.5\n4.0\n\n\ny\n11\n0\n-9\n-16\n-21\n-24\n-25\n-24\n-21\n-16\n-9\n0\n11\n\n\n\n\n(b)(i) The graph\n(b)(ii)(\\(\\alpha\\), deduce that 4x\\(^2\\) - 8x - 21 = 3 - 21 so that y = -18. From the graph, the point of intersection of y = -18 and y = 4x\\(^2\\) - 8x - 21 was atx = {-0.35 \\(\\pm\\) 0.1, 2.3 \\(\\pm\\) 0.1}\n\n(b)(ii)(\\(\\beta\\)), the equation4x\\(^2\\) - 8x - 21 = 0 which can be written as4x\\(^2\\) - x - 7x - 21 = -x. This implies that4x\\(^2\\) - 8x - 21 = -x.\nBut, y =4x\\(^2\\) - 8x - 21 so that y = -x, Next was to draw the line y = -x and from the graph, the point of intersection with the curve y =4x\\(^2\\) - 8x - 21 was at x = {3.3 \\(\\pm\\) 0.1, -1.6 \\(\\pm\\) 0.1}\n\n\n\n', '(a) They completed the table of values as shown\n\n\n\nx\n-2.0\n-1.5\n-1.0\n0.5\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\n3.0\n3.5\n4.0\n\n\ny\n11\n0\n-9\n-16\n-21\n-24\n-25\n-24\n-21\n-16\n-9\n0\n11\n\n\n\n\n(b)(i) The graph\n(b)(ii)(\\(\\alpha\\), deduce that 4x\\(^2\\) - 8x - 21 = 3 - 21 so that y = -18. From the graph, the point of intersection of y = -18 and y = 4x\\(^2\\) - 8x - 21 was atx = {-0.35 \\(\\pm\\) 0.1, 2.3 \\(\\pm\\) 0.1}\n~(b)(i) The graph\n(b)(ii)(\\(\\alpha\\), deduce that 4x\\(^2\\) - 8x - 21 = 3 - 21 so that y = -18. From the graph, the point of intersection of y = -18 and y = 4x\\(^2\\) - 8x - 21 was atx = {-0.35 \\(\\pm\\) 0.1, 2.3 \\(\\pm\\) 0.1}\n\n(b)(ii)(\\(\\beta\\)), the equation4x\\(^2\\) - 8x - 21 = 0 which can be written as4x\\(^2\\) - x - 7x - 21 = -x. This implies that4x\\(^2\\) - 8x - 21 = -x.\nBut, y =4x\\(^2\\) - 8x - 21 so that y = -x, Next was to draw the line y = -x and from the graph, the point of intersection with the curve y =4x\\(^2\\) - 8x - 21 was at x = {3.3 \\(\\pm\\) 0.1, -1.6 \\(\\pm\\) 0.1}\n\n\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(745, '2019', '\n\nQuestion\n\n(a) The curved surface areas of two cones are equal. The base radius of one is 5 cm and its slant height is 12cm. calculate the height of the second cone if its base radius is 6 cm.\n(b) Given the matrices A = \\(\\begin{pmatrix} 2 & 5 \\\\ -1 & -3 \\end{pmatrix}\\) and B =\\(\\begin{pmatrix} 3 & -2 \\\\ 4 & 1 \\end{pmatrix}\\), find:\n\n(i) BA;\n(ii) the determinant of BA.\n\n', '', '(a) The curved surface areas of two cones are equal. The base radius of one is 5 cm and its slant height is 12cm. calculate the height of the second cone if its base radius is 6 cm.\n(b) Given the matrices A = \\(\\begin{pmatrix} 2 & 5 \\\\ -1 & -3 \\end{pmatrix}\\) and B =\\(\\begin{pmatrix} 3 & -2 \\\\ 4 & 1 \\end{pmatrix}\\), find:\n\n(i) BA;\n(ii) the determinant of BA.', '(a) The curved surface areas of two cones are equal. The base radius of one is 5 cm and its slant height is 12cm. calculate the height of the second cone if its base radius is 6 cm.~(b) Given the matrices A = \\(\\begin{pmatrix} 2 & 5 \\\\ -1 & -3 \\end{pmatrix}\\) and B =\\(\\begin{pmatrix} 3 & -2 \\\\ 4 & 1 \\end{pmatrix}\\), find:\n\n(i) BA;\n(ii) the determinant of BA.', NULL, '\n\nExplanation\n(a) since the curved surface areas were the same, it was expected that they have 5 x 12\\(pi\\) = 6 \\(\\pi\\)land solving for the slant height to get l= 10 cm.\nThen by the use of Pythagoras theorem, the height of the second cone is h\\(^2\\)= 10\\(^2\\) - 6\\(^2\\) and when simplified will result in h = 8 cm.\n\n(b(i), they were to find BA = \\(\\begin{pmatrix} 3 & -2 \\\\4 & 1\\end{pmatrix}\\) \\(\\begin{pmatrix} 2 & 5 \\\\ -1 & -3\\end{pmatrix}\\) =\\(\\begin{pmatrix} 8 & 21 \\\\ 7 & 17 \\end{pmatrix}\\)\n(b)(ii), the determinant of BA =(8 x 17) - (21 x 7) = 136 - 147 = -11\n\n', '', 'Explanation\n(a) since the curved surface areas were the same, it was expected that they have 5 x 12\\(pi\\) = 6 \\(\\pi\\)land solving for the slant height to get l= 10 cm.\nThen by the use of Pythagoras theorem, the height of the second cone is h\\(^2\\)= 10\\(^2\\) - 6\\(^2\\) and when simplified will result in h = 8 cm.\n\n(b(i), they were to find BA = \\(\\begin{pmatrix} 3 & -2 \\\\4 & 1\\end{pmatrix}\\) \\(\\begin{pmatrix} 2 & 5 \\\\ -1 & -3\\end{pmatrix}\\) =\\(\\begin{pmatrix} 8 & 21 \\\\ 7 & 17 \\end{pmatrix}\\)\n(b)(ii), the determinant of BA =(8 x 17) - (21 x 7) = 136 - 147 = -11\n\n', '(a) since the curved surface areas were the same, it was expected that they have 5 x 12\\(pi\\) = 6 \\(\\pi\\)land solving for the slant height to get l= 10 cm.\nThen by the use of Pythagoras theorem, the height of the second cone is h\\(^2\\)= 10\\(^2\\) - 6\\(^2\\) and when simplified will result in h = 8 cm.\n\n(b(i), they were to find BA = \\(\\begin{pmatrix} 3 & -2 \\\\4 & 1\\end{pmatrix}\\) \\(\\begin{pmatrix} 2 & 5 \\\\ -1 & -3\\end{pmatrix}\\) =\\(\\begin{pmatrix} 8 & 21 \\\\ 7 & 17 \\end{pmatrix}\\)~(b)(ii), the determinant of BA =(8 x 17) - (21 x 7) = 136 - 147 = -11\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(746, '2019', '\n\nQuestion\n\n(a) Given that 110\\(_x\\) - 40\\(_{five}\\). find the value of x\n(b) Simplify \\(\\frac{15}{\\sqrt{75}} - \\sqrt{432}\\), leaving the answer in the form a\\(\\sqrt{b}\\), where a and b are positive integers.\n\n\n', '', '(a) Given that 110\\(_x\\) - 40\\(_{five}\\). find the value of x\n(b) Simplify \\(\\frac{15}{\\sqrt{75}} - \\sqrt{432}\\), leaving the answer in the form a\\(\\sqrt{b}\\), where a and b are positive integers.\n', '(a) Given that 110\\(_x\\) - 40\\(_{five}\\). find the value of x~(b) Simplify \\(\\frac{15}{\\sqrt{75}} - \\sqrt{432}\\), leaving the answer in the form a\\(\\sqrt{b}\\), where a and b are positive integers.\n', NULL, '\n\nExplanation\n(a) Conveting to bese ten and when simplified yielded x\\(^2\\) + x - 20 = 0 and when solves ; (x + 5)(x - 4) = 0\nx = 4 or x = -5 But x cabbot be negative since it is the base, therefore, x = 4.\n(b) Simplify \\(\\frac{15}{\\sqrt{75}}\\) = \\(\\frac{3}{\\sqrt{3}}\\) which will yield \\(\\sqrt{3}\\) when rationalized. Similarly, \\(\\sqrt{108}\\) = 6\\(\\sqrt{3}\\) and \\(\\sqrt{432}\\) = 12\\(\\sqrt{3}\\). Thus, substracting and simplifying will yield \\(\\sqrt{3} + 12\\sqrt{3} = 19\\sqrt{3}\\)\n\n\n', '', 'Explanation\n(a) Conveting to bese ten and when simplified yielded x\\(^2\\) + x - 20 = 0 and when solves ; (x + 5)(x - 4) = 0\nx = 4 or x = -5 But x cabbot be negative since it is the base, therefore, x = 4.\n(b) Simplify \\(\\frac{15}{\\sqrt{75}}\\) = \\(\\frac{3}{\\sqrt{3}}\\) which will yield \\(\\sqrt{3}\\) when rationalized. Similarly, \\(\\sqrt{108}\\) = 6\\(\\sqrt{3}\\) and \\(\\sqrt{432}\\) = 12\\(\\sqrt{3}\\). Thus, substracting and simplifying will yield \\(\\sqrt{3} + 12\\sqrt{3} = 19\\sqrt{3}\\)\n\n\n', '(a) Conveting to bese ten and when simplified yielded x\\(^2\\) + x - 20 = 0 and when solves ; (x + 5)(x - 4) = 0\nx = 4 or x = -5 But x cabbot be negative since it is the base, therefore, x = 4.~(b) Simplify \\(\\frac{15}{\\sqrt{75}}\\) = \\(\\frac{3}{\\sqrt{3}}\\) which will yield \\(\\sqrt{3}\\) when rationalized. Similarly, \\(\\sqrt{108}\\) = 6\\(\\sqrt{3}\\) and \\(\\sqrt{432}\\) = 12\\(\\sqrt{3}\\). Thus, substracting and simplifying will yield \\(\\sqrt{3} + 12\\sqrt{3} = 19\\sqrt{3}\\)\n\n', 'WAEC-PK-1', 'WAEC-MATH', 1),
(747, '2019', '\n\nQuestion\n\n(a)\n\nIn the diagram. \\(\\over{Rs}\\) and \\(\\over{RT}\\) are tangent to the circle with centre O, < TUS = 68\\(^o\\), < SRT = x and < UTO = y. Find the value of x.\n\n(b) Two tanks A and B are filled to capacity with diesel. Tank A holds 600 litres diesel more than tank B. If 100 litres of diesel was pumped cut of each tank, tank A would then contain 3 times as much as tank B. Find the capacity of each tank.\n', '', '(a)\n\nIn the diagram. \\(\\over{Rs}\\) and \\(\\over{RT}\\) are tangent to the circle with centre O, < TUS = 68\\(^o\\), < SRT = x and < UTO = y. Find the value of x.\n\n(b) Two tanks A and B are filled to capacity with diesel. Tank A holds 600 litres diesel more than tank B. If 100 litres of diesel was pumped cut of each tank, tank A would then contain 3 times as much as tank B. Find the capacity of each tank.\n', '(a)\n\nIn the diagram. \\(\\over{Rs}\\) and \\(\\over{RT}\\) are tangent to the circle with centre O, < TUS = 68\\(^o\\), < SRT = x and < UTO = y. Find the value of x.\n~(b) Two tanks A and B are filled to capacity with diesel. Tank A holds 600 litres diesel more than tank B. If 100 litres of diesel was pumped cut of each tank, tank A would then contain 3 times as much as tank B. Find the capacity of each tank.\n', NULL, '\n\nExplanation\n(a). < SOT = 2 < SOT = 2 x 68° =136.\nObserve that < OSR = < OTR = 90\\(^o\\)\nSo that < OSR + x + < OTR + < SOT = 360\\(^o\\). Next is to substitute and simplified to get x + 316\\(o\\) = 360\\(o\\) so that x = 44\\(o\\)\n\n(b) If we let capacity of tank A = a and capacity of tank B = b, then\na = 600 + b......(1)\na - 100 = 3(b - 100)\na = 3b - 200........(2)\nSubstituting (2) into (1) yielded 3b - 200 = 600 + b and solving for b, b = 400.\nTherefore. Capacity of tank B = 400litres\nSubstituting b in (1) yielded A = 600 + 400 = 1000\nCapacity of A =1000.\n\n', '', 'Explanation\n(a). < SOT = 2 < SOT = 2 x 68° =136.\nObserve that < OSR = < OTR = 90\\(^o\\)\nSo that < OSR + x + < OTR + < SOT = 360\\(^o\\). Next is to substitute and simplified to get x + 316\\(o\\) = 360\\(o\\) so that x = 44\\(o\\)\n\n(b) If we let capacity of tank A = a and capacity of tank B = b, then\na = 600 + b......(1)\na - 100 = 3(b - 100)\na = 3b - 200........(2)\nSubstituting (2) into (1) yielded 3b - 200 = 600 + b and solving for b, b = 400.\nTherefore. Capacity of tank B = 400litres\nSubstituting b in (1) yielded A = 600 + 400 = 1000\nCapacity of A =1000.\n\n', '(a). < SOT = 2 < SOT = 2 x 68° =136.\nObserve that < OSR = < OTR = 90\\(^o\\)\nSo that < OSR + x + < OTR + < SOT = 360\\(^o\\). Next is to substitute and simplified to get x + 316\\(o\\) = 360\\(o\\) so that x = 44\\(o\\)\n~(b) If we let capacity of tank A = a and capacity of tank B = b, then\na = 600 + b......(1)\na - 100 = 3(b - 100)\na = 3b - 200........(2)\nSubstituting (2) into (1) yielded 3b - 200 = 600 + b and solving for b, b = 400.\nTherefore. Capacity of tank B = 400litres\nSubstituting b in (1) yielded A = 600 + 400 = 1000\nCapacity of A =1000.\n', 'WAEC-PK-1', 'WAEC-MATH', 1);

-- --------------------------------------------------------

--
-- Table structure for table `grading_system`
--

CREATE TABLE `grading_system` (
  `id` int(11) NOT NULL,
  `score_from` int(11) NOT NULL,
  `score_to` int(11) NOT NULL,
  `grade` varchar(2) NOT NULL,
  `descrption` varchar(100) NOT NULL,
  `exm_type` varchar(100) NOT NULL COMMENT 'WAEC, NECO, JAMB',
  `status` int(1) NOT NULL DEFAULT 1,
  `created_at` timestamp NOT NULL DEFAULT current_timestamp(),
  `updated_at` timestamp NOT NULL DEFAULT current_timestamp() ON UPDATE current_timestamp()
) ENGINE=InnoDB DEFAULT CHARSET=latin1;

--
-- Dumping data for table `grading_system`
--

INSERT INTO `grading_system` (`id`, `score_from`, `score_to`, `grade`, `descrption`, `exm_type`, `status`, `created_at`, `updated_at`) VALUES
(1, 75, 100, 'A1', 'EXCELLENT', 'WAEC', 1, '2017-08-19 22:51:43', '2021-06-24 12:54:58'),
(2, 70, 74, 'B2', 'VERY GOOD', 'WAEC', 1, '2017-08-19 22:51:43', '2021-06-24 12:55:06'),
(3, 65, 69, 'B3', 'GOOD', 'WAEC', 1, '2017-08-19 22:53:03', '2021-06-24 12:55:15'),
(4, 60, 64, 'C4', 'CREDIT', 'WAEC', 1, '2017-08-19 22:53:03', '2021-06-24 12:55:19'),
(5, 55, 59, 'C5', 'CREDIT', 'WAEC', 1, '2017-08-19 22:54:28', '2021-06-24 12:55:23'),
(6, 50, 54, 'C6', 'CREDIT', 'WAEC', 1, '2017-08-19 22:54:28', '2021-06-24 12:55:28'),
(7, 45, 49, 'D7', 'PASS', 'WAEC', 1, '2017-08-19 22:55:21', '2021-06-24 12:55:32'),
(8, 40, 44, 'E8', 'PASS', 'WAEC', 1, '2017-08-19 22:55:21', '2021-06-24 12:55:36'),
(9, 0, 39, 'F9', 'FAIL', 'WAEC', 1, '2017-08-19 22:55:54', '2021-06-24 12:55:41');

-- --------------------------------------------------------

--
-- Table structure for table `labelled_parameter`
--

CREATE TABLE `labelled_parameter` (
  `id` int(11) NOT NULL,
  `question_id` varchar(200) NOT NULL,
  `label_id` varchar(200) NOT NULL,
  `topic_name` longtext NOT NULL,
  `user_id` varchar(200) NOT NULL,
  `status` int(1) NOT NULL,
  `approved` int(2) NOT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4;

--
-- Dumping data for table `labelled_parameter`
--

INSERT INTO `labelled_parameter` (`id`, `question_id`, `label_id`, `topic_name`, `user_id`, `status`, `approved`) VALUES
(21, '1', 'DL-2', 'nn', 'DL-USER-2', 1, 1),
(22, '2', 'DL-2', '', 'DL-USER-2', 0, 1),
(23, '3', 'DL-2', '', 'DL-USER-2', 0, 0),
(24, '4', 'DL-2', '', 'DL-USER-2', 0, 1),
(25, '5', 'DL-2', '', 'DL-USER-2', 0, 0),
(26, '1', 'DL-1', 'csf', 'DL-USER-3', 1, 1),
(27, '2', 'DL-1', 'volumes', 'DL-USER-3', 1, 1),
(28, '3', 'DL-1', 'quadratic equations', 'DL-USER-3', 1, 1),
(29, '6', 'DL-2', 'angles of elevation and depression', 'DL-USER-3', 0, 0),
(30, '7', 'DL-2', 'percentages', 'DL-USER-3', 0, 0),
(31, '8', 'DL-2', 'plane geometry', 'DL-USER-3', 1, 1),
(32, '5', 'DL-1', 'simplify', 'DL-USER-3', 1, 1),
(33, '6', 'DL-1', 'quadratic equations', 'DL-USER-3', 1, 1),
(34, '7', 'DL-1', 'set', 'DL-USER-3', 1, 1),
(35, '9', 'DL-2', 'angles of elevation and depression', 'DL-USER-3', 0, 0),
(36, '10', 'DL-2', 'plane geometry', 'DL-USER-3', 0, 0),
(37, '11', 'DL-2', 'angles of elevation and depression', 'DL-USER-3', 0, 1);

