Year :
2001
Title :
Mathematics (Core)
Exam :
WASSCE/WAEC MAY/JUNE
Paper 1 | Objectives
11 - 20 of 49 Questions
| # | Question | Ans |
|---|---|---|
| 11. |
Evaluate \(\frac{1}{2}+\frac{3}{4}of\frac{2}{5}\div 1\frac{3}{5}\) A. \(\frac{15}{16}\) B. \(\frac{11}{16}\) C. \(\frac{49}{50}\) D. \(3\frac{1}{5}\) Detailed Solution\(\frac{1}{2} + (\frac{3}{4} \text{ of } \frac{2}{5}) \div 1\frac{3}{5}\)= \(\frac{1}{2} + (\frac{3}{4} \times \frac{2}{5}) \div \frac{8}{5}\) = \(\frac{1}{2} + \frac{3}{10} \div \frac{8}{5}\) = \(\frac{1}{2} + (\frac{3}{10} \times \frac{5}{8})\) = \(\frac{1}{2} + \frac{3}{16}\) = \(\frac{11}{16}\) |
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| 12. |
A man is four times as old as his son. The difference between their ages is 36 years Find the sum of their ages A. 45 years B. 48 years C. 60 years D. 74 years Detailed SolutionLet the sons age be x. The father is 4x∴ 4x - x = 36; 3x = 36; x = 12 The son is 12 years and the father is 12 x 4 = 48. The sum of their ages (12 + 48) years = 60years |
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| 13. |
Given that y = px + q and y = 5 when x = 3, while y = 4 when x = 2, find the value of p and q. A. p = 1, q = 3 B. p = 1, q = 2 C. p = -2, q = 3 D. p = 3, q = -2 Detailed Solutiony = px + q5 = 3p + q ... (i) 4 = 2p + q ... (ii) (i) - (ii) : p = 1 \(\therefore\) 5 = 3(1) + q \(\implies\) q = 5 - 3 = 2 (p, q) = (1, 2) |
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| 14. |
Evaluate \(\frac{x^2 + x - 2}{2x^2 + x -3}\) when x = -1 A. -2 B. -1 C. \(-\frac{1}{2}\) D. 1 Detailed Solution\(\frac{x^2 + x - 2}{2x^2 + x - 3}\)= \(\frac{x^2 + 2x - x - 2}{2x^2 + 3x - 2x - 3}\) = \(\frac{x(x + 2) - 1(x + 2)}{x(2x + 3) - 1(2x + 3)}\) = \(\frac{(x - 1)(x + 2)}{(x - 1)(2x + 3)}\) = \(\frac{x + 2}{2x + 3}\) At x = -1, = \(\frac{-1 + 2}{2(-1) + 3}\) = \(\frac{1}{1}\) = 1 |
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| 15. |
Factorize \(6x^2 + 7x - 20\) A. (6x - 5)(x + 4) B. 2(3x-5)(x+2) C. (3x+4)(2x-5) D. (3x-4)(2x+5) Detailed Solution\(6x^2 + 7x - 20\)= \(6x^2 + 15x - 8x - 20\) = \(3x(2x + 5) - 4(2x + 5)\) = \((3x - 4)(2x + 5)\) |
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| 16. |
Simplify \(\frac{2x-1}{3}-\frac{x+3}{2}\) A. \(\frac{x+3}{6}\) B. \(\frac{x+8}{6}\) C. \(\frac{x-11}{6}\) D. \(\frac{x-4}{6}\) Detailed Solution\(\frac{2x - 1}{3} - \frac{x + 3}{2}\)= \(\frac{2(2x - 1) - 3(x + 3)}{6}\) = \(\frac{4x - 2 - 3x - 9}{6}\) = \(\frac{x - 11}{6}\) |
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| 17. |
If \(\frac{y-3}{2}<\frac{2y-1}{3}\), which of the following is true? A. y > 7 B. y < -7 C. y > -7 D. y < 7 Detailed Solution\(\frac{y - 3}{2} < \frac{2y - 1}{3}\)\(3(y - 3) < 2(2y - 1)\) \(3y - 9 < 4y - 2\) \(3y - 4y < -2 + 9\) \(-y < 7\) \(y > -7\) |
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| 18. |
If \(\frac{4m+3n}{4m-3n}=\frac{5}{2}\), find the ratio m:n A. 7:4 B. 4:3 C. 3:4 D. 4:7 Detailed Solution\(\frac{4m + 3n}{4m - 3n} = \frac{5}{2}\)\(5(4m - 3n) = 2(4m + 3n)\) \(20m - 15n = 8m + 6n\) \(20m - 8m = 6n + 15n\) \(12m = 21n\) \(\frac{21}{12} = \frac{m}{n}\) \(m : n = 7 : 4\) |
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| 19. |
If \(2x^2 + kx - 14 = (x+2)(2x-7)\), find the value of K A. -3 B. 5 C. 9 D. 11 Detailed Solution\(2x^2 + kx - 14 = (x+2)(2x-7)\\∴2x^2 + kx - 14 = 2x^2 - 3x - 14\) equating coefficient K = -3 |
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| 20. |
Which of the following is not quadratic expression? A. \(y = 2x^2 - 5x\) B. \(y=x(x-5)\) C. \(y = x^2 - 5\) D. y = 5(x-1) Detailed SolutionA quadratic equation is an equation of the second order. The highest power in the equation is 2. |
