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POST UTME UNN 2025 Mathematics | Objective

Are you preparing for POST UTME UNN 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.

A. 48\pi

B. 64\pi

Correct C. 72\pi

D. 80\pi

Correct Answer: C

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Question 2

Solve the inequality \frac{x^2 - 4x - 5}{x^2 - 2x - 6} > 0.

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

B. \( -\infty, -2 \) \cup \( 1, \infty \)

C. \( -\infty, -3 \) \cup \( -2, \infty \)

D. \( -\infty, -2 \) \cup \( -3, \infty \)

Correct Answer: A

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Question 3

Find the area under the curve y = 2x^2 + 3x - 4 from x = 0 to x = 2.

A. 14

B. 16

Correct C. 18

D. 20

Correct Answer: C

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Question 4

Simplify the expression \sqrt{8} + \sqrt{18} + \sqrt{32}.

A. 10\sqrt{2}

B. 12\sqrt{2}

Correct C. 14\sqrt{2}

D. 16\sqrt{2}

Correct Answer: C

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Question 5

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 = x - 1

D. y = x + 1

Correct Answer: A

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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 fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 7?

A. 1/6

Correct B. 1/3

C. 1/2

D. 2/3

Correct Answer: B

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Question 8

Solve the system of equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix} \).

A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

Correct B. \begin{bmatrix} -1 \ 2 \end{bmatrix}

C. \begin{bmatrix} 1 \ -2 \end{bmatrix}

D. \begin{bmatrix} -1 \ -2 \end{bmatrix}

Correct Answer: B

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Question 9

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

A. y = 2x - 1

Correct B. y = 2x + 1

C. y = -2x + 1

D. y = -2x - 1

Correct Answer: B

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Question 10

A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 11

In a set of consecutive integers, the sum of the first five terms is 15 more than the sum of the last five terms. If the middle term is 11, find the sum of all the terms in the set.

A. 150

B. 200

Correct C. 250

D. 300

Correct Answer: C

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Question 12

A right circular cone has a height of 20 cm and a radius of 10 cm. Find the volume of the cone in cubic centimeters.

A. 1000\pi

Correct B. 2000\pi

C. 3000\pi

D. 4000\pi

Correct Answer: B

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Question 13

In a geometric sequence, the first term is 2 and the common ratio is 3. Find the sum of the first six terms.

A. 731

B. 741

C. 751

Correct D. 761

Correct Answer: D

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Question 14

A solid sphere has a radius of 5 cm. Find the surface area of the sphere in square centimeters.

Correct A. 314.16

B. 314.17

C. 314.18

D. 314.19

Correct Answer: A

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Question 15

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

Correct B. 8.16

C. 8.18

D. 8.20

Correct Answer: B

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Question 16

Find the value of x in the equation \( \frac{x}{2} + 5 = 11 \).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 17

Solve for y in the equation \( y^2 + 4y - 5 = 0 \).

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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Question 18

Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, 54, ... ).

Correct A. 120

B. 140

C. 160

D. 180

Correct Answer: A

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Question 19

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 20

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

Correct A. x > 4

B. x < 4

C. x > 2

D. x < 2

Correct Answer: A

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Question 21

Find the equation of the circle with center at (2, 3) and pas\sing through the point (4, 5).

Correct A. \boxed{\( x - 2 \)^2 + \( y - 3 \)^2 = 5}

B. \( x - 2 \)^2 + \( y - 3 \)^2 = 10

C. \( x - 2 \)^2 + \( y - 3 \)^2 = 15

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 20

Correct Answer: A

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Question 22

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

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

B. \( -3, -1 \) \cup (1, 3) \cup (4, 6)

C. \( -3, -1 \) \cup (1, 3) \cup \( -6, -4 \)

D. \( -3, -1 \) \cup (1, 3) \cup (4, 6) \cup \( -6, -4 \)

Correct Answer: A

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Question 23

Find the derivative of the function f(x) = \frac{1}{x^2 + 1} u\sing the chain rule.

Correct A. -\frac{2x}{\( x^2 + 1 \)^2}

B. \frac{2x}{\( x^2 + 1 \)^2}

C. -\frac{2}{\( x^2 + 1 \)^2}

D. \frac{2}{\( x^2 + 1 \)^2}

Correct Answer: A

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Question 24

Solve the vector equation \overrightarrow{a} \cdot \overrightarrow{b} = 0.

Correct A. \overrightarrow{a} = \overrightarrow{0} \text{ or } \overrightarrow{b} = \overrightarrow{0}

B. \overrightarrow{a} = \overrightarrow{b}

C. \overrightarrow{a} \perp \overrightarrow{b}

D. \overrightarrow{a} \parallel \overrightarrow{b}

Correct Answer: A

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Question 25

Find the volume of the solid formed by revolving the region bounded by the curves y = x^2 and y = x^3 about the x-axis.

Correct A. \frac{\pi}{6}

B. \frac{\pi}{12}

C. \frac{\pi}{24}

D. \frac{\pi}{48}

Correct Answer: A

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