-- --------------------------------------------------------

--
-- Table structure for table `labelling`
--

CREATE TABLE `labelling` (
  `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` varchar(500) NOT NULL,
  `topic` varchar(500) NOT NULL,
  `package_id` varchar(200) NOT NULL,
  `subject_id` varchar(200) NOT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4;

--
-- Dumping data for table `labelling`
--

INSERT INTO `labelling` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`) VALUES
(1, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(2, '1989', 'If 3loga + 5loga - 6loga = log64, what is a?', '', '', '32', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(3, '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?', '', '', '68', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(4, '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.', '', '', ' 19cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(5, '1989', 'In the diagram O is the center of the circle, if ', '', '', ' 90o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(6, '1989', 'Evaluate, using logarithm tables5.34 x 67.4/2.7', '', '', '13.32', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(7, '1989', 'Factorize 35 - 2b - b2', '', '', ' (7+b)(5+b)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(8, '1989', 'Evaluate 0.009 / 0.012, leaving your answer in standard form', '', '', ' 7.5 x 10-3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(9, '1989', 'The graph above is that of a quadratic function y = 2x2 - x - 6.The roots of the equation are', '', '', ' -1, 6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(10, '1989', 'Factorize the following expression; 2x2 + x - 15', '', '', ' (2x+5)(x+3)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(11, '1989', 'The angle of elevation of X from Y is 30o. If XY = 40m, how high is X above the level of Y?', '', '', ' 50m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(12, '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.', '', '', '0.154', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(13, '1989', 'In the diagram above, ', '', '', ' x = 2p', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(14, '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.', '', '', ' 48.8cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(15, '1989', 'Using the above graph, if 10o < x < 60o, what is the value of x for which sin x = cos x?', '', '', ' 50o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(16, '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?', '', '', '85', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(17, '1989', 'An arc of a circle radius 7cm is 14cm long. What angle does the arc subtend at the center of circle?', '', '', ' 114.55o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(18, '1989', 'If 5 times a certain integer is subtracted from twice the integer, the result is 63. Find the integer.', '', '', '3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(19, '1989', 'If 3 y = 243, find the value of y', '', '', '6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(20, '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', '', '', ' 336o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(21, '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 ', '', '', ' 15cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(22, '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.', '', '', ' 253.5cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(23, '1989', 'Solve the following equation: 6x2 - 7x - 5 = 0', '', '', ' x = 5/6 or x = -1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(24, '1989', 'What angle represents grown up girls ? Correct to one decimal place', '', '', ' 3.75o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(25, '1989', 'What percentage of the population are married? correct to one decimal place', '', '', '0.365', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(26, '1989', 'If A = (a,b,c), B = (a,b,c,d,e) and C = (a,b,c,d,e,f). Find (A', '', '', ' ', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(27, '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', '', '', '7', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(28, '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?', '', '', '10', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(29, '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?', '', '', '10', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(30, '1989', 'In the diagram above O is the center of the circle, if ', '', '', ' 210o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(31, '1989', 'Simplify 91/2/272/3', '', '', ' 1/27', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(32, '1989', 'In the diagram above, what is the size of angle ACB.', '', '', ' 100o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(33, '1989', 'With reference to the graph above, which f the following solution sets is represented by ΔOPQ?', '', '', ' y ≤ x, y ≥ 0, y + x ≥ 7', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(34, '1989', 'Find the volume of a cone of radius 3.5cm and vertical height 12cm ', '', '', ' 154.0cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(35, '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?', '', '', ' 3/4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(36, '1989', 'The angle of a sector of a circle of diameter 8cm ', '', '', ' 313/7cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(37, '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.', '', '', ' 20o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(38, '1989', 'Which of the following gives the point of intersection of the graph y = x2 and y = x + 6 shown above?', '', '', ' (-2,2)(3,6)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(39, '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. ', '', '', ' 90.2cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(40, '1989', 'If logax = p, express x in terms  of a and p', '', '', ' x = ap', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(41, '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. ', '', '', ' 50.3cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(42, '1989', 'In the diagram above, O is the center of the circle. If ', '', '', ' 54o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(43, '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', '', '', ' 13.9m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(44, '1989', 'Solve for x: (x2 + 2x + 1) = 25', '', '', ' 5, 5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(45, '1989', 'Given that logp = 2 logx + 3logq, which of the following expresses p in terms of x and q?', '', '', ' p = x2q3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(46, '1989', 'sinθ = 1/2 and cosθ = -√3/2, what is the value of  θ?', '', '', ' 150 o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(47, '1989', 'What is the probability that 3 customers waiting in a bank will be served in the sequence of their arrival at the bank', '', '', ' 5/6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(48, '1989', 'In the diagram, O is the center of the circle, If ', '', '', ' 32o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(49, '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', '', '', ' 51/2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(50, '1990', 'What must be added to 4x2 - 4 to make it a perfect square?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(51, '1990', 'Each of the interior angles of a regular polygon is 140o. How many sides has the polygon?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(52, '1990', 'If sin x = cos 50o, then x equals', '', '', ' 130o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(53, '1990', 'Simplify 125-1/3 x 49-1/2 x 100', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(54, '1990', 'If 32x = 27, what is x?', '', '', '40.5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(55, '1990', 'Express 0.00562 in standard form', '', '', ' 5.62 x 103', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(56, '1990', 'Given that 1/3log10 P = 1, find the value of P', '', '', '1000', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(57, '1990', 'Simplifylog√8/log8', '', '', ' 1/2log√2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(58, '1990', 'Evaluate using the logarithm table, log(0.65)2', '', '', '1.6272', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(59, '1990', 'If log x = 2.3675 an log y = 0.9750, what is the value of x + y? Correct to three significant figures', '', '', '9.46', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(60, '1990', 'While doing his physics practical, Idowu recorded a reading as 1.12cm instead of 1.21cm. Calculate his percentage error', '', '', '0.09', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(61, '1990', 'Find the 4th term of an A.P, whose first term is 2 and the common difference is 0.5', '', '', '4.5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(62, '1990', 'From the graph determine the roots of the equation y = 2x2 + x - 6', '', '', ' 2, 1.5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(63, '1990', 'Find the values of x for which y = 5', '', '', ' 0, 0', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(64, '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?', '', '', ' 168o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(65, '1990', 'Find the sum of the first five terms of the G.P 2.6 18 ....', '', '', '121', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(66, '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?', '', '', '50', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(67, '1990', 'The area shaded with horizontal lines is the solution set of the inequalities:', '', '', ' y ≤ x, y ≤ 2x - 3, x ≥ 3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(68, '1990', 'The area shaded with vertical lines is the solution set of the inequalities:', '', '', ' y ≥ x, y + 2x ≥ 3, x ≤ 3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(69, '1990', 'In the diagram above, O is the center of the circle with radius 10cm, and ', '', '', ' 31.4cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(70, '1990', 'Factorize x2 + 4x - 192', '', '', ' (x+12) (x+16)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(71, '1990', 'Factorize 2e2 - 3e + 1', '', '', ' (e2-3(2e-1)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(72, '1990', 'Solve the equation 7y2 = 3y', '', '', ' y = 0 or 10', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(73, '1990', 'Find the value of m which makes x2 + 8 + m a perfect square', '', '', '16', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(74, '1990', 'Solve the equation 2a2 - 3a - 27 = 0', '', '', ' -3, 9/2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(75, '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  ', '', '', ' 206o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(76, '1990', 'calculate the surface area of a sphere of radius 7cm ', '', '', ' 4312cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(77, '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?', '', '', ' 0o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(78, '1990', 'A cylindrical container closed at both ends, has a radius of 7cm and height 5cm ', '', '', ' 770cm3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(79, '1990', 'In the diagram above, |PQ| = |PR| = |RS| and ', '', '', ' 26o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(80, '1990', 'In the diagram above, WXYZ is a rhombus and ', '', '', ' 70o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(81, '1990', 'In the diagram above PS||RQ, |RQ| = 6.4cm and perpendicular PH = 3.2cm. Find the area of SQR.', '', '', ' 40.96cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(82, '1990', 'Which angle is equal to ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(83, '1990', 'Which triangle is equal in area to ΔVWZ', '', '', ' ΔWYZ', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(84, '1990', 'In the diagram above, PQRS s a cyclic quadrilateral, ', '', '', ' 38o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(85, '1990', 'In the diagram below, O is the center of the circle if ', '', '', ' 20o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(86, '1990', 'In the diagram above, PQ is a tangent at T to the circle ABT. ABC is a straight line and TC bisects ', '', '', ' 50o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(87, '1990', 'Which of the sketches above gives a correct method for constructed an angle of 120o at the point P?', '', '', ' I, II and III', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(88, '1990', 'Use mathematical table to evaluate (cos40o - sin30o)', '', '', '1.532', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(89, '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?', '', '', ' 0o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(90, '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', '', '', ' 26.1m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(91, '1990', 'The bearing of a point x from a point y is 074o. What is the bearing of y from x?', '', '', ' 286o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(92, '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?', '', '', ' N2,300.00', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(93, '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', '', '', ' N4,000.00', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(94, '1990', 'The table shows that the amount of money (in naira) collected through voluntary donations in a secondary school.What is the mode?', '', '', ' N15', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(95, '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?', '', '', ' N18.00', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(96, '1990', 'If a student in favour of the proposal is selected for a post, what is the probability that he is from group A?', '', '', ' 4/5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(97, '1990', 'If a student is chosen at random, what is probability that he is against the proposal?', '', '', ' 10/19', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(98, '1991', 'Simplify 11+√511+√5\\frac{1}{1 + \\sqrt{5}} - 11−√511−√5\\frac{1}{1 - \\sqrt{5}}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(99, '1991', 'The population of a village is 6538. Express this number to three significant figures.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(100, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(101, '1991', 'A headmaster contributes 7% of his income into a fund and his wife contributes 4% of her income. If the husband earns ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(102, '1991', 'Given that 1/2 log10 P = 1, find the value Of P', '', '', ' 10-1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(103, '1991', 'In the diagram above, |PQ| = |QR|, |PS| = |RS|, ', '', '', ' 55o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(104, '1991', 'Express 0.0462 in standard form', '', '', ' 4.62 x 103', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(105, '1991', 'Simplify: log6 + log2 --  log12', '', '', '4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(106, '1991', 'Find the number whose logarithm to base 10 is 2.6025', '', '', '0.0004004', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(107, '1991', 'Simplify: (1)-11/2/4', '', '', '8', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(108, '1991', 'For what value of y is the expression (y + 2)/y2 - 3y- 10 undefined?', '', '', ' y = 10', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(109, '1991', 'Factorize 3a2 - 11a + 6', '', '', ' (2a-3)(a + 2)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(110, '1991', 'Solve the equation: 3a + 10 = a2', '', '', ' a = 5 or a = -2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(111, '1991', 'Simplify 3x+152y+6xy3x+152y+6xy\\frac{3}{x} + \\frac{15}{2y} + \\frac{6}{xy}', '', '', ' 42y−5x42y−5x\\frac{4}{2y - 5x}', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(112, '1991', 'Simplify: 1/4(2n - 2n+2)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(113, '1991', 'Find the equation whose roots are -2/3 and -1/4', '', '', ' x2 - 11/12x - 2 = 0', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(114, '1991', 'Solve: 6(x - 4) + 3(x + 7) = 3', '', '', ' o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(115, '1991', 'If 2x + y = 7 and 3x - 2y = 3, by how much is 7x greater than 10?', '', '', '17', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(116, '1991', 'A car is travelling at an average speed of 80km/hr. Its speed in meters per second (m/s) is', '', '', ' 1333.3m/s', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(117, '1991', 'Mrs. Kofi sold an article for C7.50 instead of C12.75. Calculate her percentage of error, correct to one decimal place.', '', '', '0.014', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(118, '1991', 'Find the area of the enclosed region, PXROY correct to the nearest whole number.', '', '', ' 385cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(119, '1991', 'Find the perimeter of the region.', '', '', ' 66cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(120, '1991', 'The shaded portion shows the outer boundary of the half plane defined by the inequality', '', '', ' 4x < 6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(121, '1991', 'Find the coordinates of point B.', '', '', ' (11/2, 0)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(122, '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.', '', '', ' 2a + 4d', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(123, '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,', '', '', '90', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(124, '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 ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(125, '1991', 'The graph above is a sketch of', '', '', ' y = 2cos x', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(126, '1991', 'Given that sin 9 = -0.9063, where O ≤≤\\leq θθ\\theta o ≤≤\\leq 270o.Find θθ\\theta.', '', '', ' 265o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(127, '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.', '', '', ' √3/25 m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(128, '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.', '', '', ' √3√3\\sqrt{3}/13m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(129, '1991', 'In the diagram above, ATR is a tangent at the point T; to the circle centre O, if ', '', '', ' 65o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(130, '1991', 'P=(2, 1,3, 9, 1/2)Q=(1,21/2,3, 7)and R=(5, 4, 21/2)Find P', '', '', ' (1/2, 1, 2, 21/2, 3, 4, 5, 7, 9)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(131, '1991', 'P=(2, 1,3, 9, 1/2)Q=(1,21/2,3, 7)andR=(5, 4, 21/2)Find P∩Q∩R', '', '', ' (5,7,9)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(132, '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?', '', '', '50', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(133, '1991', 'Which of the following is not a measure ofDispersion?', '', '', ' Standard deviation', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(134, '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', '', '', '3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(135, '1991', 'Find the mean of the distribution.', '', '', '5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(136, '1991', 'Find the mode of the distribution.', '', '', '2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(137, '1991', 'Find the median of the distribution.', '', '', '4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(138, '1991', 'If events X and Y are mutually exclusive, .P(X) = 1/3 and P(Y) = 2/5,P(X∩Y) is', '', '', '1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(139, '1991', 'If events X and Y are mutually exclusive, .P(X) = 1/3 and P(Y) = 2/5,P(X', '', '', '1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(140, '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?', '', '', ' 3/10', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(141, '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?', '', '', ' 3/4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(142, '1991', 'Which of the following about a rhombus may notBe true?', '', '', ' Opposite angles are equal', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(143, '1991', 'The angles of a pentagon are xo, 2xo (x + 6O) o,(X + 10) o, (x -1O) o. Find the value of x', '', '', '90', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(144, '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?', '', '', '12', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(145, '1991', 'In the diagram above, O is the center of the circle, |SQ| = |QR| and ', '', '', ' 68o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(146, '1991', 'Find the area of an equivalent triangle of side 16cm', '', '', ' 128cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(147, '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.', '', '', ' 4:9', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(148, '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.', '', '', ' 120cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(149, '1991', 'In the diagram above , |AD| = 10cm, |DC| = 8cm and |CF| = 15cm.Which of the following is correct?', '', '', ' Area DABO = Area CFEO', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(150, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(151, '1992', 'What must be added to expression x2−18xx2−18xx^2 - 18x to make a perfect square?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(152, '1992', 'The area of a parallelogram is 513cm22^2 and the height is 19cm, calculate the base.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(153, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(154, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(155, '1992', 'Let U = (1, 2, 3, 4), P = (2, 3) and Q = (2, 4). What is (P∩Q)\'?', '', '', ' (1, 4)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(156, '1992', 'Simplify (3/4 + 1/3) x 41/3 + 31/4', '', '', ' 13/9', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(157, '1992', 'If x varies over the set of real numbers, which of', '', '', ' x≥2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(158, '1992', 'Convert 77 to a number in base two', '', '', '10011', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(159, '1992', 'The nth term of a sequence is given by 3.2n+2Write down the first three terms of the sequence.', '', '', ' 2/3, 3, 1/3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(160, '1992', 'Simplify: (16/81) 1/4', '', '', ' -4/3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(161, '1992', 'Evaluate log1025 + log1032 - log108', '', '', '490', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(162, '1992', 'Factorize the expression 2y2 + xy - 3x2', '', '', ' (X ', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(163, '1992', 'Construct a quadratic equation whose roots are-1/2 and 2.', '', '', ' 2x2-3x-2=0', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(164, '1992', 'Write a single fraction1/1 - x +2/1 + x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(165, '1992', 'Solve the equationm/3 +1/2 =3/4 +m/4', '', '', '4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(166, '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.', '', '', ' 16/10cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(167, '1992', 'The curved surface area of a cylindrical tin is704cm2. Calculate the height when the radius is8cm. ', '', '', ' 32cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(168, '1992', 'The volume of a cone of height 9cm is 1848cm', '', '', ' 196cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(169, '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. ', '', '', ' 6 1/6cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(170, '1992', 'In the diagram above PQT is a tangent to the circle QRS at Q. Angle QTR = 48o and ', '', '', ' 30o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(171, '1992', 'In the diagram above, O is the center of the circle and ', '', '', ' 54o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(172, '1992', 'In the diagram above, TR = TS and ', '', '', '150', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(173, '1992', 'In the diagram above, O is the center of the circle PQRS and ', '', '', ' 288o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(174, '1992', 'In the diagram above, O is the center of the circle QOR is a diameter and ', '', '', ' 147o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(175, '1992', 'In the diagram above, ML//PQ and NP//QR, if ', '', '', ' 55o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(176, '1992', 'The angles marked in the diagram above are measured in degrees. Find x.', '', '', ' 48o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(177, '1992', 'Find the value of t in the diagram above.', '', '', ' 7.0cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(178, '1992', 'A regular polygon has each of its exterior angles as 18o. How many sides has the polygon', '', '', '24', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(179, '1992', 'In the diagram above, PQT is an isosceles triangle.