Year :
2011
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
31 - 40 of 46 Questions
| # | Question | Ans |
|---|---|---|
| 31. |
A man walks 100 m due West from a point X to Y, he then walks 100 m due North to a point Z. Find the bearing of X from Z. A. 195o B. 135o C. 225o D. 045o |
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| 32. |
The derivatives of (2x + 1)(3x + 1) is A. 12x + 1 B. 6x + 5 C. 6x + 1 D. 12x + 5 Detailed Solution2x + 1 \(\frac{d(3x + 1)}{\mathrm d x}\) + (3x + 1) \(\frac{d(2x + 1)}{\mathrm d x}\)2x + 1 (3) + (3x + 1) (2) 6x + 3 + 6x + 2 = 12x + 5 There is an explanation video available below. |
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| 33. |
\(\begin{array}{c|c} Class Intervals & 0 - 2 & 3 - 5 & 6 - 8 & 9 - 11 & \\ \hline Frequency & 3 & 2 & 5 & 3 &\end{array}\) A. 9 B. 8 C. 10 D. 7 |
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| 34. |
Find the value of x at the minimum point of the curve y = x3 + x2 - x + 1 A. \(\frac{1}{3}\) B. -\(\frac{1}{3}\) C. 1 D. -1 Detailed Solutiony = x3 + x2 - x + 1\(\frac{dy}{dx}\) = \(\frac{d(x^3)}{dx}\) + \(\frac{d(x^2)}{dx}\) - \(\frac{d(x)}{dx}\) + \(\frac{d(1)}{dx}\) \(\frac{dy}{dx}\) = 3x2 + 2x - 1 = 0 \(\frac{dy}{dx}\) = 3x2 + 2x - 1 At the maximum point \(\frac{dy}{dx}\) = 0 3x2 + 2x - 1 = 0 (3x2 + 3x) - (x - 1) = 0 3x(x + 1) -1(x + 1) = 0 (3x - 1)(x + 1) = 0 therefore x = \(\frac{1}{3}\) or -1 For the maximum point \(\frac{d^2y}{dx^2}\) < 0 \(\frac{d^2y}{dx^2}\) 6x + 2&l |
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| 35. |
Evaluate \(\int^{1}_{0}\)(3 - 2x)dx A. 33m B. 5 C. 2 D. 6 Detailed Solution\(\int^{1}_{0}\)(3 - 2x)dx[3x - x\(^2\)]\(_{0} ^{1}\) [3(1) - (1)\(^2\)] - [3(0) - (0)\(^2\)] (3 - 1) - (0 - 0) = 2 - 0 = 2 There is an explanation video available below. |
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| 36. |
Find \(\int\) cos4 x dx A. \(\frac{3}{4}\) sin 4x + k B. -\(\frac{1}{4}\) sin 4x + k C. -\(\frac{3}{4}\) sin 4x + k D. \(\frac{1}{4}\) sin 4x + k Detailed Solution\(\int\) cos4 x dxlet u = 4x \(\frac{dy}{dx}\) = 4 dx = \(\frac{dy}{4}\) \(\int\)cos u. \(\frac{dy}{4}\) = \(\frac{1}{4}\)\(\int\)cos u du = \(\frac{1}{4}\) sin u + k = \(\frac{1}{4}\) sin4x + k There is an explanation video available below. |
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| 37. |
The sum of four consecutive integers is 34. Find the least of these numbers A. 7 B. 6 C. 8 D. 5 |
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| 38. |
\(\begin{array}{c|c} No & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline Frequency & 1 & 4 & 3 & 8 & 2 & 5 \end{array}\). From the table above, find the median and range of the data respectively. A. (8,5) B. (3, 5) C. (5 , 8) D. (5 , 3) |
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| 39. |
\(\begin{array}{c|c} A. √5 B. √6 C. √7 D. √2 |
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| 40. |
In how many was can the letters of the word ELATION be arranged? A. 6! B. 7! C. 5! D. 8! Detailed SolutionELATIONSince there are 7 letters. The first letter can be arranged in 7 ways, , the second letter in 6 ways, the third letter in 5 ways, the 4th letter in four ways, the 3rd letter in three ways, the 2nd letter in 2 ways and the last in one way. therefore, 7 x 6 x 5 x 4 x 3 x 2 x 1 = 7! ways There is an explanation video available below. |
