POST UTME FUTO 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > \frac{3}{2}
B. x < -1 or x < \frac{3}{2}
C. x > -1 or x > \frac{3}{2}
D. x > -1 or x < \frac{3}{2}
Question 2
A circle has a radius of 4 cm. Find the area of the circle.
A. 50.24 cm^2
B. 100.48 cm^2
C. 200.96 cm^2
D. 400.96 cm^2
Question 3
A right circular cone has a height of 10 cm and a base radius of 5 cm. Find the volume of the cone.
A. 250π
B. 500π
C. 1000π
D. 2000π
Question 4
Solve the inequality \( \frac{x - 2}{x + 1} > 0 \).
A. \( -∞, -1 \) ∪ (1, ∞)
B. \( -∞, -1 \) ∪ (1, 2)
C. \( -∞, -1 \) ∪ (2, ∞)
D. \( -∞, 1 \) ∪ (2, ∞)
Question 5
The surface area of a cube with side length $s$ is given by the formula $6s^2$. Find the surface area of a cube with a side length of 5 cm.
A. 150 cm^2
B. 120 cm^2
C. 100 cm^2
D. 90 cm^2
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 = 16
C. \( x+2 \)^2 + \( y-3 \)^2 = 4
D. \( x-2 \)^2 + \( y+3 \)^2 = 4
Question 7
A company produces two products, A and B. Product A requires 2 hours of labor and 3 hours of machine time, while product B requires 3 hours of labor and 2 hours of machine time. If the company has 120 hours of labor and 180 hours of machine time available, how many units of product A and product B should the company produce to maximize profit?
A. 10 units of A, 15 units of B
B. 15 units of A, 10 units of B
C. 20 units of A, 20 units of B
D. 25 units of A, 25 units of B
Question 8
A histogram of exam scores is shown below. If the mean score is 75, find the value of k.
A. 5
B. 10
C. 15
D. 20
Question 9
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = -1 \end{cases} \).
A. \( x = 1, y = 3 \)
B. \( x = 3, y = 1 \)
C. \( x = 2, y = 2 \)
D. \( x = 4, y = 0 \)
Question 10
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 11
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. \( y = \frac{1}{2}x + \frac{1}{2} \)
B. \( y = 2x - 1 \)
C. \( y = \frac{1}{2}x - 1 \)
D. \( y = 2x + 1 \)
Question 12
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.
A. 32π
B. 64π
C. 128π
D. 256π
Question 13
Solve for x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ), given that \( \sin\( x \ \) = \frac{3}{5} ).
A. x = \frac{\pi}{4}
B. x = \frac{3\pi}{4}
C. x = \frac{5\pi}{4}
D. x = \frac{7\pi}{4}
Question 14
Solve the inequality \( \frac{2x + 5}{x - 2} > 0 \) for \( x in \( -infty, infty \ \) ).
A. \( -2, 2 \) cup (5, infty)
B. \( -infty, -2 \) cup (2, 5)
C. \( -infty, -2 \) cup (2, 5) cup (5, infty)
D. \( -infty, -2 \) cup (2, 5)
Question 15
A histogram of exam scores is shown below. If the mean score is 75, what is the median score?
A. 70
B. 75
C. 80
D. 85

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