|PQ| = |QT|, ', '', '', ' 75o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(180, '1992', 'Sin 60o has the same value as I. Sin 120o II. cos 240o III. -sin 150o IV. cos 210o V. sin 240o', '', '', ' IV and V only', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(181, '1992', 'The value of sin 210o is', '', '', ' √3/2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(182, '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.', '', '', ' 10m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(183, '1992', 'Points X and Y are respectively 12m Nonh and5m of point Z. Calculate XY', '', '', ' 18m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(184, '1992', 'Find the median of the following set of scores:65, 72, 55, 48, 78', '', '', '72', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(185, '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?', '', '', '20', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(186, '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', '', '', '6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(187, '1992', 'The data below shows the frequency distribution of marks scored by a group of students in a class test.Find the mean mark.', '', '', '3.8', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(188, '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.', '', '', ' 72o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(189, '1992', 'The table above shows the scores of 15 students in a Physics test.How many students scored at least 5?', '', '', '14', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(190, '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?', '', '', ' 7/10', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(191, '1992', 'What is the probability of throwing a number greater than 2 with a single fair die', '', '', ' 5/6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(192, '1992', 'A fair die is rolled once. What is the probability ofObtaining 4 or 6?', '', '', ' 2/3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(193, '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?', '', '', ' 5/243', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(194, '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?', '', '', ' 1/4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(195, '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.', '', '', ' 3/4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(196, '1993', 'Simplify 1p1p\\frac{1}{p} - 1q1q\\frac{1}{q} + pqpq\\frac{p}{q} - qpqp\\frac{q}{p}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(197, '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.', '', '', '-1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(198, '1993', 'S = (1, 2, 3, 4, 5, 6), T = (2,4,5,7) and R = (1,4, 5), and (S∩T) ', '', '', ' (1, 2, 3, 4, 5)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(199, '1993', 'Simplify: 3/4 + 11/4 x (11/2-2/3)', '', '', ' 18/25', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(200, '1993', 'Solve the inequality: 3m + 3 > 9', '', '', ' m>12', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(201, '1993', 'Convert 89ten to a number in base two.', '', '', '11001', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(202, '1993', 'A stick of length 1.75m was measured by a boy as 1.80m. Find the percentage error in his measurement', '', '', ' 284/7%.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(203, '1993', 'Simplify:4-1/2 x 163/4/41/2', '', '', '4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(204, '1993', 'Simplify:log√27/log81', '', '', '6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(205, '1993', 'Factorize the expression 2s2 - 3st - 2t2.', '', '', ' (2s + t)(s + 2t)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(206, '1993', 'Solve the equation x2 - 2x - 3 = 0', '', '', ' (-1, 3).', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(207, '1993', 'Write as a single fraction5/6r -3/4r', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(208, '1993', 'Factorize 2x2 - 21x + 45', '', '', ' (2x - 9)(x + 5)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(209, '1993', 'Solve the simultaneous equations y = 3x; 4y - 5x =14', '', '', ' -1,-3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(210, '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 ', '', '', ' 95cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(211, '1993', 'Calculate the total surface area of a cone of height 12cm and base radius 5cm. ', '', '', ' 361 3/7cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(212, '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.', '', '', ' 445.5cm3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(213, '1993', 'The area and a diagonal of a rhombus are 60cm and 12cm respectively. Calculate the length of the other diagonal.', '', '', ' 15cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(214, '1993', 'The angle of a sector of a circle radius 10.5cm is 120o. Find the perimeter of the sector ', '', '', ' 115.5cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(215, '1993', 'In the diagram, PQR is a tangent to the circle QST at Q. If |QT| = |ST| and ', '', '', ' 73o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(216, '1993', 'The sum of an interior angles of a regular polygon is 30 right angles. How many sides has the polygon?', '', '', ' 15 sides', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(217, '1993', 'In the diagram above, |QR| = 12cm and |QS| = 10cm. If ', '', '', ' 6.6cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(218, '1993', 'Two chords PQ and RS of a circle when produced meet at K. If ', '', '', ' 149o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(219, '1993', 'In the diagram above, QRS is a straight line, QP//RT, PRQ = 56o, ', '', '', '124', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(220, '1993', 'Simplify2.25/0.015 leaving your answer in standard form', '', '', ' 1.5 x 102', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(221, '1993', 'State the fifth and seventh terms of the sequence -2, -3, -41/2 ...........', '', '', ' -21/8, 32/618', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(222, '1993', 'If x is a rational number, which of the following is represented on the number line?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(223, '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?', '', '', ' 240km', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(224, '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?', '', '', ' 84km', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(225, '1993', 'Given that tan x = 5/12, what is the value of sin x + cos x ?', '', '', ' 5/12', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(226, '1993', 'Cos 75o has the same value as', '', '', ' -sin 255o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(227, '1993', 'If sin x = 12/13, where 0o< x < 90o, find the value of 1-cos2x', '', '', ' 8/13', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(228, '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.', '', '', ' 60cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(229, '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,', '', '', ' 500m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(230, '1993', 'Find the median of the following set of numbers: 28, 29, 39, 38, 33, 37, 26, 20, 15, 25', '', '', '28', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(231, '1993', 'What is A∩B in the diagram above?', '', '', ' (6,4,7)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(232, '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', '', '', ' (9,5)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(233, '1993', 'The table above shows the scores of a group of 40 students in a physics test.What is the mean of the distribution?', '', '', '5.2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(234, '1993', 'Find the median of the set of numbers 12, 15, 13, 14, 12, 12.', '', '', '14', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(235, '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', '', '', ' 54o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(236, '1993', 'How many students took the examination?', '', '', '24', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(237, '1993', 'How many students scored less than 7 marks?', '', '', '25', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(238, '1993', 'What is the probability that an integer selected from the set of integers (20, 21, ...., 30) is a prime number', '', '', ' 2/3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(239, '1993', 'A fair die is rolled once. What is the probability of obtaining a number less than 3?', '', '', ' 5/6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(240, '1993', 'What is the probability of having an even number in a single toss of a fair die?', '', '', ' 5/6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(241, '1993', 'What is the probability that the total sum of seven would appear in toss of a fair die?', '', '', '1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(242, '1993', 'A die is rolled 200 times the outcomes obtained are shown in the table below. Find the probability of obtaining 2.', '', '', '0.2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(243, '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 ?', '', '', '0.725', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(244, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(245, '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', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(246, '1994', 'If sinθθ \\theta  = K find tanθθ \\theta , 0o ≤≤ \\leq  θθ \\theta  ≤≤ \\leq  90o', '', '', ' k√k2−1kk2−1 \\frac{k}{\\sqrt{ k^2 - 1}} ', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(247, '1994', 'Simplify: (21/3) / (22/3) x (11/7)', '', '', '4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(248, '1994', 'Which of the following is equal to 7212572125 \\frac{72}{125} ', '', '', ' 22×32×425222×32×4252 \\frac{2^2 \\times 3^2 \\times 4^2}{5^2} ', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(249, '1994', 'Express in 8.750.0258.750.025 \\frac{8.75}{0.025} standard form', '', '', ' 3.5 x 103', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(250, '1994', 'Evaluate 271316−14271316−14 \\frac{27^{\\frac{1}{3}}}{16^{-\\frac{1}{4}}} ', '', '', '2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(251, '1994', 'Simplify: 165/4 x 2-3 x 30', '', '', '20', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(252, '1994', 'simplify; 2log36 + log312 - log316', '', '', ' 4 - log32', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(253, '1994', 'What is the number whose logarithm to base 10Is 3.4771?', '', '', '0.0003', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(254, '1994', 'A house bought for N100,000 was later auctioned for N80.000. Find the loss percent.', '', '', '0.6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(255, '1994', 'A string is 4.8m. A boy measured it to be 4.95m. Find the percentage error.', '', '', '0.25', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(256, '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.', '', '', '24', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(257, '1994', 'E = (integers 20), P = (multiples of 3), Q = (multiples of 4), what are the elements of P\'∩Q?', '', '', ' (3, 4, 6, 8, 9, 12, 15, 16, 18, 20)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(258, '1994', 'Given that 2p - m = 6 and 2p + 4m = 1, find the value of (4p + 3m).', '', '', '9', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(259, '1994', 'Which of the following is a point on the curve y = x2 -4x + 7?', '', '', ' (3,2)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(260, '1994', 'If 8x- 4 = 6x- 10, find the value of 5x,', '', '', '7', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(261, '1994', 'For what value of x is the expressionx2 + 15x + 50/x - 5 not defined ?', '', '', '10', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(262, '1994', 'In the graph above, the gradient of the curve at the point P is', '', '', '113', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(263, '1994', 'What is the equation of the line PQ?', '', '', ' y = 2x - 3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(264, '1994', 'Which of the following equations can be solved by the points of intersection P and Q of the curve and the line PQ?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(265, '1994', 'Which of the following is not a factors of 2p2 - 2?', '', '', ' 2p + 1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(266, '1994', 'Find the quadratic equation whose roots are 3 and 2/3.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(267, '1994', 'Which of the following is a root of the equation x2 +6x = 0?', '', '', ' It does not have any root.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(268, '1994', 'Factorise: 6x2 + 7xy - 5y2', '', '', ' (2x + y)(3x - 5y)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(269, '1994', 'Solve the equation log8x - 4log8x = 2', '', '', '4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(270, '1994', 'The angle subtended at the centre by a chord of a circle radius 6cm is 120°', '', '', ' 6√l3cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(271, '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)', '', '', ' 10cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(272, '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 ', '', '', ' 3,200km', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(273, '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. ', '', '', ' 110cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(274, '1995', 'Find (1012)2, expressing the answer in base 2.', '', '', '10110', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(275, '1995', 'If three children shares N10.50 among themselves in ratio 6:7:8, how much is the largest share?', '', '', ' N5.00', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(276, '1995', 'Express 0.000834 in standard form', '', '', ' 8.34 x 106', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(277, '1995', 'Given that log2a = log84, find a', '', '', '23', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(278, '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?', '', '', ' N200.00', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(279, '1995', 'Find the nth term Un of the A.P., 11, 4, -3,....... .', '', '', ' Un= 17-7n', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(280, '1995', 'lf 16/9 , x, 1, y are in Geometric Progression (GP), find the product of x and y.', '', '', ' 16/6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(281, '1995', 'If R = ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(282, '1995', 'Find the values of x for which the expression is underlined;6x - 1/x2 + 4x - 5', '', '', ' +4 -1', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(283, '1995', 'Which of the following could be the inequality illustrated in the sketch graph above?', '', '', ' y≥3x+2.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(284, '1995', 'Solve the inequality: 1/3(2x - 1) 5', '', '', ' x < 16', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(285, '1995', 'What is the smaller value  of x for which x2 - 3x + 2=O?', '', '', '5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(286, '1995', 'Factorize the expression x(a - c) + y(c - a)', '', '', ' (a - c)(x + y)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(287, '1995', 'If y = 1/x and x= 3 when y=4, find y when x=2', '', '', '21', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(288, '1995', 'Solve the equation 3x2 + 25x -18 = 0', '', '', ' 2/3, 9.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(289, '1995', 'Solve the equation (x +2)(x - 7) = 0', '', '', ' x= -5or -2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(290, '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', '', '', ' 31/2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(291, '1995', 'Use the graph of y = 3x2 + x - 7 above to answer the question.What is the minimum value of y?', '', '', '2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(292, '1995', 'Use the graph of y = 3x2 + x - 7 above to answer the question.Find the roots of the equation y=3x2 + x - 7', '', '', ' 2.4 and -2.0', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(293, '1995', 'In the diagram above. |AB| = 12cm, |AE| = 8cm, |DCl = 9cm and AB||DC. Calculate |EC|.', '', '', ' 6cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(294, '1995', 'The diagonals AC and BD of a rhombus ABCD are 16cm and 12cm long respectively. Calculate the area of the rhombus.', '', '', ' 96cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(295, '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? ', '', '', ' 375000 litres', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(296, '1995', 'A cylindrical container, closed at both ends, has a radius of 7cm and height 5cm ', '', '', ' 770cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(297, '1995', 'Find the total surface area of solid circular cone with base radius 3cm and slant height 4cm. ', '', '', ' 88cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(298, '1995', 'A hollow sphere has a volume of kcm3 and a surface area of kcm2. Calculate the diameter of the sphere.', '', '', ' More information is needed', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(299, '1995', 'The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone.', '', '', ' 30cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(300, '1995', 'The positions of two countries P and Q are (15oN, 12oE) and (65oN, 12oE) respectively. What is the difference in latitude?', '', '', ' 24o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(301, '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', '', '', ' 13 3/5cm,', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(302, '1995', 'In the diagram above; O is the centre of the circle and |BD| = |DC|. If ', '', '', ' 40o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(303, '1995', 'In the in diagram above, AO is perpendicular to OB. Find x.', '', '', ' 38.6o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(304, '1995', 'In the diagram above, PQ is parallel to TU, ', '', '', ' 96o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(305, '1995', 'In the diagram above, AB//CD, the bisector of ', '', '', ' 90o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(306, '1995', 'In the diagram above, AB//CD. What is the size of the angle marked x?', '', '', ' 52o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(307, '1995', 'The locus of a point which is equidistant from two given fixed points is the', '', '', ' a line making an acute angle with the line joining the two points', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(308, '1995', 'In the diagram above, the value of angles b + c is', '', '', ' do', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(309, '1995', 'Which of the following angles is an exterior angle of a regular polygon?', '', '', ' 72o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(310, '1995', 'In ΔABC above, BC is produced to D, /AB/ = /AC/ and ', '', '', ' 115o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(311, '1995', 'Without using tables, find the value of sin20', '', '', '-2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(312, '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.', '', '', ' 5m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(313, '1995', 'What is the mode of the numbers 8, 10, 9, 9, 10, 8, 11, B, 10, 9, 8 and 14?', '', '', '14', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(314, '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.', '', '', '2.56', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(315, '1995', 'Find the median of the following numbers 2.64, 2.50, 2.72, 2.91 and 2.35.', '', '', '2.35', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(316, '1995', 'Two fair dice are tossed together once. Find the probability that the sum of the outcome is at least 10.', '', '', ' 5/18', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(317, '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?', '', '', ' 11/13', 'None', '', 'WAEC-PK-1', 'WAEC-PHY');
INSERT INTO `labelling` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`) VALUES
(318, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(319, '1996', 'Find the 9th term of the arithmetic progression 18, 12, 6, 0, -6, ...', '', '', '54', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(320, '1996', 'The 6th term of a G.P is -2 and its first term is 18. What is the common ratio?', '', '', '3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(321, '1996', 'Convert the decimal number 89 to a binary number', '', '', '1011001', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(322, '1996', 'simplify  (21/6 -  12/3) / 22/3', '', '', '10.4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(323, '1996', 'Simplify 56x-4 / 14x-8', '', '', ' 4x-4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(324, '1996', 'Simplufy Log104 + Log1025', '', '', '5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(325, '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?', '', '', '0.001', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(326, '1996', 'Expand (2x - 5)(x - 3)', '', '', ' 2x2 - 6x + 15', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(327, '1996', 'Simplify5/x - y -4/y - x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(328, '1996', 'If 3p - q = 6 and 2p + 3q = 4, find q', '', '', ' 33/7', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(329, '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/3p2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(330, '1996', 'If x is a real number which of the following is more illustrated on the number line?', '', '', ' -2 ≤ x < 4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(331, '1996', 'Solve the equation4/a +1/5a = 3', '', '', ' 1/3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(332, '1996', 'Make p the subject if formula y =a + p/a - p', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(333, '1996', 'Factorize 32x3 - 8xy2', '', '', ' 4(2x + y)(4x - y)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(334, '1996', 'The roots of a quadratic equation are -1/4 and 3. The quadratic equation is', '', '', ' 3x2 - 11x + 3 = 0', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(335, '1996', 'The graph of 2y = 5x2 - 3x2 - 2 cuts the y axis at the point', '', '', ' (0, 1)', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(336, '1996', 'In the diagram above, O is the center of the circle of radius 3.5cm, ', '', '', ' 71/3cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(337, '1996', 'If the hypotenuse of a right-angle isosceles triangle is 2, what is the length of each of the other side?', '', '', ' √3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(338, '1996', 'Find, correct to 1 decimal place, the volume of cylinder of height 8cm and base radius 3cm. ', '', '', ' 150.9cm3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(339, '1996', 'One side of a rectangle is 8cm and the diagonal is 10cm. What is the area of the rectangle?', '', '', ' 24cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(340, '1996', 'The angle of a sector of a circle of radius 35cm is 288o. Find the perimeter of the sector. ', '', '', ' 44cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(341, '1996', 'How many sides has a polygon if the sum of its interior angle is 1440o?', '', '', '10', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(342, '1996', 'Each interior angle of a regular nonagon(nine sided polygon) is equal to', '', '', ' 36o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(343, '1996', 'In the diagram above, find x correct to the nearest degree.', '', '', ' 72o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(344, '1996', 'In the diagram above, TRQ is a straight line. Find p, if p = 1/3(a + b + c).', '', '', ' 150o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(345, '1996', 'Which of the following is not true? You may construct a', '', '', ' parallelogram given two adjacent sides and the diagonal joining them', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(346, '1996', 'In the diagram above, PQ is parallel to RST. /RS/ = /SQ/ = /TQ/ and ', '', '', ' 110o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(347, '1996', 'In the diagram above, /PQ/ = /PS/ and /QR/ = /SR/. Which of the following is/are true?  i. the line PR bisects ', '', '', ' I, II and III', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(348, '1996', 'In the diagram, ', '', '', ' 6cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(349, '1996', 'In the diagram above, PQ is a tangent to the circle MTN at T. What is the size of ', '', '', ' 128o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(350, '1996', 'In the diagram above, KLMN is a cyclic quadrilateral. /KL/ = /KN/, ', '', '', ' 55o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(351, '1996', 'Two angles (a + 31) and (b - 49o) are adjacent angles on a straight line. Which of the following is true', '', '', ' a + b = 80o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(352, '1996', 'The trapezium PQRS parallel to SR, ', '', '', ' 112o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(353, '1996', 'In the diagram above, AB, CD and XY are straight lines intersecting at W. Find ', '', '', ' 140o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(354, '1996', 'If sinθθ\\theta cosθθ\\theta, for 0o ≤≤\\leq θ ≤≤\\leq 360o, find the value of θθ\\theta', '', '', ' 45o, 135o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(355, '1996', 'If tan x = 2252252\\frac{2}{5}, find the value of sin x; 0 ≤≤\\leq x ≤≤\\leq 90o', '', '', ' 13/12', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(356, '1996', 'A town P is 150km from a town Q in the direction 050o. What is the bearing of Q from P?', '', '', ' 310o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(357, '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.', '', '', ' 65m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(358, '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?', '', '', '2.15', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(359, '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?', '', '', '7', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(360, '1996', 'The cumulative frequency curve may be used to find the', '', '', ' mean', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(361, '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', '', '', ' II and III only', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(362, '1996', 'What percentage of observation lie outside interquartile range of any distribution?', '', '', '0.75', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(363, '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', '', '', ' 5/48', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(364, '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?', '', '', ' 17/25', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(365, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(366, '1997', 'Express (0.0425 / 2.5)   as a fraction', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(367, '1997', 'If P = {3, 5, 6} and Q = {4, 5, 6} then P∩Q equals', '', '', ' {3, 5}', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(368, '1997', 'A and B are two sets. The number of elements in A', '', '', '7', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(369, '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.', '', '', '0.2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(370, '1997', 'Simplify log39 + log315 - log35', '', '', ' o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(371, '1997', 'Solve me equation: 2/3 (x + 5) = 1/4(5x - 3)', '', '', '7', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(372, '1997', 'Which of the following equations has its roots as 4and 5?', '', '', ' x2 - x - 20 = 0', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(373, '1997', 'Solve the equations: 4x -y = 11 5x + 2y = 4', '', '', ' x = 2, y = 3.