POST UTME AL-HIKMAH UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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. 15
C. 20
D. 25
Question 2
The equation of a circle is given by \( x^2 + y^2 - 6x + 8y + 12 = 0 \). Find the center and radius of the circle.
A. Center: \( 3, -4 \ \) ), Radius: ( 2 )
B. Center: ( (4, 3) ), Radius: ( 2 )
C. Center: ( (3, 4) ), Radius: ( 2 )
D. Center: \( 4, -3 \ \) ), Radius: ( 2 )
Question 3
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
C. 4.5
D. 5.5
Question 4
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 5
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 6
A histogram is shown below. Find the mean of the data.
A. 10
B. 15
C. 20
D. 25
Question 7
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 8
In the diagram below, what is the value of x?
A. 3
B. 4
C. 5
D. 6
Question 9
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
C. 36
D. 42
Question 10
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
D. 30
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
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 13
If f(x) = x^3 - 2x^2 + x - 1, find f'(x) u\sing the chain rule.
A. \frac{d}{dx} \( x^3 - 2x^2 + x - 1 \) = 3x^2 - 4x + 1
B. \frac{d}{dx} \( x^3 - 2x^2 + x - 1 \) = 3x^2 - 4x - 1
C. \frac{d}{dx} \( x^3 - 2x^2 + x - 1 \) = 3x^2 - 4x + 2
D. \frac{d}{dx} \( x^3 - 2x^2 + x - 1 \) = 3x^2 - 4x - 2
Question 14
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 15
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. \( \frac{1}{15} \)

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