Year :
1995
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
11 - 20 of 46 Questions
| # | Question | Ans |
|---|---|---|
| 11. |
Finds a positive value of p if the expression 2x2 - px + p leaves a remainder 6 when divided by x - p and q A. 1 B. 2 C. 3 D. 4 Detailed Solutionx - p,x = p2p2 - p2 + p = 6 = p2 + p - 6 = 0 p = 3, 2 |
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| 12. |
Find T in terms of K, Q and S if S = 2r(\(\piQT + K) A. \(\frac{S^2}{2 \pi r^2Q} - \frac{k}{Q}\) B. \(\frac{S^2}{2 \pi r^2Q}\) - k C. \(\frac{S^2}{4 \pi r^2Q} - \frac{k}{Q}\) D. \(\frac{s^2}{4 \pi r^2Q}\) Detailed Solution\(\frac{s^2}{4r^2}\) = QT\(\pi\) + KT\(\frac{s^2}{4r^2}\) - k\(\pi\) = QT\(\pi\) T = \(\frac{s^2}{4Q\pi r^2}\) - k |
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| 13. |
The graph of f(x) = x2 - 5x + 6 crosses the x-axis at the points A. (-6, 0), (-1, 0) B. (-3, 0), (-2,0) C. (-6, 0),(1, 0) D. (2, 0), (3, 0) Detailed SolutionWhen X = 3, Y = 0(3, 0),When x = 2, y = 0(2, 0) |
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| 14. |
Factorize completely the expression \(abx^2 + 6y - 3ax - 2byx\) A. (ax - 2y)(bx - 3) B. (bx + 3)(2y - ax) C. (bx + 3)(ax - 2y) D. (ax - 2y)(ax - b) Detailed Solution\(abx^{2} + 6y - 3ax - 2byx\)Collecting like terms, we have \(abx^{2} - 3ax + 6y - 2byx\) = \(ax(bx - 3) + 2y(3 - bx)\) = \(ax(bx - 3) - 2y(bx - 3)\) = \((ax - 2y)(bx - 3)\) |
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| 15. |
Solve the inequality (x - 3)(x - 4) \(\leq\) 0 A. 3 \(\leq\) x \(\leq\) 4 B. 3 < x < 4 C. 3 \(\leq\) x < 4 D. 3 < x \(\leq\) 4 Detailed Solution(x - 3)(x - 4) \(\leq\) 0Case 1 (+, -) = x - 3 \(\geq\) 0, X - 4 \(\geq\) 0 = X \(\leq\) 3, x \(\geq\) 4 = 3 < x \(\geq\) 4 (solution) Case 2 = (-, +) = x - 3 \(\leq\) 0, x - 4 \(\geq\) 0 = x \(\leq\) 3, x \(\geq\) 4 therefore = 3 \(\leq\) x \(\leq\) 4 |
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| 16. |
The 4th term of an A.P. is 13 while the 10th term is 31. Find the 21st term. A. 175 B. 85 C. 64 D. 45 Detailed Solutiona + 3d = 13a + 9d = 31 6d = 18 = d = 3 a = 13 - 9 = 4 a + 20d = 4 + (20 x 3) = 64 |
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| 17. |
Simplify \(\frac{x^2 - 1}{x^3 + 2x^2 - x - 2}\) A. \(\frac{1}{x + 2}\) B. \(\frac{x - 1}{x + 1}\) C. \(\frac{x - 1}{x + 2}\) D. \(\frac{1}{x - 2}\) Detailed Solution\(\frac{x^2 - 1}{(x - 1)(x + 2)(x + 1)}\) = \(\frac{(x -1)(x + 1)}{(x - 1)(x + 2)(x + 1)}\) = \(\frac{1}{x + 2}\) |
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| 18. |
