POST UTME SUMMIT UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \).
A. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
B. \left\( -\infty, -\frac{3}{2} \right \) \cap \left\( \frac{3}{2}, \infty \right \)
C. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( -\frac{3}{2}, \frac{3}{2} \right \)
D. \left\( -\infty, -\frac{3}{2} \right \) \cap \left\( -\frac{3}{2}, \frac{3}{2} \right \)
Question 2
Solve the inequality \(2x^2-5x-3>0\).
A. \( -\infty,-3)\cup\( 1,\infty \ \)
B. \( -\infty,-3)\cup\( 1,\infty \ \)
C. \( -\infty,-3)\cup\( 1,\infty \ \)
D. \( -\infty,-3)\cup\( 1,\infty \ \)
Question 3
A circle with center ( (0, 0) ) and radius ( 4 ) has an equation of the form \( x^2 + y^2 = r^2 \). Find the value of ( r ).
A. 4
B. 8
C. 16
D. 32
Question 4
A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:4, how many loaves of whole wheat bread are sold per day?
A. 200
B. 250
C. 300
D. 350
Question 5
A company produces two products, A and B. The profit from product A is $10 per unit, and the profit from product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?
A. $1500
B. $2000
C. $2500
D. $3000
Question 6
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 = 32
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 64
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 128
Question 7
A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). Find ( 2 ast 3 ).
A. 13
B. 14
C. 15
D. 16
Question 8
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > 3/2
B. x > -1 or x < 3/2
C. x < 3/2 or x > -1
D. x > 3/2 or x < -1
Question 9
Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ 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 solid right circular cone has a height of 20 cm and a base radius of 8 cm. Find the volume of the cone in terms of π.
A. 64\pi\text{ cm}^3
B. 128\pi\text{ cm}^3
C. 256\pi\text{ cm}^3
D. 512\pi\text{ cm}^3
Question 11
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 12
Solve the inequality \( \frac{x+2}{x^2-4} > 0 \) for \( x in \( -infty, infty \ \) ).
A. \( -2, -1 \) ∪ (1, ∞)
B. \( -∞, -2 \) ∪ \( -1, 1 \)
C. \( -∞, -2 \) ∪ (1, ∞)
D. \( -2, 1 \)
Question 13
Solve the inequality \frac{x-1}{x+1} > 0.
A. x < -1 \text{ or } x > 1
B. x < -1 \text{ or } x > 1
C. x < -1 \text{ or } x > 1
D. x < -1 \text{ or } x > 1
Question 14
Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}.
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 1 \ 2 \end{bmatrix}
C. \begin{bmatrix} 1 \ 2 \end{bmatrix}
D. \begin{bmatrix} 1 \ 2 \end{bmatrix}
Question 15
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = -1
C. x = 0
D. x = 1

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