Year :
2002
Title :
Mathematics (Core)
Exam :
WASSCE/WAEC MAY/JUNE
Paper 1 | Objectives
21 - 30 of 49 Questions
| # | Question | Ans |
|---|---|---|
| 21. |
For what values of x is the expression \(\frac{3x-2}{4x^2+9x-9}\) undefined? A. \(\frac{-3}{4} \hspace{1mm}or \hspace{1mm}3\) B. \(\frac{-2}{3} \hspace{1mm}or \hspace{1mm}-3\) C. \(\frac{2}{3} \hspace{1mm}or \hspace{1mm}3\) D. \(\frac{3}{4} \hspace{1mm}or \hspace{1mm}-3\) Detailed SolutionThe equation \(\frac{3x - 2}{4x^2 + 9x - 9}\) is undefined when the denominator = 0.\(4x^2 + 9x - 9 = 0\) \(4x^2 + 12x - 3x - 9 = 0\) \(4x(x + 3) - 3(x + 3) = 0\) \((4x - 3)(x + 3) = 0\) x = \(\frac{3}{4}\) or x = -3. |
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| 22. |
Simplify \(\frac{1}{1-x} + \frac{2}{1+x}\) A. \(\frac{x+3}{1-x^2}\) B. \(\frac{x-3}{1+x^2}\) C. \(\frac{3-x}{1-x^2}\) D. \(\frac{3-x}{1+x^2}\) Detailed Solution\(\frac{1}{1-x} + \frac{2}{1+x}\\\frac{1+x+2-2x}{(1-x)(1+x)} = \(\frac{3-x}{1-x^2}\)\) |
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| 23. |
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. A. 5cm B. 7cm C. 10cm D. 15cm Detailed Solution\(\frac{1}{2}(a+b)\times h = 105cm^2\\\frac{1}{2}(9+12)\times h = 105\\ h = \frac{105 \times 2}{21} = 10cm\) |
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| 24. |
The base diameter of a cone is 14cm, and its volume is 462 cm3. Find its height. [Taken \(\pi = \frac{22}{7}\)] A. 3.5cm B. 5cm C. 7cm D. 9cm Detailed SolutionFrom \(V = \frac{1}{3}\pi r^2 h. \hspace{1mm} r =\frac{14}{2}\\462 = \frac{1}{3} \times \frac{22}{7} \times 7^2 \times h \\ h = \frac{3 \times 462}{22 \times 7}\\ h = 9\) |
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| 25. |
A number is selected at random from the set Y = {18, 19, 20, . . . 28, 29}. Find the probability that the number is prime. A. \(\frac{1}{4}\) B. \(\frac{3}{11}\) C. \(\frac{1}{2}\) D. \(\frac{3}{4}\) Detailed SolutionY = {18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29}Number of prime numbers = 3 Prob(picking a prime number) = \(\frac{3}{12}\) = \(\frac{1}{4}\) |
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| 26. |
 The median of the distribution is A. 25 B. 17.5 C. 15 D. 12.5 |
C |
| 27. |
 The range of the distribution is A. 50 B. 30 C. 25 D. 15 |
C |
| 28. |
 The upper quartile of the distribution is A. 30 B. 27.5 C. 25 D. 17.75 |
D |
| 29. |
 In the diagram O and O' are the centres of the circles radii 15cm and 8cm respectively. If PQ = 12cm, find |OO'|. A. 8.46cm B. 19.04cm C. 20.81cm D. 26.16cm Detailed SolutionIn \(\Delta\) POQ,\(12^2 = 15^2 + 15^2 - 2(15)(15) \cos < POQ\) \(144 = 450 - 450\cos < POQ\) \(450 \cos < POQ = 450 - 144 = 306\) \(\cos <POQ = \frac{306}{450} = 0.68\) \(< POQ = 47.2°\) In \(\Delta\) PO'Q, \(12^2 = 8^2 + 8^2 - 2(8)(8) \cos <PO'Q\) \(144 - 128 = -128 \cos < PO'Q\) \(\cos < PO'Q = - 0.125\) \(< PO'Q = 97.2°\)  In \(\Delta\) POQ, \(\co |
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| 30. |