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(374, '1997', 'Make q the subject of the relation t = √pq/r ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(375, '1997', 'P varies inversely as the square of W. When W = 4, P = 9. Find the value of P when W = 9', '', '', ' 4/3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(376, '1997', 'If x varies over the set of real numbers, which of the following is illustrated in the diagram above?', '', '', ' x ≥ 3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(377, '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.', '', '', ' 23cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(378, '1997', 'Two points P and Q are on longitude 67oW. Their latitudes differ by 90o. Calculate their distance apart in terms of ', '', '', ' 3200km/', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(379, '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', '', '', ' 300cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(380, '1997', 'Calculate the total surface area of a solid cone of slant height 15cm and base radius 8cm in terms of ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(381, '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', '', '', ' 24Ocm3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(382, '1997', 'Find the radius of a circle in which an arc of length 44cm subtends angle 200° at the centre of the circle. ', '', '', ' 124.5cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(383, '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.', '', '', ' 40o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(384, '1997', 'Which of the following is not necessarily sufficient for the construction of a Q triangle?', '', '', ' Two angles and a side.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(385, '1997', 'In the diagram, EF//QR, PE = 2cm, EQ = 4cm and FR = 6cm. Find x.', '', '', ' 6cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(386, '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', '', '', ' I and II', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(387, '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?', '', '', ' Parallelogram PQRS = Parallelogram GHRS', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(388, '1997', 'From the diagram above, which of the following is true?', '', '', ' a ', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(389, '1997', 'The interior angles of a pentagon are 126o, 114o, y, 92o and 83o. Find the value of y.', '', '', ' 125o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(390, '1997', 'Solve the inequality 3x - 8 ≥ 5x', '', '', ' x < 2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(391, '1997', 'Divide 3.6721 by 4', '', '', '1.918', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(392, '1997', 'The eleventh term of an AP, is 25 and its first term is -3. Find its common difference.', '', '', ' 24/5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(393, '1997', 'Find the common ratio in the GP: log 3, log 9, log 81 ..........', '', '', '9', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(394, '1997', 'Find the value oft for which 64/27 = (3/4)t-1', '', '', '4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(395, '1997', 'O is the centre of the circle PQRS. PR and QS intersect at T POR is a diameter, ', '', '', ' 22o.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(396, '1997', 'TR is the tangent to the circle PQR with centre O. Find the size of ', '', '', ' 118o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(397, '1997', 'If two triangles are similar, which of the following is true? Their', '', '', ' perimeters are equal', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(398, '1997', 'Which of the following is not necessarily true of aRectangle?', '', '', ' Each diagonal divides the rectangle into two congruent triangles', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(399, '1997', 'A chord is 5cm from the centre of a circle of diameter 26cm. Find the length of the chord', '', '', ' 51.1cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(400, '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?', '', '', ' 27m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(401, '1997', 'Express the true bearing of 250o as a compass bearing', '', '', ' S70oE', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(402, '1997', 'Cos 65o has the same value as', '', '', ' Cos 295o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(403, '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.', '', '', ' 53o.', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(404, '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?', '', '', ' P', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(405, '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.', '', '', ' 4/25', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(406, '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?', '', '', ' 1/6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(407, '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?', '', '', ' 3/14', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(408, '1998', 'In the venn diagram, the shaded region is', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(409, '1998', 'A chord of circle radius 26cm is 10cm from the centre of the circle. Calculate the length of the chord.', '', '', ' 48cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(410, '1998', 'Find the value of x in the diagram.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(411, '1998', 'Find the root of the equation 2x2 - 3x - 2 = 0', '', '', ' x = -1/2 or 2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(412, '1998', 'What value of k makes the given expression a perfect square ? m2 - 8m + k = 0', '', '', '64', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(413, '1998', 'If log10q = 2.7078, what is q?', '', '', '51.02', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(414, '1998', 'Simplify 0.663954 + 0.003 giving your answer correct to two signifiicant figures', '', '', '21', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(415, '1998', 'If log10a = 4; what is a?', '', '', '10000', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(416, '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?', '', '', ' 4.788m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(417, '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?', '', '', ' 1700m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(418, '1998', 'Convert 35 to a number in base two', '', '', ' 110001two', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(419, '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, 0, 6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(420, '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', '', '', '0.393', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(421, '1998', 'Simplify 823', '', '', '4', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(422, '1998', 'Solve the equation 5x2 - 4x - 1 = 0', '', '', ' -1, 5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(423, '1998', 'p and q are two positive numbers such that p > 2q. Which one of the following statements is not true?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(424, '1998', 'For what value of x is the expressionx - 5/x2 - 2x - 3 not defined?', '', '', ' 1, -3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(425, '1998', 'Make S the subject of the formula: V=K√T−SV=K√T−SV = \\frac{K}{\\sqrt{T-S}}', '', '', ' T−KV2=ST-\\frac{K}{V^2} = S', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(426, '1998', 'Find the equation whose roots are 23and−14\\frac{2}{3}and \\frac{-1}{4}', '', '', ' 12x2+11x+2=012x^2+11x+2=0', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(427, '1998', 'Find (X-Y) if 4x - 3y = 7 and 3x - 2y = 5', '', '', '-3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(428, '1998', 'Solve the inequality: (y−3)<y3(y−3)<y3(y−3)<\\frac{y}{3}.', '', '', ' y > 0', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(429, '1998', 'If h(m+n) = m(h+r) find h in terms of m, n and r', '', '', ' h=mrnh=mrnh=\\frac{mr}{n}', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(430, '1998', 'Given that 6x−yx+2y=26x−yx+2y=2\\frac{6x-y}{x+2y}=2, find the value of xyxy\\frac{x}{y}', '', '', ' 8585\\frac{8}{5}', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(431, '1998', 'The radius of a geographical globe is 60cm. Find the length of the parallel of latitude 60oN', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(432, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(433, '1998', 'Express as a single fraction: xx−2−x+2x+3xx−2−x+2x+3\\frac{x}{x-2}-\\frac{x+2}{x+3}', '', '', ' 3x−4(x−2)(x+3)3x−4(x−2)(x+3)\\frac{3x - 4}{(x-2)(x+3)}', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(434, '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?', '', '', '0.5', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(435, '1998', 'A die with faces numbered 1 to 6 is rolled once. What is the probability of obtaining  4?', '', '', ' 2323\\frac{2}{3}', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(436, '1998', 'In the diagram above, the area of triangle ABC is 35cm2, find the value of y.', '', '', ' 70cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(437, '1998', 'The graph of the quadratic expression', '', '', ' y=x2−2x−2y=x2−2x−2y=x^2 - 2 x - 2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(438, '1998', 'The values of x when y = -1 are approximately', '', '', ' 1.6 and 1.6', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(439, '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?', '', '', ' 5656\\frac{5}{6}', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(440, '1998', 'In ', '', '', ' 1cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(441, '1998', 'In the diagram, PQ||SR. Find the value of Z.', '', '', ' 120o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(442, '1998', 'In sin(X+30)o=cos40osin(X+30)o=cos40osin(X+30)^o=cos40^o,find X', '', '', ' 90o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(443, '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', '', '', ' 38.7o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(444, '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?', '', '', ' 10√3m10√3m10\\sqrt{3}m', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(445, '1998', 'Two chords PQ and RS of a circle intersected at right angles at a point inside the circle. If ', '', '', ' 90o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(446, '1998', 'In the diagram, O is the center of the circle and the reflex angle ROS is 264o. Find ', '', '', ' 192o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(447, '1998', 'If the exterior angles of quadrilateral are yo, (y + 5)o, (y + 10)o and (y + 25)o, find y', '', '', ' 80o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(448, '1998', 'In the diagram PQ is a diameter of circle PMQN center O, if ', '', '', ' 27o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(449, '1998', 'In the diagram O is the center of circle PRQ. The radius is 3.5cm and ', '', '', ' 3.1cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(450, '1998', 'Calculate the perimeter of the trapezium PQRS.', '', '', ' 520cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(451, '1998', 'The length of an arc of a circle of radius 5cm is 4cm. Find the area of the sector', '', '', ' 20cm2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(452, '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', '', '', '750', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(453, '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?', '', '', '0.14', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(454, '1998', 'The diagram above is a rectangle. If the perimeter is 36m, find the area of the rectangle.', '', '', ' 275m2275m2275m^2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(455, '1998', 'Find the value of x in the diagram above', '', '', ' 5.6cm', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(456, '1998', 'Find the angle x in the diagram above.', '', '', ' 100o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(457, '1998', 'The diagonal and one side of a square are x and y units respectively. Find an expression for y in terms of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(458, '1998', 'Find the curved surface area of a cone of radius 3cm and slant height 7cm (take', '', '', ' 198cm2198cm^2', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(459, '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?', '', '', '144', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(460, '1998', 'Three of the angles of a hexagon are each Xo. The others are each 3Xo. Find X', '', '', ' 120o', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(461, '1998', 'Evaluate √20×(√5)3\\sqrt{20}\\times (\\sqrt{5})^3', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(462, '1998', 'If P = {3, 7, 11, 13} and Q = {2, 4, 8, 16}, which of the following is correct', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(463, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(464, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(465, '1998', 'A trader makes a loss of 15% when selling an article. Find the ratio, selling price : cost price', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(466, '1998', 'The side of a square is increased from 20cm to 21cm. Calculate the percentage increase in its area', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(467, '1998', 'Arrange in ascending order of magnitude 268,367,and259268,367,and25926', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(468, '1999', 'An interior angle of a regular polygon is 5 times each exterior angle. How many sides has the polygon?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(469, '1999', 'if y=√ax−by=√ax−by = \\sqrt{ax-b} express x in terms of y and b', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(470, '1999', 'The side of a rhombus is 10cm long, correct to the nearest whole number. Between what limits should the perimeter P lie?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(471, '1999', 'Simplify log82−log72+log74log82−log72+log74log', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(472, '1999', 'If K√28+√63−√7=0,findKK√28+√63−√7=0,findKK\\sqrt{28}+\\sqrt{63}-\\sqrt{7}=0, find \\hspace{1mm} K', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(473, '1999', 'From a set A=', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(474, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(475, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(476, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(477, '1999', 'Which of the following figures have one line of symmetry only? I. Isosceles triangle II. Rhombus III. Kite', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(478, '1999', 'In the diagram above, |XR| = |RY| = |YZ| and ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(479, '1999', 'In the diagram above, RST is a tangent to circle VSU center O ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(480, '1999', 'Calculate the value of Y in the diagram.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(481, '1999', 'In the diagram, POR is a circle with center O. ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(482, '1999', 'Given that m = -3 and n = 2 find the value of 3n2−2m3m3n2−2m3m\\frac{3n^2 - 2m^3}{m}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(483, '1999', 'Simplify 2−18m21+3m\\frac{2-18m^2}{1+3m}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(484, '1999', 'If y=√ax−by = \\sqrt{ax-b} express x in terms of y, a and b', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(485, '1999', 'Given that 81×22n−2=K,find√K81\\times 2^{2n-2} = K, find \\sqrt{K}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(486, '1999', 'Simplify 4x+1−3x−1\\frac{4}{x+1}-\\frac{3}{x-1}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(487, '1999', 'If y varies inversely as x2, how does x vary with y?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(488, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(489, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(490, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(491, '1999', 'In the diagram, PQST and QRST are parallelograms. Calculate the area of the trapezium PRST.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(492, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(493, '1999', 'Simplify 3.72 x 0.025 and express your answer in the standard form', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(494, '1999', 'Two numbers 24 and 31 are equal in value when converted to base ten. Find the equation connecting x and y', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(495, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(496, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(497, '1999', 'Water flows from a tap into cylindrical container at the rate 5', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(498, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(499, '1999', 'Which of the following pairs of inequalities is represented on the number line?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(500, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(501, '1999', 'The root of a quadratic equation in x, are -m and 2n. Find the equation', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(502, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(503, '1999', 'In the diagram, DE||BC, |AD| = x cm and |DB| = |AE| = ycm. Find |CE| in terms of x and y.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(504, '1999', 'Describe the locus L shown in the diagram below.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(505, '1999', 'Which of the following statements is true from the diagram above?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(506, '1999', 'In the diagram, O is the centre of the circle ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(507, '1999', 'The sides of a right angle triangle in ascending order of magnitude are 8cm, (x-2)cm and x cm. Find x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(508, '1999', 'In the diagram, CDE is a triangle, ABEF is cyclic quadrilateral, AB||CD, ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(509, '2000', 'Express 398753 correct to three significant figures', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(510, '2000', 'Express 719719\\frac{7}{19} as a percentage, correct to 1 decimal place.', '', '', '0.422', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(511, '2000', 'Find the missing number in the addition of the following numbers, in base seven.43211234', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(512, '2000', 'What fraction must be subtracted from the sum of 2162162\\frac{1}{6} and 3143143\\frac{1}{4}?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(513, '2000', 'Simplify (1681)−34×√10081(1681)−34×√10081\\left(\\frac{16}{81}\\right)^{-\\frac{3}{4}}\\times \\sqrt{\\frac{100}{81}}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(514, '2000', 'Which of the following numbers is perfect cube?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(515, '2000', 'If 104x=68104x=68104', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(516, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(517, '2000', 'Given that log4X=−3,log4X=−3,log', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(518, '2000', 'Given that the logarithm of a number is 1.8732, find, correct to 2 significant figures the square root of the mumber', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(519, '2000', 'A car moves at an average speed of 30kmh-1 how long does it take to cover 200 meters?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(520, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(521, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(522, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(523, '2000', 'Which of the following bearings is equivalent to S50oW?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(524, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(525, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(526, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(527, '2000', 'Calculate the standard deviation of the following marks; 2, 3, 6, 2, 5, 0, 4, 2', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(528, '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\\)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(529, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(530, '2000', 'In the diagram, PQRS is a circle center O. PQR is a diameter and ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(531, '2000', 'Each side of a regular convex polygon subtends an angle of 30o at its center. Calculate each interior angle', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(532, '2000', 'If the interior angles of hexagon are 107', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(533, '2000', 'In the diagram, POS and ROT are straight lines, OPQR is a parallelogram. |OS| = |OT| and ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(534, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(535, '2000', 'Given that \\(27^{(1+x)}=9,)\\ find x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(536, '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}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(537, '2000', 'Given that (2x + 7) is a factor of 2x2+3x−142x2+3x−142x^2 + 3x - 14, find the other factor', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(538, '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}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(539, '2000', 'For an inequality for a distance of meters which is more than 18m, but not more than 23m', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(540, '2000', 'Find the equation whose roots are -8 and 5', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(541, '2000', 'Make t the subject of formula k=m√t−prk=mt−prk = m\\sqrt{\\frac{t-p}{r}}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(542, '2000', 'Solve the equation 3y2=27y3y2=27y3y^2 = 27y', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(543, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(544, '2000', 'Given that p varies directly as q while q varies inversely as r, which of the following statements is true?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(545, '2000', 'In the diagram, PQS is a circle with center O. RST is a tangent at S and ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(546, '2000', 'A bicycle wheel of radius 42cm is rolled over a distance 66 meters. How many revolutions does it make?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(547, '2000', 'The height for a pyramid on  square base is 15cm. if the volume is 80cm^3, find the area of the square base.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(548, '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)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(549, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(550, '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 ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(551, '2000', 'In the diagram, |PQ| = |PS|, which of the following statements is true?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(552, '2000', 'The area of a circle is 38.5cm2. Find its diameter ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(553, '2000', 'Find the volume (in cm3) of the solid shown above.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(554, '2000', 'Solve the equation 3 + 5x - 2x2 = 0', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(555, '2000', 'If the simple interest on N2000 after 9 months is N60, at what rate per annum is the interest charged?