POST UTME ESUT 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. ( 32 )
B. ( 64 )
C. ( 16 )
D. ( 128 )
Question 2
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 3
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 4
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 5
Find the sum of the first 10 terms of the geometric series \( 2x^2 - 3x + 1 \) with common ratio \( r = 2 \).
A. \( 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + cdots + 2x^2 - 3x + 1 \)
B. \( 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + cdots + 2x^2 - 3x + 1 \)
C. \( 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + cdots + 2x^2 - 3x + 1 \)
D. \( 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + cdots + 2x^2 - 3x + 1 \)
Question 6
A fair six-sided die is rolled. What is the probability that the number rolled is either 1, 2, or 3?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 7
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} ) for \( x = 1, 2, 3 \). Find the expected value of ( X ).
A. ( 2 )
B. ( 3 )
C. ( 4 )
D. ( 5 )
Question 8
A circuit consists of a battery, a resistor, and a capacitor in series. If the capacitor is charged to 5V and the resistor is 10Ω, what is the current flowing through the circuit?
A. 0.5A
B. 1A
C. 2A
D. 5A
Question 9
Let ( f(x) = \frac{1}{\sqrt{x^2 - 4}} ). Find the domain of ( f(x) ) in interval notation.
A. \( -∞, -2 \) ∪ (2, ∞)
B. \( -∞, 2 \) ∪ (2, ∞)
C. \( -∞, -2 \) ∪ (2, ∞)
D. \( -∞, 2 \)
Question 10
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -1 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) u\sing the formula \( \text{proj}_mathbf{a} mathbf{b} = \frac{mathbf{a} cdot mathbf{b}}{| mathbf{a} |^2} mathbf{a} \).
A. \( \begin{pmatrix} \frac{5}{13} \frac{15}{13} \end{pmatrix} \ \)
B. \( \begin{pmatrix} \frac{2}{13} \frac{6}{13} \end{pmatrix} \ \)
C. \( \begin{pmatrix} \frac{1}{13} \frac{3}{13} \end{pmatrix} \ \)
D. \( \begin{pmatrix} \frac{3}{13} \frac{9}{13} \end{pmatrix} \ \)
Question 11
A set of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the z-score of a score of 90?
A. 1.5
B. 2.0
C. 2.5
D. 3.0
Question 12
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?
A. 30
B. 40
C. 50
D. 60
Question 13
Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.
A. 24π cm³
B. 48π cm³
C. 96π cm³
D. 192π cm³
Question 14
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \).
A. -2
B. 2
C. 4
D. 6
Question 15
Solve the equation \( 2^x + 2^x = 100 \) for x.
A. 4
B. 5
C. 6
D. 7

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