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POST UTME AL-HIKMAH UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME AL-HIKMAH 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

Solve the inequality \( \frac{x^2 - 4}{x + 2} geq 0 \) for ( x in mathbb{R} ).

Correct A. \( x leq -2 \) or ( x geq 2 )

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

C. ( x leq 2 ) or \( x geq -2 \)

D. \( x = -2 \) or \( x = 2 \)

Correct Answer: A

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Question 2

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

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

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

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

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

Correct Answer: A

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Question 3

The equation of a circle is given by \( x^2 + y^2 - 6x + 8y + 12 = 0 \). Find the center and radius of the circle.

Correct A. Center: \( 3, -4 \ \) ), Radius: ( 2 )

B. Center: ( (4, 3) ), Radius: ( 2 )

C. Center: ( (3, 4) ), Radius: ( 2 )

D. Center: \( 4, -3 \ \) ), Radius: ( 2 )

Correct Answer: A

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Question 4

A polynomial function is defined as ( f(x) = x^3 - 6x^2 + 11x - 6 ). Find the value of \( f\( -1 \ \) ).

Correct A. ( 4 )

B. ( 5 )

C. ( 6 )

D. ( 7 )

Correct Answer: A

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Question 5

Two events A and B are indep\endent. If ( P(A) = \frac{1}{3} ) and ( P(B) = \frac{2}{5} ), find the probability that both events occur.

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

Correct B. \( \frac{2}{15} \)

C. \( \frac{4}{15} \)

D. \( \frac{1}{15} \)

Correct Answer: B

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Question 6

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 7

A survey of 100 students found that 60% preferred Mathematics, 20% preferred Science, and 20% preferred both. What is the number of students who prefer Mathematics but not Science?

A. 24

B. 30

Correct C. 36

D. 42

Correct Answer: C

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Question 8

In the diagram below, what is the value of x?

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 9

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

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 10

A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed for the round trip?

A. 45

B. 50

Correct C. 55

D. 60

Correct Answer: C

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Question 11

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

A. 24

B. 30

Correct C. 36

D. 42

Correct Answer: C

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Question 12

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

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 13

A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first five terms of the sequence.

A. 30

Correct B. 35

C. 40

D. 45

Correct Answer: B

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Question 14

A histogram is shown below. Find the mean of the data.

A. 10

B. 15

Correct C. 20

D. 25

Correct Answer: C

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Question 15

A vector ( mathbf{a} ) is defined by \( mathbf{a} = 2mathbf{i} + 3mathbf{j} \). Find the magnitude of ( mathbf{a} ).

A. 2.5

B. 3.5

Correct C. 4.5

D. 5.5

Correct Answer: C

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Question 16

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

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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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. 10

B. 12

Correct C. 15

D. 20

Correct Answer: C

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Question 18

The first term of an arithmetic progression is ( a ) and the common difference is ( d ). Find the sum of the first five terms of the progression.

Correct A. \frac{5}{2}\( 2a + 3d \)

B. \frac{5}{2}\( a + 3d \)

C. \frac{5}{2}\( 2a + d \)

D. \frac{5}{2}\( a + d \)

Correct Answer: A

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Question 19

A solid cylinder has a radius of 4 cm and a height of 10 cm. Find the volume of the cylinder.

A. 800\pi

Correct B. 1600\pi

C. 3200\pi

D. 6400\pi

Correct Answer: B

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Question 20

The mean of a set of numbers is 25. If the sum of the numbers is 100, find the mode of the set.

A. 20

Correct B. 25

C. 30

D. 35

Correct Answer: B

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Question 21

Simplify the expression \( \sqrt{\frac{16}{25}} \ \).

Correct A. \frac{4}{5}

B. \frac{2}{5}

C. \frac{4}{3}

D. \frac{2}{3}

Correct Answer: A

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Question 22

Find the value of ( x ) in the equation \( 2^x = 64 \).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 23

A histogram has a mean of 25 and a s\tandard deviation of 5. Find the range of the histogram.

A. 20

B. 25

C. 30

Correct D. 35

Correct Answer: D

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Question 24

Simplify the expression \( \log_{10}\( 1000 \ \).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 25

A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first five terms of the sequence.

A. 15

B. 20

C. 25

Correct D. 30

Correct Answer: D

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