Year :
1991
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
11 - 20 of 48 Questions
| # | Question | Ans |
|---|---|---|
| 11. |
Rationalize \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\) A. 5 - 2\(\sqrt{6}\) B. 5 + 2\(\sqrt{6}\) C. 5\(\sqrt{6}\) D. 5 Detailed Solution\(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\)= \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\) x \(\frac{3\sqrt{2} + 2 \sqrt{3}}{3\sqrt{2} - 2 \sqrt{3}}\) \(\frac{4(3) + 9(2) + 2(6) \sqrt{6}}{9(2) - 4(3)}\) \(\frac{12 + 18 + 12\sqrt{6}}{1`8 - 12}\) = \(\frac{30 + 12\sqrt{6}}{6}\) = 5 + 2\(\sqrt{6}\) |
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| 12. |
Multiply (x2 - 3x + 1) by (x - a) A. x3 - (3 + a) x2 + (1 + 3a)x - a B. x3 - (3 - a)x2 + 3ax - a C. x3 - (3 - a)x2 - (1 = 3a) - a D. x3 + (3 - a)x2 + (1 + 3a) - a Detailed Solution(x2 - 3x + 1)(x - a) = x3 - 3x2 + x - ax2 + 3ax - a= x3 - (3 + a) x2 + (1 + 3a)x - a |
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| 13. |
Evaluate \(\frac{xy^2 - x^2y}{x^2 - xy^1}\) When x = -2 and y = 3 A. 3 B. -\(\frac{3}{5}\) C. \(\frac{3}{5}\) D. -3 Detailed Solution\(\frac{xy^2 - x^2y}{x^2 - xy^1}\)= \(\frac{(-2)(3)^2 - (-2)^2(3)}{(-2)^2 - (-2)(3)}\) = \(\frac{-30}{10}\) = -3 |
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| 14. |
A car travels from calabar to Enugu, a distance of P km with an average speed of U km per hour and continues to benin, a distance of Q km, with an average speed of Wkm per hour. Find its average speed from Calabar to Benin A. \(\frac{(p + q)}{pw + qu}\) B. \(\frac{uw(p + q)}{pw + qu}\) C. \(\frac{uw(p + q)}{pw}\) D. \(\frac{uw}{pw + qu}\) Detailed SolutionAverage speed = \(\frac{\text{total Distance}}{\text{Total Time}\)from Calabar to Enugu in time t1, hence t1 = \(\frac{P}{U}\) also from Enugu to Benin t2 \(\frac{q}{w}\) Av. speed = \(\frac{p + q}{t_1 + t_2} = \(\frac{p + q}{\frac{p}{u} + \frac{q}{w}\) = p + q x \(\frac{uw}{pw + qu}\) = \(\frac{uw(p + q)}{pw + qu}\) |
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| 15. |
If w varies inversely as \(\frac{uv}{u + v}\) and is equal to 8 when A. uvw = 16(u + v) B. 16ur = 3w(u + v) C. uvw = 12(u + v) D. 12uvw = u + v Detailed SolutionW \(\alpha\) \(\frac{\frac{1}{uv}}{u + v}\)∴ w = \(\frac{\frac{k}{uv}}{u + v}\) = \(\frac{k(u + v)}{uv}\) w = \(\frac{k(u + v)}{uv}\) w = 8, u = 2 and v = 6 8 = \(\frac{k(2 + 6)}{2(6)}\) = \(\frac{k(8)}{12}\) k = 12 i.e 12 ( u + v) = uwv |
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| 16. |
If g(x) = x2 + 3x + 4, find g(x + 1) - g(x) A. (x + 2) B. 2(x + 2) C. (2x + 1) D. (x2 + 4) Detailed Solutiong(x) = x2 + 3x + 4= g(x + 1) = (x + 1)^2 + 3(x + 1) + 4 = x2 + 1 + 2x + 3x + 3 + 4 = x2 + 5x + 8 g(x + 1) - g(x) = x2 + 5x + 8 - (x2 + 3x + 4) = x2 + 5x + 8 - x2 + 3x + 4 = 2x + 4 = 2(x + 2) |
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| 17. |
