Year :
2002
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
1 - 10 of 48 Questions
| # | Question | Ans |
|---|---|---|
| 1. |
Without using tables, evaluate \((343)^{\frac{1}{3}} \times (0.14)^{-1} \times (25)^{-\frac{1}{2}}\) A. 10 B. 12 C. 8 D. 7 Detailed Solution\((343)^{\frac{1}{3}} \times (0.14)^{-1} \times (25)^{-\frac{1}{2}}\)= \(\sqrt[3]{343} \times (\frac{14}{100})^{-1} \times (\sqrt{25})^{-1}\) = \(7 \times \frac{100}{14} \times \frac{1}{5}\) = 10. |
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| 2. |
In a school, 220 students offer Biology or Mathematics or both. 125 offer Biology and 110 mathematics. How many offer Biology but not Mathematics? A. 95 B. 80 C. 125 D. 110 Detailed SolutionHint: Represent the question in a venn diagram, such thatn(B ∩ M) = x n(B) only = 125-x n(M) only = 110-x => 125-x + 110-x + x = 220 => x = 15. n(B) only = 125 - 15 = 110 |
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| 3. |
Simplify 52.4 - 5.7 - 3.45 - 1.75 A. 41.4 B. 41.5 C. 42.1 D. 42.2 Detailed Solution52.4 - 5.7 - 3.45 - 1.75= 52.4 - (5.7 + 3.45 + 1.75) = 52.4 - 10.90 = 41.5 |
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| 4. |
Simplify \((\sqrt{0.7} + \sqrt{70})^{2}\) A. 84.7 B. 70.7 C. 217.7 D. 168.7 Detailed Solution\((\sqrt{0.7} + \sqrt{70})^{2}\)= \((\sqrt{0.7} + \sqrt{70})(\sqrt{0.7} + \sqrt{70})\) = \(0.7 + 2\sqrt{0.7 \times 70} + 70\) = \(0.7 + 14 + 70 \) = 84.7 |
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| 5. |
Evaluate: \(\frac{0.21 \times 0.072 \times 0.00054}{0.006 \times 1.68 \times 0.063}\) A. 0.01286 B. 0.01285 C. 0.1286 D. 0.1285 Detailed Solution\(\frac{0.21 \times 0.072 \times 0.00054}{0.006 \times 1.68 \times 0.063}\)= \(\frac{9 \times 10^{-10}}{7 \times 10^{-8}}\) = \(1.2857 \times 10^{-2}\) = \(0.012857 \approxeq 0.01286\) (to 4 s.f) |
|
| 6. |
A trader bought goats for N4000 each. He sold them for N180,000 at a loss of 25%. How many goats did he buy? A. 60 B. 50 C. 45 D. 36 Detailed SolutionLet the number of goats be XC.P of X goats = N4000X S.P of X goats = (75/100) x 4000X = N3000X 3000X = 180,000 => X = 180000/3000 = 60. X = 60 goats |
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| 7. |
If dy/dx = 2x - 3 and y = 3 when x = 0, find y in terms of x. A. 2x2 - 3x B. x2 - 3x C. x2 - 3x - 3 D. x2 - 3x + 3 Detailed Solutiondy/dx = 2x - 3y = ∫2x - 3 dx => y = x2 - 3x + c 3 = (0)2 - 3(0) + c => c = 3 Thus y = x2 - 3x + 3 |
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| 8. |
Find the derivative of \(y = \sin^{2} (5x)\) with respect to x. A. 10 sin 5x cos 5x B. 5 sin5x cos 5x C. 2 sin 5x cos 5x D. 15 sin 5x cos 5x Detailed Solution\(y = \sin^{2} (5x)\)Let u = sin 5x \(\frac{\mathrm d u}{\mathrm d x} = 5 \cos 5x\) \(\therefore y = u^{2}\) \(\frac{\mathrm d y}{\mathrm d u} = 2u\) \(\frac{\mathrm d y}{\mathrm d x} = 2u . 5 \cos 5x\) = \(10u \cos 5x\) = \(10 \sin 5x \cos 5x\) |
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| 9. |
The slope of the tangent to the curve y = 3x\(^2\) - 2x + 5 at the point (1, 6) is A. 4 B. 1 C. 6 D. 5 Detailed Solutiony = 3x\(^2\) - 2x + 5Slope = \(\frac{\mathrm d y}{\mathrm d x} = 6x - 2\) At x = 1, Slope : 6(1) - 2 = 4. |
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| 10. |
