Year :
2008
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
31 - 40 of 49 Questions
| # | Question | Ans |
|---|---|---|
| 31. |
Find the derivative of \(y=\frac{x^7 - x^5}{x^4}\) A. x(x2-1) B. 3x(x2-1) C. 3x2-1 D. 7x6-5x4 Detailed Solution\(y=\frac{x^7 - x^5}{x^4}\\y = \frac{x^7}{x^4} \div \frac{x^5}{x^4}\\ y = x^3 - x \\ \frac{dy}{dx} = 3x^2 - 1\) There is an explanation video available below. |
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| 32. |
Differentiate sin x - x cos x A. x cos x B. x sin x C. -x cos x D. -x sin x Detailed Solutionsin x - x cos xdy/dx = cos x - [1.cos x + x -sin x] = co x - [cos x - x sin x] = cos x - cos x + x sin x = x sin x There is an explanation video available below. |
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| 33. |
Find the minimum value of the function y = x(1+x) A. -1/4 B. -1/2 C. 1/4 D. 1/2 Detailed Solutiony = x(1+x)= x + x2 dy/dx = 1 + 2x As dy/dy → 0 1 + 2x = 0 2x = -1 X = -1/2 Y = x(1+x) = -1/2(1 - 1/2) at x = -1/2 = -1/2(1/2) = -1/4 There is an explanation video available below. |
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| 34. |
Evaluate \(\int_1 ^2(6x^2-2x)dx\) A. 16 B. 13 C. 12 D. 11 Detailed Solution\(\int_1 ^2(6x^2-2x)dx=[\frac{6x^3}{3}-\frac{2x^2}{2}]_1 ^2\\= [2x^3 - x^2]_1^2\) = [2(2)3 - (2)2] – [2(1)3 - (1)2] = [16-4] – [2-1] = 12 – 1 = 11 There is an explanation video available below. |
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| 35. |
Evaluate \(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx\) A. zero B. 1 C. 2 D. 3 Detailed Solution\(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx = [sinx]^{\frac{\pi}{2}} _{\frac{-\pi}{2}}\\=sin\frac{\pi}{2} - sin\frac{-\pi}{2}\) = sin90 – sin-90 = sin90 – sin270 = 1 – (-1) = 1+1 = 2 There is an explanation video available below. |
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| 36. |
On a pie chart there are six sectors of which four angles are 30°, 45°, 60°, 90° and the remaining two angles are in the ratio 2:1. Find the smallest angles of the remaining two angles. A. 15o B. 30o C. 45o D. 60o Detailed Solution30 + 45 + 60 + 90 + 2x + x = 360°225 + 3x = 360 3x = 360 - 225 3x = 135 x = 45° There is an explanation video available below. |
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| 37. |
 The bar chart above shows the number of times the word "a, and , in, it, the ,to" appear in a paragraph in a book.What is the ratio of the least frequent word to the most frequent word? A. 1/6 B. 1/3 C. 2/3 D. 3/4 Detailed SolutionRatio of least to most = 2:12= 2/12 = 1/6 There is an explanation video available below. |
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| 38. |
What is the mean of the data t, 2t-1, t-2, 2t -1, 4t and 2t+2? A. 2t B. 2t-1 C. 2/3t+1 D. 2t-1/3 Detailed Solution\(Mean = \frac{t+2t-1+t-2+2t-1+4t+2t+2}{6}\\Mean = \frac{12t-2}{6}\\ =\frac{2(6t-1)}{6}\\ =\frac{6t-1}{3}\\ =\frac{6t}{3}- \frac{1}{3}\\ =2t-\frac{1}{3}\) There is an explanation video available below. |
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| 39. |
Find the median of 4, 1, 4, 1, 0, 4, 4, 2 and 0 A. zero B. 1 C. 2 D. 4 Detailed Solution4, 4, 1, 0, 4, 4, 2, 0Arrange in ascending order: 0, 0, 1, 1, 2, 4, 4, 4, 4 Position of median = N+1 / 2 = 9+1 / 2 = 5th Median = 2 There is an explanation video available below. |
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| 40. |
If x > 0, find the range of number x-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x and 3x+1 A. 3x+3 B. 3x+1 C. 2x+5 D. 2x+1 Detailed Solutionx-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x, 3x+1Range = 4x - (x-3) = 3x + 3 There is an explanation video available below. |