Express \(\frac{5x - 12}{(x - 2)(x - 3)}\) in partial fractions A. \(\frac{2}{x + 2} - \frac{3}{x - 3}\) B. \(\frac{2}{x - 2} + \frac{3}{x - 3}\) C. \(\frac{2}{x - 3} - \frac{3}{x - 2}\) D. \(\frac{5}{x - 3} - \frac{4}{x - 2}\) Detailed Solution\(\frac{5x - 12}{(x - 2)(x - 3)} = \frac{A}{x - 2} + \frac{B}{x - 3}\)= \(\frac{A(x - 3) + B(x - 2)}{(x - 2)(x - 3)}\) \(\implies 5x - 12 = Ax - 3A + Bx - 2B\) \(A + B = 5 ... (i)\) \(-(3A + 2B) = -12 \implies 3A + 2B = 12 ... (ii)\) From (i), \(A = 5 - B\) \(3(5 - B) + 2B = 12\) \(15 - 3B + 2B = 12 \implies B = 3\) \(A + 3 = 5 \implies A = 2\) \(\frac{5x - 12}{(x - 2)(x - 3)} = \frac{2}{x - 2} + \frac{3}{x - 3}\) |
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| 19. |
Which of the following binary operations is cumulative on the set of integers? A. a \(\ast\) b = a + 2b B. a \(\ast\) b = a + b - ab C. a \(\ast\) b = a2 + b D. a \(\ast\) b = \(\frac{a(b + 1)}{2}\) Detailed Solution\(a \ast b = a + b - ab\)\(b \ast a = b + a - ba\) On the set of integers, the two above are cumulative as multiplication and addition are cumulative on the set of integers. |
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| 20. |
If a \(\ast\) b = + \(\sqrt{ab}\), evaluate 2 \(\ast\)(12 \(\ast\) 27) A. 12 B. 9 C. 6 D. 2 Detailed Solution\(2 \ast (12 \ast 27)\)\(12 \ast 27 = + \sqrt{12 \times 27}\) = \(+ \sqrt{324} = 18\) \(2 \ast 18 = + \sqrt{2 \times 18}\) = \(+ \sqrt{36} = 6\) |
| 11. |
Finds a positive value of p if the expression 2x2 - px + p leaves a remainder 6 when divided by x - p and q A. 1 B. 2 C. 3 D. 4 Detailed Solutionx - p,x = p2p2 - p2 + p = 6 = p2 + p - 6 = 0 p = 3, 2 |
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| 12. |
Find T in terms of K, Q and S if S = 2r(\(\piQT + K) A. \(\frac{S^2}{2 \pi r^2Q} - \frac{k}{Q}\) B. \(\frac{S^2}{2 \pi r^2Q}\) - k C. \(\frac{S^2}{4 \pi r^2Q} - \frac{k}{Q}\) D. \(\frac{s^2}{4 \pi r^2Q}\) Detailed Solution\(\frac{s^2}{4r^2}\) = QT\(\pi\) + KT\(\frac{s^2}{4r^2}\) - k\(\pi\) = QT\(\pi\) T = \(\frac{s^2}{4Q\pi r^2}\) - k |
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| 13. |
The graph of f(x) = x2 - 5x + 6 crosses the x-axis at the points A. (-6, 0), (-1, 0) B. (-3, 0), (-2,0) C. (-6, 0),(1, 0) D. (2, 0), (3, 0) Detailed SolutionWhen X = 3, Y = 0(3, 0),When x = 2, y = 0(2, 0) |
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| 14. |
Factorize completely the expression \(abx^2 + 6y - 3ax - 2byx\) A. (ax - 2y)(bx - 3) B. (bx + 3)(2y - ax) C. (bx + 3)(ax - 2y) D. (ax - 2y)(ax - b) Detailed Solution\(abx^{2} + 6y - 3ax - 2byx\)Collecting like terms, we have \(abx^{2} - 3ax + 6y - 2byx\) = \(ax(bx - 3) + 2y(3 - bx)\) = \(ax(bx - 3) - 2y(bx - 3)\) = \((ax - 2y)(bx - 3)\) |
