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POST UTME SKYLINE UNIVERSITY 2017 Mathematics | Objective

Are you preparing for POST UTME SKYLINE UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the area under the curve $ y = \frac{1}{2}x^2 + 3x - 2 $ from $ x = 0 $ to $ x = 4 $.

A. $ \frac{1}{2} $

B. ( 3 )

C. ( 4 )

Correct D. ( 6 )

Correct Answer: D

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Question 2

Solve for ( x ) in the equation $ 2^x + 3^x = 5^x $.

Correct A. $ x = 1 $

B. $ x = 2 $

C. $ x = 3 $

D. $ x = 4 $

Correct Answer: A

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Question 3

Find the value of $ \log_{10} \( 1000 \ $ ).

A. ( 3 )

Correct B. ( 4 )

C. ( 5 )

D. ( 6 )

Correct Answer: B

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Question 4

Solve the inequality $ x^2 - 4x - 5 > 0 $.

Correct A. $ x < -1 $ or $ x > 5 $

B. $ x < 1 $ or $ x > 5 $

C. $ x < -1 $ or $ x < 5 $

D. $ x < 1 $ or $ x > 5 $

Correct Answer: A

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Question 5

Find the value of $ \sin \( 2\theta \ $ ) given that $ \sin \theta = \frac{1}{2} $ and $ \cos \theta = \frac{\sqrt{3}}{2} $.

Correct A. $ \frac{\sqrt{3}}{2} $

B. $ \frac{1}{2} $

C. $ \frac{\sqrt{5}}{2} $

D. $ \frac{1}{\sqrt{2}} $

Correct Answer: A

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Question 6

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 48\pi

B. 64\pi

Correct C. 80\pi

D. 96\pi

Correct Answer: C

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Question 7

Solve the equation $ x^3 - 6x^2 + 11x - 6 = 0 $ u\sing the factor theorem.

Correct A. $ x - 1 $$ x - 2 $$ x - 3 $

B. $ x - 1 $$ x - 2 $$ x - 4 $

C. $ x - 1 $$ x - 3 $$ x - 4 $

D. $ x - 2 $$ x - 3 $$ x - 4 $

Correct Answer: A

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Question 8

Find the magnitude of the vector $ \vec{a} = 3\hat{i} + 4\hat{j} $ and the angle it makes with the positive x-axis.

A. \sqrt{5}

Correct B. \sqrt{10}

C. \sqrt{20}

D. \sqrt{25}

Correct Answer: B

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Question 9

Solve the equation $ \sin^2 x + \cos^2 x = 1 $ for $ x $ in the interval $ [0, 2\pi] $.

Correct A. 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}

B. \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}

C. \frac{\pi}{6}, \frac{\pi}{3}, \frac{2\pi}{3}, \frac{5\pi}{6}

D. \frac{\pi}{8}, \frac{3\pi}{8}, \frac{5\pi}{8}, \frac{7\pi}{8}

Correct Answer: A

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Question 10

Find the derivative of the function $ f(x) = \frac{1}{x^2 + 1} $ u\sing the chain rule.

Correct A. \frac{-2x}{$ x^2 + 1 $^2}

B. \frac{2x}{$ x^2 + 1 $^2}

C. \frac{-2}{$ x^2 + 1 $^2}

D. \frac{2}{$ x^2 + 1 $^2}

Correct Answer: A

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Question 11

Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 12

A binary operation \ast on the set of integers is defined as a \ast b = ab + 1. Find the value of 2 \ast 3.

A. 7

Correct B. 9

C. 11

D. 13

Correct Answer: B

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Question 13

Find the area under the curve y = x^3 - 6x^2 + 9x + 2 from x = 0 to x = 4.

A. 64

B. 128

Correct C. 192

D. 256

Correct Answer: C

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Question 14

Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...

A. 123

B. 124

C. 125

Correct D. 126

Correct Answer: D

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Question 15

Find the derivative of the function f(x) = 2x^3 - 5x^2 + 3x - 1.

A. 6x^2 - 10x + 3

B. 12x^2 - 20x + 6

Correct C. 24x^2 - 40x + 12

D. 48x^2 - 80x + 24

Correct Answer: C

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Question 16

Find the equation of the circle with center at $ -2, 3 $ and radius 4.

Correct A. \boxed{$ x + 2 $^2 + $ y - 3 $^2 = 16}

B. $ x - 2 $^2 + $ y + 3 $^2 = 16

C. $ x + 2 $^2 + $ y + 3 $^2 = 16

D. $ x - 2 $^2 + $ y - 3 $^2 = 16

Correct Answer: A

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Question 17

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its surface area.

Correct A. 2(6)(4) + 2(6)(3) + 2(4)(3) = 48 + 36 + 24 = 108

B. 2(6)(4) + 2(6)(3) + 2(4)(3) = 48 + 36 + 24 = 108

C. 2(6)(4) + 2(6)(3) + 2(4)(3) = 48 + 36 + 24 = 108

D. 2(6)(4) + 2(6)(3) + 2(4)(3) = 48 + 36 + 24 = 108

Correct Answer: A

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Question 18

Simplify the expression: \frac{2x^2 + 5x - 3}{x + 3}

Correct A. \frac{2x^2 + 5x - 3}{x + 3} = 2x - 1

B. \frac{2x^2 + 5x - 3}{x + 3} = 2x + 1

C. \frac{2x^2 + 5x - 3}{x + 3} = x - 1

D. \frac{2x^2 + 5x - 3}{x + 3} = x + 1

Correct Answer: A

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Question 19

Find the derivative of the function: f(x) = 3x^2 + 2x - 5

Correct A. f'(x) = 6x + 2

B. f'(x) = 6x - 2

C. f'(x) = 3x^2 + 2

D. f'(x) = 3x^2 - 2

Correct Answer: A

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Question 20

Solve the system of equations: x + y = 4 and x - y = 2

Correct A. x = 3, y = 1

B. x = 1, y = 3

C. x = 2, y = 2

D. x = 4, y = 0

Correct Answer: A

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Question 21

Find the equation of the line pas\sing through the points (2, 3) and (4, 5)

Correct A. y = 1x + 1

B. y = 1x - 1

C. y = -1x + 1

D. y = -1x - 1

Correct Answer: A

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Question 22

A circle has a radius of 4 cm and a center at (0, 0). Find the equation of the circle.

Correct A. x^2 + y^2 = 16

B. x^2 + y^2 = 4

C. x^2 - y^2 = 16

D. x^2 - y^2 = 4

Correct Answer: A

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Question 23

Find the volume of the rec\tangular prism with length 6 cm, width 4 cm, and height 3 cm.

A. 6(4)(3) = 72

B. 6(4)(3) = 64

C. 6(4)(3) = 80

D. 6(4)(3) = 96

Correct Answer: VIEW ANSWER

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Question 24

In a circle with center $O$, a chord $AB$ is drawn such that $OA=3$ and $OB=4$. If $M$ is the midpoint of $AB$, find the area of $\triangle OMA$.

Correct A. 12

B. 16

C. 20

D. 24

Correct Answer: A

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Question 25

Let $f(x)=\frac{x^2+1}{x^2-1}$. Find the value of $f^{-1}(2)$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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