POST UTME ACHIEVERS UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the matrix equation \( \begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 3 \end{bmatrix} \).
A. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 1 \end{bmatrix}
B. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 2 \end{bmatrix}
C. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 3 \end{bmatrix}
D. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 4 \ 4 \end{bmatrix}
Question 2
Solve the inequality: \( x^2 - 4x + 3 > 0 \).
A. \( -infty, 1 \) cup (3, infty)
B. \( -infty, 3 \) cup (1, infty)
C. \( -infty, 1 \) cup (1, 3)
D. \( -infty, 3 \) cup (3, infty)
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 = 4
C. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
D. \( x - 3 \)^2 + \( y - 2 \)^2 = 4
Question 4
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.
A. 30
B. 60
C. 90
D. 120
Question 5
Find the volume of the sphere with radius 5.
A. \frac{4}{3}pi(5)^3
B. \frac{1}{3}pi(5)^3
C. \frac{2}{3}pi(5)^3
D. \frac{1}{4}pi(5)^3
Question 6
Find the area under the curve $y = 2x^3 - 5x^2 + x + 1$ from $x = 0$ to $x = 2$.
A. \frac{23}{3}
B. \frac{47}{6}
C. \frac{97}{12}
D. \frac{191}{15}
Question 7
In a set A = {1, 2, 3, 4, 5}, find the number of subsets that contain exactly two elements.
A. 5
B. 10
C. 15
D. 20
Question 8
Solve the system of linear equations \( \begin{bmatrix} 1 & 2 \ 2 & 1 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 3 \end{bmatrix} \).
A. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 1 \end{bmatrix}
B. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 2 \end{bmatrix}
C. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 3 \end{bmatrix}
D. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 4 \ 4 \end{bmatrix}
Question 9
Determine the volume of the solid formed by rotating the region bounded by $y = x^2$ and $y = 4x$ about the x-axis.
A. \frac{16\pi}{3}
B. \frac{32\pi}{3}
C. \frac{64\pi}{3}
D. \frac{128\pi}{3}
Question 10
A circle has a radius of 4 cm. Find the area of the circle.
A. 50.24
B. 100.48
C. 201.06
D. 314.16
Question 11
Solve the system of linear equations: \begin{align*} x + y &= 2 \ 2x - y &= 3 \end{align*}
A. x = 1, y = 1
B. x = 2, y = 0
C. x = 0, y = 2
D. x = 1, y = 0
Question 12
Find the sum of the first 10 terms of the geometric series 2, 6, 18, ...
A. 1023
B. 1024
C. 1025
D. 1026
Question 13
Find the area of the region bounded by the parabola y = x^2, the x-axis, and the line x = 4.
A. 64
B. 128
C. 256
D. 512
Question 14
Solve the trigonometric equation \( 2 \sin^2 x + 3 \cos x - 1 = 0 \).
A. \sin x = \frac{1}{2}
B. \sin x = \frac{1}{3}
C. \cos x = \frac{1}{2}
D. \cos x = \frac{1}{3}
Question 15
Solve the system of equations: \( x + y = 2 \) and \( x - y = 0 \).
A. (0, 2)
B. (1, 1)
C. (2, 0)
D. (0, 0)

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