Year :
2009
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
11 - 20 of 50 Questions
| # | Question | Ans |
|---|---|---|
| 11. |
A polynomial in x whose roots are 4/3 and -3/5 is? A. 15x2 - 11x – 12 B. 15x2 + 11x – 12 C. 12x2 - x – 12 D. 12x2 + 11x – 15 Detailed SolutionIf 4/3 and -3/5 are roots of a polynomialImply x = 4/3 and - 3/5 3x = 4 and 5x = -3 ∴3x-4 = 0 and 5x+3 = 0 are factors (3x-4)(5x+3) = 0 product of the factors 15x2 + 9x – 20x – 12 = 0 By expansion 15x2 - 11x – 12 = 0 There is an explanation video available below. |
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| 12. |
 Which of the following equations represent the graph above? A. y = 2+7x+4x2 B. y = 2-7x+4x2 C. y = 2+7x-4x2 D. y = 2-7x-4x2 Detailed Solutionx = -2 and x = 1/4x = -2 and 4x = 1 x+2 and 4x-1 (x+2)(4x-1) = 0 4x2 - x + 8x -2 = 0 4x2 + 7x – 2 = 0 but y intercept is positive. Multiply the equation by -1 -4x2 - 7x + 2 = 0 ∴y = 2 – 7x – 4x2 There is an explanation video available below. |
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| 13. |
W is directly proportional to U. If W = 5 when U = 3, find U when W = 2/7 A. 6/35 B. 10/21 C. 21/10 D. 35/6 Detailed Solution\(W ∝ U\\W = KU\\ K = \frac{W}{U}\\ K = \frac{5}{3}\\ W = \frac{5}{3}U\\ \frac{2}{7} = \frac{5}{3}U\\ U = \frac{2}{7} \times \frac{3}{5}\\ U = \frac{6}{35}\) There is an explanation video available below. |
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| 14. |
Determine the value of x for which (x\(^2\) - 1) > 0? A. x < -1 or x > 1 B. -1 < x < 1 C. x > 0 D. x < -1 Detailed Solution
(x+1)(x-1) > 0 x = 1 or -1 -1 < x < 1 There is an explanation video available below. |
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| 15. |
Find the range of values of x for which 3x - 7 \(\leq\) 0 and x + 5 > 0? A. -5 < x < \(\frac{7}{3}\) B. -5 \(\leq\) x \(\leq\) \(\frac{7}{3}\) C. -5 < x \(\leq\) \(\frac{7}{3}\) D. -5 \(\leq\) x < \(\frac{7}{3}\) Detailed Solution3x - 7 \(\leq\) 0 and x + 5 > 03x \(\leq\) 7 and x > -5 x \(\leq\) \(\frac{7}{3}\) ∴ Range -5 < x \(\leq\) \(\frac{7}{3}\) There is an explanation video available below. |
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| 16. |
The sum of the first n terms of the arithmetic progression 5, 11, 17, 23, 29, 35, ... is? A. n(3n - 0.5) B. n(3n + 2) C. n(3n + 2.5) D. n(3n + 5) Detailed Solutiona = 5, d = 6, n = nSn = n/2(2a + (n-1)d) = n/2(2(5) + (n-1)6) = n/2(10 + 6n-6) = n/2(6n+4) = 6n2/2 + 4n/2 = 32 + 2n = n(3n + 2) There is an explanation video available below. |
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| 17. |
Find to infinity, the sum of the sequence \(1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3,.....\) A. 10 B. 9 C. 10/9 D. 9/10 Detailed Solution\(a=1, r=\frac{9}{10}\\S_n = \frac{a}{1-r}\\ S_n = \frac{1}{1-\frac{9}{10}}\\ =1\div \frac{1}{10}\\ =1\times \frac{10}{1}\\ 10\) |
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| 18. |
If m * n = n - (m+2) for any real number m and n find the value of 3*(-5)? A. -6 B. -8 C. -10 D. -12 Detailed Solutionm * n = n - (m+2)= -5 - (3+2) = -5-5 = -10 There is an explanation video available below. |
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| 19. |
A binary operation ⊗ defined on the set of integers is such that m⊗n = m + n + mn for all integers m and n. Find the inverse of -5 under this operation, if the identity element is 0? A. -5/4 B. -5/6 C. zero D. 5 Detailed Solution\(m \otimes n = m + n + mn\)Let the inverse of -5 be n. \(\therefore -5 \otimes n = 0\) \(-5 + n + (-5n) = 0\) \(n - 5n = 5 \implies -4n = 5\) \(n = -\frac{5}{4}\) There is an explanation video available below. |
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| 20. |
If Q is\( \left[ \begin{array}{cc} A. -50 B. -22 C. 22 D. 50 Detailed SolutionQ = \( \left[ \begin{array}{ccc}9 & -2 \\ -7 & 4 \\ \end{array} \right]\) |Q| = 9x4 - (-2x7) = 36 - 14 = 22 There is an explanation video available below. |