| 31. |
A man walks 100 m due West from a point X to Y, he then walks 100 m due North to a point Z. Find the bearing of X from Z. A. 195o B. 135o C. 225o D. 045o |
|
| 32. |
The derivatives of (2x + 1)(3x + 1) is A. 12x + 1 B. 6x + 5 C. 6x + 1 D. 12x + 5 Detailed Solution2x + 1 \(\frac{d(3x + 1)}{\mathrm d x}\) + (3x + 1) \(\frac{d(2x + 1)}{\mathrm d x}\)2x + 1 (3) + (3x + 1) (2) 6x + 3 + 6x + 2 = 12x + 5 There is an explanation video available below. |
|
| 33. |
\(\begin{array}{c|c} Class Intervals & 0 - 2 & 3 - 5 & 6 - 8 & 9 - 11 & \\ \hline Frequency & 3 & 2 & 5 & 3 &\end{array}\) A. 9 B. 8 C. 10 D. 7 |
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| 34. |
Find the value of x at the minimum point of the curve y = x3 + x2 - x + 1 A. \(\frac{1}{3}\) B. -\(\frac{1}{3}\) C. 1 D. -1 Detailed Solutiony = x3 + x2 - x + 1\(\frac{dy}{dx}\) = \(\frac{d(x^3)}{dx}\) + \(\frac{d(x^2)}{dx}\) - \(\frac{d(x)}{dx}\) + \(\frac{d(1)}{dx}\) \(\frac{dy}{dx}\) = 3x2 + 2x - 1 = 0 \(\frac{dy}{dx}\) = 3x2 + 2x - 1 At the maximum point \(\frac{dy}{dx}\) = 0 3x2 + 2x - 1 = 0 (3x2 + 3x) - (x - 1) = 0 3x(x + 1) -1(x + 1) = 0 (3x - 1)(x + 1) = 0 therefore x = \(\frac{1}{3}\) or -1 For the maximum point \(\frac{d^2y}{dx^2}\) < 0 \(\frac{d^2y}{dx^2}\) 6x + 2&l |
|
| 35. |
Evaluate \(\int^{1}_{0}\)(3 - 2x)dx A. 33m B. 5 C. 2 D. 6 Detailed Solution\(\int^{1}_{0}\)(3 - 2x)dx[3x - x\(^2\)]\(_{0} ^{1}\) [3(1) - (1)\(^2\)] - [3(0) - (0)\(^2\)] (3 - 1) - (0 - 0) = 2 - 0 = 2 There is an explanation video available below. |
| 36. |
Find \(\int\) cos4 x dx A. \(\frac{3}{4}\) sin 4x + k B. -\(\frac{1}{4}\) sin 4x + k C. -\(\frac{3}{4}\) sin 4x + k D. \(\frac{1}{4}\) sin 4x + k Detailed Solution\(\int\) cos4 x dxlet u = 4x \(\frac{dy}{dx}\) = 4 dx = \(\frac{dy}{4}\) \(\int\)cos u. \(\frac{dy}{4}\) = \(\frac{1}{4}\)\(\int\)cos u du = \(\frac{1}{4}\) sin u + k = \(\frac{1}{4}\) sin4x + k There is an explanation video available below. |
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| 37. |
The sum of four consecutive integers is 34. Find the least of these numbers A. 7 B. 6 C. 8 D. 5 |
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| 38. |
\(\begin{array}{c|c} No & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline Frequency & 1 & 4 & 3 & 8 & 2 & 5 \end{array}\). From the table above, find the median and range of the data respectively. A. (8,5) B. (3, 5) C. (5 , 8) D. (5 , 3) |
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| 39. |
\(\begin{array}{c|c} A. √5 B. √6 C. √7 D. √2 |
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| 40. |
In how many was can the letters of the word ELATION be arranged? A. 6! B. 7! C. 5! D. 8! Detailed SolutionELATIONSince there are 7 letters. The first letter can be arranged in 7 ways, , the second letter in 6 ways, the third letter in 5 ways, the 4th letter in four ways, the 3rd letter in three ways, the 2nd letter in 2 ways and the last in one way. therefore, 7 x 6 x 5 x 4 x 3 x 2 x 1 = 7! ways There is an explanation video available below. |