Year :
2013
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
11 - 20 of 48 Questions
| # | Question | Ans |
|---|---|---|
| 11. |
The remainder when 6p3 - p2 - 47p + 30 is divided by p - 3 is A. 21 B. 42 C. 63 D. 18 |
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| 12. |
P varies jointly as m and u, and varies inversely as q. Given that p = 4, m = 3 and u = 2 and q = 1, find the value of p when m = 6, u = 4 and q =\(\frac{8}{5}\) A. 12\(\frac{8}{5}\) B. 15 C. 10 D. 28\(\frac{8}{5}\) |
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| 13. |
If r varies inversely as the square root of s and t, how does s vary with r and t? A. s varies inversely as r and t2 B. s varies inverely as r2 and t C. s varies directly as r2 and t2 D. s varies directly as r and t |
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| 14. |
Evaluate 3(x + 2) > 6(x + 3) A. x < 4 B. x > -4 C. x < -4 D. x > 4 |
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| 15. |
Solve for x: |x - 2| < 3 A. x < 5 B. -2 < x < 3 C. -1 < x < 5 D. x < 1 Detailed Solution|x - 2| < 3 implies-(x - 2) < 3 .... or .... +(x - 2) < 3 -x + 2 < 3 .... or .... x - 2 < 3 -x < 3 - 2 .... or .... x < 3 + 2 x > -1 .... or .... x < 5 combining the two inequalities results, we get; -1 < x < 5 There is an explanation video available below. |
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| 16. |
The nth term of the progression \(\frac{4}{2}\), \(\frac{7}{3}\), \(\frac{10}{4}\), \(\frac{13}{5}\) is ... A. \(\frac{1 - 3n}{n + 1}\) B. \(\frac{3n + 1}{n + 1}\) C. \(\frac{3n + 1}{n - 1}\) D. \(\frac{3n - 1}{n + 1}\) |
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| 17. |
If a binary operation * is defined by x * y = x + 2y, find 2 * (3 * 4) A. 24 B. 16 C. 14 D. 26 |
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| 18. |
If P = \(\begin{pmatrix} 5 & 3 \\ 2 & 1 \end{pmatrix}\) and Q = \(\begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}\), find 2P + Q A. \(\begin{vmatrix} 7 & 7 \\ 14 & 8 \end{vmatrix}\) B. \(\begin{vmatrix} 14 & 8 \\ 7 & 7 \end{vmatrix}\) C. \(\begin{vmatrix} 7 & 7 \\ 8 & 14 \end{vmatrix}\) D. \(\begin{vmatrix} 8 & 14 \\ 7 & 7 \end{vmatrix}\) Detailed Solution2P + Q = 2\(\begin{pmatrix} 5 & 3 \\ 2 & 1 \end{pmatrix}\) + \(\begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}\)= \(\begin{pmatrix} 10 & 6 \\ 4 & 2 \end{pmatrix}\) + \(\begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}\) = \(\begin{pmatrix} 14 & 8 \\ 7 & 7 \end{pmatrix}\) There is an explanation video available below. |
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| 19. |
Find the inverse \(\begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix}\) A. \(\begin{vmatrix} 2 & -\frac{3}{2} \\ -3 & -\frac{5}{2} \end{vmatrix}\) B. \(\begin{vmatrix} 2 & -\frac{3}{2} \\ -3 & \frac{5}{2} \end{vmatrix}\) C. \(\begin{vmatrix} 2 & \frac{3}{2} \\ -3 & \frac{5}{2} \end{vmatrix}\) D. \(\begin{vmatrix} 2 & \frac{3}{2} \\ -3 & \frac{5}{2} \end{vmatrix}\) Detailed SolutionLet A = \(\begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix}\)Then |A| = \(\begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix}\) = 20 - 18 = 2 Hence A-1 = \(\frac{1}{|A|}\begin{pmatrix} 4 & -3 \\ -6 & 5 \end{pmatrix}\) = \(\frac{1}{2}\begin{pmatrix} 4 & -3 \\ -6 & 5 \end{pmatrix}\) = \(\begin{pmatrix} 4 \times 1/2 & -3 \times 1/2 \\ -6 \times 1/2 & 5 \times 1/2 \end{pmatrix}\) = \(\begin{pmatrix} 2 & -\frac{3}{2} \\ -3 & \frac{5}{2} \end{pmatrix}\) There is an explanation video available |
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| 20. |
