Year :
1990
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
11 - 20 of 44 Questions
| # | Question | Ans |
|---|---|---|
| 11. |
Simplify (\(\frac{1}{x^{-1}} + \frac{1}{y^{-1}}\))-1 A. \(\frac{x}{y}\) B. xy C. \(\frac{x}{y}\) D. (xy)-1 Detailed SolutionSimplify (\(\frac{1}{x^{-1}} + \frac{1}{y^{-1}}\))-1 = (\(\frac{1}{x^{-1}} + \frac{1}{y^{-1}}\))-1= (x + y)-1 = \(\frac{(x)}{y}\) = \(\frac{x}{y}\) |
|
| 12. |
If a = 2, b = -2 and c = -\(\frac{1}{2}\), evaluate (ab2 - bc2)(a2c - abc) A. 2 B. -28 C. -30 D. -34 Detailed Solution(ab2 - bc2)(a2c - abc)[2(2)2 - (- 2x\(\frac{1}{2}\))] [22(-\(\frac{1}{2}\)) - 2(-2)(-\(\frac{1}{2}\))] [8 = \(\frac{1}{2}\)][-2 - 2] = \(\frac{17}{2}\) x 42 = -34 |
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| 13. |
If f(x - 4) = x2 + 2x + 3, Find, f(2) A. 6 B. 11 C. 27 D. 51 Detailed Solutionf(x - 4) = x2 + 2x + 3To find f(2) = f(x - 4) = f(2) x - 4 = 2 x = 6 f(2) = 62 + 2(6) + 3 = 36 + 12 + 3 = 51 |
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| 14. |
Factorize 9(x + y)2 - 4(x - y)2 A. (x + y)(5x + y) B. (x + y)2 C. (x + 5y)(5x + y) D. 5(x + y)2 Detailed Solution9(x + y)2 - 4(x - y)2Using difference of two squares which says a2 - b2 = (a + b)(a - b) = 9(x + y)2 - 4(x - y)2 = [3(x + y)]2 - [2(x - y)]-2 = [3(x + y) + 2(x - y) + 2(x - y)][3(x + y) - 2(x - y)] = [3x +3y + 2x - 2y][3x + 3y - 2x + 2y] = (5x + y)(x + 5y) |
|
| 15. |
If a2 + b2 = 16 and 2ab = 7.Find all the possible values of (a - b) A. 3, -3 B. 2, -2 C. 1, -1 D. 3, -1 Detailed Solutiona2 + b2 = 16 and 2ab = 7To find all possible values = (a - b)2 + b2 - 2ab Substituting the given values = (a - b)2 = 16 - 7 = 9 (a - b) = \(\pm\)9 = \(\pm\)3 OR a - b = 3, -3 |
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| 16. |
Divide x3 - 2x2 - 5x + 6 by (x - 1) A. x2 - x - 6 B. x2 - 5x + 6 C. x2 - 7x + 6 D. x2 - 5x - 6 Detailed SolutionStep 1: Just multiply each of the options by ( x - 1 )Step 2: Then collect like terms to derive the same equation found in the question. Hope this helps! |
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| 17. |
If x + \(\frac{1}{x}\) = 4, find x2 + \(\frac{1}{x^2}\) A. 16 B. 14 C. 12 D. 9 Detailed Solutionx + \(\frac{1}{x}\) = 4, find x2 + \(\frac{1}{x^2}\)= (x + \(\frac{1}{x}\))2 = x2 + \(\frac{1}{x^2}\) + 2 x2 + \(\frac{1}{x^2}\) = ( x + \(\frac{1}{x^2}\))2 - 2 = (4)2 - 2 = 16 - 2 = 14 |
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| 18. |
What must be added to 4x2 - 4 to make it a perfect square? A. \(\frac{-1}{x^2}\) B. \(\frac{1}{x^2}\) C. 1 D. -1 Detailed Solution(2x \(\frac{-1}{4}\)2 = 4x2 + \(\frac{1}{x^2}\) - 4what must be added is +\(\frac{1}{x^2}\) |
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| 19. |
Find the solution of the equation x - 8\(\sqrt{x}\) + 15 = 0 A. 3, 5 B. -3, -5 C. 9, 25 D. -9, 25 Detailed Solutionx - 8\(\sqrt{x}\) + 15 = 0x + 15 = 8\(\sqrt{x}\) square both sides = (x + 15)2 = (8 \(\sqrt{x}\)2 x2 + 225 + 30x = 64x x2 + 225 + 30x - 64x = 0 x2 - 34x + 225 = 0 (x - 9)(x - 25) = 0 x = 9 or 25 |
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| 20. |
The perimeter of a rectangular lawn is 24m. If the area of the lawn is 35m2; how wide is the lawn? A. 5cm B. 7m C. 12m D. 14m |
