POST UTME ACHIEVERS UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A rec\tangular solid has dimensions 5 cm, 6 cm, and 7 cm. Find the volume of the solid.
A. 210
B. 220
C. 230
D. 240
Question 2
A solid right circular cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone in cubic centimeters.
A. 256\pi
B. 512\pi
C. 1024\pi
D. 2048\pi
Question 3
Solve the inequality \( \frac{x^2 - 9}{x^2 - 4} < 0 \).
A. \( -∞, -2 \) ∪ (2, ∞)
B. \( -∞, -2 \) ∪ (2, 3)
C. \( -∞, -2 \) ∪ (3, ∞)
D. \( -∞, 3 \) ∪ (4, ∞)
Question 4
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 5
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 2).
A. 6
B. 8
C. 10
D. 12
Question 6
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 12
B. 16
C. 20
D. 24
Question 7
A vector \overrightarrow{a} has a magnitude of 6 units and makes an angle of 30° with the positive x-axis. Find the x and y components of \overrightarrow{a}.
A. 3\hat{i} + 3\hat{j}
B. 6\hat{i} + 3\hat{j}
C. 3\hat{i} + 6\hat{j}
D. 6\hat{i} + 6\hat{j}
Question 8
Find the area of the triangle formed by the points ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).
A. 6
B. 8
C. 10
D. 12
Question 9
A circle has a diameter of 10 cm. Find the area of the circle.
A. 50
B. 100
C. 200
D. 500
Question 10
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 11
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 4
B. 8
C. 16
D. 32
Question 12
Solve the inequality 2x^2 + 5x - 3 > 0.
A. x < -1 or x > 3/2
B. x < 1 or x > 3
C. x < -3 or x > 1
D. x < 1 or x < 3
Question 13
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 14
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}}
B. f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}}
C. f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}}
D. f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}}
Question 15
Find the derivative of the function f(x) = \( \frac{1}{x^2 + 1} \) u\sing the chain rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2})
B. \( \frac{2x}{\( x^2 + 1 \ \)^2})
C. \( \frac{1}{\( x^2 + 1 \ \)^2})
D. \( \frac{-1}{\( x^2 + 1 \ \)^2})

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