POST UTME UNILAG 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \frac{x-2}{x+1} > 0.
A. x < -1 \text{ or } x > 2
B. x < -1 \text{ or } x < 2
C. x > -1 \text{ or } x > 2
D. x > -1 \text{ or } x < 2
Question 2
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 = 3x - 2
D. y = 3x + 2
Question 3
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is the volume of the prism?
A. 72
B. 80
C. 90
D. 100
Question 4
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. 0
B. -2
C. -1
D. 1
Question 5
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 be produced to maximize profit?
A. 20 units of A, 30 units of B
B. 30 units of A, 20 units of B
C. 40 units of A, 10 units of B
D. 10 units of A, 40 units of B
Question 6
A circle has a radius of 5 cm. Find the area of the circle.
A. 25\pi
B. 50\pi
C. 75\pi
D. 100\pi
Question 7
Find the volume of a rec\tangular prism with a length of 6 cm, a width of 4 cm, and a height of 3 cm.
A. 72
B. 96
C. 120
D. 144
Question 8
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 5:3, how many loaves of whole wheat bread are sold per day?
A. 150
B. 200
C. 250
D. 300
Question 9
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 10
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) u\sing the formula \( \text{proj}_{mathbf{a}} mathbf{b} = \frac{mathbf{a} cdot mathbf{b}}{| mathbf{a} |^2} mathbf{a} \).
A. \begin{pmatrix} 0.2 \ 0.3 \end{pmatrix}
B. \begin{pmatrix} 0.4 \ -0.6 \end{pmatrix}
C. \begin{pmatrix} 0.6 \ -0.9 \end{pmatrix}
D. \begin{pmatrix} 0.8 \ -1.2 \end{pmatrix}
Question 11
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 12
In a triangle ABC, the coordinates of A, B, and C are (2, 3), (4, 6), and (8, 2) respectively. Find the equation of the median from vertex A to side BC.
A. \frac{x}{2} + 3 = 0
B. \frac{x}{2} + 3 = 1
C. \frac{x}{2} + 3 = 2
D. \frac{x}{2} + 3 = 3
Question 13
Determine the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24π cm³
B. 48π cm³
C. 96π cm³
D. 192π cm³
Question 14
A polynomial function is defined as ( f(x) = ax^3 + bx^2 + cx + d ). If ( f(1) = 5 ), \( f\( -1 \ \) = -3 ), and ( f(2) = 17 ), find the value of ( a ).
A. 1
B. 2
C. 3
D. 4
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70

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