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POST UTME ABU 2025 Mathematics | Objective

Are you preparing for POST UTME ABU 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

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

Correct A. 48\pi cm^3

B. 64\pi cm^3

C. 96\pi cm^3

D. 128\pi cm^3

Correct Answer: A

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Question 2

A bakery sells a total of 250 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. 125

Correct B. 150

C. 175

D. 200

Correct Answer: B

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Question 3

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side.

A. 8 cm

Correct B. 6\sqrt{5} cm

C. 8\sqrt{5} cm

D. 12 cm

Correct Answer: B

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Question 4

A set of 4 coins contains 2 nickels and 2 dimes. If a coin is selected at random, what is the probability that it is a nickel?

Correct A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 5

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 = 25

C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49

Correct Answer: A

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Question 6

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new median?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 7

Solve for x in the equation \( \frac{1}{x} + 2 = \frac{3}{x} \).

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 8

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pi

Correct B. 48\pi

C. 72\pi

D. 96\pi

Correct Answer: B

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Question 9

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \). If \( a_1 = 2 \), find the value of \( a_{10} \).

A. 1023

Correct B. 1024

C. 1025

D. 1026

Correct Answer: B

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Question 10

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( -\infty, -1 \) \cup \( 3, \infty \)

B. \( -\infty, 1 \) \cup \( 3, \infty \)

C. \( -\infty, -1 \) \cup \( 1, \infty \)

D. \( -\infty, 1 \) \cup \( 1, \infty \)

Correct Answer: A

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Question 11

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

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)

D. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \times 4 \)

Correct Answer: A

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Question 12

Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.

Correct A. \( x = \frac{-5 pm \sqrt{25 + 24}}{4} \)

B. \( x = \frac{-5 pm \sqrt{25 - 24}}{4} \)

C. \( x = \frac{-5 pm \sqrt{25 + 24}}{2} \)

D. \( x = \frac{-5 pm \sqrt{25 - 24}}{2} \)

Correct Answer: A

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Question 13

Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( x = 2 \) about the x-axis.

Correct A. \( \frac{4}{3} pi \times 2^3 \)

B. \( \frac{4}{3} pi \times 2^2 \)

C. \( \frac{4}{3} pi \times 2 \)

D. \( \frac{4}{3} pi \times 2^2 \times 2 \)

Correct Answer: A

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Question 14

A particle moves along the curve \( y = x^3 - 6x^2 + 9x + 2 \) with a velocity of \( \frac{dy}{dx} = 3x^2 - 12x + 9 \). Find the acceleration of the particle at the point where \( x = 1 \).

Correct A. \( 6x - 12 \)

B. \( 3x^2 - 12x + 9 \)

C. \( 6x^2 - 12x + 9 \)

D. \( 3x^2 - 12x + 9 \)

Correct Answer: A

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Question 15

A rec\tangular box has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the surface area of the box.

Correct A. \( 2 \times \( 5 \times 3 + 3 \times 2 + 2 \times 5 \ \) )

B. \( 2 \times \( 5 \times 3 + 3 \times 2 + 2 \times 5 + 5 \times 2 \ \) )

C. \( 2 \times \( 5 \times 3 + 3 \times 2 + 2 \times 5 + 5 \times 2 + 3 \times 2 \ \) )

D. \( 2 \times \( 5 \times 3 + 3 \times 2 + 2 \times 5 + 5 \times 2 + 3 \times 2 + 2 \times 5 \ \) )

Correct Answer: A

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Question 16

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 17

A matrix A is given by \( A = \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \). Find the determinant of A.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 18

A quadratic equation is given by \( x^2 + 4x + 4 = 0 \). Solve for x.

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 19

A probability experiment consists of rolling two fair six-sided dice. What is the probability that the sum of the numbers on the dice is 7?

Correct A. 1/6

B. 1/12

C. 1/18

D. 1/36

Correct Answer: A

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Question 20

A trigonometric equation is given by \( \sin^2 x + \cos^2 x = 1 \). Simplify the equation.

Correct A. \sin^2 x = 1

B. \cos^2 x = 1

C. \sin x = \cos x

D. \sin x = -\cos x

Correct Answer: A

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Question 21

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pi

B. 48\pi

Correct C. 96\pi

D. 192\pi

Correct Answer: C

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Question 22

Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.

Correct A. \( -3, -2 \) \cup (2, 3)

B. \( -3, -2 \) \cup (2, 3) \cup (4, 5)

C. \( -3, -2 \) \cup (2, 3) \cup \( -5, -4 \)

D. \( -3, -2 \) \cup (2, 3) \cup (4, 5) \cup \( -5, -4 \)

Correct Answer: A

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Question 23

Find the equation of the \tangent line to the curve y = x^2 + 2x - 3 at the point (1, 2).

Correct A. y = 4x - 1

B. y = 4x + 1

C. y = 4x - 3

D. y = 4x + 3

Correct Answer: A

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Question 24

Solve the system of equations \begin{align*} x + y &= 4 \ x - y &= 2 \end{align*}.

Correct A. \begin{pmatrix} 1 \ 3 \end{pmatrix}

B. \begin{pmatrix} 2 \ 2 \end{pmatrix}

C. \begin{pmatrix} 3 \ 1 \end{pmatrix}

D. \begin{pmatrix} 4 \ 0 \end{pmatrix}

Correct Answer: A

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Question 25

Find the area of the region bounded by the curves y = x^2 and y = 2x.

Correct A. 4/3

B. 2/3

C. 1/3

D. 4/5

Correct Answer: A

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