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(556, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(557, '2001', 'A boy estimated his transport fare for a journey as ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(558, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(559, '2001', 'A man is four times as old as his son. The difference between their ages is 36. Find the sum of their ages', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(560, '2001', 'The variance of a given distribution is 25. What is the standard deviation?', '', '', '3', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(561, '2001', 'Which of the following correctly expresses 48 as a product of prime factors?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(562, '2001', 'Evaluate (20three)2−(11three)2(20three)2−(11three)2(20', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(563, '2001', 'Evaluate log105+log1020log105+log1020log', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(564, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(565, '2001', 'If N varies directly as M and N = 8 when M = 20 find M when N = 7', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(566, '2001', 'Evaluate 525×(23)2', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(567, '2001', 'The nth term of a sequence is 22n−12^{2n-1}. Which term of the sequence is 29?2^9?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(568, '2001', 'Evaluate 12+34of25', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(569, '2001', 'Evaluate x2+x−22x2+x−3\\frac{x^2 + x - 2}{2x^2 + x -3} when x = -1', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(570, '2001', 'Factorize 6x2+7x−206x^2 + 7x - 20', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(571, '2001', 'Simplify 2x−13−x+32\\frac{2x-1}{3}-\\frac{x+3}{2}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(572, '2001', 'If y−32<2y−13\\frac{y-3}{2} <', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(573, '2001', 'if 4m+3n4m−3n=52\\frac{4m+3n}{4m-3n}=\\frac{5}{2}, find the ratio m:n', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(574, '2001', 'The number line represents', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(575, '2001', 'If 2x2+kx−14=(x+2)(2x−7)2x^2 + kx - 14 = (x+2)(2x-7), find the value of K', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(576, '2001', 'which of the following is not quadratic expression?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(577, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(578, '2001', 'Subtract (-y + 3x + 5z) from (4y - x - 2z)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(579, '2001', 'If y', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(580, '2001', 'If 2x : (x +1) = 3:2, what is the value of x?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(581, '2001', 'The bearing S40oE is the same as', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(582, '2001', 'Given that sin P=513P = \\frac{5}{13}, where p is acute, find the value of cos p - tan p', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(583, '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|', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(584, '2001', 'Express 25o 45l in decimal (Hint 1o = 60l)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(585, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(586, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(587, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(588, '2001', 'What is the range of their age?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(589, '2001', 'What is the mode?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(590, '2001', 'How many students are there in the group?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(591, '2001', 'Which of the following is not the the size of an exterior angle of a regular polygon?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(592, '2001', 'In the diagram, PQR is a triangle.|PQ| = |PR|, |PS| = |SQ| and PRS = 50o. What is the size of ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(593, '2001', 'PQRS is a rhombus of side 16cm. The diagonal |QS| = 20cm. Calculate, correct to the nearest degree, ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(594, '2001', 'In the diagram, PQ is a diameter of the circle and ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(595, '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 ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(596, '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 ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(597, '2001', 'In the diagram, MN||PQ, |LM| = 3cm and |LP| = 4cm. If the area of ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(598, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(599, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(600, '2001', 'A solid cylinder of radius 7cm is 10cm long. Find its total surface area', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(601, '2001', 'PQRS is a trapezium in which |PS| = 9cm, |QR| = 15m, |PQ| = 2√32√32\\sqrt{3}, ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(602, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(603, '2001', 'What is the length of ¯RP¯RP\\bar{RP}?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(604, '2002', 'Simplify 35', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(605, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(606, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(607, '2002', 'The height of a night circular cone is 4cm. The radius of its base is 3cm. Find the curve surface area', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(608, '2002', 'Find the value of x in 0.5x + 2.6 = 5x + 0.35', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(609, '2002', 'If M5ten=1001011twoM5ten=1001011twoM5', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(610, '2002', 'What is the value of y at Q?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(611, '2002', 'When y=312y=312y = 3\\frac{1}{2}, what is the positive value of x?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(612, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(613, '2002', 'If log2 = 0.3010 and log2y = 1.8062, find; correct to the nearest whole number, the value of y', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(614, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(615, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(616, '2002', 'If (x + 3) varies directly as y and x = 3 when y = 12, what is the value of x when y = 8?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(617, '2002', 'From the diagram, find the bearing of Q from P.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(618, '2002', 'Find the nth term of the sequence 4, 10, 16 ,...', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(619, '2002', 'If (-3, -4) is a point on the line y = mx + 2 find the value of m.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(620, '2002', 'Which of the following is represented by the above sketch?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(621, '2002', 'In the diagram, SQ is a tangent to the circle at P, XP||YQ, ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(622, '2002', 'For what values of x is the expression 3x−24x2+9x−93x−24x2+9x−9\\frac{3x-2}{4x^2+9x-9} undefined?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(623, '2002', 'Simplify 11−x+21+x11−x+21+x\\frac{1}{1-x} + \\frac{2}{1+x}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(624, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(625, '2002', 'The base diameter of a cone is 14cm, and its volume is 462 cm3. Find its height. ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(626, '2002', 'A number is selected at random from the set Y = {18, 19, 2O, . . . 28, 29). Find the probability that the number is prime', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY');
INSERT INTO `labelling` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`) VALUES
(627, '2002', 'The median of the distribution is', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(628, '2002', 'The range of the distribution is', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(629, '2002', 'The upper quartile of the distribution is', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(630, '2002', 'In the diagram O and OI are the centres of the circles radii 15cm and 8cm respectively. If PQ = 12cm, find |OOI|.', '', '', ' no option', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(631, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(632, '2002', 'Simplify 212×8124212×8124\\frac{2^{\\frac{1}{2}}\\times 8^{\\frac{1}{2}}}{4}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(633, '2002', 'In the diagram, |SR| = |RQ| and ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(634, '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|.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(635, '2002', 'The volume of a cylinder of radius 14cm is 210cm3. What is the curved surface area of the cylinder?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(636, '2002', 'Simplify 2√3+10√3−6−323+103−6−32\\sqrt{3} + 10\\sqrt{3} - \\frac{6}{-3}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(637, '2002', 'Factorize m(2a-b)-2n(b-2a)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(638, '2002', 'If q oranges are sold for t Naira, how many oranges can be bought for p naira?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(639, '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|.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(640, '2002', 'In the diagram, calculate the value of x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(641, '2002', 'In the diagram, ¯PSand¯QTPS¯andQT¯\\bar{PS}\\hspace{1mm} and \\hspace{1mm}\\bar{QT} are two altitudes of ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(642, '2002', 'In the diagram, |QR| = 10cm, PR', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(643, '2002', 'Calculate and correct to two significant figures, the percentage error in approximating 0.375 to 0.4', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(644, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(645, '2002', 'In the diagram, QR||TPQR||TPQR||TP and W', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(646, '2002', 'In the diagram O is the center of the circle, ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(647, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(648, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(649, '2002', 'Which of the following is not a rational number?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(650, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(651, '2003', 'In the diagram, STUV is a straight line. < TSY = < UXY = 40o and < VUW = 110o. Calculate < TYW', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(652, '2003', 'Simplify (34−13)×413', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(653, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(654, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(655, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(656, '2003', 'Interpret the inequality represented on the number line.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(657, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(658, '2003', 'Simplify 4a−3−1a+34a−3−1a+3\\frac{4}{a-3}-\\frac{1}{a+3}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(659, '2003', 'Simplify 4√18√84188\\frac{4\\sqrt{18}}{\\sqrt{8}}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(660, '2003', 'In the diagram, PQ/RT /RS/ =/QS/, ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(661, '2003', 'Three men, Bedu, Bakre and Kofi shared\' N500 in the ratio 3:2: x respectively. If Bedu', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(662, '2003', 'Simplify (123)2(23)2(123)2(23)2\\left(1\\frac{2}{3}\\right)^2\\left(\\frac{2}{3}\\right)^2', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(663, '2003', 'Find the value of x which satisfies the equation5(x-7)=7-2x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(664, '2003', 'Evaluate log8log(14)log8log(14)\\frac{log8}{log\\left(\\frac{1}{4}\\right)}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(665, '2003', 'A pyramid of volume 120cm3 has a rectangular base which measures 5cm by 6cm. Calculate the height of the pyramid', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(666, '2003', 'PQRS is a cyclic quadrilateral. If ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(667, '2003', 'In the diagram, ZM is a straight line. Calculate the value of x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(668, '2003', 'Find the value of x in the equation 3x2 - 8x - 3 = 0', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(669, '2003', 'In', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(670, '2003', 'Given, that 4P45=119104P45=119104P4', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(671, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(672, '2003', 'What is the size of angle x in the diagram?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(673, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(674, '2003', 'Calculate the value of y in the diagram.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(675, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(676, '2003', 'Find the values of x for which 12x2−13x+15 \\frac{1}{2x^2 - 13x +15}  is not defined,', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(677, '2003', 'In the diagram, P', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(678, '2003', 'Evaluate (111two)2=−(101two)2(111', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(679, '2003', 'Given that x ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(680, '2003', 'If 3(1−n)9−2n=19\\frac{3^{(1-n)}}{9^{-2n}}=\\frac{1}{9} find n', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(681, '2003', 'Which of the following is/are not the interior angle(s) of a regular polygon? I.108o II. 116o III. 120o', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(682, '2003', 'In a ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(683, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(684, '2003', 'Use the Venn diagram to answer the question below.How many elements are in P∩Q?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(685, '2003', 'Use the Venn diagram to answer Question belowFind Ql∩R', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(686, '2003', 'The square root of a number is 2k. What is half of the number', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(687, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(688, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(689, '2003', 'The locus of points equidistant from two intersecting straight lines PQ and PR is', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(690, '2003', 'In the diagram, PR is a tangent at T to the circle O. Find the value of x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(691, '2003', 'Find the equation whose roots are −23−23-\\frac{2}{3} and 3', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(692, '2003', 'Evaluate Cos 45o Cos 30o - Sin 45o Sin 30o leaving the answer in surd form', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(693, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(694, '2003', 'In the diagram /PS/ = 9 cm, /OR/ = 5cm, P', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(695, '2003', 'A right circular cone is such that its radius r is twice its height h. Find its volume in terms of h', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(696, '2003', 'A man made a loss of 15% by selling an article for N595. Find the cost price of the article', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(697, '2003', 'The bearing of P from Q is x, where 270o< x < 360o. Find the bearing of Q from P.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(698, '2003', 'Which of the following is not a measure of dispersion?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(699, '2004', 'Find the average of the first four prime numbers greater than 10.', '', '', '13', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(700, '2004', 'Find the mean deviation of 6, 7, 8, 9, 10.', '', '', '10', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(701, '2004', '1. Evaluate 2022three−1122three2022three−1122three 202^2', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(702, '2004', 'If y=23five+101threey = 23', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(703, '2004', 'Solve for t in the equation 34t+13(21−t)\\frac{3}{4}t+\\frac{1}{3}(21-t) = 11,', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(704, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(705, '2004', 'In the diagram, R', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(706, '2004', 'There are m boys and 12 girls in a class. What is the probability of selecting at random a girl from the class?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(707, '2004', 'Simplify 712−(212+3)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(708, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(709, '2004', 'Find the area of a rectangle of length 4cm and whose diagonal is 6cm, (Leave your answer in surd form)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(710, '2004', 'Given that x + y = 7 and 3x-y = 5, evaluate y2−3\\frac{y}{2}-3.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(711, '2004', 'In the diagram, PDQ is the diameter of the circle centre O. Calculate ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(712, '2004', 'If (14)(2−y)\\left(\\frac{1}{4}\\right)^{(2-y)}, find y.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(713, '2004', 'Calculate the total surface area of a cupboard which measures 12cm by 10cm by 8cm', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(714, '2004', 'If xa+1+yb\\frac{x}{a+1}+\\frac{y}{b} 1. Make y the subject of the relation', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(715, '2004', 'lf logpp=rlog^p', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(716, '2004', 'Find the next two terms of the sequence1, 5, 14, 30, 50 ....,. ,', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(717, '2004', 'Each interior angle of a regular polygon is 108o. How many sides has it?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(718, '2004', 'Solve the equation 10-3x-x2 = 0', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(719, '2004', 'Find, correct to two decimal places, the mean of9, 13, 16, 17, 19, 23, 24.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(720, '2004', 'Factorise 27p2x2 - 48y2.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(721, '2004', 'What is the volume of a solid cylinder of diameter 7cm and height 7cm? (Take ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(722, '2004', 'Find the sum of the roots of the equation 2x2 + 3x - 9 = 0', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(723, '2004', 'Given that ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(724, '2004', 'In the diagram, KS is a tangent to the circle centre O at R and ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(725, '2004', 'A point X is on the bearing 342o from a point Y. What is the bearing of Y from X?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(726, '2004', 'In the diagram, O is the centre of the circle where OS//QR and ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(727, '2004', 'Given that √128+√18−√k√128+√18−√k\\sqrt{128}+\\sqrt{18}-\\sqrt{k}, find K,', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(728, '2004', 'In the diagram, PQRW is a circle. Line P, V and QR are produced to meet at M, where ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(729, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(730, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(731, '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}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(732, '2004', 'A boy walks 800m in 20 minutes. Calculate his average speed in km per hour', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(733, '2004', 'Simplify 2a+b−1a−b\\frac{2}{a+b}-\\frac{1}{a-b}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(734, '2004', 'The diagram is a circle centre O. Find the value of x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(735, '2004', 'Use the graph to answer the question below.What are the roots of the equation x2 + 3x - 4 = 0?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(736, '2004', 'The values of x when y = 3 are approximately', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(737, '2004', 'Which of the following quadratic equations has −12−12-\\frac{1}{2} and 3434\\frac{3}{4}  as its roots?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(738, '2004', 'The locus of a point which moves in a plane such that it is equidistant from two fixed points X and Y is', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(739, '2004', 'Given that P', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(740, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(741, '2004', 'The sides of two cubes are in the ratio 215. What is the ratio of their volumes?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(742, '2004', 'Given that p = 2, q = -5 and r = - 4, evaluate 3p2 - q2 - r3', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(743, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(744, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(745, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(746, '2005', 'If (x - a) is a factor of bx - ax + x2, find the other factor.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(747, '2005', 'Each of the interior angles of a regular polygon is 140o. Calculate the sum of all the interior angles of the polygon', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(748, '2005', 'In the diagram, find the size of the angle marked ao', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(749, '2005', 'Correct 0.04945 to two significant figures', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(750, '2005', 'Simplify 5√3−3√25√3−3√2\\frac{5}{\\sqrt{3}}-\\frac{3}{\\sqrt{2}}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(751, '2005', 'Evaluate, correct to the nearest whole number 712−(212+3)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(752, '2005', 'Simplify the expression log1018−log102.88+log1016log1018−log102.88+log1016log', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(753, '2005', 'Find the equation whose roots are 2 and −312-3\\frac{1}{2}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(754, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(755, '2005', 'From a point P, R is 5km due west and 12km due south. Find the distance between P and R', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(756, '2005', 'A fair die is tossed once, what is the probability of obtaining neither 5 or 2', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(757, '2005', 'In the diagram, KL//MN, ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(758, '2005', 'In the diagram, PR is a diameter, ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(759, '2005', 'Convert 101101two to a number in base ten', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(760, '2005', 'Solve the equation 27=85−x2^7 = 8^{5-x}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(761, '2005', 'expand (2x-3y)(x-5y)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(762, '2005', 'Make f the subject of the relation v=u+ftv = u + ft', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(763, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(764, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(765, '2005', 'In the diagram PQ and MN are straight lines. Find the value of x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(766, '2005', 'In the diagram, PQRS is a parallelogram and ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(767, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(768, '2005', 'What is the diameter of a circle of area 77cm2 ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(769, '2005', 'Solve the equation 2x - 3y = 22; 3x + 2y = 7', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(770, '2005', 'Solve the equation 2y−13−3y−14=1\\frac{2y-1}{3} - \\frac{3y-1}{4} = 1', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(771, '2005', 'If log9x=1.5log', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(772, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(773, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(774, '2005', 'Find the mean of the numbers 1, 3, 4, 8, 8, 4 and 7', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(775, '2005', 'What is the total surface area of a closed cylinder of height 10cm and diameter 7cm? ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(776, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(777, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(778, '2005', 'P = {3, 9, 11, 13} and Q = {3, 7, 9, 15} are subset of the universal set ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(779, '2005', 'A train moving at a uniform speed covers 36km in 21 minutes. How long does it take to cover 60km?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(780, '2005', 'The salary of a man was increased in the ratio 40:47. calculate the percentage increase in the salary', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(781, '2005', 'A regular polygon has 9 sides. What is the size of one of its exterior angles?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(782, '2005', 'Simplify: 23xy−3yz\\frac{2}{3xy} - \\frac{3}{yz}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(783, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(784, '2005', 'For what values of y is the expression 6y−1y2−y−6\\frac{6y-1}{y^2 - y-6}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(785, '2005', 'What are the roots of the equation?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(786, '2005', 'What is the equation of the curve?