Year :
2017
Title :
Mathematics (Core)
Exam :
WASSCE/WAEC MAY/JUNE
Paper 1 | Objectives
11 - 20 of 49 Questions
| # | Question | Ans |
|---|---|---|
| 11. |
Solve: - \(\frac{1}{4}\) < \(\frac{3}{4}\) (3x - 2) < \(\frac{1}{2}\) A. -\(\frac{5}{9}\) < x <\(\frac{8}{9}\) B. -\(\frac{8}{9}\) < x <\(\frac{7}{9}\) C. -\(\frac{8}{9}\) < x <\(\frac{5}{9}\) D. -\(\frac{7}{9}\) < x <\(\frac{8}{9}\) Detailed Solution\(\frac{3}{4}\) (3x - 2) < \(\frac{1}{2}\); \(\frac{3}{4}\) (3x - 2) > - \(\frac{1}{4}\)3(3x - 2) < 2; 3(3x - 2) > -1 9x - 6 < 2; 9x - 6 > -1 9x < 8; 9x > 5 x < \(\frac{5}{9}\); x > \(\frac{8}{9}\) |
|
| 12. |
Simplify; 3x - (p - x) - (r - p) A. 2x - r B. 2x + r C. 4x - r D. 2x - 2p - r Detailed Solution3x - (p - x) - ( r - p)= 3x - p + x - r + p = 4x - r |
|
| 13. |
An arc of a circle of radius 7.5cm is 7.5cm long. Find, correct to the nearest degree, the angle which the arc subtends at the centre of the circle. [Take \(\pi = \frac{22}{7}\)] A. 29\(^o\) B. 57\(^o\) C. 65\(^o\) D. 115\(^o\) Detailed Solutionlac = \(\frac{\theta}{360}\) x 2\(\pi\)r7.5 = \(\frac{\theta}{360}\) x 2 x \(\frac{22}{7}\) x 7.5 7.5 = \(\frac{330\theta}{2520}\) \(\theta\) = \(\frac{7.5}{0.1309}\) \(\theta\) = 57.29 \(\theta\) = 57 \(^o\) |
|
| 14. |
Water flows out of a pipe at a rate of 40\(\pi cm^2\) per seconds into an empty cylinder container of base radius 4cm. Find the height of water in the container after 4 seconds. A. 10 cm B. 14 cm C. 16 cm D. 20 cm Detailed SolutionVolume of a cylinder = \(\pi r^2h\)40\(\pi cm^3\) = \(\pi. 4^2h\) 40\(cm^3\) = 16h h = 2.5cm/sec In 4 seconds, 2.5cm x 4 = 10cm |
|
| 15. |
The dimensions of water tank are 13cm, 10cm and 70cm. If it is half-filled with water, calculate the volume of water in litres A. 4.55 litres B. 7.50 litres C. 8.10 litres D. 9.55 litres Detailed SolutionVol of a cubiod = L x b x hv = 13cm x 10cm x 70cm = 9100cm Since it is half-filled = \(\frac{9100}{2}\)cm = 4550cm 4550cm \(\to\) 4.55 litres |
|
| 16. |
If the total surface area of a solid hemisphere is equal to its volume, find the radius A. 3.0cm B. 4.5cm C. 5.0cm D. 9.0cm Detailed SolutionT.S.A of hemisphere = 3\(\pi r^2\)vol of hemisphere = \(\frac{2}{3} \pi r^2\) 3\(\pi r^2\) = \(\frac{2}{3} \pi r^2\) 3 = \(\frac{2}{3} \pi r\) 9 = 2r r = \(\frac{9}{2}\) r = 4.5cm |
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| 17. |
Which of the following is true about parallelogram? A. opposite angles are supplementary B. opposite angles are complementary C. opposite angles are equal D. opposite angles are reflex angles |
C |
| 18. |
Calculate the gradient (slope) of the joining points (-1, 1) and (2, -2) A. -1 B. \(\frac{-1}{2}\) C. \(\frac{1}{2}\) D. 1 Detailed SolutionGradient = m = \(\frac{y_2 - y_1}{x_2 - x_1}\)= \(\frac{-2 -1}{2 + 1}\) = \(\frac{-3}{3}\) = -1 |
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| 19. |
If P(2,3) and Q)2, 5) are points on a graph, calculate the length PQ A. 6 units B. 5 units C. 4 units D. 2 units Detailed Solution\(\sqrt{(x_2 - x_1)^2 + (y_2 - Y_1)^2}\)= \(\sqrt{(2 - 2)^2 + (5 - 3)^2}\) = \(\sqrt{0^2 + 2^2}\) = \(\sqrt{4}\) = 2 units |
|
| 20. |
