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POST UTME CRAWFORD UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME CRAWFORD UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2025 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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.

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

B. \frac{64\pi}{5}

C. \frac{128\pi}{5}

D. \frac{256\pi}{5}

Correct Answer: A

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Question 2

Solve the inequality \frac{x^2 - 4}{x^2 + 4} > 0.

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

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

C. \( -2, 2 \)

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

Correct Answer: A

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Question 3

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

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

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

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

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

Correct Answer: A

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Question 4

Solve the equation x^2 + 4x + 4 = 0.

Correct A. x = -2

B. x = -1

C. x = 1

D. x = 2

Correct Answer: A

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Question 5

Find the sum of the first 5 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 2 + 6 + 18 + 54 + 162

B. 2 + 6 + 18 + 54 + 162

C. 2 + 6 + 18 + 54 + 162

D. 2 + 6 + 18 + 54 + 162

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 for x in the equation \( \log_{10} \( x^2 \) = 4 \).

A. 10^4

Correct B. 10^8

C. 10^12

D. 10^16

Correct Answer: B

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Question 8

A circle passes through the points (2, 3) and (4, 5). Find the equation of the circle.

Correct A. \( x - 3 \)^2 + \( y - 4 \)^2 = 5^2

B. \( x - 2 \)^2 + \( y - 3 \)^2 = 4^2

C. \( x - 4 \)^2 + \( y - 5 \)^2 = 3^2

D. \( x - 5 \)^2 + \( y - 3 \)^2 = 4^2

Correct Answer: A

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Question 9

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

A. 6

Correct B. 12

C. 18

D. 24

Correct Answer: B

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Question 10

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 11

Determine the value of x in the equation \( \sin^2 x + \cos^2 x = 1 \) if \( \sin x = \frac{3}{5} \).

A. \( \frac{\sqrt{16}}{5} \)

B. \( \frac{\sqrt{9}}{5} \)

C. \( \frac{\sqrt{25}}{5} \)

Correct D. \( \frac{\sqrt{36}}{5} \)

Correct Answer: D

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Question 12

Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).

Correct A. \( \frac{pi}{4} \)

B. \( \frac{pi}{2} \)

C. \( \frac{pi}{6} \)

D. \( \frac{pi}{3} \)

Correct Answer: A

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Question 13

Solve the inequality \( \frac{x^2 - 4x + 3}{x^2 - 2x - 3} > 0 \).

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

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

C. \( x < -1 \) or \( x < 3 \)

D. \( x > 1 \) or \( x < 3 \)

Correct Answer: A

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Question 14

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

Correct A. \( y = 2x - 1 \)

B. \( y = 2x + 1 \)

C. \( y = x - 1 \)

D. \( y = x + 1 \)

Correct Answer: A

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Question 15

Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).

Correct A. \( x = 1 \) or \( x = 2 \) or \( x = 3 \)

B. \( x = 1 \) or \( x = 2 \) or \( x = 4 \)

C. \( x = 1 \) or \( x = 3 \) or \( x = 4 \)

D. \( x = 2 \) or \( x = 3 \) or \( x = 4 \)

Correct Answer: A

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Question 16

Find the area under the curve \( y = \frac{1}{x^2} \) from \( x = 1 \) to \( x = 2 \).

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

B. \( \frac{1}{3} \)

C. \( \frac{1}{4} \)

D. \( \frac{1}{5} \)

Correct Answer: A

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Question 17

Solve the inequality \( |x - 2| geq 3 \).

Correct A. \( x leq -1 \) or ( x geq 5 )

B. ( x leq 1 ) or ( x geq 5 )

C. \( x leq -1 \) or ( x geq 4 )

D. ( x leq 0 ) or ( x geq 4 )

Correct Answer: A

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Question 18

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

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

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

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

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

Correct Answer: A

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Question 19

Solve the equation \( 2 \sin^2 x + 3 \sin x - 2 = 0 \).

Correct A. \( \sin x = -1 \) or \( \sin x = \frac{2}{3} \)

B. \( \sin x = 1 \) or \( \sin x = -\frac{2}{3} \)

C. \( \sin x = -\frac{1}{2} \) or \( \sin x = \frac{2}{3} \)

D. \( \sin x = \frac{1}{2} \) or \( \sin x = -\frac{2}{3} \)

Correct Answer: A

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Question 20

Find the area of the triangle with vertices (A(1, 2)), (B(3, 4)), and (C(2, 1)).

Correct A. ( 5 )

B. ( 10 )

C. ( 15 )

D. ( 20 )

Correct Answer: A

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Question 21

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

Correct A. \frac{-x}{\( x^2 + 1 \)^{3/2}}

B. \frac{x}{\( x^2 + 1 \)^{3/2}}

C. \frac{1}{\( x^2 + 1 \)^{3/2}}

D. \frac{-1}{\( x^2 + 1 \)^{3/2}}

Correct Answer: A

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Question 22

Solve for x in the equation \( 2^x + 2^x = 2^{x+1} \).

Correct A. x = 1

B. x = 2

C. x = 3

D. x = 4

Correct Answer: A

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Question 23

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \frac{1}{6}

B. \frac{2}{6}

C. \frac{3}{6}

Correct D. \frac{4}{6}

Correct Answer: D

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Question 24

Find the equation of the circle with center \( -2, 3 \) and radius 4.

Correct A. \( x + 2 \)^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 25

Solve for x in the equation \( 2^x = 16 \).

Correct A. x = 2

B. x = 3

C. x = 4

D. x = 5

Correct Answer: A

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