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POST UTME ACHIEVERS UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME ACHIEVERS UNIVERSITY 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.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the volume of the solid formed by rotating the region bounded by $y = x^2$ and $y = 4x$ about the x-axis.

Correct A. \frac{16\pi}{3}

B. \frac{32\pi}{3}

C. \frac{64\pi}{3}

D. \frac{128\pi}{3}

Correct Answer: A

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Question 2

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 85?

A. 0.1587

B. 0.3413

C. 0.4772

Correct D. 0.6915

Correct Answer: D

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Question 3

Find the area under the curve $y = 2x^3 - 5x^2 + x + 1$ from $x = 0$ to $x = 2$.

A. \frac{23}{3}

Correct B. \frac{47}{6}

C. \frac{97}{12}

D. \frac{191}{15}

Correct Answer: B

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Question 4

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

A. 30

B. 60

Correct C. 90

D. 120

Correct Answer: C

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Question 5

A circle has a radius of 4 cm. Find the area of the circle.

A. 50.24

B. 100.48

C. 201.06

Correct D. 314.16

Correct Answer: D

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Question 6

A solid right circular cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone in cubic centimeters.

A. 256\pi

Correct B. 512\pi

C. 1024\pi

D. 2048\pi

Correct Answer: B

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Question 7

Find the area of the region bounded by the parabola y = x^2, the x-axis, and the line x = 4.

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 8

A vector \overrightarrow{a} has a magnitude of 6 units and makes an angle of 30° with the positive x-axis. Find the x and y components of \overrightarrow{a}.

Correct A. 3\hat{i} + 3\hat{j}

B. 6\hat{i} + 3\hat{j}

C. 3\hat{i} + 6\hat{j}

D. 6\hat{i} + 6\hat{j}

Correct Answer: A

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Question 9

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

Correct A. x < -1 or x > 3/2

B. x < 1 or x > 3

C. x < -3 or x > 1

D. x < 1 or x < 3

Correct Answer: A

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Question 10

A binary operation \ast is defined as a \ast b = ab + 1. Find the value of $ 2 \ast 3 $ \ast 4.

A. 25

Correct B. 26

C. 27

D. 28

Correct Answer: B

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Question 11

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 = x - 1

D. y = x + 1

Correct Answer: B

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Question 12

Solve the system of linear equations: \begin{align*} x + y &= 2 \ 2x - y &= 3 \end{align*}

Correct A. x = 1, y = 1

B. x = 2, y = 0

C. x = 0, y = 2

D. x = 1, y = 0

Correct Answer: A

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Question 13

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 2).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 14

Solve the quadratic equation: x^2 + 5x + 6 = 0.

Correct A. x = -2, x = -3

B. x = -1, x = -6

C. x = 2, x = 3

D. x = 1, x = 6

Correct Answer: A

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Question 15

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 = 4

C. $ x - 3 $^2 + $ y - 2 $^2 = 16

D. $ x - 3 $^2 + $ y - 2 $^2 = 4

Correct Answer: A

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Question 16

Solve the system of linear equations: \begin{align*} x + y &= 2 \ x - y &= 1 \end{align*}

A. x = 1, y = 1

Correct B. x = 2, y = 0

C. x = 0, y = 2

D. x = 1, y = 0

Correct Answer: B

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Question 17

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 2).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 18

Solve the quadratic equation: x^2 + 5x + 6 = 0.

A. x = -2, x = -3

B. x = -1, x = -6

C. x = 2, x = 3

D. x = 1, x = 6

Correct Answer: VIEW ANSWER

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Question 19

Let X be a random variable with probability density function (pdf) given by f(x) = $ \frac{1}{2}e^{-|x|} $ for -∞ < x < ∞. Find the probability that X lies in the interval $ -2, 3 $.

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 20

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

Correct A. $ -∞, -3 $ ∪ (2, ∞)

B. $ -∞, -3 $ ∪ (2, 3)

C. $ -∞, -3 $ ∪ (3, ∞)

D. $ -∞, 3 $ ∪ (4, ∞)

Correct Answer: A

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Question 21

Find the sum of the infinite geometric series $ sum_{n=1}^{infty} \frac{2}{3^n} $.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 22

Let A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}. Find the symmetric difference of A and B.

Correct A. {1, 2, 3}

B. {4, 5, 6, 7, 8}

C. {1, 2, 3, 4, 5}

D. {6, 7, 8}

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{1}{\( x^2 + 1 \ $^2})

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

Correct Answer: A

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Question 24

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

A. 2

B. 4

Correct C. 10

D. 20

Correct Answer: C

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Question 25

Let X be a random variable with probability density function (pdf) given by f(x) = $ \frac{1}{2}e^{-|x|} $ for -∞ < x < ∞. Find the probability that X lies in the interval $ -3, 2 $.

A. 0.6

Correct B. 0.7

C. 0.8

D. 0.9

Correct Answer: B

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