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POST UTME UNIBEN 2017 Mathematics | Objective

Are you preparing for POST UTME UNIBEN 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 of the function ( f(x) = \frac{1}{2}x^2 + 3x - 2 ) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{1}{2} \)

B. ( 3 )

C. ( 4 )

D. ( 6 )

Correct Answer: A

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Question 2

A set of 10 numbers has a mean of 20 and a s\tandard deviation of 5. What is the probability that a randomly selected number from this set will be greater than 25?

A. 0.25

B. 0.5

Correct C. 0.75

D. 0.9

Correct Answer: C

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Question 3

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( x < -1 \) or \( x > 3 \)

B. \( x < -3 \) or \( x > 1 \)

C. \( x < -2 \) or \( x > 2 \)

D. \( x < -4 \) or \( x > 4 \)

Correct Answer: A

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Question 4

Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).

A. \( 2 + 6 + 18 + ldots + 972 \)

B. \( 2 + 6 + 18 + ldots + 1024 \)

Correct C. \( 2 + 6 + 18 + ldots + 1026 \)

D. \( 2 + 6 + 18 + ldots + 1028 \)

Correct Answer: C

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Question 5

A polynomial function has a degree of 4 and has zeros at \( x = -2 \), \( x = 1 \), and \( x = 3 \). Find the polynomial function.

A. \( x + 2 \)\( x - 1 \)\( x - 3 \ \) )

Correct B. \( x + 2 \)\( x - 1 \)\( x - 3 \)\( x + 1 \ \) )

C. \( x + 2 \)\( x - 1 \)\( x - 3 \)\( x - 4 \ \) )

D. \( x + 2 \)\( x - 1 \)\( x - 3 \)\( x + 4 \ \) )

Correct Answer: B

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Question 6

Solve the inequality \( \frac{x}{x-2} > 0 \) for \( x in \( -infty, infty \ \) ).

Correct A. \( -\infty, 2 \) \cup \( 2, \infty \)

B. \( -\infty, 2 \) \cap \( 2, \infty \)

C. \( -\infty, 2 \) \cup \( 2, \infty \)

D. \( -\infty, 2 \) \cap \( 2, \infty \)

Correct Answer: A

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Question 7

Find the value of ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.

Correct A. -\frac{5}{4}

B. \frac{3}{2}

C. -\frac{3}{2}

D. \frac{5}{4}

Correct Answer: A

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Question 8

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the z-score of a score of 70?

A. 0.5

B. 1.0

Correct C. 1.5

D. 2.0

Correct Answer: C

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Question 9

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the power rule.

Correct A. 6x + 2

B. 6x - 2

C. 3x^2 + 2

D. 3x^2 - 2

Correct Answer: A

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Question 10

A circle has a radius of 4 cm. What is the area of the circle?

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 11

Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x = 1 - \cos^2 x \).

Correct A. x = \frac{\pi}{4}

B. x = \frac{3\pi}{4}

C. x = \frac{\pi}{2}

D. x = \frac{5\pi}{4}

Correct Answer: A

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Question 12

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

Correct A. f'(x) = \frac{-2x}{\( x^2 + 1 \)^2}

B. f'(x) = \frac{2x}{\( x^2 + 1 \)^2}

C. f'(x) = \frac{1}{\( x^2 + 1 \)^2}

D. f'(x) = \frac{-1}{\( x^2 + 1 \)^2}

Correct Answer: A

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Question 13

Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.

Correct A. x < -1 or x > \frac{3}{2}

B. x < -1 or x < \frac{3}{2}

C. x > -1 or x > \frac{3}{2}

D. x < -1 or x < \frac{3}{2}

Correct Answer: A

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Question 14

Find the mean and s\tandard deviation of the data set {1, 2, 3, 4, 5} u\sing the formulas \( \bar{x} = \frac{\sum x_i}{n} \) and \( s = \sqrt{\frac{\sum \( x_i - \bar{x} \ \)^2}{n - 1}} ).

Correct A. \bar{x} = 3, s = 1.414

B. \bar{x} = 3, s = 1.732

C. \bar{x} = 2, s = 1.414

D. \bar{x} = 2, s = 1.732

Correct Answer: A

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Question 15

Graph the function \( y = \sin x \) over the interval \( [0, 2\pi] \) u\sing the unit circle.

A. A graph of the function y = \sin x over the interval [0, 2π] showing the unit circle.

B. A graph of the function y = \sin x over the interval [0, 2π] showing the \sine wave.

Correct C. A graph of the function y = \sin x over the interval [0, 2π] showing the unit circle and the \sine wave.

D. A graph of the function y = \sin x over the interval [0, 2π] showing only the unit circle.

Correct Answer: C

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Question 16

If ( f(x) = \frac{1}{x^2 + 1} ), find \( lim_{x \to infty} f\( x \ \) ).

Correct A. 0

B. \frac{1}{2}

C. \frac{1}{\infty}

D. \frac{\infty}{\infty}

Correct Answer: A

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Question 17

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( -\infty, -1 \) \cup \( 3, \infty \)

B. \( -\infty, -3 \) \cup \( 1, \infty \)

C. \( -\infty, 1 \) \cup \( 3, \infty \)

D. \( -\infty, -3 \) \cup \( 1, \infty \)

Correct Answer: A

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Question 18

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. \frac{1}{4}

B. \frac{1}{3}

Correct C. \frac{2}{5}

D. \frac{3}{5}

Correct Answer: C

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Question 19

Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( x = 2 \) about the x-axis.

Correct A. \frac{32\pi}{5}

B. \frac{16\pi}{3}

C. \frac{8\pi}{3}

D. \frac{4\pi}{3}

Correct Answer: A

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Question 20

If ( f(x) = \sin x ), find ( f'(x) ).

Correct A. \cos x

B. \sin x

C. \tan x

D. \csc x

Correct Answer: A

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Question 21

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

A. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

B. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

Correct C. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

D. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

Correct Answer: C

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Question 22

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)

B. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)

C. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)

D. \( x > -\frac{5}{4} \) or \( x > \frac{3}{2} \)

Correct Answer: A

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Question 23

Find the sum of the first 10 terms of the arithmetic progression ( 2, 5, 8, ldots ).

Correct A. ( 55 )

B. ( 65 )

C. ( 75 )

D. ( 85 )

Correct Answer: A

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Question 24

Solve the equation \( \sin^2 x + \cos^2 x = 1 \).

A. \( x = \frac{pi}{2} \)

Correct B. \( x = \frac{pi}{4} \)

C. \( x = \frac{3pi}{4} \)

D. \( x = \frac{5pi}{4} \)

Correct Answer: B

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Question 25

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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