| 11. |
Evaluate \(\frac{1}{2}+\frac{3}{4}of\frac{2}{5}\div 1\frac{3}{5}\) A. \(\frac{15}{16}\) B. \(\frac{11}{16}\) C. \(\frac{49}{50}\) D. \(3\frac{1}{5}\) Detailed Solution\(\frac{1}{2} + (\frac{3}{4} \text{ of } \frac{2}{5}) \div 1\frac{3}{5}\)= \(\frac{1}{2} + (\frac{3}{4} \times \frac{2}{5}) \div \frac{8}{5}\) = \(\frac{1}{2} + \frac{3}{10} \div \frac{8}{5}\) = \(\frac{1}{2} + (\frac{3}{10} \times \frac{5}{8})\) = \(\frac{1}{2} + \frac{3}{16}\) = \(\frac{11}{16}\) |
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| 12. |
A man is four times as old as his son. The difference between their ages is 36 years Find the sum of their ages A. 45 years B. 48 years C. 60 years D. 74 years Detailed SolutionLet the sons age be x. The father is 4x∴ 4x - x = 36; 3x = 36; x = 12 The son is 12 years and the father is 12 x 4 = 48. The sum of their ages (12 + 48) years = 60years |
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| 13. |
Given that y = px + q and y = 5 when x = 3, while y = 4 when x = 2, find the value of p and q. A. p = 1, q = 3 B. p = 1, q = 2 C. p = -2, q = 3 D. p = 3, q = -2 Detailed Solutiony = px + q5 = 3p + q ... (i) 4 = 2p + q ... (ii) (i) - (ii) : p = 1 \(\therefore\) 5 = 3(1) + q \(\implies\) q = 5 - 3 = 2 (p, q) = (1, 2) |
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| 14. |
Evaluate \(\frac{x^2 + x - 2}{2x^2 + x -3}\) when x = -1 A. -2 B. -1 C. \(-\frac{1}{2}\) D. 1 Detailed Solution\(\frac{x^2 + x - 2}{2x^2 + x - 3}\)= \(\frac{x^2 + 2x - x - 2}{2x^2 + 3x - 2x - 3}\) = \(\frac{x(x + 2) - 1(x + 2)}{x(2x + 3) - 1(2x + 3)}\) = \(\frac{(x - 1)(x + 2)}{(x - 1)(2x + 3)}\) = \(\frac{x + 2}{2x + 3}\) At x = -1, = \(\frac{-1 + 2}{2(-1) + 3}\) = \(\frac{1}{1}\) = 1 |
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| 15. |
Factorize \(6x^2 + 7x - 20\) A. (6x - 5)(x + 4) B. 2(3x-5)(x+2) C. (3x+4)(2x-5) D. (3x-4)(2x+5) Detailed Solution\(6x^2 + 7x - 20\)= \(6x^2 + 15x - 8x - 20\) = \(3x(2x + 5) - 4(2x + 5)\) = \((3x - 4)(2x + 5)\) |
| 16. |
Simplify \(\frac{2x-1}{3}-\frac{x+3}{2}\) A. \(\frac{x+3}{6}\) B. \(\frac{x+8}{6}\) C. \(\frac{x-11}{6}\) D. \(\frac{x-4}{6}\) Detailed Solution\(\frac{2x - 1}{3} - \frac{x + 3}{2}\)= \(\frac{2(2x - 1) - 3(x + 3)}{6}\) = \(\frac{4x - 2 - 3x - 9}{6}\) = \(\frac{x - 11}{6}\) |
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| 17. |
If \(\frac{y-3}{2}<\frac{2y-1}{3}\), which of the following is true? A. y > 7 B. y < -7 C. y > -7 D. y < 7 Detailed Solution\(\frac{y - 3}{2} < \frac{2y - 1}{3}\)\(3(y - 3) < 2(2y - 1)\) \(3y - 9 < 4y - 2\) \(3y - 4y < -2 + 9\) \(-y < 7\) \(y > -7\) |
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| 18. |
If \(\frac{4m+3n}{4m-3n}=\frac{5}{2}\), find the ratio m:n A. 7:4 B. 4:3 C. 3:4 D. 4:7 Detailed Solution\(\frac{4m + 3n}{4m - 3n} = \frac{5}{2}\)\(5(4m - 3n) = 2(4m + 3n)\) \(20m - 15n = 8m + 6n\) \(20m - 8m = 6n + 15n\) \(12m = 21n\) \(\frac{21}{12} = \frac{m}{n}\) \(m : n = 7 : 4\) |
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| 19. |
If \(2x^2 + kx - 14 = (x+2)(2x-7)\), find the value of K A. -3 B. 5 C. 9 D. 11 Detailed Solution\(2x^2 + kx - 14 = (x+2)(2x-7)\\∴2x^2 + kx - 14 = 2x^2 - 3x - 14\) equating coefficient K = -3 |
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| 20. |
Which of the following is not quadratic expression? A. \(y = 2x^2 - 5x\) B. \(y=x(x-5)\) C. \(y = x^2 - 5\) D. y = 5(x-1) Detailed SolutionA quadratic equation is an equation of the second order. The highest power in the equation is 2. |