POST UTME COAL CITY UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 128
Question 2
In a 3x3 matrix, if the determinant is 12, and the first row is [2, 3, 4], find the value of the element in the second row and third column.
A. 5
B. 6
C. 7
D. 8
Question 3
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 4
Solve for x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ).
A. \( x = \frac{pi}{4} \)
B. \( x = \frac{pi}{2} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{pi}{6} \)
Question 5
A rec\tangular prism has a length of 5cm, a width of 3cm, and a height of 2cm. Find its surface area.
A. 35
B. 40
C. 45
D. 50
Question 6
Find the volume of the solid formed by rotating the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 7
Solve the inequality \frac{x}{x-1} > 2.
A. x < -1 or x > 2
B. x < 1 or x > 2
C. x < -1 or x < 2
D. x > -1 or x > 2
Question 8
Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for \( x in \( -infty, -2 \ \) cup \( -2, infty \) ).
A. \( -2, -1 \) ∪ (1, ∞)
B. \( -∞, -2 \) ∪ (0, ∞)
C. \( -∞, -2 \) ∪ (1, ∞)
D. \( -∞, -1 \) ∪ (0, ∞)
Question 9
Find the determinant of the matrix \( \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 10
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the sum of the first 5 terms of the sequence.
A. 65
B. 67
C. 69
D. 71
Question 11
A survey of 100 students found that 60% preferred Mathematics, 20% preferred Science, and 20% preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?
A. 0.8
B. 0.7
C. 0.6
D. 0.5
Question 12
A circle with center (0, 0) and radius 4 passes through the point (3, 4). Find the equation of the circle.
A. x^2 + y^2 = 16
B. x^2 + y^2 = 20
C. x^2 + y^2 = 24
D. x^2 + y^2 = 28
Question 13
A histogram of exam scores is shown below. If the mean score is 75, and the range is 20, what is the mode?
A. 60
B. 70
C. 80
D. 90
Question 14
A particle moves in a straight line with a velocity of \( 5 , \text{m/s} \) and an acceleration of \( 2 , \text{m/s}^2 \). Find its position after ( 3 ) seconds.
A. 15
B. 20
C. 25
D. 30
Question 15
In a set of 10 numbers, the mean is 20 and the s\tandard deviation is 5. If the numbers are normally distributed, what is the probability that a randomly selected number is between 15 and 25?
A. 0.5
B. 0.6
C. 0.7
D. 0.8

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