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(787, '2005', 'In the diagram PQRS is a circle, |PT| = |QT| and ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(788, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(789, '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 ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(790, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(791, '2005', 'Ladi sold  a car for N84,000 at a loss of 4%. How much did ladi buy the car', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(792, '2005', 'The monthly salary of a man increased from N2,700 to N3,200. Find the percentage increase', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(793, '2005', 'In the diagram, O is the center of the circle, ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(794, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(795, '2006', 'A machine valued at ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(796, '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 ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(797, '2006', 'Evaluate (0.13)33^3correct to three significant figures', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(798, '2006', 'Simplify: 1101122', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(799, '2006', 'Simplify 2523', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(800, '2006', 'Simplify x−44−x−36x−44−x−36\\frac{x - 4}{4} - \\frac{x - 3}{6}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(801, '2006', 'Given that y = 1 - 2x4x−3\\frac{2x}{4x - 3}, find the value of x for which y is undefined', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(802, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(803, '2006', 'A fair coin is tossed three times. Find the probability of getting two heads and one tail.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(804, '2006', 'If 30% of y is equal to x, what in terms of x, is 30% of 3y?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(805, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(806, '2006', 'If tan y = 0.404, where y is acute, find cos 2y', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(807, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(808, '2006', 'x14py0.512.5x14py0.512.5\\begin{array}{c|c} x ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(809, '2006', 'Given that (2x - 1)(x + 5) = 2x2 - mx - 5, what is the value of m', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(810, '2006', 'What is the place value of 9 in the number 3.0492?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(811, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(812, '2006', 'If 2x + y = 10, and y ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(813, '2006', 'If x + y = 12 and 3x - y = 20, find the value of 2x - y', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(814, '2006', 'Which of these equations best describes the points of intersection of the curve and the line?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(815, '2006', 'If loga270 - loga10 + loga 1313\\frac{1}{3} = 2, what is the value of a?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(816, '2006', 'a conical water-jug is 7cm in diameter and 6cm deep. find the volume of water it can hold. ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(817, '2006', 'If p = ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(818, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(819, '2006', 'The wheel of a tractor has a diameter 1.4m. What distance does it cover in 100 complete revolutions? ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(820, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(821, '2006', 'The values of three angles at a point are 3y - 45o, y + 25o and yo . Find the value of y.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(822, '2006', 'A rectangular carpet 2.5m long and 2.4m wide covers 5% of a rectangular floor. Calculate the area of the floor', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(823, '2006', 'Which of the following is not a measure of centre tendency?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(824, '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?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(825, '2006', 'Simplify 205√28−2√6320528−263\\frac{20}{5\\sqrt{28} - 2 \\sqrt{63}}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(826, '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', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(827, '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.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(828, '2006', 'In the diagram, |QR| = 5cm, PQR = 60o and PSR = 45o. Find |PS|, leaving your answer in surd form.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(829, '2006', 'In the diagram, PQRSPQRS\\frac{PQ}{RS}, find xo + yo.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(830, '2006', 'In the diagram, PR is a diameter of the circle centre O. RS is a tangent at R and QPR = 58o. Find < QRS.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(831, '2006', 'In the diagram, the two circles have a common centre O. If the area of the larger circle is 100', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(832, '2006', 'In the diagram, PQR is a straight line, QRST is a parallelogram, < TPQ = 72o and < RST = 126o. What type of triangle is ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(833, '2006', 'How many pupils took the test?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(834, '2006', 'If the pass mark was 4. What percentage of the pupils failed the test?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(835, '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. ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(836, '2006', 'In the diagram what is x + y in terms of z?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(837, '2006', 'In the diagram |XY| = 12cm, |XZ| = 9cm, |ZN| = 3cm and ZY||NM, calculate |MY|.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(838, '2007', 'Evaluate (111two)2(111', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(839, '2007', 'Find the LCM of 23×3×52,2×32×5and22×32×52^{3}\\times 3\\times 5^{2}, 2\\times 3^{2}\\times 5 \\hspace{1mm}and \\hspace{1mm}2^{2}\\times 3^{2}\\times 5', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(840, '2007', 'Simplify (0.3×105)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(841, '2007', 'If p', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(842, '2007', 'Simplify 3√45−12√5+16√203\\sqrt{45}-12\\sqrt{5}+16\\sqrt{20}leaving your answer in surd form', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(843, '2007', 'Simplify3x3(3x)3\\frac{3x^{3}}{(3x)^{3}}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(844, '2007', 'N140,000 is shared between ABU, Kayode and Uche. Abu has twice as much as Kayode, and Kayode has twice as much as Uche. What is Kayode\'s share?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(845, '2007', 'I am x years old and my brother is 3 years older how old was my brother last year', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(846, '2007', 'For what value of x is the expression 2x−1x+32x−1x+3\\frac{2x-1}{x+3}not defined?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(847, '2007', 'If x =3, y = 2 and z = 4 what is the value of 3x2−2y+z3x2−2y+z3x^{2}-2y+z', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(848, '2007', 'Solve the simultaneous equation: x+y=2 and 3x-2y=1', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(849, '2007', 'If 8x+1=148x+1=148^{x+1}=\\frac{1}{4}, find x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(850, '2007', 'The area of a square field is 110.25m2. Find the cost of fencing it round at N75.00 per meter square', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(851, '2007', 'A chord of length 6cm is drawn in a circle of radius 5cm. Find the distance of the chord from the center of the circle', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(852, '2007', 'A sector of a circle of radius 14cm containing an angle 60o is folded to form a cone. Calculate the radius of the base of the cone.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(853, '2007', 'IN the diagram, |LN| = 4cm, LNM = 90o and tan y = 2/3. What is the area of the ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(854, '2007', 'Evaluate(111two)2 and leave your answer in base 2.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(855, '2007', 'Find the LCM of 23 x 3 x 52, 2 x 32 x 5 and 23 x 33 x 5', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(856, '2007', 'Simplify(0.3 x 105) ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(857, '2007', 'If p ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(858, '2007', 'Simplify 3√45−12√15+16√2045−1215+1620\\sqrt{45} - 12\\sqrt{15} + 16\\sqrt{20}, leaving your answer in surd form', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(859, '2007', 'Simplify 3x3(3x)33x3(3x)3\\frac{3x^3}{(3x)^3}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(860, '2007', 'N140,000 is shared between Abu, Kayode and Uche. Abu has twice as much as Kayode and Kayode has twice as much as Uche. What is Kayode\'sshare?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(861, '2007', 'I am x years old and my brother is 3 years older. How old was my brother last year?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(862, '2007', 'For what value of x is the expression 2x−1x+32x−1x+3\\frac{2x - 1}{x + 3} not defined?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(863, '2007', 'If x = 3, Y = 2 and z = 4, what is the value of 3x2 - 2y + z?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(864, '2007', 'Solve the simultaneous equations x + y = 2 and 3x - 2y = 1', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(865, '2007', 'If 8x-1 = 1414\\frac{1}{4}, find x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(866, '2007', 'A chord of length 6cm is drawn in a circle of radius 5cm. Find the distance of the chord from the centre of the circle.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(867, '2007', 'The area of a square field is 110.25m2. Find the cost of fencing it round at N75.00 per metre', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(868, '2007', 'A sector of a circle of radius 14cm containing an angle 60o is folded to form a cone. Calculate the radius of the base of the cone', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(869, '2007', 'Find the volume of a solid cylinder with base radius 10cm and height 14cm.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(870, '2007', 'In a , < PQR = < PRQ = 45o. which of the following statements is/are correct?  i. ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(871, '2007', 'The table above gives the distribution of the marks of a number of students in a test.Mark123456Frequency536425Mark123456Frequency536425\\begin{array}{c|c} Mark ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(872, '2007', 'If the probability of an event occurring is x, what is the probability of the event not occurring?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(873, '2007', 'The table shows the ages (in years) of twenty children chosen at random from a community. What is the mean age?Age (years)12345Number of children23564Age (years)12345Number of children23564\\begin{array}{c|c} \\text{Age (years)} ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(874, '2007', 'The table shows the ages (in years) of twenty children chosen at random from a community. What is the median of the distribution?Age (years)12345Number of children23564Age (years)12345Number of children23564\\begin{array}{c|c} \\text{Age (years)} ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(875, '2007', 'Divide the sum of 8, 6, 7, 2, 0, 4, 7, 2, 3, by their mean', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(876, '2007', 'Q is 32 km away from P on a bearing 042o and R is 25km from P on a bearing of 132o. Calculate the bearing of R from Q.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(877, '2007', 'The bearing of a point P from another point Q is 310o. If |PQ| = 200m, how far west of Q is P?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(878, '2007', 'Find the value of a if log10 a2 + log10a2 = 0.9030', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(879, '2007', 'A messenger was paid N2.50 an hour during the normal working hours and 4.00 n hour during overtime. If he received N31.00 for 10 hours work, how many hours are for overtime?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(880, '2007', 'At what rate per cent per annum will N520.00 yield a simple interest of N39.00 in three years?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(881, '2007', 'PQR is an equilateral triangle with sides 2√3cm√3cm\\sqrt{3cm}. calculate its height', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(882, '2007', 'Which of the following is a factor of 2 - x - x2?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(883, '2007', 'make w the subject of the relation a+bcwd+fa+bcwd+f\\frac{a + bc}{wd + f} = g', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(884, '2007', 'For what range of values of x is 4x - 3(2x - 1) > 1?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(885, '2007', 'Find the smallest value of k such that 22 x 32 5 x k is a perfect square', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(886, '2007', 'Expand the expression(3a - xy)(3a + xy)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(887, '2007', 'Simplify 42x−2x+xx42x−2x+xx\\frac{4}{2x} - \\frac{2x + x}{x}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(888, '2007', 'Two circles have radii 16cm and 23cm. What is the difference between their circumference? take ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(889, '2007', 'The volume of a cylinder is 1200cm3 and the area of its base is 1500cm2. Find the height of the cylinder.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(890, '2007', 'In the diagram |LN| = 4cm, LNM = 90o and tan y = 2323\\frac{2}{3}. What is the area of the ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(891, '2007', 'From the diagram, find the value of x in the diagram.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(892, '2007', 'In the diagram, |SP| = |SR| and < PRS = 50o. Calculate < PQR', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(893, '2007', 'The venn diagram shows the choice of food of a number of visitors to a canteen. If there were 35 visitors in all, find the value of x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(894, '2007', 'The Venn diagram shows the choice of food of a number of visitors to a canteen. How many people took at least two kinds of food?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(895, '2007', 'If the ratio x:y = 3:5 and y:z = 4:7, find the ratio x:y:z', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(896, '2007', 'In the diagram, |XR| = 4cm, |RZ| = 12cm, |SR| = n, |XZ| = m and SR||YZ. Find m in terms of n.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(897, '2007', 'In the diagram, O is the centre of the circle and PQ is a diameter. Triangle RSO is an equilateral triangle of side 4cm. Find the area of the shaded region.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(898, '2007', 'Find the product of 0.0409 and 0.0021 leaving your answer in the standard form', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(899, '2007', 'Convert 425 to base three numeral', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(900, '2008', 'The volume of a cube is 512cm3. Find the length of its side', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(901, '2008', 'Simplify x2−y22x2+xy−y2x2−y22x2+xy−y2\\frac{x^2 - y^2}{2x^2 + xy - y^2}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(902, '2008', 'A train travels 60km in M minutes. If its average speed is 400km per hour, find the value of M.', '', '', '7', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(903, '2008', 'If x% of 240 equals 12, find x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(904, '2008', 'Evaluate (3.2)2−(4.8)23.2+4.8(3.2)2−(4.8)23.2+4.8\\frac{(3.2)^2 - (4.8)^2}{3.2 + 4.8}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(905, '2008', 'Simplify √50+10√2\\sqrt{50} + \\frac{10}{\\sqrt{2}}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(906, '2008', 'P naira invested for 4 years at r% simple interest per annum yields 0.36 p naira interest. Find the value of r.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(907, '2008', 'A trader bought 100 tubers at 5 for N350.00. She sold them in sets of 4 for N290.00. Find her gain percent.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(908, '2008', 'If p-2g + 1 = g + 3p and p - 2 = 0, find g', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(909, '2008', 'Simplify 1x+1yx+y\\frac{\\frac{1}{x} + \\frac{1}{y}}{x + y}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(910, '2008', 'Simplify 3√27x3y93√27x3y9\\sqrt', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(911, '2008', 'Given that x = 2 and y = -14\\frac{1}{4}, evaluate x2y−2xy5\\frac{x^2y - 2xy}{5}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(912, '2008', 'Factorize 5y2 + 2ay - 3a2', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(913, '2008', 'If 4y is 9 greater than the sum of y and 3x, by how much is y greater than x?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(914, '2008', 'If p = 35√qr\\frac{3}{5} \\sqrt{\\frac{q}{r}}, express q in terms of p and r', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(915, '2008', 'PQR is a sector of a circle centre O, radius 4cm. If PQR = 30o, find, correct to 3 significant figures, the area of sector PQR. ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(916, '2008', 'The angles of a quadrilateral are (x + 10)o, 2yo, 90o and (100 - y)o, Find y in terms of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(917, '2008', 'If xo is obtuse, which of the following is true?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(918, '2008', 'If tan x = 1, evaluate sin x + cos x, leaving your answer in the surd form', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(919, '2008', 'If cos (x + 25)o = sin 45o, find the value of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(920, '2008', 'If 2n = 128, find the value of (2n - 1)(5n - 2)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(921, '2008', 'If x ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(922, '2008', 'Simplify log√8log4−log2\\frac{\\log \\sqrt{8}}{\\log 4 - \\log 2}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(923, '2008', 'An arc of a circle, radius 14cm, is 18.33cm long. Calculate to the nearest degree, the angle which the arc subtends at the centre of the circle. ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(924, '2008', 'What is the length of an edge of a cube whose total surface area is X cm2 and whose volume is X2\\frac{X}{2}cm3?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(925, '2008', 'XY is a chord of circle centre O and radius 7cm. The chord XY which is 8cm long subtends an angle of 120o at the centre of the circle. Calculate the perimeter of the minor segment. ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(926, '2008', 'If p = 12\\frac{1}{2} and 1p−1=2p+x\\frac{1}{p - 1} = \\frac{2}{p + x}, find the value of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(927, '2008', 'Find the quadratic equation whose roots are c and -c', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(928, '2008', 'Given the sets A = ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(929, '2008', 'Find the mean deviation of these numbers 10, 12, 14, 15, 17, 19.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(930, '2008', 'In the diagram, < QPR = 90o. If q2 = 25 - r2. Find the value of p.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(931, '2008', 'In the diagram, /PQ/ = /QR/ and /PR/ = /RS/ = /SP/, calculate the side of < QRS.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(932, '2008', 'In the diagram, PQRS is a rhombus. /PR/ = 10cm and /QS/ = 24cm. Calculate the perimeter of the rhombus', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(933, '2008', 'In the figure shown, PQS is a straight line. What is the value of ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(934, '2008', 'In the diagram, PQ//RS, QU//PT and < PSR = 42o. Find angle x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(935, '2008', 'In the figure /PX/ = /XQ/, PQ//YZ and XV//QR. What is the ratio of the area of XYZQ to te area of ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(936, '2008', 'In the diagram, O is the centre of the circle and PQRS is a cyclic quadrilateral. Find the value of x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(937, '2008', 'If the perimeter of ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(938, '2008', 'In the diagram, PX is a tangent to the circle and RST is an equilateral triangle. Calculate < PTS.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(939, '2008', 'In the diagram, o, o, o, o, o and RS//TU, calculate y.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(940, '2008', 'Every staff in an office owns either a Mercedes and/or a Toyota car. 20 own Mercedes, 15 own Toyota and 5 own both. How many staff are there in the office?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(941, '2009', 'Simplify: (312+413)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(942, '2009', 'If log 2 = x, log 3 = y and log 7 = z, find, in terms of x, y and z, the value of log (283283\\frac{28}{3})', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(943, '2009', 'Arrange the following numbers in descending orders of magnitude: 22three, 34five, 21six', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(944, '2009', 'Find the value to which N3000.00 will amount in 5 years at 6% per annum simple interest', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(945, '2009', 'Express the square root of 0.000144 in the standard form', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(946, '2009', 'Two sets are disjoint if', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(947, '2009', 'If 32x−23x=432x−23x=4\\frac{3}{2x} - \\frac{2}{3x} = 4, solve for x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(948, '2009', 'If (2x + 3)3 = 125, find the value of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(949, '2009', 'Factorize x2 - 2x - 3xy completely', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(950, '2009', 'The diameter of a bicycle wheel is 42cm. If the wheel makes 16 complete revolution, what will be the total distance covered by the wheel? ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(951, '2009', 'The interior angles of a pentagon are (2x + 5)o, (x + 20)o, xo, (3x - 20)o and (x + 15)o. Find the value of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(952, '2009', 'If M and N are two fixed points in a plane. Find the locus L = ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(953, '2009', 'Given that sin 60o = √32√32\\frac{\\sqrt{3}}{2} and cos 60o = 1212\\frac{1}{2}, evaluate 1−sin60o1+cos60o1−sin60o1+cos60o\\frac{1 - sin 60^o}{1 + cos 60^o}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(954, '2009', 'In an examination, Kofi scored x% in Physics, 50% in Chemistry and 70% in Biology. If his mean score for the three subjects was 55%, find x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(955, '2009', 'What is the median of the following scores: 22 35 41 63 74 82', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(956, '2009', 'Express 2.7864 x 10-3 to 2 significant figures', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(957, '2009', 'If 92x = 1313\\frac{1}{3}(27x), find x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(958, '2009', 'If 85% of x is N3230, what is the value of x?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(959, '2009', 'The capacity of a water tank is 1,800 litres. If the tank is in form of a cuboid with base 600cm by 150 cm. Find the height of the tank', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(960, '2009', 'An arc of a circle subtends an angle of 60o at the centre. If the radius of the circle is 3cm, find , in terms of ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(961, '2009', 'solve 2x+16−3x−142x+16−3x−14\\frac{2x + 1}{6} - \\frac{3x - 1}{4} = 0', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY');
INSERT INTO `labelling` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`) VALUES