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| 15. |
Solve the inequality (x - 3)(x - 4) \(\leq\) 0 A. 3 \(\leq\) x \(\leq\) 4 B. 3 < x < 4 C. 3 \(\leq\) x < 4 D. 3 < x \(\leq\) 4 Detailed Solution(x - 3)(x - 4) \(\leq\) 0Case 1 (+, -) = x - 3 \(\geq\) 0, X - 4 \(\geq\) 0 = X \(\leq\) 3, x \(\geq\) 4 = 3 < x \(\geq\) 4 (solution) Case 2 = (-, +) = x - 3 \(\leq\) 0, x - 4 \(\geq\) 0 = x \(\leq\) 3, x \(\geq\) 4 therefore = 3 \(\leq\) x \(\leq\) 4 |
| 16. |
The 4th term of an A.P. is 13 while the 10th term is 31. Find the 21st term. A. 175 B. 85 C. 64 D. 45 Detailed Solutiona + 3d = 13a + 9d = 31 6d = 18 = d = 3 a = 13 - 9 = 4 a + 20d = 4 + (20 x 3) = 64 |
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| 17. |
Simplify \(\frac{x^2 - 1}{x^3 + 2x^2 - x - 2}\) A. \(\frac{1}{x + 2}\) B. \(\frac{x - 1}{x + 1}\) C. \(\frac{x - 1}{x + 2}\) D. \(\frac{1}{x - 2}\) Detailed Solution\(\frac{x^2 - 1}{(x - 1)(x + 2)(x + 1)}\) = \(\frac{(x -1)(x + 1)}{(x - 1)(x + 2)(x + 1)}\) = \(\frac{1}{x + 2}\) |
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| 18. |
Express \(\frac{5x - 12}{(x - 2)(x - 3)}\) in partial fractions A. \(\frac{2}{x + 2} - \frac{3}{x - 3}\) B. \(\frac{2}{x - 2} + \frac{3}{x - 3}\) C. \(\frac{2}{x - 3} - \frac{3}{x - 2}\) D. \(\frac{5}{x - 3} - \frac{4}{x - 2}\) Detailed Solution\(\frac{5x - 12}{(x - 2)(x - 3)} = \frac{A}{x - 2} + \frac{B}{x - 3}\)= \(\frac{A(x - 3) + B(x - 2)}{(x - 2)(x - 3)}\) \(\implies 5x - 12 = Ax - 3A + Bx - 2B\) \(A + B = 5 ... (i)\) \(-(3A + 2B) = -12 \implies 3A + 2B = 12 ... (ii)\) From (i), \(A = 5 - B\) \(3(5 - B) + 2B = 12\) \(15 - 3B + 2B = 12 \implies B = 3\) \(A + 3 = 5 \implies A = 2\) \(\frac{5x - 12}{(x - 2)(x - 3)} = \frac{2}{x - 2} + \frac{3}{x - 3}\) |
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| 19. |
Which of the following binary operations is cumulative on the set of integers? A. a \(\ast\) b = a + 2b B. a \(\ast\) b = a + b - ab C. a \(\ast\) b = a2 + b D. a \(\ast\) b = \(\frac{a(b + 1)}{2}\) Detailed Solution\(a \ast b = a + b - ab\)\(b \ast a = b + a - ba\) On the set of integers, the two above are cumulative as multiplication and addition are cumulative on the set of integers. |
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| 20. |
If a \(\ast\) b = + \(\sqrt{ab}\), evaluate 2 \(\ast\)(12 \(\ast\) 27) A. 12 B. 9 C. 6 D. 2 Detailed Solution\(2 \ast (12 \ast 27)\)\(12 \ast 27 = + \sqrt{12 \times 27}\) = \(+ \sqrt{324} = 18\) \(2 \ast 18 = + \sqrt{2 \times 18}\) = \(+ \sqrt{36} = 6\) |