Year :
2000
Title :
Mathematics (Core)
Exam :
WASSCE/WAEC MAY/JUNE
Paper 1 | Objectives
31 - 40 of 48 Questions
| # | Question | Ans |
|---|---|---|
| 31. |
Simplify \(\frac{1}{x-3}-\frac{3(x-1)}{x^2 - 9}\) A. \(\frac{x-1}{x-3}\) B. \(\frac{-2}{x+3}\) C. \(\frac{x-1}{x+3}\) D. \(\frac{4x}{x^2-9}\) Detailed Solution\(\frac{1}{x-3}-\frac{3(x-1)}{x^2 - 9}\\\frac{1}{x-3}-\frac{3(x-1)}{(x-3)(x+3)}\\ \frac{x+3-3x+3}{(x-3)(x+3)};\frac{-2x+6}{(x-3)(x+3)}\\ \frac{-2(x-3)}{(x-3)(x+3)}=\frac{-2}{x+3}\) |
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| 32. |
Form an inequality for a distance d meters which is more than 18m, but not more than 23m A. 18 ≤ d ≤ 23 B. 18 < d ≤ 23 C. 18 ≤ d < 23 D. d < 18 or d > 23 |
B |
| 33. |
Find the equation whose roots are -8 and 5 A. \(x^2 + 13x + 40=0\) B. \(x^2 - 13x - 40=0\) C. \(x^2 - 3x +40=0\) D. \(x^2 + 3x - 40=0\) Detailed SolutionEquation with roots -8 and 5: (x + 8)(x - 5) = 0\(x^2 - 5x + 8x - 40 = 0\) \(x^2 + 3x - 40 = 0\) |
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| 34. |
Make t the subject of formula \(k = m\sqrt{\frac{t-p}{r}}\) A. \(\frac{rk^2 + p}{m^2}\) B. \(\frac{rk^2+pm^2}{m^2}\) C. \(\frac{rk^2-p}{m^2}\) D. \(\frac{rk^2-p^2}{m^2}\) Detailed Solution\(k = m\sqrt{\frac{t - p}{r}}\)\(\frac{k}{m} = \sqrt{\frac{t - p}{r}}\) \((\frac{k}{m})^2 = \frac{t - p}{r}\) \(rk^2 = m^2 (t - p)\) \(\therefore m^2 t = rk^2 + m^2 p\) \(t = \frac{rk^2 + m^2 p}{m^2}\) |
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| 35. |
Solve the equation \(3y^2 = 27y\) A. y = o or 3 B. y = 0 or 9 C. y = -3 or 3 D. y = 3 or 9 Detailed Solution\(3y^2 = 27y\\3y^2 - 27y = 0\\ 3y(y - 9) = 0\\ 3y = 0 or y - 9 = 0\\ y = 0 or y = 9\\ y = 0 or 9\) |
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| 36. |
Find the value of x such that the expression \(\frac{1}{x}+\frac{4}{3x}-\frac{5}{6x}+1\) equals zero A. \(\frac{1}{6}\) B. \(\frac{1}{4}\) C. \(\frac{-3}{2}\) D. \(\frac{-7}{6}\) Detailed Solution\(\frac{1}{x} + \frac{4}{3x} - \frac{5}{6x} + 1 = 0\)\(\frac{6 + 8 - 5 + 6x}{6x} = 0\) \(\frac{9 + 6x}{6x} = 0 \implies 9 + 6x = 0\) \(6x = -9 \implies x = \frac{-3}{2}\) |
|
| 37. |
Given that p varies directly as q while q varies inversely as r, which of the following statements is true? A. r varies directly as p B. p varies inversely as r C. p varies directly as r D. q varies inversely as p |
B |
| 38. |
 In the diagram, PQS is a circle with center O. RST is a tangent at S and ∠SOP = 96o. Find ∠PST A. 42o B. 48o C. 60o D. 66o |
B |
| 39. |
A bicycle wheel of radius 42cm is rolled over a distance 66 meters. How many revolutions does it make?[Take \(\pi = \frac{22}{7}\)] A. 2.5 B. 5 C. 25 D. 50 Detailed Solutioncircumference of the bicycle wheel\(= 2\pi r = 2 \times \frac{22}{7} \times 42 - 264cm = 2.64m\\\) Number of revolution \(=\frac{66}{2.64} = 25\) |
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| 40. |
The height of a pyramid on square base is 15cm. if the volume is 80cm^3, find the area of the square base. A. 8cm2 B. 9.6cm2 C. 16cm2 D. 25cm2 Detailed SolutionVolume of pyramid with square base = \(\frac{\text{base area} \times height}{3}\)\(80 = \frac{\text{base area} \times 15}{3}\) \(80 = 5 \times \text{base area}\) \(\text{Base area} = 16 cm^2\) |
