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POST UTME MOUNTAIN TOP UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME MOUNTAIN TOP 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.

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Question 1

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. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 2

A particle moves along the curve y = x² + 2x + 1. Find the area under the curve between x = 0 and x = 2.

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 3

Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 4

Solve the quadratic equation x² + 5x + 6 = 0.

Correct A. x = -2, x = -3

B. x = -1, x = -6

C. x = 2, x = 3

D. x = 1, x = 6

Correct Answer: A

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Question 5

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 = 4

C. \( x + 2 \)² + \( y + 3 \)² = 16

D. \( x + 2 \)² + \( y + 3 \)² = 4

Correct Answer: A

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Question 6

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 7

A circle with center ( C(2, 3) ) and radius 4 passes through the point ( P(6, 5) ). Find the equation of the circle.

Correct A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )

B. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 20 )

C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 24 )

D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 28 )

Correct Answer: A

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Question 8

Two events ( A ) and ( B ) are indep\endent. If ( P(A) = 0.3 ) and ( P(B) = 0.4 ), find \( P\( A \cap B \ \) ).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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

B. \( x = \frac{\pi}{2} \ \) or \( x = \frac{3\pi}{2} \ \)

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

D. \( x = \frac{\pi}{2} \ \) or \( x = \frac{5\pi}{2} \ \)

Correct Answer: A

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Question 10

Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix} \ \).

A. 0

Correct B. 10

C. 20

D. 30

Correct Answer: B

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Question 11

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the cross product formula.

Correct A. \( egin{pmatrix} 6 \ -4 \end{pmatrix} \)

B. \( egin{pmatrix} 4 \ -6 \end{pmatrix} \)

C. \( egin{pmatrix} 3 \ -2 \end{pmatrix} \)

D. \( egin{pmatrix} 2 \ -3 \end{pmatrix} \)

Correct Answer: A

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Question 12

Find the derivative of ( 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{x^2}{\( x^2 + 1 \ \)^2} )

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

Correct Answer: A

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Question 13

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

Correct A. 30

B. 50

C. 60

D. 70

Correct Answer: A

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Question 14

Simplify the expression \( \frac{1}{2} \times \frac{3}{4} \) u\sing binary operations.

Correct A. \( \frac{3}{8} \)

B. \( \frac{1}{8} \)

C. \( \frac{3}{4} \)

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

Correct Answer: A

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Question 15

Find the surface area of a sphere with a radius of 4 cm.

Correct A. 201.06

B. 202.06

C. 203.06

D. 204.06

Correct Answer: A

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Question 16

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 17

A set ( A ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( A ) that contain exactly two elements.

A. 6

Correct B. 10

C. 12

D. 15

Correct Answer: B

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Question 18

The first five terms of a geometric sequence are ( 2, 6, 18, 54, 162 ). Find the common ratio.

Correct A. 3

B. 4

C. 5

D. 6

Correct Answer: A

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Question 19

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the highest score is 95, find the lowest score.

A. 55

B. 60

C. 65

Correct D. 70

Correct Answer: D

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Question 20

A number is divisible by 3 if the sum of its digits is divisible by 3. Find the smallest number greater than 1000 that is divisible by 3.

Correct A. 1002

B. 1005

C. 1008

D. 1011

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) in the coordinate plane.

Correct A. y = 2x + 1

B. y = 3x - 2

C. y = x + 2

D. y = 2x - 3

Correct Answer: A

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Question 22

A coin is tossed 5 times. What is the probability that exactly 3 heads appear?

A. 1/32

Correct B. 5/32

C. 10/32

D. 15/32

Correct Answer: B

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Question 23

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).

Correct A. x = -2

B. x = 2

C. x = -1

D. x = 1

Correct Answer: A

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Question 24

Find the mean of the following data set: 2, 4, 6, 8, 10.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 25

A set of numbers has a mean of 10 and a s\tandard deviation of 2. What is the probability that a randomly selected number from this set is greater than 12?

Correct A. 0.25

B. 0.5

C. 0.75

D. 1

Correct Answer: A

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