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POST UTME UNILAG 2025 Mathematics | Objective

Are you preparing for POST UTME UNILAG exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2025 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 2

Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 3

Find the area under the curve \( y = \frac{1}{x} \) from x = 1 to x = 2.

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 4

A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?

A. 18

Correct B. 19

C. 20

D. 21

Correct Answer: B

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Question 5

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?

A. ₦1,250

B. ₦1,500

C. ₦1,750

Correct D. ₦2,000

Correct Answer: D

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Question 6

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 7

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

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 8

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.

Correct A. 72

B. 80

C. 90

D. 100

Correct Answer: A

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Question 9

Find the determinant of the matrix \( egin{bmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{bmatrix} \).

A. 10

B. 15

Correct C. 20

D. 25

Correct Answer: C

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Question 10

A set of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score will be greater than 80.

A. 0.25

B. 0.30

Correct C. 0.35

D. 0.40

Correct Answer: C

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Question 11

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

Correct C. \frac{x}{2} + 3 = 2

D. \frac{x}{2} + 3 = 3

Correct Answer: C

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Question 12

Find the value of x in the equation \log_{10} \( x^2 \) = 4.

A. 10

B. 20

C. 40

Correct D. 80

Correct Answer: D

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Question 13

Solve the inequality \frac{x-2}{x+1} > 0.

Correct 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

Correct Answer: A

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Question 14

Find the equation of the circle with center (2, 3) and radius 4.

Correct 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 = 256

Correct Answer: A

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Question 15

Find the value of x in the equation \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2}.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 16

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 17

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

Correct C. 250

D. 300

Correct Answer: C

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Question 18

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?

Correct A. 72

B. 80

C. 90

D. 100

Correct Answer: A

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Question 19

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is blue?

A. 0.2

Correct B. 0.25

C. 0.3

D. 0.35

Correct Answer: B

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Question 20

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?

Correct 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

Correct Answer: A

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Question 21

Determine the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.

A. 64π cm³

Correct B. 128π cm³

C. 256π cm³

D. 512π cm³

Correct Answer: B

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Question 22

A set of 5 integers has an average of 20. If the largest integer is 35, and the second largest is 25, what is the sum of the remaining 3 integers?

A. 50

B. 60

Correct C. 70

D. 80

Correct Answer: C

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Question 23

Find the equation of the line pas\sing through the points (2,3) and (4,5).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = 3x - 2

D. y = 3x + 2

Correct Answer: A

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Question 24

A sequence is defined by the recurrence relation a_n = 2a_\( n-1 \) + 1, with a_1 = 3. Find the value of a_5.

A. 31

B. 32

Correct C. 33

D. 34

Correct Answer: C

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Question 25

A histogram has a mean of 25 and a s\tandard deviation of 5. If the largest value is 40, what is the sum of the remaining 4 values?

A. 80

B. 90

Correct C. 100

D. 110

Correct Answer: C

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