(962, '2009', 'If a positive integer, list the values of x which satisfy the equation 3x - 4 < 6 and x - 1 > 0', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(963, '2009', 'If c and k are the roots of 6 - x - x2 = 0, find c + k', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(964, '2009', 'A bucket holds 10 litres of water. How many buckets of water will fill a reservoir of size 8m x 7m x 5m.(1 litre = 1000cm3)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(965, '2009', 'A box contains black, white and red identical balls. The probability of picking a black ball at random from the box is 310310\\frac{3}{10} and the probability of picking a white ball at random is 2525\\frac{2}{5}. If there are 30 balls in the box, how many of them are red?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(966, '2009', 'Simplify; 12√32−√18√21232−182\\frac{1}{2}\\sqrt{32} - \\sqrt{18}  \\sqrt{2}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(967, '2009', 'The angles of triangle are (x + 10)o, (2x - 40)o and (3x - 90)o. Which of the following accurately describes the triangle?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(968, '2009', 'Simplify (x - 3y)2 - (x + 3y)2', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(969, '2009', 'Find the quadratic equation whose roots are -1212\\frac{1}{2} and 3', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(970, '2009', 'The following is the graph of a quadratic friction, find the co-ordinates of point P.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(971, '2009', 'The following is the graph of a quadratic friction, find the value of x when y = 0.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(972, '2009', 'PQRS is a trapezuim. QR//PS, /PQ/ = 5cm, /OR/ = 6cm, /PS/ = 10cm and angle QPS = 42o. Calculate the perpendicular distance between the parallel sides', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(973, '2009', 'PQRS is a trapezium. QR//PS, /PQ/ = 5cm, /OR/ = 6cm, /PS/ = 10cm and angle QPS = 42o. Calculate, correct to the nearest cm2, the area of the trapezium (h = 3.35cm2 )', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(974, '2009', 'In the diagram, /TP/ = 12cm and it is 6cm from O, the centre of the circle, Calculate ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(975, '2009', 'In the diagram, IG is parallel to JE, JEF = 120o and FHG = 130o, find the angle marked t.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(976, '2009', 'In the diagram, \\SQ\\ = 4cm, \\PT\\ = 7cm. /TR/ = 5cm and ST//OR. If /SP/ = xcm, find the value of x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(977, '2009', 'Using the diagram, find the bearing of X from Y.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(978, '2009', 'If /XY/ = 50m, how far cast of X is Y?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(979, '2009', 'In the diagram, angle 20o is subtended at the centre of the circle, find the value of x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(980, '2009', 'The pie chart shows the distribution of 4320 students who graduated from four departments in a university. How many students graduated from the science department?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(981, '2009', 'The pie chart shows the distribution of 4320 students who graduated from four departments in a university. If a student is picked at random from the four departments, what id the probability that he is not from the education department?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(982, '2009', 'From the diagram which of the following statements are correct? i. XQ is a radius of a circle centre Q. ii. /XQ/ = /QY/. iii. /QX/ = /XY/', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(983, '2010', 'If 2 logx (33838\\frac{3}{8}) = 6, find the value of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(984, '2010', 'Simplify (1681)14', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(985, '2010', 'Solve the inequality -6(x + 3) ≤≤\\leq 4(x - 2)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(986, '2010', 'Simplify 0.000215 x 0.000028 and express your answer in standard form', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(987, '2010', 'Factorize: x + y - ax = ay', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(988, '2010', 'A car uses one litre of petrol for every 14km. If one of petrol cost N63.00, how far can the car go with N900.00 worth of petrol?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(989, '2010', 'Correct 0.002473 to 3 significant figure', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(990, '2010', 'The sum of 2 consecutive whole numbers is 5656\\frac{5}{6} of their product, find the numbers', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(991, '2010', 'A casting is made up of Copper and Zinc. If 65% of the casting is Zinc and there are 147g of Copper. What is the mass of the casting?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(992, '2010', 'Given that P = {x : 1 ≤x≤6≤x≤6\\leq x \\leq 6}, and Q = {x : 2 ≤x≤10\\leq x \\leq 10} where x is an integer. Find n(P ∩\\cap)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(993, '2010', 'The sum of 6 and one-third of x is one more than twice x, find x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(994, '2010', 'An empty rectangular tank is 250cm long and 120cm wide. If 180 litres of water is poured into the tank. Calculate the height of the water', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(995, '2010', 'Given that 5n+3252n−2\\frac{5^{n +3}}{25^{2n -2}} = 5o, find n', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(996, '2010', 'No. of pets01234No. of students845103\\begin{array}{c|c} \\text{No. of pets} ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(997, '2010', 'Simplify 2√3\\sqrt{3} - 6√3+3√27\\frac{6}{\\sqrt{3}} + \\frac{3}{\\sqrt{27}}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(998, '2010', 'If sin 3y = cos 2y and 0o ≤\\leq 90o, find the value of y', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(999, '2010', 'A rectangle has length xcm and width (x - 1)cm. If the perimeter is 16cm. Find the value of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1000, '2010', 'Given that tan x = 1, where 0o ≥\\geq x 90o, evaluate 1−sin2xcosx\\frac{1 - \\sin^2 x}{\\cos x}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1001, '2010', 'What is the length of a rectangular garden whose perimeter is 32cm and area 39cm2?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1002, '2010', 'Simplify 22+x+22−x\\frac{2}{2 + x} + \\frac{2}{2 - x}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1003, '2010', 'The sum of the exterior of an n-sided convex polygon is half the sum of its interior angle. find n', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1004, '2010', 'If y = y(2√x2+m)3N\\frac{y(2\\sqrt{x^2 + m})}{3N}, make x the subject of the formular', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1005, '2010', 'The nth term of the sequence -2, 4, -8, 16.... is given by', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1006, '2010', 'How many times, correct to the nearest whole number, will a man run round  circular track of diameter 100m to cover a distance of 1000m?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1007, '2010', 'Bola sold an article for N6,900.00 and made a profit of 15%. If he sold it for N6,600.00 he would make a', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1008, '2010', 'The mean age of R men in a club is 50 years, Two men aged 55 and 63, left the club and the mean age reduced by 1 year. Find the value of R', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1009, '2010', 'x0246y1234\\begin{array}{c|c} x ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1010, '2010', 'What is the value of x when y = 5?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1011, '2010', 'The subtraction below is in base seven. Find the missing number.5 1 6 2seven-2 6 4 4seven--------2 * 1 5--------', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1012, '2010', 'If the sum of the roots of the equation (x - p)(2x - 1) - 0 is 1, find the value of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1013, '2010', 'If x km/h = y m/s, then y =', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1014, '2010', 'The mean of the numbers 2, 5, 2x and 7 is less than or equal to 5. Find the range of the values of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1015, '2010', 'In an athletic composition, the probability that an athlete wins a 100m race is 18\\frac{1}{8} and the probability that he wins in high jump is 14\\frac{1}{4}. What is the probability that he wins only one of the events?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1016, '2010', 'In the diagram, < PSR = 220o, < SPQ = 58o and < PQR = 41o. Calculate the obtuse angle QRS.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1017, '2010', 'The bar chart shows the marks distribution in am English test. If 50% is the pass mark, how many students passed the test?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1018, '2010', 'The bar chart shows the marks distribution in am English test. What percentage of the students had marks ranging from 35 to 50?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1019, '2010', 'What is the value of m in the diagram?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1020, '2010', 'In the diagram, QR//ST, /PQ/ = /PR/ and < PST = 75o. Find the value of y.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1021, '2010', 'In the diagram, triangles HKL and HIJ are similar. Which of the following ratios is equal to LHJH\\frac{LH}{JH}?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1022, '2010', 'In the diagram, < ROS = 66o and < POQ = 3x. some construction lines are shown. Calculate the value of x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1023, '2010', 'In the diagram, O is the centre of the circle, < SQR = 60o, < SPR = y and < SOR = 3x. Find the value of (x + y).', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1024, '2010', 'The shaded portion in the diagram is the solution of', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1025, '2010', 'In the diagram, GI is a tangent to the circle at H. If EF//GI, calculate the size of ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1026, '2010', 'The diagram is a net right rectangular pyramid. Calculate the total surface area.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1027, '2010', 'The diagram shows a rectangular cardboard from which a semi-circle is cut off. Calculate the area of the remaining part.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1028, '2010', 'In the diagram, 0 is the centre of the circle. Find the value x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1029, '2010', 'In the diagram, < WOX = 60o, < YOE = 50o and < OXY = 30o. What is the bearing of x from y?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1030, '2011', 'Simplify 1025−623+31025−623+310\\frac{2}{5} - 6 \\frac{2}{3} + 3', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1031, '2011', 'Solve the inequality -6(x + 3) ≤\\leq 4(x - 2)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1032, '2011', 'If N112.00 exchanges for D14.95, calculate the value of D1.00 in naira', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1033, '2011', 'Solve for x in the equation; 35\\frac{3}{5}(2x - 1) = 14\\frac{1}{4}(5x - 3)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1034, '2011', 'Given that cos xo = 1r\\frac{1}{r}, express tan x in terms of r', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1035, '2011', 'Solve the equation; 3x - 2y = 7, x + 2y = -3', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1036, '2011', 'If a number is chosen at random from the set {x: 4 ≤x≤45\\leq x \\leq 45}. Find the probability that it is a multiple of 3 or a multiple of 4', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1037, '2011', 'One of the factors of (mn - nq - n2 + mq) is (m - n). The other factor is', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1038, '2011', 'A cylindrical container has a base radius of 14cm and height 18cm. How many litres of liquid can it hold?  correct to the nearest litre ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1039, '2011', 'A regular polygon of n sides has each exterior angle to 45o. Find the value of n', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1040, '2011', 'Esther was facing S 20o W. She turned 90o in the clock wise direction. What direction is she facing?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1041, '2011', 'The cross section section of a uniform prism is a right-angled triangle with sides 3cm. 4cm and 5cm. If its length is 10cm. Calculate the total surface area', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1042, '2011', 'From the equation whose roots are x = 12\\frac{1}{2} and -23\\frac{2}{3}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1043, '2011', 'Simplify log√27log√81\\frac{\\log \\sqrt{27}}{\\log \\sqrt{81}}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1044, '2011', 'Which of these angles can be constructed using ruler and a pair of compasses only?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1045, '2011', 'The perimeter of a sector of a circle of radius 4cm is (', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1046, '2011', 'The length of a piece of stick is 1.75m. A girl measured it as 1.80m. Find the percentage error', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1047, '2011', 'What is the value of 3 in the number 42.7531?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1048, '2011', 'The height of a cylinder is equal to its radius. If the volume is 0.216 ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1049, '2011', 'Factorize the expression: am + bn - an - bm', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1050, '2011', 'The graph represents the relation y = x2 - 3x - 3. Find the value of x for which x2 - 3x = 7.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1051, '2011', 'Simplify mn+(m−1)5n=(m−2)10nmn+(m−1)5n=(m−2)10n\\frac{m}{n} + \\frac{(m - 1)}{5n} = \\frac{(m - 2)}{10n} where n ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1052, '2011', 'If √72+√32−3√18=x√8\\sqrt{72} + \\sqrt{32} - 3 \\sqrt{18} = x \\sqrt{8}, Find the value of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1053, '2011', 'G varies directly as the square of H, If G is 4 when H is 3, find H when G = 100', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1054, '2011', 'Given that n(p) = 19, m(P ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1055, '2011', 'What must be added to (2x - 3y) to get (x 0 2y)?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1056, '2011', 'Find the smaller value of x that satisfies the equation x2 + 7x + 10 = 0', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1057, '2011', 'The perpendicular bisectors of the sides of an acute-angled triangle are drawn. Which of these statements is correct? They intersect', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1058, '2011', 'A rectangular garden measures 18.6m by 12.5m. Calculate, correct to three significant figures, the area of the garden', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1059, '2011', 'John pours 96 litres of red oil into a rectangular container with length 220cm and breadth 40cm. Calculate, correct to the nearest cm, the height of the oil in the container', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1060, '2011', 'in a quiz competition, a student answers n questions correctly and was given D(n + 50) for each question correctly answered. If he gets D600.00 altogether, how many questions did he answer correctly?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1061, '2011', 'If 27x = 9y. Find the value of xy\\frac{x}{y}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1062, '2011', 'a boy looks through a window of a building and sees a mango fruit on the ground 50m away from the foot of the building. If the window is 9m from the ground, calculate, correct to the nearest degree, the angle of depression of the mango from the window', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1063, '2011', 'The diagram shows a cyclic quadrilateral PQRS with its diagonals intersecting at K. Which of the following triangles is similar to triangle QKR?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1064, '2011', 'In the diagram, PO and OR are radii, |PQ| = |QR| and reflex o. Calculate the value x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1065, '2011', 'Find the size of the angle marked x in the diagram.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1066, '2011', 'The histogram shows the age distribution of members of a club. How many members are in the club?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1067, '2011', 'The histogram shows the age distribution of members of a club. What is their modal age?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1068, '2011', 'In the diagram, /MN/, /OP/, /QOP/ = 125o. What is the size of ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1069, '2011', 'The graph represents the relation y = x2 - 3x - 3. What is the equation of the line of symmetry of the graph?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1070, '2011', 'From the diagram, Which of the following statements are true? i. m = q ii. n = q iii. n + p = 180o iv. p + m = 180o', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1071, '2011', 'Using the cumulative frequency curve, estimate the median of the data represented on the graph.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1072, '2011', 'Using the cumulative frequency curve. What is the 80th percentile?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1073, '2011', 'The Venn diagram shows the number of students in a class who like reading(R), dancing(D) and swimming(S). How many students like dancing and swimming?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1074, '2012', 'Find the coefficient of m in the expression of (m2−112)(m+23)(\\frac{m}{2} - 1\\frac{1}{2})(m + \\frac{2}{3})', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1075, '2012', 'The volume of a cuboid is 54 cm3. If the length, width and height of the cuboid are in the ratio 2:1:2 respectively, find its total surface area', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1076, '2012', 'A side and a diagonal of a rhombus are 10cm and 12cm respectively, Find its area', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1077, '2012', 'Factorise completely: 32x2y - 3y3', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1078, '2012', 'In the diagram, MN, PQ and RS are three intersecting straight lines. Which of the following statements is/are true?  i. t = y  ii. x + y + z + m = 180°  iii. x + m + n = 180°  iv. x + n = m + z', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1079, '2012', 'The bar chart shows the frequency distribution of marks scored by students in a class test. How many students are in the class?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1080, '2012', 'The bar chart shows the frequency distribution of marks scored by students in a class test. What is the median of the distribution?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1081, '2012', '', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1082, '2012', 'The diagram is a circle of radius |QR| = 4cm. ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1083, '2012', 'Simplify 1p\\frac{1}{p} - 1q\\frac{1}{q} + pq\\frac{p}{q} - qp\\frac{q}{p}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1084, '2012', 'Express 302.10495 correct to five significant figures', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1085, '2012', 'Simplify; 3√5×4√62√2×3√2\\frac{3\\sqrt{5} \\times 4\\sqrt{6}}{2 \\sqrt{2} \\times 3\\sqrt{2}}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1086, '2012', 'In 1995, the enrollment of two schools X and Y were 1,050 and 1,190 respectively. Find the ration of the enrollments of X and Y', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1087, '2012', 'Convert 3510 to number in base 2', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1088, '2012', 'The nth term of a sequence is Tn = 5 + (n - 1)2. Evaluate T4 - T6', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1089, '2012', 'Mr. Manu travelled from Accra to Pamfokromb a distance of 720km in 8 hours. What will be his speed in m/s?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1090, '2012', 'If N2,500.00 amounted to N3,50.00 in 4 years at simple interest, find the rate at which the interest was charged', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1091, '2012', 'Solve for x in the equation; 1x+23x=13\\frac{1}{x} + \\frac{2}{3x} = \\frac{1}{3}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1092, '2012', 'Simplify: 54k2−63k+1\\frac{54k^2 - 6}{3k + 1}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1093, '2012', 'Make p the subject of the relation: q = 3pr+s23pr+s2\\frac{3p}{r} + \\frac{s}{2}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1094, '2012', 'If x + y = 2y - x + 1 = 5, find the value of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1095, '2012', 'The sum of 12 and one third of n is 1 more than twice n. Express the statement in the form of an equation', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1096, '2012', 'Solve the inequality: −m2−54≥5m12−76−m2−54≥5m12−76\\frac{-m}{2} - \\frac{5}{4} \\geq \\frac{5m}{12} - \\frac{7}{6}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1097, '2012', 'The curved surface area of a cylindrical tin is 704cm2. If the radius of its base is 8cm, find the height. ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1098, '2012', 'The lengths of the minor and major arcs 54cm and 126cm respectively. Calculate the angle of the major sector', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1099, '2012', 'If cos(x + 40)o = 0.0872, what is the value of x?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1100, '2012', 'A kite flies on a taut string of length 50m inclined at tan angle 54o to the horizontal ground. The height of the kite above the ground is', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1101, '2012', 'Given that the mean of the scores 15, 21, 17, 26, 18 and 29 is 21, calculate the standard deviation of the scores', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1102, '2012', 'A bag contains 4 red and 6 black balls of the same size. If the balls are shuffled briskly and two balls are drawn one after the other without replacement, find the probability of picking balls of different colours', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1103, '2012', 'Which of these statements about y = 8√m\\sqrt{m} is correct?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1104, '2012', 'If x + 0.4y = 3 and y = 12\\frac{1}{2}x, find the value of (x + y)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1105, '2012', 'Express 3 - ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1106, '2012', 'If p = {prime factors of 210} and Q = {prime less than 10}, find p ∩\\cap Q', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1107, '2012', 'Alfred spent 14\\frac{1}{4} of his money on food, 13\\frac{1}{3} on clothing and save the rest. If he saved N72,20.00, how much did he spend on food?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1108, '2012', 'If x and y are variables and k is a constant, which of the following describes an inverse relationship between x and y?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1109, '2012', 'In the diagram, |QR| = 10m, |SR| = 8m, < QPS = 30o, < QRP = 90o and |PS| = x, Find x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1110, '2012', 'In the diagram, O is a circle centre of the circle PQRS and < PSR = 86o. If < PQR = xo, find x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1111, '2012', 'The diagram is a circle centre O. If < SPR = 2m and < SQR = n, express m in terms of n.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1112, '2012', 'In the diagram, MQ//RS, < TUV = 70o and < RLV = 30o. Find the value of x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1113, '2012', 'The position of three ships P,Q and R at sea are illustrated in the diagram. The arrows indicated the North direction. The bearing of Q from P is 050o and < PQR = 72o. Calculate the bearing of R and Q.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1114, '2012', 'In the diagram, MN//PO, < PMN = 112o, < PNO = 129o', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1115, '2012', 'The diagram is a circle with centre P. PRST are points on the circle. Find the value of ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1116, '2012', 'In the diagram, |SR| = |QR|. o and o, find ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1117, '2012', 'The graph is that of y = 2x2 - 5x - 3. For what value of x will y be negative? For what value of x will y be negative?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1118, '2012', 'The diagram is a polygon. Find the largest of its interior angles.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1119, '2012', 'Simplify 3x+152y+6xy\\frac{3}{x} + \\frac{15}{2y} + \\frac{6}{xy}', '', '', ' 42y−5x\\frac{4}{2y - 5x}', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1120, '2013', 'In what number base is the addition 465 + 24 + 225 = 1050?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1121, '2013', 'Simplify 178×225634', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1122, '2013', 'If √50−K√8=2√250−K8=22\\sqrt{50} - K\\sqrt{8} = \\frac{2}{\\sqrt{2}}, find KKK', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1123, '2013', 'Four oranges sell for ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1124, '2013', 'Simplify: x2−y2(x+y)2+(x−y)2(3x+3y)x2−y2(x+y)2+(x−y)2(3x+3y)\\frac{x^2 - y^2}{(x + y)^2} + \\frac{(x - y)^2}{(3x + 3y)}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1125, '2013', 'If x=64x=64x = 64 and y=27,y=27,y = 27, evaluate: x12−y13y−x23x12−y13y−x23\\frac{x^{\\frac{1}{2}} - y^{\\frac{1}{3}}}{y - x^{\\frac{2}{3}}}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1126, '2013', 'A chord is 2cm from the centre of a circle. If the radius of the circle is 5cm, find the length of the chord', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1127, '2013', 'A cube and cuboid have the same base area. The volume of the cube is 64 cm3 while that of the cuboid is 80 cm3. Find the height of the cuboid', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1128, '2013', 'If sin x = 513513\\frac{5}{13} and 0° ≤≤\\leq x ≤≤\\leq 90°, find the value of (cos x - tan x)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1129, '2013', 'An object is 6m away from the base of a mast. The angle of depression of the object from the top of the mast is 50°, Find, correct to 2 decimal places, the height of the mast', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1130, '2013', 'Which of the following is not a probability of Mary scoring 85% in a mathematics test?