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POST UTME PAN-ATLANTIC UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME PAN-ATLANTIC 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

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

Correct Answer: A

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Question 2

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

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 3

Find the value of \( \log_{10} \( x^2 \ \) ) given that \( \log_{10} \( x \ \) = 2 ).

Correct A. ( 4 )

B. ( 2 )

C. ( 8 )

D. ( 16 )

Correct Answer: A

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Question 4

A circle with center ( (0, 0) ) and radius ( 4 ) has a chord of length ( 6 ). Find the dis\tance from the center to the chord.

Correct A. \( 2 \sqrt{3} \)

B. \( 4 \sqrt{3} \)

C. \( 6 \sqrt{3} \)

D. \( 8 \sqrt{3} \)

Correct Answer: A

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Question 5

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

A. ( 15 )

B. ( 25 )

C. ( 35 )

Correct D. ( 45 )

Correct Answer: D

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Question 6

Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1, and f_Y(y) = 3y^2, 0 < y < 1. Find the probability that X + Y < 1.

A. 1/4

Correct B. 1/2

C. 3/4

D. 1

Correct Answer: B

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Question 7

Find the derivative of the function f(x) = \( 2x^3 + 5x^2 - 3x + 1 \) / \( x^2 + 2x - 1 \) u\sing the quotient rule.

Correct A. \frac{6x^2 + 10x - 3}{\( x^2 + 2x - 1 \)^2}

B. \frac{6x^2 + 10x - 3}{\( x^2 + 2x - 1 \)^2} + 1

C. \frac{6x^2 + 10x - 3}{\( x^2 + 2x - 1 \)^2} - 1

D. \frac{6x^2 + 10x - 3}{\( x^2 + 2x - 1 \)^2} + 2

Correct Answer: A

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Question 8

A circle with center (2, 3) and radius 4 passes through the point (1, 1). Find the equation of the circle.

Correct A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16

B. \( x - 1 \)^2 + \( y - 1 \)^2 = 16

C. \( x - 2 \)^2 + \( y - 3 \)^2 = 25

D. \( x - 1 \)^2 + \( y - 1 \)^2 = 25

Correct Answer: A

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Question 9

Find the determinant of the matrix \[ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \].

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 10

A line passes through the points (1, 2) and (3, 4). Find the equation of the line.

Correct A. y = 2x

B. y = 2x + 1

C. y = 2x - 1

D. y = 2x + 2

Correct Answer: A

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Question 11

Find the sum of the first 10 terms of the geometric series 4, 12, 36, ...

A. 1,048,576

Correct B. 4,194,304

C. 8,388,608

D. 16,777,216

Correct Answer: B

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Question 12

A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 80?

A. 0.135

B. 0.341

C. 0.674

Correct D. 0.954

Correct Answer: D

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Question 13

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

A. 32\pi

B. 64\pi

C. 128\pi

Correct D. 256\pi

Correct Answer: D

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Question 14

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

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

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

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

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

Correct Answer: A

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Question 15

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

Correct A. 1/2

B. 1/3

C. 2/5

D. 3/8

Correct Answer: A

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Question 16

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 cm^3

Correct B. 48\pi cm^3

C. 96\pi cm^3

D. 192\pi cm^3

Correct Answer: B

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Question 17

Solve the system of linear equations u\sing matrices: \begin{align*} x + 2y - z &= 3 \ 2x - 3y + 4z &= 5 \ -x + y - 2z &= -2 \end{align*}

Correct A. \begin{pmatrix} 1 \ 2 \ -1 \end{pmatrix}

B. \begin{pmatrix} 2 \ -1 \ 3 \end{pmatrix}

C. \begin{pmatrix} 3 \ 4 \ -2 \end{pmatrix}

D. \begin{pmatrix} 5 \ 6 \ -3 \end{pmatrix}

Correct Answer: A

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Question 18

Find the area under the curve \[ y = \frac{1}{x^2 + 1} \] from x = 0 to x = 1.

Correct A. \frac{\pi}{4}

B. \frac{\pi}{2}

C. \frac{\pi}{3}

D. \frac{\pi}{6}

Correct Answer: A

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Question 19

A binary operation \(*\) on the set \{0, 1\} is defined as \[ a * b = \begin{cases} 1 & \text{if } a = 0 \text{ and } b = 1 \ 0 & \text{otherwise} \end{cases} \] Find the value of \[ \( 1 * 0 \) * \( 0 * 1 \) \]

A. 0

Correct B. 1

C. 10

D. 11

Correct Answer: B

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Question 20

Find the volume of the sphere with radius 4 cm.

Correct A. 268.08 cm^3

B. 268.08 cm^3

C. 268.08 cm^3

D. 268.08 cm^3

Correct Answer: A

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Question 21

Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{1}{2^n} \) u\sing the formula \( S = \frac{a}{1 - r} \), where (a) is the first term and (r) is the common ratio.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 22

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

Correct A. -5 < x < -1 or x > 5

B. -5 < x < 1 or x > 5

C. -5 < x < 5

D. -5 < x < 1

Correct Answer: A

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Question 23

Find the area under the curve \( y = x^2 + 2x + 1 \) from \( x = 0 \) to \( x = 2 \).

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 24

Solve the equation \( x^3 - 2x^2 - 5x + 6 = 0 \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 25

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

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

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

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

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

Correct Answer: A

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