| 11. |
A polynomial in x whose roots are 4/3 and -3/5 is? A. 15x2 - 11x – 12 B. 15x2 + 11x – 12 C. 12x2 - x – 12 D. 12x2 + 11x – 15 Detailed SolutionIf 4/3 and -3/5 are roots of a polynomialImply x = 4/3 and - 3/5 3x = 4 and 5x = -3 ∴3x-4 = 0 and 5x+3 = 0 are factors (3x-4)(5x+3) = 0 product of the factors 15x2 + 9x – 20x – 12 = 0 By expansion 15x2 - 11x – 12 = 0 There is an explanation video available below. |
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| 12. |
Which of the following equations represent the graph above? A. y = 2+7x+4x2 B. y = 2-7x+4x2 C. y = 2+7x-4x2 D. y = 2-7x-4x2 Detailed Solutionx = -2 and x = 1/4x = -2 and 4x = 1 x+2 and 4x-1 (x+2)(4x-1) = 0 4x2 - x + 8x -2 = 0 4x2 + 7x – 2 = 0 but y intercept is positive. Multiply the equation by -1 -4x2 - 7x + 2 = 0 ∴y = 2 – 7x – 4x2 There is an explanation video available below. |
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| 13. |
W is directly proportional to U. If W = 5 when U = 3, find U when W = 2/7 A. 6/35 B. 10/21 C. 21/10 D. 35/6 Detailed Solution\(W ∝ U\\W = KU\\ K = \frac{W}{U}\\ K = \frac{5}{3}\\ W = \frac{5}{3}U\\ \frac{2}{7} = \frac{5}{3}U\\ U = \frac{2}{7} \times \frac{3}{5}\\ U = \frac{6}{35}\) There is an explanation video available below. |
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| 14. |
Determine the value of x for which (x\(^2\) - 1) > 0? A. x < -1 or x > 1 B. -1 < x < 1 C. x > 0 D. x < -1 Detailed Solution
(x+1)(x-1) > 0 x = 1 or -1 -1 < x < 1 There is an explanation video available below. |
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| 15. |
Find the range of values of x for which 3x - 7 \(\leq\) 0 and x + 5 > 0? A. -5 < x < \(\frac{7}{3}\) B. -5 \(\leq\) x \(\leq\) \(\frac{7}{3}\) C. -5 < x \(\leq\) \(\frac{7}{3}\) D. -5 \(\leq\) x < \(\frac{7}{3}\) Detailed Solution3x - 7 \(\leq\) 0 and x + 5 > 03x \(\leq\) 7 and x > -5 x \(\leq\) \(\frac{7}{3}\) ∴ Range -5 < x \(\leq\) \(\frac{7}{3}\) There is an explanation video available below. |
| 16. |
The sum of the first n terms of the arithmetic progression 5, 11, 17, 23, 29, 35, ... is? A. n(3n - 0.5) B. n(3n + 2) C. n(3n + 2.5) D. n(3n + 5) Detailed Solutiona = 5, d = 6, n = nSn = n/2(2a + (n-1)d) = n/2(2(5) + (n-1)6) = n/2(10 + 6n-6) = n/2(6n+4) = 6n2/2 + 4n/2 = 32 + 2n = n(3n + 2) There is an explanation video available below. |
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| 17. |
Find to infinity, the sum of the sequence \(1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3,.....\) A. 10 B. 9 C. 10/9 D. 9/10 Detailed Solution\(a=1, r=\frac{9}{10}\\S_n = \frac{a}{1-r}\\ S_n = \frac{1}{1-\frac{9}{10}}\\ =1\div \frac{1}{10}\\ =1\times \frac{10}{1}\\ 10\) |
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| 18. |
If m * n = n - (m+2) for any real number m and n find the value of 3*(-5)? A. -6 B. -8 C. -10 D. -12 Detailed Solutionm * n = n - (m+2)= -5 - (3+2) = -5-5 = -10 There is an explanation video available below. |
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| 19. |
A binary operation ⊗ defined on the set of integers is such that m⊗n = m + n + mn for all integers m and n. Find the inverse of -5 under this operation, if the identity element is 0? A. -5/4 B. -5/6 C. zero D. 5 Detailed Solution\(m \otimes n = m + n + mn\)Let the inverse of -5 be n. \(\therefore -5 \otimes n = 0\) \(-5 + n + (-5n) = 0\) \(n - 5n = 5 \implies -4n = 5\) \(n = -\frac{5}{4}\) There is an explanation video available below. |
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| 20. |
If Q is\( \left[ \begin{array}{cc} A. -50 B. -22 C. 22 D. 50 Detailed SolutionQ = \( \left[ \begin{array}{ccc}9 & -2 \\ -7 & 4 \\ \end{array} \right]\) |Q| = 9x4 - (-2x7) = 36 - 14 = 22 There is an explanation video available below. |