If y = x sin x, find \(\frac{\delta y}{\delta x}\) A. sin x - cos x B. cos x - x sin x C. cos x + x sin x D. sin x + x cos x |
| 11. |
The remainder when 6p3 - p2 - 47p + 30 is divided by p - 3 is A. 21 B. 42 C. 63 D. 18 |
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| 12. |
P varies jointly as m and u, and varies inversely as q. Given that p = 4, m = 3 and u = 2 and q = 1, find the value of p when m = 6, u = 4 and q =\(\frac{8}{5}\) A. 12\(\frac{8}{5}\) B. 15 C. 10 D. 28\(\frac{8}{5}\) |
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| 13. |
If r varies inversely as the square root of s and t, how does s vary with r and t? A. s varies inversely as r and t2 B. s varies inverely as r2 and t C. s varies directly as r2 and t2 D. s varies directly as r and t |
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| 14. |
Evaluate 3(x + 2) > 6(x + 3) A. x < 4 B. x > -4 C. x < -4 D. x > 4 |
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| 15. |
Solve for x: |x - 2| < 3 A. x < 5 B. -2 < x < 3 C. -1 < x < 5 D. x < 1 Detailed Solution|x - 2| < 3 implies-(x - 2) < 3 .... or .... +(x - 2) < 3 -x + 2 < 3 .... or .... x - 2 < 3 -x < 3 - 2 .... or .... x < 3 + 2 x > -1 .... or .... x < 5 combining the two inequalities results, we get; -1 < x < 5 There is an explanation video available below. |
| 16. |
The nth term of the progression \(\frac{4}{2}\), \(\frac{7}{3}\), \(\frac{10}{4}\), \(\frac{13}{5}\) is ... A. \(\frac{1 - 3n}{n + 1}\) B. \(\frac{3n + 1}{n + 1}\) C. \(\frac{3n + 1}{n - 1}\) D. \(\frac{3n - 1}{n + 1}\) |
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| 17. |
If a binary operation * is defined by x * y = x + 2y, find 2 * (3 * 4) A. 24 B. 16 C. 14 D. 26 |
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| 18. |
If P = \(\begin{pmatrix} 5 & 3 \\ 2 & 1 \end{pmatrix}\) and Q = \(\begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}\), find 2P + Q A. \(\begin{vmatrix} 7 & 7 \\ 14 & 8 \end{vmatrix}\) B. \(\begin{vmatrix} 14 & 8 \\ 7 & 7 \end{vmatrix}\) C. \(\begin{vmatrix} 7 & 7 \\ 8 & 14 \end{vmatrix}\) D. \(\begin{vmatrix} 8 & 14 \\ 7 & 7 \end{vmatrix}\) Detailed Solution2P + Q = 2\(\begin{pmatrix} 5 & 3 \\ 2 & 1 \end{pmatrix}\) + \(\begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}\)= \(\begin{pmatrix} 10 & 6 \\ 4 & 2 \end{pmatrix}\) + \(\begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}\) = \(\begin{pmatrix} 14 & 8 \\ 7 & 7 \end{pmatrix}\) There is an explanation video available below. |
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| 19. |
Find the inverse \(\begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix}\) A. \(\begin{vmatrix} 2 & -\frac{3}{2} \\ -3 & -\frac{5}{2} \end{vmatrix}\) B. \(\begin{vmatrix} 2 & -\frac{3}{2} \\ -3 & \frac{5}{2} \end{vmatrix}\) C. \(\begin{vmatrix} 2 & \frac{3}{2} \\ -3 & \frac{5}{2} \end{vmatrix}\) D. \(\begin{vmatrix} 2 & \frac{3}{2} \\ -3 & \frac{5}{2} \end{vmatrix}\) Detailed SolutionLet A = \(\begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix}\)Then |A| = \(\begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix}\) = 20 - 18 = 2 Hence A-1 = \(\frac{1}{|A|}\begin{pmatrix} 4 & -3 \\ -6 & 5 \end{pmatrix}\) = \(\frac{1}{2}\begin{pmatrix} 4 & -3 \\ -6 & 5 \end{pmatrix}\) = \(\begin{pmatrix} 4 \times 1/2 & -3 \times 1/2 \\ -6 \times 1/2 & 5 \times 1/2 \end{pmatrix}\) = \(\begin{pmatrix} 2 & -\frac{3}{2} \\ -3 & \frac{5}{2} \end{pmatrix}\) There is an explanation video available |
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| 20. |
If y = x sin x, find \(\frac{\delta y}{\delta x}\) A. sin x - cos x B. cos x - x sin x C. cos x + x sin x D. sin x + x cos x |