Factorize m3 - 2m2 - m + 2 A. (m2 + 1)(m - 2) B. (m - 1)(m + 1)(m + 2) C. (m - 2)(m + 1)(m - 1) D. (m2 + 2)(m - 1) Detailed Solutionm3 - 2m2 - m + 2Let f(m) = m3 - 2m2 - m2 + 2 = f(1) = 1 - 2 - 2 + 2 = 0 ∴ m - 1 is factor \(\frac{m^3 - 2m^2 - m^2 + 2}{m - 1}\) = m2 - m - 2 = (m - 1)m2 - m - 2 = (m - 1)(m + 1)(m - 2) |
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| 18. |
Factorize 1 - (a - b)2 A. (1 - a - b)(1 - a + b) B. (1 + a - b)(1 - a + b) C. (1 - a + b)(1 - a + b) D. (1 + a + b)(1 + a + b) Detailed Solution1 - (a - b)2 = [1 + (a - b)][1 - a + b]= (1 + a - b)(1 - a + b) |
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| 19. |
Which of the following is a factor of rs + tr - pt - ps? A. (p - s) B. (s - p) C. r - p) D. r + p) Detailed Solutionrs + tr - pt - ps = rs - ps - tr - pt= (r - p)s + (r - p)t = (r - p)(s + t), hence r - p is a factor |
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| 20. |
Find the two values of y which satisfy the simultaneous equation 3x + y = 8, x\(^2\) + xy = 6. A. -1 and 5 B. -5 and 1 C. 1 and 5 D. 1 and 1 Detailed Solution\(3x + y = 8 ... (i)\)\(x^{2} + xy = 6 ... (ii)\) From (i), \(y = 8 - 3x\) From (ii), \(xy = 6 - x^{2} \implies y = \frac{6 - x^{2}}{x}\) Equating the two values of y, we have \(8 - 3x = \frac{6 - x^{2}}{x} \implies x(8 - 3x) = 6 - x^{2}\) \(8x - 3x^{2} = 6 - x^{2} \implies 6 - x^{2} - 8x + 3x^{2} = 0\) \(2x^{2} - 8x + 6 = 0\) \(x^{2} - 4x + 3 = 0\) \(x^{2} - 3x - x + 3 = 0 \implies x(x - 3) - 1(x - 3) = 0\) \((x - 1)(x - 3) = 0 \therefore \text{x = 1 or 3}\) \(y = 8 - 3x \) When x = 1, \(y = 8 - 3(1) = 5\) When x = 3, \(y = 8 - 3(3) = -1\) \(\therefore \text{y = -1 or 5}\) |
| 11. |
Rationalize \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\) A. 5 - 2\(\sqrt{6}\) B. 5 + 2\(\sqrt{6}\) C. 5\(\sqrt{6}\) D. 5 Detailed Solution\(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\)= \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\) x \(\frac{3\sqrt{2} + 2 \sqrt{3}}{3\sqrt{2} - 2 \sqrt{3}}\) \(\frac{4(3) + 9(2) + 2(6) \sqrt{6}}{9(2) - 4(3)}\) \(\frac{12 + 18 + 12\sqrt{6}}{1`8 - 12}\) = \(\frac{30 + 12\sqrt{6}}{6}\) = 5 + 2\(\sqrt{6}\) |
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| 12. |
Multiply (x2 - 3x + 1) by (x - a) A. x3 - (3 + a) x2 + (1 + 3a)x - a B. x3 - (3 - a)x2 + 3ax - a C. x3 - (3 - a)x2 - (1 = 3a) - a D. x3 + (3 - a)x2 + (1 + 3a) - a Detailed Solution(x2 - 3x + 1)(x - a) = x3 - 3x2 + x - ax2 + 3ax - a= x3 - (3 + a) x2 + (1 + 3a)x - a |
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| 13. |
Evaluate \(\frac{xy^2 - x^2y}{x^2 - xy^1}\) When x = -2 and y = 3 A. 3 B. -\(\frac{3}{5}\) C. \(\frac{3}{5}\) D. -3 Detailed Solution\(\frac{xy^2 - x^2y}{x^2 - xy^1}\)= \(\frac{(-2)(3)^2 - (-2)^2(3)}{(-2)^2 - (-2)(3)}\) = \(\frac{-30}{10}\) = -3 |
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| 14. |
