POST UTME AL-HIKMAH UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of ( x ) in the equation \( 2^x = 64 \).
A. 3
B. 4
C. 5
D. 6
Question 2
A histogram is shown below. Find the mean of the data.
A. 10
B. 15
C. 20
D. 25
Question 3
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
B. 25
C. 30
D. 35
Question 4
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.
A. \frac{5}{2}\( 2a + 3d \)
B. \frac{5}{2}\( a + 3d \)
C. \frac{5}{2}\( 2a + d \)
D. \frac{5}{2}\( a + d \)
Question 5
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 12
C. 14
D. 16
Question 6
Solve the equation x^2 + 4x + 4 = 0 u\sing the quadratic formula.
A. x = -2 \pm 0i
B. x = -2 \pm 2i
C. x = -2 \pm 4i
D. x = -2 \pm 6i
Question 7
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
C. 15
D. 20
Question 8
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \frac{1}{3}
B. \frac{2}{3}
C. \frac{1}{2}
D. \frac{2}{6}
Question 9
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
C. 55
D. 60
Question 10
A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first five terms of the sequence.
A. 30
B. 35
C. 40
D. 45
Question 11
A polynomial function is defined as ( f(x) = x^3 - 6x^2 + 11x - 6 ). Find the value of \( f\( -1 \ \) ).
A. ( 4 )
B. ( 5 )
C. ( 6 )
D. ( 7 )
Question 12
Solve the inequality \( \frac{x^2 - 4}{x + 2} geq 0 \) for ( x in mathbb{R} ).
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 \( x = 2 \)
Question 13
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. \( \frac{1}{5} \)
B. \( \frac{2}{15} \)
C. \( \frac{4}{15} \)
D. \( \frac{1}{15} \)
Question 14
Simplify the expression \( \sqrt{\frac{16}{25}} \ \).
A. \frac{4}{5}
B. \frac{2}{5}
C. \frac{4}{3}
D. \frac{2}{3}
Question 15
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
C. 50
D. 60

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