Mathematics (Core), 2000, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

2000

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

11 - 20 of 45 Questions

#	Question	Ans
11.	The 3rd term of an A.P is 4x - 2y and the 9th term is 10x - 8y. Find the common difference. A. 19x - 17y B. 8x - 4y C. x - y D. 2x Show Content Detailed Solution n = 3, U\(_3\) = 4x - 2y, U\(_n\) = a + (n+1)d, 4x - 2y = a + 2d... (1) U\(_9\) = 10x - 8y, 10x - 8y = a + 8d... (2) Solving (1) and (2), d = 6(x-y)/6 d = x-y.	C
12.	Find the inverse of p under the binary operation * defined by pq = p + q - pq, where p and q are real numbers and zero is the identity A. p B. p -1 C. p/(p-1) D. p/(p+1) Show Content Detailed Solution If P-1 is the inverse of P and O is the identity, Then P-1 P = P * P-1 = 0 i.e. P-1 + P - P-1.P = 0 P-1 - P-1.P = -P P-1(1 - P) = -P P-1 = -P/(P-1) = P/(P-1)	C
13.	Evaluate (1/2 - 1/4 - 1/8 - 1/16 + ...) - 1 A. 2/3 B. zero C. -2/3 D. -1 Show Content Detailed Solution S = a/(1+r), where a = 1/2, r = 1/2. S = 1/2 3/2 = 1/2 x 3/2 = 1/3. 1/3 - 1 = -2/3	C
14.	If (x - 1), (x + 1) and (x - 2) are factors of the polynomial ax³ + bx² + cx - 1, find a, b, c in that order. A. -1/2, 1., 1/2 B. 1/2, 1, 1/2 C. 1/2, 1, -1/2 D. 1/2, -1, 1/2 Show Content Detailed Solution This is a polynomial of the 3rd order, thus x should have three answers. Use the factors given to get values of x as 1, -1 and -2. Form three equations, and carry out elimination and subsequent substitution to get a = -1/2, b = 1, and c = 1/2	A
15.	A trader realizes 10x - x\(^2\) naira profit from the sale of x bags on corn. How many bags will give him the desired profit? A. 4 B. 5 C. 6 D. 7 Show Content Detailed Solution y = 10x - x\(^2\) dy/dx = 10 - 2x As dy/dx = 0, 10 - 2x = 0 2x = 10 x = 5	B
16.	Solve the inequality 2 - x > x\(^2\). A. x < -2 or x > 1 B. x > 2 or x< -1 C. -1 < x < 2 D. -2 < x < 1 Show Content Detailed Solution 2 - x > x\(^2\) 2 - x - x\(^2\) > 0 (x+2)(x-1) < 0 Either (x + 2) > 0 and (x - 1) < 0. x + 2 > 0 \(\implies\) x > -2. -2 < x < 1	D
17.	If α and β are the roots of the equation 3x\(^2\) + 5x - 2 = 0, find the value of 1/α + 1/β A. -5/3 B. -2/3 C. 1/2 D. 5/2 Show Content Detailed Solution 1/α + 1/β = β+α/αβ 3x\(^2\) + 5x - 2 = 0 x\(^2\) + 5x/3 - 2/3 = 0 αβ = -2/3 β+α = -5/3 Thus; β+α/αβ = -5/3 ÷ -2/3 = -5/2	D
18.	A frustrum of pyramid with square base has its upper and lower sections as squares of sizes 2m and 5m respectively and the distance between them 6m. Find the height of the pyramid from which the frustrum was obtained. A. 8.0 m B. 8.4 m C. 9.0 m D. 10.0 m Show Content Detailed Solution The lateral view of the frustrum \(\tan \theta = \frac{6}{1.5} = 4\) \(\theta = \tan^{-1} 4 = 75.96°\) Extending to the full height of the pyramid, we have The height of the pyramid which formed the frustrum = (6 + x)m, \(\tan 75.96 = \frac{6 + x}{2.5}\) \(6 + x = 2.5 \times 4 = 10.0\) \(\therefore \text{The height of the pyramid} = 1	D
19.	P is a point on one side of the straight line UV and P moves in the same direction as UV. If the straight line ST is on the locus of P and angle VUS = 60°, find angle UST. A. 310° B. 130° C. 80° D. 50° Show Content Detailed Solution Make a good sketch of the question, and follow this steps. Since ST is parallel to UV => angle USR = 50°(alternate to VUS. Angle UST = 180° - 50° = 130° (angle on a straight line)	B
20.	An equilateral triangle of side √3cm is inscribed in a circle. Find the radius of the circle. A. 2/3 cm B. 2 cm C. 1 cm D. 3 cm Show Content Detailed Solution Since the inscribed triangle is equilateral, therefore the angles at all the points = 60° Using the formula for inscribed circle, 2R = \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\) where R = radius of the circle; a, b and c are the sides of the triangle. ⇒ 2R = \(\frac{\sqrt{3}}{\sin 60}\) 2R = \(\frac{\sqrt{3}}{\frac{\sqrt{3}}{2}}\) 2R = 2 R = 1cm	C