A car travels from calabar to Enugu, a distance of P km with an average speed of U km per hour and continues to benin, a distance of Q km, with an average speed of Wkm per hour. Find its average speed from Calabar to Benin A. \(\frac{(p + q)}{pw + qu}\) B. \(\frac{uw(p + q)}{pw + qu}\) C. \(\frac{uw(p + q)}{pw}\) D. \(\frac{uw}{pw + qu}\) Detailed SolutionAverage speed = \(\frac{\text{total Distance}}{\text{Total Time}\)from Calabar to Enugu in time t1, hence t1 = \(\frac{P}{U}\) also from Enugu to Benin t2 \(\frac{q}{w}\) Av. speed = \(\frac{p + q}{t_1 + t_2} = \(\frac{p + q}{\frac{p}{u} + \frac{q}{w}\) = p + q x \(\frac{uw}{pw + qu}\) = \(\frac{uw(p + q)}{pw + qu}\) |
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| 15. |
If w varies inversely as \(\frac{uv}{u + v}\) and is equal to 8 when A. uvw = 16(u + v) B. 16ur = 3w(u + v) C. uvw = 12(u + v) D. 12uvw = u + v Detailed SolutionW \(\alpha\) \(\frac{\frac{1}{uv}}{u + v}\)∴ w = \(\frac{\frac{k}{uv}}{u + v}\) = \(\frac{k(u + v)}{uv}\) w = \(\frac{k(u + v)}{uv}\) w = 8, u = 2 and v = 6 8 = \(\frac{k(2 + 6)}{2(6)}\) = \(\frac{k(8)}{12}\) k = 12 i.e 12 ( u + v) = uwv |
| 16. |
If g(x) = x2 + 3x + 4, find g(x + 1) - g(x) A. (x + 2) B. 2(x + 2) C. (2x + 1) D. (x2 + 4) Detailed Solutiong(x) = x2 + 3x + 4= g(x + 1) = (x + 1)^2 + 3(x + 1) + 4 = x2 + 1 + 2x + 3x + 3 + 4 = x2 + 5x + 8 g(x + 1) - g(x) = x2 + 5x + 8 - (x2 + 3x + 4) = x2 + 5x + 8 - x2 + 3x + 4 = 2x + 4 = 2(x + 2) |
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| 17. |
Factorize m3 - 2m2 - m + 2 A. (m2 + 1)(m - 2) B. (m - 1)(m + 1)(m + 2) C. (m - 2)(m + 1)(m - 1) D. (m2 + 2)(m - 1) Detailed Solutionm3 - 2m2 - m + 2Let f(m) = m3 - 2m2 - m2 + 2 = f(1) = 1 - 2 - 2 + 2 = 0 ∴ m - 1 is factor \(\frac{m^3 - 2m^2 - m^2 + 2}{m - 1}\) = m2 - m - 2 = (m - 1)m2 - m - 2 = (m - 1)(m + 1)(m - 2) |
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| 18. |
Factorize 1 - (a - b)2 A. (1 - a - b)(1 - a + b) B. (1 + a - b)(1 - a + b) C. (1 - a + b)(1 - a + b) D. (1 + a + b)(1 + a + b) Detailed Solution1 - (a - b)2 = [1 + (a - b)][1 - a + b]= (1 + a - b)(1 - a + b) |
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| 19. |
Which of the following is a factor of rs + tr - pt - ps? A. (p - s) B. (s - p) C. r - p) D. r + p) Detailed Solutionrs + tr - pt - ps = rs - ps - tr - pt= (r - p)s + (r - p)t = (r - p)(s + t), hence r - p is a factor |
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| 20. |
Find the two values of y which satisfy the simultaneous equation 3x + y = 8, x\(^2\) + xy = 6. A. -1 and 5 B. -5 and 1 C. 1 and 5 D. 1 and 1 Detailed Solution\(3x + y = 8 ... (i)\)\(x^{2} + xy = 6 ... (ii)\) From (i), \(y = 8 - 3x\) From (ii), \(xy = 6 - x^{2} \implies y = \frac{6 - x^{2}}{x}\) Equating the two values of y, we have \(8 - 3x = \frac{6 - x^{2}}{x} \implies x(8 - 3x) = 6 - x^{2}\) \(8x - 3x^{2} = 6 - x^{2} \implies 6 - x^{2} - 8x + 3x^{2} = 0\) \(2x^{2} - 8x + 6 = 0\) \(x^{2} - 4x + 3 = 0\) \(x^{2} - 3x - x + 3 = 0 \implies x(x - 3) - 1(x - 3) = 0\) \((x - 1)(x - 3) = 0 \therefore \text{x = 1 or 3}\) \(y = 8 - 3x \) When x = 1, \(y = 8 - 3(1) = 5\) When x = 3, \(y = 8 - 3(3) = -1\) \(\therefore \text{y = -1 or 5}\) |