| 31. |
Simplify \(\frac{1}{x-3}-\frac{3(x-1)}{x^2 - 9}\) A. \(\frac{x-1}{x-3}\) B. \(\frac{-2}{x+3}\) C. \(\frac{x-1}{x+3}\) D. \(\frac{4x}{x^2-9}\) Detailed Solution\(\frac{1}{x-3}-\frac{3(x-1)}{x^2 - 9}\\\frac{1}{x-3}-\frac{3(x-1)}{(x-3)(x+3)}\\ \frac{x+3-3x+3}{(x-3)(x+3)};\frac{-2x+6}{(x-3)(x+3)}\\ \frac{-2(x-3)}{(x-3)(x+3)}=\frac{-2}{x+3}\) |
|
| 32. |
Form an inequality for a distance d meters which is more than 18m, but not more than 23m A. 18 ≤ d ≤ 23 B. 18 < d ≤ 23 C. 18 ≤ d < 23 D. d < 18 or d > 23 |
B |
| 33. |
Find the equation whose roots are -8 and 5 A. \(x^2 + 13x + 40=0\) B. \(x^2 - 13x - 40=0\) C. \(x^2 - 3x +40=0\) D. \(x^2 + 3x - 40=0\) Detailed SolutionEquation with roots -8 and 5: (x + 8)(x - 5) = 0\(x^2 - 5x + 8x - 40 = 0\) \(x^2 + 3x - 40 = 0\) |
|
| 34. |
Make t the subject of formula \(k = m\sqrt{\frac{t-p}{r}}\) A. \(\frac{rk^2 + p}{m^2}\) B. \(\frac{rk^2+pm^2}{m^2}\) C. \(\frac{rk^2-p}{m^2}\) D. \(\frac{rk^2-p^2}{m^2}\) Detailed Solution\(k = m\sqrt{\frac{t - p}{r}}\)\(\frac{k}{m} = \sqrt{\frac{t - p}{r}}\) \((\frac{k}{m})^2 = \frac{t - p}{r}\) \(rk^2 = m^2 (t - p)\) \(\therefore m^2 t = rk^2 + m^2 p\) \(t = \frac{rk^2 + m^2 p}{m^2}\) |
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| 35. |
Solve the equation \(3y^2 = 27y\) A. y = o or 3 B. y = 0 or 9 C. y = -3 or 3 D. y = 3 or 9 Detailed Solution\(3y^2 = 27y\\3y^2 - 27y = 0\\ 3y(y - 9) = 0\\ 3y = 0 or y - 9 = 0\\ y = 0 or y = 9\\ y = 0 or 9\) |
| 36. |
Find the value of x such that the expression \(\frac{1}{x}+\frac{4}{3x}-\frac{5}{6x}+1\) equals zero A. \(\frac{1}{6}\) B. \(\frac{1}{4}\) C. \(\frac{-3}{2}\) D. \(\frac{-7}{6}\) Detailed Solution\(\frac{1}{x} + \frac{4}{3x} - \frac{5}{6x} + 1 = 0\)\(\frac{6 + 8 - 5 + 6x}{6x} = 0\) \(\frac{9 + 6x}{6x} = 0 \implies 9 + 6x = 0\) \(6x = -9 \implies x = \frac{-3}{2}\) |
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| 37. |
Given that p varies directly as q while q varies inversely as r, which of the following statements is true? A. r varies directly as p B. p varies inversely as r C. p varies directly as r D. q varies inversely as p |
B |
| 38. |
In the diagram, PQS is a circle with center O. RST is a tangent at S and ∠SOP = 96o. Find ∠PST A. 42o B. 48o C. 60o D. 66o |
B |
| 39. |
A bicycle wheel of radius 42cm is rolled over a distance 66 meters. How many revolutions does it make?[Take \(\pi = \frac{22}{7}\)] A. 2.5 B. 5 C. 25 D. 50 Detailed Solutioncircumference of the bicycle wheel\(= 2\pi r = 2 \times \frac{22}{7} \times 42 - 264cm = 2.64m\\\) Number of revolution \(=\frac{66}{2.64} = 25\) |
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| 40. |
The height of a pyramid on square base is 15cm. if the volume is 80cm^3, find the area of the square base. A. 8cm2 B. 9.6cm2 C. 16cm2 D. 25cm2 Detailed SolutionVolume of pyramid with square base = \(\frac{\text{base area} \times height}{3}\)\(80 = \frac{\text{base area} \times 15}{3}\) \(80 = 5 \times \text{base area}\) \(\text{Base area} = 16 cm^2\) |