11.	The 3rd term of an A.P is 4x - 2y and the 9th term is 10x - 8y. Find the common difference. A. 19x - 17y B. 8x - 4y C. x - y D. 2x Show Content Detailed Solution n = 3, U\(_3\) = 4x - 2y, U\(_n\) = a + (n+1)d, 4x - 2y = a + 2d... (1) U\(_9\) = 10x - 8y, 10x - 8y = a + 8d... (2) Solving (1) and (2), d = 6(x-y)/6 d = x-y.	C
12.	Find the inverse of p under the binary operation * defined by pq = p + q - pq, where p and q are real numbers and zero is the identity A. p B. p -1 C. p/(p-1) D. p/(p+1) Show Content Detailed Solution If P-1 is the inverse of P and O is the identity, Then P-1 P = P * P-1 = 0 i.e. P-1 + P - P-1.P = 0 P-1 - P-1.P = -P P-1(1 - P) = -P P-1 = -P/(P-1) = P/(P-1)	C
13.	Evaluate (1/2 - 1/4 - 1/8 - 1/16 + ...) - 1 A. 2/3 B. zero C. -2/3 D. -1 Show Content Detailed Solution S = a/(1+r), where a = 1/2, r = 1/2. S = 1/2 3/2 = 1/2 x 3/2 = 1/3. 1/3 - 1 = -2/3	C
14.	If (x - 1), (x + 1) and (x - 2) are factors of the polynomial ax³ + bx² + cx - 1, find a, b, c in that order. A. -1/2, 1., 1/2 B. 1/2, 1, 1/2 C. 1/2, 1, -1/2 D. 1/2, -1, 1/2 Show Content Detailed Solution This is a polynomial of the 3rd order, thus x should have three answers. Use the factors given to get values of x as 1, -1 and -2. Form three equations, and carry out elimination and subsequent substitution to get a = -1/2, b = 1, and c = 1/2	A
15.	A trader realizes 10x - x\(^2\) naira profit from the sale of x bags on corn. How many bags will give him the desired profit? A. 4 B. 5 C. 6 D. 7 Show Content Detailed Solution y = 10x - x\(^2\) dy/dx = 10 - 2x As dy/dx = 0, 10 - 2x = 0 2x = 10 x = 5	B

16.	Solve the inequality 2 - x > x\(^2\). A. x < -2 or x > 1 B. x > 2 or x< -1 C. -1 < x < 2 D. -2 < x < 1 Show Content Detailed Solution 2 - x > x\(^2\) 2 - x - x\(^2\) > 0 (x+2)(x-1) < 0 Either (x + 2) > 0 and (x - 1) < 0. x + 2 > 0 \(\implies\) x > -2. -2 < x < 1	D
17.	If α and β are the roots of the equation 3x\(^2\) + 5x - 2 = 0, find the value of 1/α + 1/β A. -5/3 B. -2/3 C. 1/2 D. 5/2 Show Content Detailed Solution 1/α + 1/β = β+α/αβ 3x\(^2\) + 5x - 2 = 0 x\(^2\) + 5x/3 - 2/3 = 0 αβ = -2/3 β+α = -5/3 Thus; β+α/αβ = -5/3 ÷ -2/3 = -5/2	D
18.	A frustrum of pyramid with square base has its upper and lower sections as squares of sizes 2m and 5m respectively and the distance between them 6m. Find the height of the pyramid from which the frustrum was obtained. A. 8.0 m B. 8.4 m C. 9.0 m D. 10.0 m Show Content Detailed Solution The lateral view of the frustrum \(\tan \theta = \frac{6}{1.5} = 4\) \(\theta = \tan^{-1} 4 = 75.96°\) Extending to the full height of the pyramid, we have The height of the pyramid which formed the frustrum = (6 + x)m, \(\tan 75.96 = \frac{6 + x}{2.5}\) \(6 + x = 2.5 \times 4 = 10.0\) \(\therefore \text{The height of the pyramid} = 1	D
19.	P is a point on one side of the straight line UV and P moves in the same direction as UV. If the straight line ST is on the locus of P and angle VUS = 60°, find angle UST. A. 310° B. 130° C. 80° D. 50° Show Content Detailed Solution Make a good sketch of the question, and follow this steps. Since ST is parallel to UV => angle USR = 50°(alternate to VUS. Angle UST = 180° - 50° = 130° (angle on a straight line)	B
20.	An equilateral triangle of side √3cm is inscribed in a circle. Find the radius of the circle. A. 2/3 cm B. 2 cm C. 1 cm D. 3 cm Show Content Detailed Solution Since the inscribed triangle is equilateral, therefore the angles at all the points = 60° Using the formula for inscribed circle, 2R = \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\) where R = radius of the circle; a, b and c are the sides of the triangle. ⇒ 2R = \(\frac{\sqrt{3}}{\sin 60}\) 2R = \(\frac{\sqrt{3}}{\frac{\sqrt{3}}{2}}\) 2R = 2 R = 1cm	C