 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 III. a + b = c A. I and II only B. II and III only C. II only D. III only |
A |
| 21. |
For what values of x is the expression \(\frac{3x-2}{4x^2+9x-9}\) undefined? A. \(\frac{-3}{4} \hspace{1mm}or \hspace{1mm}3\) B. \(\frac{-2}{3} \hspace{1mm}or \hspace{1mm}-3\) C. \(\frac{2}{3} \hspace{1mm}or \hspace{1mm}3\) D. \(\frac{3}{4} \hspace{1mm}or \hspace{1mm}-3\) Detailed SolutionThe equation \(\frac{3x - 2}{4x^2 + 9x - 9}\) is undefined when the denominator = 0.\(4x^2 + 9x - 9 = 0\) \(4x^2 + 12x - 3x - 9 = 0\) \(4x(x + 3) - 3(x + 3) = 0\) \((4x - 3)(x + 3) = 0\) x = \(\frac{3}{4}\) or x = -3. |
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| 22. |
Simplify \(\frac{1}{1-x} + \frac{2}{1+x}\) A. \(\frac{x+3}{1-x^2}\) B. \(\frac{x-3}{1+x^2}\) C. \(\frac{3-x}{1-x^2}\) D. \(\frac{3-x}{1+x^2}\) Detailed Solution\(\frac{1}{1-x} + \frac{2}{1+x}\\\frac{1+x+2-2x}{(1-x)(1+x)} = \(\frac{3-x}{1-x^2}\)\) |
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| 23. |
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. A. 5cm B. 7cm C. 10cm D. 15cm Detailed Solution\(\frac{1}{2}(a+b)\times h = 105cm^2\\\frac{1}{2}(9+12)\times h = 105\\ h = \frac{105 \times 2}{21} = 10cm\) |
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| 24. |
The base diameter of a cone is 14cm, and its volume is 462 cm3. Find its height. [Taken \(\pi = \frac{22}{7}\)] A. 3.5cm B. 5cm C. 7cm D. 9cm Detailed SolutionFrom \(V = \frac{1}{3}\pi r^2 h. \hspace{1mm} r =\frac{14}{2}\\462 = \frac{1}{3} \times \frac{22}{7} \times 7^2 \times h \\ h = \frac{3 \times 462}{22 \times 7}\\ h = 9\) |
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| 25. |
A number is selected at random from the set Y = {18, 19, 20, . . . 28, 29}. Find the probability that the number is prime. A. \(\frac{1}{4}\) B. \(\frac{3}{11}\) C. \(\frac{1}{2}\) D. \(\frac{3}{4}\) Detailed SolutionY = {18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29}Number of prime numbers = 3 Prob(picking a prime number) = \(\frac{3}{12}\) = \(\frac{1}{4}\) |
| 26. |
The median of the distribution is A. 25 B. 17.5 C. 15 D. 12.5 |
C |
| 27. |
The range of the distribution is A. 50 B. 30 C. 25 D. 15 |
C |
| 28. |
The upper quartile of the distribution is A. 30 B. 27.5 C. 25 D. 17.75 |
D |
| 29. |
In the diagram O and O' are the centres of the circles radii 15cm and 8cm respectively. If PQ = 12cm, find |OO'|. A. 8.46cm B. 19.04cm C. 20.81cm D. 26.16cm Detailed SolutionIn \(\Delta\) POQ,\(12^2 = 15^2 + 15^2 - 2(15)(15) \cos < POQ\) \(144 = 450 - 450\cos < POQ\) \(450 \cos < POQ = 450 - 144 = 306\) \(\cos <POQ = \frac{306}{450} = 0.68\) \(< POQ = 47.2°\) In \(\Delta\) PO'Q, \(12^2 = 8^2 + 8^2 - 2(8)(8) \cos <PO'Q\) \(144 - 128 = -128 \cos < PO'Q\) \(\cos < PO'Q = - 0.125\) \(< PO'Q = 97.2°\) In \(\Delta\) POQ, \(\co |
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| 30. |
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 III. a + b = c A. I and II only B. II and III only C. II only D. III only |
A |