Year :
2000
Title :
Mathematics (Core)
Exam :
WASSCE/WAEC MAY/JUNE
Paper 1 | Objectives
41 - 48 of 48 Questions
| # | Question | Ans |
|---|---|---|
| 41. |
A tap leaks at the rate of 2cm\(^3\) per seconds. How long will it take the tap to fill a container of 45 liters capacity? (1 liters = 1000cm\(^3\)) A. 8 hours B. 6hr 15min C. 4hr 25min D. 3hr Detailed SolutionTotal capacity of the container = 45 liters = 45 x 1000= 45000 cm\(^3\) Time to fill the container = \(\frac{45000}{2}\) = 22500 seconds = \(\frac{22500}{3600}\) = 6 hr 15 mins |
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| 42. |
The length of the parallel sides of a trapezium are 5cm and 7cm. If its area is 120cm\(^2\), find the perpendicular distance between the parallel sides A. 5.0cm B. 6.9cm C. 10.0cm D. 20.0cm Detailed SolutionArea of trapezium = \(\frac{1}{2} (a + b)h\)\(120 = \frac{1}{2} (5 + 7) \times h\) \(120 = 6h\) \(h = 20 cm\) |
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| 43. |
The arc of a circle 50 cm long, subtends angle of 75° at the center of the circle. Find correct to 3 significant figures, the radius of the circle. Take \(\pi = \frac{22}{7}\) A. 8.74cm B. 38.2cm C. 61.2cm D. 76.4cm Detailed SolutionLength of arc = \(\frac{\theta}{360} \times 2\pi r\)\(50 = \frac{75}{360} \times 2 \times \frac{22}{7} \times r\) \(r = \frac{50 \times 360 \times 7}{75 \times 2 \times 22}\) \(r = \frac{420}{11}\) = 38.18 cm \(\approxeq\) 38.2 cm (3 sig. figs) |
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| 44. |
 In the diagram, |PQ| = |PS| Which of the following statements is true? A. ∠QPS = QRS B. |PO| = |RO| C. QR||PS D. ∠PQR=∠PSR |
D |
| 45. |
The area of a circle is 38.5cm2. Find its diameter [take \(\pi = \frac{22}{7}\)] A. 22cm B. 14cm C. 7cm D. 6cm Detailed Solution\(\pi r^2 = 38.5\\\frac{}{} = r^2 = 38.5\\ r^2 = \frac{38.5 \times 7}{22}\\ r = \sqrt{12.25} = 3.5\\ diameter = 2r = 2 \times 3.5 = 7cm\) |
|
| 46. |
 Find the volume (in cm\(^3\)) of the solid shown above A. 100cm3 B. 150cm3 C. 175cm3 D. 250cm3 Detailed SolutionTotal volume = (5 x 5) x 5 + (5 x 5) x 2= 125 + 50 = 175 cm\(^3\) |
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| 47. |
Solve the equation 3 + 5x - 2x2 = 0 A. \(-\frac{1}{2},-3\) B. 2, 3 C. -2, 3 D. \(-\frac{1}{2},3\) Detailed Solution\(3 + 5x - 2x^2 = 0\\3 + 6x - x - 2x^2 = 0\\ 3(1 + 2x) - x(1 + 2x) = 0\\ (3-x)(1+2x)=0\\ 3-x = 0 \hspace{1mm}or \hspace{1mm}1+2x = 0\\ x = 3\hspace{1mm} x = -\frac{1}{2}\\ x = 3 \hspace{1mm}or\hspace{1mm} x =-\frac{1}{2}\) |
|
| 48. |
If the simple interest on N2000 after 9 months is N60, at what rate per annum is the interest charged? A. \(2\frac{1}{4}\)% B. 4% C. 5% D. 6% Detailed Solution\(I = \frac{PRT}{100}\)\(R = \frac{100I}{PT}\) \(R = \frac{100 \times 60}{2000 \times \frac{3}{4}}\) \(R = \frac{6000}{1500}\) = 4% |
| 41. |
A tap leaks at the rate of 2cm\(^3\) per seconds. How long will it take the tap to fill a container of 45 liters capacity? (1 liters = 1000cm\(^3\)) A. 8 hours B. 6hr 15min C. 4hr 25min D. 3hr Detailed SolutionTotal capacity of the container = 45 liters = 45 x 1000= 45000 cm\(^3\) Time to fill the container = \(\frac{45000}{2}\) = 22500 seconds = \(\frac{22500}{3600}\) = 6 hr 15 mins |
|
| 42. |
The length of the parallel sides of a trapezium are 5cm and 7cm. If its area is 120cm\(^2\), find the perpendicular distance between the parallel sides A. 5.0cm B. 6.9cm C. 10.0cm D. 20.0cm Detailed SolutionArea of trapezium = \(\frac{1}{2} (a + b)h\)\(120 = \frac{1}{2} (5 + 7) \times h\) \(120 = 6h\) \(h = 20 cm\) |
|
| 43. |
The arc of a circle 50 cm long, subtends angle of 75° at the center of the circle. Find correct to 3 significant figures, the radius of the circle. Take \(\pi = \frac{22}{7}\) A. 8.74cm B. 38.2cm C. 61.2cm D. 76.4cm Detailed SolutionLength of arc = \(\frac{\theta}{360} \times 2\pi r\)\(50 = \frac{75}{360} \times 2 \times \frac{22}{7} \times r\) \(r = \frac{50 \times 360 \times 7}{75 \times 2 \times 22}\) \(r = \frac{420}{11}\) = 38.18 cm \(\approxeq\) 38.2 cm (3 sig. figs) |
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| 44. |
In the diagram, |PQ| = |PS| Which of the following statements is true? A. ∠QPS = QRS B. |PO| = |RO| C. QR||PS D. ∠PQR=∠PSR |
D |
| 45. |
The area of a circle is 38.5cm2. Find its diameter [take \(\pi = \frac{22}{7}\)] A. 22cm B. 14cm C. 7cm D. 6cm Detailed Solution\(\pi r^2 = 38.5\\\frac{}{} = r^2 = 38.5\\ r^2 = \frac{38.5 \times 7}{22}\\ r = \sqrt{12.25} = 3.5\\ diameter = 2r = 2 \times 3.5 = 7cm\) |
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| 46. |
Find the volume (in cm\(^3\)) of the solid shown above A. 100cm3 B. 150cm3 C. 175cm3 D. 250cm3 Detailed SolutionTotal volume = (5 x 5) x 5 + (5 x 5) x 2= 125 + 50 = 175 cm\(^3\) |
|
| 47. |
Solve the equation 3 + 5x - 2x2 = 0 A. \(-\frac{1}{2},-3\) B. 2, 3 C. -2, 3 D. \(-\frac{1}{2},3\) Detailed Solution\(3 + 5x - 2x^2 = 0\\3 + 6x - x - 2x^2 = 0\\ 3(1 + 2x) - x(1 + 2x) = 0\\ (3-x)(1+2x)=0\\ 3-x = 0 \hspace{1mm}or \hspace{1mm}1+2x = 0\\ x = 3\hspace{1mm} x = -\frac{1}{2}\\ x = 3 \hspace{1mm}or\hspace{1mm} x =-\frac{1}{2}\) |
|
| 48. |
If the simple interest on N2000 after 9 months is N60, at what rate per annum is the interest charged? A. \(2\frac{1}{4}\)% B. 4% C. 5% D. 6% Detailed Solution\(I = \frac{PRT}{100}\)\(R = \frac{100I}{PT}\) \(R = \frac{100 \times 60}{2000 \times \frac{3}{4}}\) \(R = \frac{6000}{1500}\) = 4% |