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1131, '2013', 'If p = (y : 2y ≥≥\\geq 6) and Q = (y : y -3 ≥≥\\geq 4), where y is an integer, find p∩∩\\capQ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1132, '2013', 'Find the values of k in the equation 6k2 = 5k + 6', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1133, '2013', 'If y varies directly as the square root of (x + 1) and y = 6 when x = 3, find x when y = 9', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1134, '2013', 'The graph of the relation y = x2 + 2x + k passes through the point (2, 0). Find the values of k', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1135, '2013', 'What is the locus of the point X which moves relative to two fixed points P and M on a plane such that', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1136, '2013', 'When a number is subtracted from 2, the result equals 2 less than one-fifth of the number. Find the number', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1137, '2013', 'Express 2x+3−1x−22x+3−1x−2\\frac{2}{x + 3} - \\frac{1}{x - 2} as a simple fraction', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1138, '2013', 'Given that P = x2 + 4x - 2, Q = 2x - 1 and Q - P = 2, find x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1139, '2013', 'A pyramid has a rectangular base with dimensions 12m by 8m. If its height is 14m, calculate the volume', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1140, '2013', 'The slant height of a cone is 5cm and the radius of its base is 3cm. Find, correct to the nearest whole number, the volume of the cone. (Take ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1141, '2013', 'The distance between two towns is 50km. It is represented on a map by 5cm. Find the scale used', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1142, '2013', 'Given that (x + 2)(x2 - 3x + 2) + 2(x + 2)(x - 1) = (x + 2) M, find M', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1143, '2013', 'An open cone with base radius 28cm and perpendicular height 96cm was stretched to form sector of a circle. Calculate the arc of the sector (Take ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1144, '2013', 'In the diagram, the height of a flagpole |TF| and the length of its shadow |FL| re in the ratio 6:8. Using k as a constant of proportionality, find the shortest distance between T and L', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1145, '2013', 'the diagrams, |XZ| = |MN|, |ZY| = |MO| and |XY| = |NO|. Which of the following statements is true?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1146, '2013', 'The pie chart shows the distribution of 600 mathematics textbooks for Arts, Business, Science and Technical Classes. How many textbooks are for the technical class?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1147, '2013', 'The pie chart shows the distribution of 600 mathematics textbooks for Arts, Business, Science and Technical Classes. What percentage of the total number of textbooks belongs to science?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1148, '2013', 'Multiply 2.7 x 10-4 by 6.3 x 106 and leave your answers in standard form', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1149, '2013', 'If 9(2 - x) = 3, find x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1150, '2013', 'If Un = n(n2 + 1), evaluate U5 - U4', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1151, '2013', 'A sales boy gave a change of N68 instead of N72. Calculate his percentage error', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1152, '2013', 'If 12\\frac{1}{2}x + 2y = 3 and 32\\frac{3}{2}x and 32\\frac{3}{2}x - 2y = 1, find (x + y)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1153, '2013', 'Given that p13\\frac{1}{3} = 3√qr\\frac{3\\sqrt{q}}{r}, make q the subject of the equation', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1154, '2013', 'The bearing of Y from X is 060o and the bearing of Z from Y = 060o. Find the bearing of X from Z', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1155, '2013', 'In the diagram, PRST is a square. If |PQ| = 24cm. |QR| = 10cm and < PQR = 90o, find the perimeter of the polygon PQRST.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1156, '2013', 'In the diagram, PQRS is a rhombus and < PSQ = 35o. Calculate the size of < PRO.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1157, '2013', 'Find the value of m in the diagram.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1158, '2013', 'In the diagram, O is the centre of the circle. OM||XZ and < ZOM = 25o.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1159, '2013', 'Using the histogram, estimate the mode of distribution.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1160, '2013', 'Using the histogram, what is the median class?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1161, '2014', 'If 23x = 325, find the value of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1162, '2014', 'Simplify: √12(√48−√3)12(48−3)\\sqrt{12} (\\sqrt{48} - \\sqrt{3})', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1163, '2014', 'Given that x > y and 3 < y, which of the following is/are true? i. y > 3 ii. x < 3 iii. x > y > 3', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1164, '2014', 'Three quarters of a number added to two and a half of the number gives 13. Find the number', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1165, '2014', 'Find the truth set of the equation x2 = 3(2x + 9)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1166, '2014', 'The coordinates of points P and Q are (4, 3) and (2, -1) respectively. Find the shortest distance between P and Q.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1167, '2014', 'Make u the subject of formula, E = m2gm2g\\frac{m}{2g}(v2 - u2)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1168, '2014', 'If x varies inversely as y and y varies directly as z, what is the relationship between x and z?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1169, '2014', 'Find the gradient of the line joining the points (2, -3) and 2, 5)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1170, '2014', 'The area of a sector a circle with diameter 12cm is 66cm2. If the sector is folded to form a cone, calculate the radius of the base of the cone ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1171, '2014', 'A chord, 7cm long, is drawn in a circle with radius 3.7cm. Calculate the distance of the chord from the centre of the circle', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1172, '2014', 'Which of the following is a measure of dispersion?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1173, '2014', 'A ship sails x km due east to a point E and continues x km due north to F. Find the bearing the bearing of f from the starting point.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1174, '2014', 'A box contains 13 currency notes, all of which are either ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1175, '2014', 'If x : y = 3 : 2 and y : z = 5 : 4, find the value of x in the ratio x : y : z', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1176, '2014', 'Given that cos x = 12131213\\frac{12}{13}, evaluate 1−tanxtanx1−tanxtanx\\frac{1 - \\tan x}{\\tan x}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1177, '2014', 'Approximate 0.0033780 to 3 significant figures', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1178, '2014', 'Simplify 82×4n+122n×1682×4n+122n×16\\frac{8^2 \\times 4^n + 1}{2^{2n} \\times 16}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1179, '2014', 'If 2x−3−3x−2\\frac{2}{x - 3} - \\frac{3}{x - 2} is equal to p(x−3)(x−2)\\frac{p}{(x - 3)(x - 2)}, find p', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1180, '2014', 'Subtract 12\\frac{1}{2}(a - b - c) from the sum of 12\\frac{1}{2}(a - b + c) and 12\\frac{1}{2}(a + b - c)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1181, '2014', 'A man\'s eye level is 1.7m above the horizontal ground and 13m from a vertical pole. If the pole is 8.3m high, calculate, correct to the nearest degree, the angle of elevation of the top of the pole from his eyes.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1182, '2014', 'A chord subtends an angle of 120° at the centre of a circle of radius 3.5cm. Find the perimeter of the minor sector containing the chord, ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1183, '2014', 'In parallelogram PQRS, QR is produced to M such that |QR| = |RM|. What fraction of the area of PQMS is the area of PRMS?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1184, '2014', 'In a cumulative frequency graph, the lower quartile is 18 years while the 60th percentile is 48 years. What percentage of the distribution is at most 18 years or greater than 48 years?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1185, '2014', 'If a number is selected at random from each of the sets p = {1, 2, 3} and Q = {2, 3, 5}, find the probability that the sum of the numbers is prime', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1186, '2014', 'If log 5.957 = 0.7750, find log 3√0.0005957\\sqrt', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1187, '2014', 'The probability of an event P happening is 15\\frac{1}{5} and that of events are independent, what is the probability that neither of them happens?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1188, '2014', 'Find the number of terms in the Arithmetic Progression (A.P): 2, -9, -20,... -141.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1189, '2014', 'In what modulus is it true that 9 + 8 = 5?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1190, '2014', 'The radii of the base of two cylindrical tins, P and Q are r and 2r respectively. If the water level in p is 10cm high, would be the height of the same quantity of water in Q?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1191, '2014', 'height23456frequency24531height23456frequency24531\\begin{array}{c|c}\\text{height} ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1192, '2014', 'Each exterior angle of a polygon is 30o. Calculate the sum of the interior angles', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1193, '2014', 'In the diagram, the value of x + y = 220o. Find the value of n.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1194, '2014', 'In the diagram < QPT = < PTS = 90o, < PQR = 110 and < TSR = 20o. Find the size of the obtuse angle QRS.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1195, '2014', 'In the diagram, PQR is a straight line, (m + n) = 120o and (n + r) = 100o. Find (m + r).', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1196, '2014', 'In the diagram, ST is parallel to UW, < WVT = xo, < VUT = yo, < RSV = 45o and < VTU = 20o. Find the value of x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1197, '2014', 'In the diagram, ST is parallel to UW, < WVT = xo, < VUT = yo, < RSV = 45o and < VTU = 20o. Calculate the value of y.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1198, '2014', 'The graph given is for the relation y = 2x2 + x - 1. What are the coordinates of the point S?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1199, '2014', 'The graph given is for the relation y = 2x2 + x - 1. Find the minimum value of y.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1200, '2014', 'In the figures, PQ is a tangent to the circle at R and UT is parallel to PQ. if < TRQ = xo, find < URT in terms of x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1201, '2014', 'Determine the value of m in the diagram.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1202, '2014', 'In the diagram, O is the centre of the circle of the circle, PR is a tangent to the circle at Q, < SOQ = 86o. Calculate the value of < SQR.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1203, '2015', 'If {X: 2 d- x d- 19; X integer} and 7 + x = 4 (mod 9), find the highest value of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1204, '2015', 'The sum 110112, 11112 and 10m10n02. Find the value of m and n.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1205, '2015', 'If 27x×31−x92x=127x×31−x92x=1\\frac{27^x \\times 3^{1 - x}}{9^{2x}} = 1, find the value of x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1206, '2015', 'Find the 7th term of the sequence: 2, 5, 10, 17, 6,...', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1207, '2015', 'Given that logx 64 = 3, evaluate x log8', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1208, '2015', 'If 2n = y, Find 2(2+n3)(2+n3)^{(2 + \\frac{n}{3})}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1209, '2015', 'Factorize completely: 6ax - 12by - 9ay + 8bx', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1210, '2015', 'Find the equation whose roots are 3434\\frac{3}{4} and -4', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1211, '2015', 'If m = 4, n = 9 and r = 16., evaluate mnmn\\frac{m}{n} - 17979\\frac{7}{9} + nrnr\\frac{n}{r}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1212, '2015', 'Adding 42 to a given positive number gives the same result as squaring the number. Find the number', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1213, '2015', 'Ada draws the graph of y = x2 - x - 2 and y = 2x - 1 on the same axes. Which of these equations is she solving?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1214, '2015', 'The volume of a cone of height 3cm is 3812\\frac{1}{2}cm3. Find the radius of its base. ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1215, '2015', 'The dimension of a rectangular tank are 2m by 7m by 11m. If its volume is equal to that of a cylindrical tank of height 4cm, calculate the base radius of the cylindrical tank. ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1216, '2015', 'In the diagram, O is the centre. If PQ//RS, what is ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1217, '2015', 'In the diagram, PTR is a tangent to the centre O. If angles TON = 180o, Calculate the size of angle PTN.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1218, '2015', 'In the diagram, PQ//RT, QR//SU, what is x?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1219, '2015', 'In the diagram, O is the centre, ¯RT\\bar{RT} is a diameter, < PQT = 33o^o and ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1220, '2015', 'In the diagram, O is the centre, ¯RT\\bar{RT} is a diameter, < PQT = 33o^o', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1221, '2015', 'x011224y0512\\begin{array}{c|c}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1222, '2015', 'PQRT is square. If x is the midpoint of PQ, Calculate correct to the nearest degree, LPXS', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1223, '2015', 'The angle of elevation of an aircraft from a point K on the horizontal ground 30', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1224, '2015', 'The population of students in a school is 810. If this is represented on a pie chart, calculate the sectoral angle for a class of 7 students', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1225, '2015', 'The scores of twenty students in a test are as follows: 44, 47, 48, 49, 50, 51, 52, 53, 53, 54, 58, 59, 60, 61, 63, 65, 67, 70, 73, 75. Find the third quartile.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1226, '2015', 'Scores0−45−910−14Frequency212\\begin{array}{c|c} Scores ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1227, '2015', 'The probability that kebba, Ebou and Omar will hit a target are 23\\frac{2}{3}, 34\\frac{3}{4} and 45\\frac{4}{5} respectively. Find the probability that only Kebba will hit the target.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1228, '2015', 'In the diagram, VW//YZ, |WX| = 6cm, |XY| = 16cm, |YZ| = 20cm and |ZX| = 12cm. Calculate |VX|.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1229, '2015', 'Tom will be 25 years old in n years\' time. If he is 5 years younger than Bade\'s present age.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1230, '2015', 'If √2+√33\\frac{\\sqrt{2} + \\sqrt{3}}{3} is simplified as m + n√6\\sqrt{6}, find the value of (m + n)', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1231, '2015', 'In the given diagram, ¯QT\\bar{QT} and ¯PR\\bar{PR} are straight lines. Find n.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1232, '2015', 'Make K the subject of the relation T = √TK−HK−HTK−HK−H\\sqrt{\\frac{TK - H}{K - H}}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1233, '2015', 'Which of the following is used to determine the mode of a grouped data?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1234, '2015', 'The area of a rhombus is 110cm', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1235, '2015', 'Simplify: 3x−yxy+2x+3y2xy+123x−yxy+2x+3y2xy+12\\frac{3x - y}{xy} +  \\frac{2x + 3y}{2xy} + \\frac{1}{2}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1236, '2015', 'A farmer uses 2525\\frac{2}{5} of his land to grow cassava, 1313\\frac{1}{3} of the remaining for yam and the rest for maize. Find the part of the land used for maize', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1237, '2015', 'The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If 4 litres of petrol is consumed on a distance of 15km. how far would the vehicle go on 9 litres of petrol?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1238, '2015', 'A trader bought 100 oranges at 5 for N40.00 and 20 for N120.00. Find the profit or loss percent', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1239, '2015', 'Find the value of p if 1414\\frac{1}{4}p + 3q = 10 and 2p - q = 7', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1240, '2015', 'Calculate the mean deviation of 5, 3, 0, 7, 2, 1', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1241, '2015', 'In the diagram, the shaded part is carpet laid in a room with dimensions 3.5m by 2.2m leaving a margin of 0.5m round it. Find area of the margin.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1242, '2015', 'Two angles of a pentagon are in the ratio 2:3. The others are 60o each. Calculate the smaller of the two angles', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1243, '2015', 'A letter is selected from the letters of the English alphabet. What is the probability that the letter selected is from the word MATHEMATICS?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1244, '2015', 'In a circle radius rcm, a chord 16√3cm√3cm\\sqrt{3}cm long is 10cmfrom the centre of the circle. Find, correct to the nearest cm, the value of r', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1245, '2015', 'In the diagram, ¯OX¯OX\\bar{OX} bisects < YXZ and ¯OZ¯OZ\\bar{OZ} bisects < YZX. If < XYZ = 68o, calculate the value of < XOZ.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1246, '2016', 'The curved surface area of a cylinder 5cm high is 110cm2. Find the radius of its base ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1247, '2016', 'Make S the subject of the relation p = s + sm2nrsm2nr\\frac{sm^2}{nr}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1248, '2016', 'Simplify:(10√3√5−√1510√3√5−√15\\frac{10\\sqrt{3}}{\\sqrt{5}} - \\sqrt{15})2', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1249, '2016', 'The distance, d, through which a stone falls from rest varies directly as the square of the time, t, taken. If the stone falls 45cm in 3 seconds, how far will it fall in 6 seconds?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1250, '2016', 'Which of following is a valid conclusion from the premise. \"Nigeria footballers are good footballers\"?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1251, '2016', 'On a map, 1cm represent 5km. Find the area on the map that represents 100km2.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1252, '2016', 'Simplify; 3n−1×27n+181n3n−1×27n+181n\\frac{3^{n - 1} \\times 27^{n + 1}}{81^{n}}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1253, '2016', 'What sum of money will amount to D10,400 in 5 years at 6% simple interest?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1254, '2016', 'The roots of a quadratic equation are 4343\\frac{4}{3} and -3737\\frac{3}{7}. Find the equation', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1255, '2016', 'Find the values of y for which the expression y2−9y+18y2+4y−21y2−9y+18y2+4y−21\\frac{y^2 - 9y + 18}{y^2 + 4y - 21} is undefined', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1256, '2016', 'Given that 2x + y = 7 and 3x - 2y = 3, by how much is 7x greater than 10?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1257, '2016', 'Simplify; 21−x−1x\\frac{2}{1 - x} - \\frac{1}{x}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1258, '2016', 'Factorize; (2x + 3y)2 - (x - 4y)2', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1259, '2016', 'The volume of a pyramid with height 15cm is 90cm3. If its base is a rectangle with dimension xcm by 6cm, find the value of x', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1260, '2016', 'Calculate the gradient of the line PQ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1261, '2016', 'A straight line passes through the point P(1,2) and Q(5,8). Calculate the length PQ.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1262, '2016', 'If cos θ\\theta = x and sin 60o = x + 0.50o < θ\\theta < 90o, find, correct to the nearest degree, the value of θ\\theta', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1263, '2016', 'Age(years)1314151617Frequency1024853Age(years)1314151617Frequency1024853\\begin{array}{c|c} Age(years) ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1264, '2016', 'In the diagram, ¯YW¯YW\\bar{YW} is a tangent to the circle at X, |UV| = |VX| and < VXW = 50o. Find the value of < VXY.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1265, '2016', 'In the diagram, ¯PF¯PF\\bar{PF}, ¯QT¯QT\\bar{QT}, ¯RG¯RG\\bar{RG} intersect at S and PG||RG. If < SPQ = 113o and < RST = 220o, find < PSQ.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1266, '2016', 'In the diagram, O is the centre of the circle, < XOZ = (10cm)o and < XWZ = mo. Calculate the value of m.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1267, '2016', 'Kweku walked 8m up to slope and was 3m above the ground. If he walks 12m further up the slope, how far above the ground will he be?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1268, '2016', 'In the diagram, TS is a tangent to the circle at S. |PR| and < PQR = 177o. Calculate < PST.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1269, '2016', 'In the diagram, PR||SV||WY|, TX||QY|, < PQT = 48o and < TXW = 60o. Find < TQU.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY');
INSERT INTO `labelling` (`id`, `examYear`, `questions`, `options`, `answer`, `explaination`, `imageDir`, `topic`, `package_id`, `subject_id`) VALUES
(1270, '2016', 'In the diagram, TX is perpendicular to UW, |UX| = 1cm and |TX| = |WX| = √3√3\\sqrt{3}cm. Find UTW.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1271, '2016', 'The figure is a pie chart which represents the expenditure of a family in a year. If the total income of the family was Le 10,800,000.00, how much was spent on food?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1272, '2016', 'A fair die is thrown two times. What is the probability that the sum of the scores is at least 10?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1273, '2016', 'The marks of eight students in a test are: 3, 10, 4, 5, 14, 13, 16 and 7. Find the range', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1274, '2016', 'If log2(3x - 1) = 5, find x.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1275, '2016', 'A sphere of radius rcm has the same volume as cylinder of radius 3cm and height 4cm. Find the value of r', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1276, '2016', 'Express 1975 correct to 2 significant figures', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1277, '2016', 'The diagram, MOPQ is a trapezium with QP||MO, MQ||NP, NQ||OP, |QP| = 9cm and the height of Δ\\Delta QNP = 6cm, calculate the area of the trapezium.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1278, '2016', 'The perimeter of a sector of a circle of radius 21cm is 64cm. Find the angle of the sector ', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1279, '2016', 'Examine M\' ∩\\cap N from the venn diagram.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1280, '2016', 'If 20(mod 9) is equivalent to y(mod 6), find y.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1281, '2016', 'Simplify (p−r)2−r22p2−4pr\\frac{(p - r)^2 - r^2}{2p^2 - 4pr}', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1282, '2016', 'In the diagram, O is the centre of the circle, < QPS = 100o, < PSQ = 60o and < QSR. Calculate < SQR.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1283, '2016', 'A bag contains 5 red and 4 blue identical balls. Id two balls are selected at random from the bag, one after the other, with replacement, find the probability that the first is red and the second is blue', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1284, '2016', 'Find the next three terms of the sequence; 0, 1, 1, 2, 3, 5, 8...', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1285, '2016', 'Find the lower quartile of the distribution illustrated by the cumulative frequency curve.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1286, '2016', 'The ratio of the exterior angle to the interior angle of a regular polygon is 1:11. How many sides has the polygon?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1287, '2016', 'Halima is n years old. Her brother\'s age is 5 years more than half of her age. How old is her brother?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1288, '2016', 'In the diagram MN is a chord of a circle KMN centre O and radius 10cm. If < MON = 140o, find, correct to the nearest cm, the length of the chord MN.', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY'),
(1289, '2016', 'From the diagram, which of the following is true?', '', '', '', 'None', '', 'WAEC-PK-1', 'WAEC-PHY');

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