A |
| 11. |
Simplify (\(\frac{1}{x^{-1}} + \frac{1}{y^{-1}}\))-1 A. \(\frac{x}{y}\) B. xy C. \(\frac{x}{y}\) D. (xy)-1 Detailed SolutionSimplify (\(\frac{1}{x^{-1}} + \frac{1}{y^{-1}}\))-1 = (\(\frac{1}{x^{-1}} + \frac{1}{y^{-1}}\))-1= (x + y)-1 = \(\frac{(x)}{y}\) = \(\frac{x}{y}\) |
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| 12. |
If a = 2, b = -2 and c = -\(\frac{1}{2}\), evaluate (ab2 - bc2)(a2c - abc) A. 2 B. -28 C. -30 D. -34 Detailed Solution(ab2 - bc2)(a2c - abc)[2(2)2 - (- 2x\(\frac{1}{2}\))] [22(-\(\frac{1}{2}\)) - 2(-2)(-\(\frac{1}{2}\))] [8 = \(\frac{1}{2}\)][-2 - 2] = \(\frac{17}{2}\) x 42 = -34 |
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| 13. |
If f(x - 4) = x2 + 2x + 3, Find, f(2) A. 6 B. 11 C. 27 D. 51 Detailed Solutionf(x - 4) = x2 + 2x + 3To find f(2) = f(x - 4) = f(2) x - 4 = 2 x = 6 f(2) = 62 + 2(6) + 3 = 36 + 12 + 3 = 51 |
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| 14. |
Factorize 9(x + y)2 - 4(x - y)2 A. (x + y)(5x + y) B. (x + y)2 C. (x + 5y)(5x + y) D. 5(x + y)2 Detailed Solution9(x + y)2 - 4(x - y)2Using difference of two squares which says a2 - b2 = (a + b)(a - b) = 9(x + y)2 - 4(x - y)2 = [3(x + y)]2 - [2(x - y)]-2 = [3(x + y) + 2(x - y) + 2(x - y)][3(x + y) - 2(x - y)] = [3x +3y + 2x - 2y][3x + 3y - 2x + 2y] = (5x + y)(x + 5y) |
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| 15. |
If a2 + b2 = 16 and 2ab = 7.Find all the possible values of (a - b) A. 3, -3 B. 2, -2 C. 1, -1 D. 3, -1 Detailed Solutiona2 + b2 = 16 and 2ab = 7To find all possible values = (a - b)2 + b2 - 2ab Substituting the given values = (a - b)2 = 16 - 7 = 9 (a - b) = \(\pm\)9 = \(\pm\)3 OR a - b = 3, -3 |
| 16. |
Divide x3 - 2x2 - 5x + 6 by (x - 1) A. x2 - x - 6 B. x2 - 5x + 6 C. x2 - 7x + 6 D. x2 - 5x - 6 Detailed SolutionStep 1: Just multiply each of the options by ( x - 1 )Step 2: Then collect like terms to derive the same equation found in the question. Hope this helps! |
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| 17. |
If x + \(\frac{1}{x}\) = 4, find x2 + \(\frac{1}{x^2}\) A. 16 B. 14 C. 12 D. 9 Detailed Solutionx + \(\frac{1}{x}\) = 4, find x2 + \(\frac{1}{x^2}\)= (x + \(\frac{1}{x}\))2 = x2 + \(\frac{1}{x^2}\) + 2 x2 + \(\frac{1}{x^2}\) = ( x + \(\frac{1}{x^2}\))2 - 2 = (4)2 - 2 = 16 - 2 = 14 |
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| 18. |
What must be added to 4x2 - 4 to make it a perfect square? A. \(\frac{-1}{x^2}\) B. \(\frac{1}{x^2}\) C. 1 D. -1 Detailed Solution(2x \(\frac{-1}{4}\)2 = 4x2 + \(\frac{1}{x^2}\) - 4what must be added is +\(\frac{1}{x^2}\) |
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| 19. |
Find the solution of the equation x - 8\(\sqrt{x}\) + 15 = 0 A. 3, 5 B. -3, -5 C. 9, 25 D. -9, 25 Detailed Solutionx - 8\(\sqrt{x}\) + 15 = 0x + 15 = 8\(\sqrt{x}\) square both sides = (x + 15)2 = (8 \(\sqrt{x}\)2 x2 + 225 + 30x = 64x x2 + 225 + 30x - 64x = 0 x2 - 34x + 225 = 0 (x - 9)(x - 25) = 0 x = 9 or 25 |
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| 20. |
The perimeter of a rectangular lawn is 24m. If the area of the lawn is 35m2; how wide is the lawn? A. 5cm B. 7m C. 12m D. 14m |
A |