Evaluate \(\int \sin 3x \mathrm d x\) A. (2/3) cos 3x + c B. (1/3) cos 3x + c C. (-1/3) cos 3x + c D. (-2/3) cos 3x + c Detailed Solution\(\int \sin 3x \mathrm d x = - \frac{\cos 3x}{3} + c\)= \(-\frac{1}{3} (\cos 3x) + c\) |
| 1. |
Without using tables, evaluate \((343)^{\frac{1}{3}} \times (0.14)^{-1} \times (25)^{-\frac{1}{2}}\) A. 10 B. 12 C. 8 D. 7 Detailed Solution\((343)^{\frac{1}{3}} \times (0.14)^{-1} \times (25)^{-\frac{1}{2}}\)= \(\sqrt[3]{343} \times (\frac{14}{100})^{-1} \times (\sqrt{25})^{-1}\) = \(7 \times \frac{100}{14} \times \frac{1}{5}\) = 10. |
|
| 2. |
In a school, 220 students offer Biology or Mathematics or both. 125 offer Biology and 110 mathematics. How many offer Biology but not Mathematics? A. 95 B. 80 C. 125 D. 110 Detailed SolutionHint: Represent the question in a venn diagram, such thatn(B ∩ M) = x n(B) only = 125-x n(M) only = 110-x => 125-x + 110-x + x = 220 => x = 15. n(B) only = 125 - 15 = 110 |
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| 3. |
Simplify 52.4 - 5.7 - 3.45 - 1.75 A. 41.4 B. 41.5 C. 42.1 D. 42.2 Detailed Solution52.4 - 5.7 - 3.45 - 1.75= 52.4 - (5.7 + 3.45 + 1.75) = 52.4 - 10.90 = 41.5 |
|
| 4. |
Simplify \((\sqrt{0.7} + \sqrt{70})^{2}\) A. 84.7 B. 70.7 C. 217.7 D. 168.7 Detailed Solution\((\sqrt{0.7} + \sqrt{70})^{2}\)= \((\sqrt{0.7} + \sqrt{70})(\sqrt{0.7} + \sqrt{70})\) = \(0.7 + 2\sqrt{0.7 \times 70} + 70\) = \(0.7 + 14 + 70 \) = 84.7 |
|
| 5. |
Evaluate: \(\frac{0.21 \times 0.072 \times 0.00054}{0.006 \times 1.68 \times 0.063}\) A. 0.01286 B. 0.01285 C. 0.1286 D. 0.1285 Detailed Solution\(\frac{0.21 \times 0.072 \times 0.00054}{0.006 \times 1.68 \times 0.063}\)= \(\frac{9 \times 10^{-10}}{7 \times 10^{-8}}\) = \(1.2857 \times 10^{-2}\) = \(0.012857 \approxeq 0.01286\) (to 4 s.f) |
| 6. |
A trader bought goats for N4000 each. He sold them for N180,000 at a loss of 25%. How many goats did he buy? A. 60 B. 50 C. 45 D. 36 Detailed SolutionLet the number of goats be XC.P of X goats = N4000X S.P of X goats = (75/100) x 4000X = N3000X 3000X = 180,000 => X = 180000/3000 = 60. X = 60 goats |
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| 7. |
If dy/dx = 2x - 3 and y = 3 when x = 0, find y in terms of x. A. 2x2 - 3x B. x2 - 3x C. x2 - 3x - 3 D. x2 - 3x + 3 Detailed Solutiondy/dx = 2x - 3y = ∫2x - 3 dx => y = x2 - 3x + c 3 = (0)2 - 3(0) + c => c = 3 Thus y = x2 - 3x + 3 |
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| 8. |
Find the derivative of \(y = \sin^{2} (5x)\) with respect to x. A. 10 sin 5x cos 5x B. 5 sin5x cos 5x C. 2 sin 5x cos 5x D. 15 sin 5x cos 5x Detailed Solution\(y = \sin^{2} (5x)\)Let u = sin 5x \(\frac{\mathrm d u}{\mathrm d x} = 5 \cos 5x\) \(\therefore y = u^{2}\) \(\frac{\mathrm d y}{\mathrm d u} = 2u\) \(\frac{\mathrm d y}{\mathrm d x} = 2u . 5 \cos 5x\) = \(10u \cos 5x\) = \(10 \sin 5x \cos 5x\) |
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| 9. |
The slope of the tangent to the curve y = 3x\(^2\) - 2x + 5 at the point (1, 6) is A. 4 B. 1 C. 6 D. 5 Detailed Solutiony = 3x\(^2\) - 2x + 5Slope = \(\frac{\mathrm d y}{\mathrm d x} = 6x - 2\) At x = 1, Slope : 6(1) - 2 = 4. |
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| 10. |
Evaluate \(\int \sin 3x \mathrm d x\) A. (2/3) cos 3x + c B. (1/3) cos 3x + c C. (-1/3) cos 3x + c D. (-2/3) cos 3x + c Detailed Solution\(\int \sin 3x \mathrm d x = - \frac{\cos 3x}{3} + c\)= \(-\frac{1}{3} (\cos 3x) + c\) |