A bearing of 320\(^o\) expressed as a compass bearing is A. N 50\(^o\) W B. N 40\(^o\) W C. N 50\(^o\) E D. N 40\(^o\) E |
B |
| 11. |
Solve: - \(\frac{1}{4}\) < \(\frac{3}{4}\) (3x - 2) < \(\frac{1}{2}\) A. -\(\frac{5}{9}\) < x <\(\frac{8}{9}\) B. -\(\frac{8}{9}\) < x <\(\frac{7}{9}\) C. -\(\frac{8}{9}\) < x <\(\frac{5}{9}\) D. -\(\frac{7}{9}\) < x <\(\frac{8}{9}\) Detailed Solution\(\frac{3}{4}\) (3x - 2) < \(\frac{1}{2}\); \(\frac{3}{4}\) (3x - 2) > - \(\frac{1}{4}\)3(3x - 2) < 2; 3(3x - 2) > -1 9x - 6 < 2; 9x - 6 > -1 9x < 8; 9x > 5 x < \(\frac{5}{9}\); x > \(\frac{8}{9}\) |
|
| 12. |
Simplify; 3x - (p - x) - (r - p) A. 2x - r B. 2x + r C. 4x - r D. 2x - 2p - r Detailed Solution3x - (p - x) - ( r - p)= 3x - p + x - r + p = 4x - r |
|
| 13. |
An arc of a circle of radius 7.5cm is 7.5cm long. Find, correct to the nearest degree, the angle which the arc subtends at the centre of the circle. [Take \(\pi = \frac{22}{7}\)] A. 29\(^o\) B. 57\(^o\) C. 65\(^o\) D. 115\(^o\) Detailed Solutionlac = \(\frac{\theta}{360}\) x 2\(\pi\)r7.5 = \(\frac{\theta}{360}\) x 2 x \(\frac{22}{7}\) x 7.5 7.5 = \(\frac{330\theta}{2520}\) \(\theta\) = \(\frac{7.5}{0.1309}\) \(\theta\) = 57.29 \(\theta\) = 57 \(^o\) |
|
| 14. |
Water flows out of a pipe at a rate of 40\(\pi cm^2\) per seconds into an empty cylinder container of base radius 4cm. Find the height of water in the container after 4 seconds. A. 10 cm B. 14 cm C. 16 cm D. 20 cm Detailed SolutionVolume of a cylinder = \(\pi r^2h\)40\(\pi cm^3\) = \(\pi. 4^2h\) 40\(cm^3\) = 16h h = 2.5cm/sec In 4 seconds, 2.5cm x 4 = 10cm |
|
| 15. |
The dimensions of water tank are 13cm, 10cm and 70cm. If it is half-filled with water, calculate the volume of water in litres A. 4.55 litres B. 7.50 litres C. 8.10 litres D. 9.55 litres Detailed SolutionVol of a cubiod = L x b x hv = 13cm x 10cm x 70cm = 9100cm Since it is half-filled = \(\frac{9100}{2}\)cm = 4550cm 4550cm \(\to\) 4.55 litres |
| 16. |
If the total surface area of a solid hemisphere is equal to its volume, find the radius A. 3.0cm B. 4.5cm C. 5.0cm D. 9.0cm Detailed SolutionT.S.A of hemisphere = 3\(\pi r^2\)vol of hemisphere = \(\frac{2}{3} \pi r^2\) 3\(\pi r^2\) = \(\frac{2}{3} \pi r^2\) 3 = \(\frac{2}{3} \pi r\) 9 = 2r r = \(\frac{9}{2}\) r = 4.5cm |
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| 17. |
Which of the following is true about parallelogram? A. opposite angles are supplementary B. opposite angles are complementary C. opposite angles are equal D. opposite angles are reflex angles |
C |
| 18. |
Calculate the gradient (slope) of the joining points (-1, 1) and (2, -2) A. -1 B. \(\frac{-1}{2}\) C. \(\frac{1}{2}\) D. 1 Detailed SolutionGradient = m = \(\frac{y_2 - y_1}{x_2 - x_1}\)= \(\frac{-2 -1}{2 + 1}\) = \(\frac{-3}{3}\) = -1 |
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| 19. |
If P(2,3) and Q)2, 5) are points on a graph, calculate the length PQ A. 6 units B. 5 units C. 4 units D. 2 units Detailed Solution\(\sqrt{(x_2 - x_1)^2 + (y_2 - Y_1)^2}\)= \(\sqrt{(2 - 2)^2 + (5 - 3)^2}\) = \(\sqrt{0^2 + 2^2}\) = \(\sqrt{4}\) = 2 units |
|
| 20. |
A bearing of 320\(^o\) expressed as a compass bearing is A. N 50\(^o\) W B. N 40\(^o\) W C. N 50\(^o\) E D. N 40\(^o\) E |
B |