| 31. |
Find the derivative of \(y=\frac{x^7 - x^5}{x^4}\) A. x(x2-1) B. 3x(x2-1) C. 3x2-1 D. 7x6-5x4 Detailed Solution\(y=\frac{x^7 - x^5}{x^4}\\y = \frac{x^7}{x^4} \div \frac{x^5}{x^4}\\ y = x^3 - x \\ \frac{dy}{dx} = 3x^2 - 1\) There is an explanation video available below. |
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| 32. |
Differentiate sin x - x cos x A. x cos x B. x sin x C. -x cos x D. -x sin x Detailed Solutionsin x - x cos xdy/dx = cos x - [1.cos x + x -sin x] = co x - [cos x - x sin x] = cos x - cos x + x sin x = x sin x There is an explanation video available below. |
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| 33. |
Find the minimum value of the function y = x(1+x) A. -1/4 B. -1/2 C. 1/4 D. 1/2 Detailed Solutiony = x(1+x)= x + x2 dy/dx = 1 + 2x As dy/dy → 0 1 + 2x = 0 2x = -1 X = -1/2 Y = x(1+x) = -1/2(1 - 1/2) at x = -1/2 = -1/2(1/2) = -1/4 There is an explanation video available below. |
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| 34. |
Evaluate \(\int_1 ^2(6x^2-2x)dx\) A. 16 B. 13 C. 12 D. 11 Detailed Solution\(\int_1 ^2(6x^2-2x)dx=[\frac{6x^3}{3}-\frac{2x^2}{2}]_1 ^2\\= [2x^3 - x^2]_1^2\) = [2(2)3 - (2)2] – [2(1)3 - (1)2] = [16-4] – [2-1] = 12 – 1 = 11 There is an explanation video available below. |
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| 35. |
Evaluate \(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx\) A. zero B. 1 C. 2 D. 3 Detailed Solution\(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx = [sinx]^{\frac{\pi}{2}} _{\frac{-\pi}{2}}\\=sin\frac{\pi}{2} - sin\frac{-\pi}{2}\) = sin90 – sin-90 = sin90 – sin270 = 1 – (-1) = 1+1 = 2 There is an explanation video available below. |
| 36. |
On a pie chart there are six sectors of which four angles are 30°, 45°, 60°, 90° and the remaining two angles are in the ratio 2:1. Find the smallest angles of the remaining two angles. A. 15o B. 30o C. 45o D. 60o Detailed Solution30 + 45 + 60 + 90 + 2x + x = 360°225 + 3x = 360 3x = 360 - 225 3x = 135 x = 45° There is an explanation video available below. |
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| 37. |
The bar chart above shows the number of times the word "a, and , in, it, the ,to" appear in a paragraph in a book.What is the ratio of the least frequent word to the most frequent word? A. 1/6 B. 1/3 C. 2/3 D. 3/4 Detailed SolutionRatio of least to most = 2:12= 2/12 = 1/6 There is an explanation video available below. |
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| 38. |
What is the mean of the data t, 2t-1, t-2, 2t -1, 4t and 2t+2? A. 2t B. 2t-1 C. 2/3t+1 D. 2t-1/3 Detailed Solution\(Mean = \frac{t+2t-1+t-2+2t-1+4t+2t+2}{6}\\Mean = \frac{12t-2}{6}\\ =\frac{2(6t-1)}{6}\\ =\frac{6t-1}{3}\\ =\frac{6t}{3}- \frac{1}{3}\\ =2t-\frac{1}{3}\) There is an explanation video available below. |
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| 39. |
Find the median of 4, 1, 4, 1, 0, 4, 4, 2 and 0 A. zero B. 1 C. 2 D. 4 Detailed Solution4, 4, 1, 0, 4, 4, 2, 0Arrange in ascending order: 0, 0, 1, 1, 2, 4, 4, 4, 4 Position of median = N+1 / 2 = 9+1 / 2 = 5th Median = 2 There is an explanation video available below. |
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| 40. |
If x > 0, find the range of number x-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x and 3x+1 A. 3x+3 B. 3x+1 C. 2x+5 D. 2x+1 Detailed Solutionx-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x, 3x+1Range = 4x - (x-3) = 3x + 3 There is an explanation video available below. |