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Subject

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POST UTME NILE UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME NILE 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

Let X be a random variable with probability density function (pdf) given by f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases}. Find the probability that X is greater than 0.5.

A. 0.25

Correct B. 0.5

C. 0.75

D. 1

Correct Answer: B

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Question 2

Find the area under the curve y = x^2 from x = 0 to x = 2.

Correct A. 4

B. 8

C. 16

D. 32

Correct Answer: A

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Question 3

Solve the vector equation \mathbf{a} \cdot \mathbf{b} = 0 where \mathbf{a} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} and \mathbf{b} = \begin{pmatrix} x \ y \ z \end{pmatrix}.

Correct A. \begin{pmatrix} 0 \ 0 \ 0 \end{pmatrix}

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

C. \begin{pmatrix} x \ y \ z \end{pmatrix}

D. \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix}

Correct Answer: A

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Question 4

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

Correct A. \frac{1}{x^3} - \frac{2\log x}{x^3}

B. \frac{2\log x}{x^3} - \frac{1}{x^3}

C. \frac{1}{x^3} + \frac{2\log x}{x^3}

D. \frac{2}{x^3} - \frac{\log x}{x^3}

Correct Answer: A

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Question 5

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

Correct A. \( -\infty, -1 \) \cup \( 0, \infty \)

B. \( -\infty, 0 \) \cup \( 1, \infty \)

C. \( -\infty, 0 \) \cup \( 1, \infty \)

D. \( -\infty, -1 \) \cup (0, 1)

Correct Answer: A

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Question 6

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

Correct A. f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

B. f'(x) = \frac{\( x^2 + 2x - 3 \)\( 2x + 2 \) - \( x^2 - 4 \)(2x)}{\( x^2 - 4 \)^2}

C. f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

D. f'(x) = \frac{\( x^2 + 2x - 3 \)\( 2x - 2 \) - \( x^2 - 4 \)(2x)}{\( x^2 - 4 \)^2}

Correct Answer: A

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Question 7

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

Correct A. 2(5 × 3) + 2(3 × 2) + 2(5 × 2)

B. 2(5 × 3) + 2(3 × 2) + 2(5 × 2) + 2(3 × 5)

C. 2(5 × 3) + 2(3 × 2) + 2(5 × 2) + 2(3 × 5) + 2(5 × 2)

D. 2(5 × 3) + 2(3 × 2) + 2(5 × 2) + 2(3 × 5) + 2(5 × 2) + 2(3 × 5)

Correct Answer: A

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Question 8

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

Correct A. x < -1 or x > \frac{3}{2}

B. x < -1 or x < \frac{3}{2}

C. x > -1 or x > \frac{3}{2}

D. x > -1 or x < \frac{3}{2}

Correct Answer: A

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Question 9

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 10

Find the vector ( mathbf{v} ) such that \( mathbf{v} cdot mathbf{i} = 3 \) and \( mathbf{v} cdot mathbf{j} = -2 \).

Correct A. \mathbf{v} = \langle 3, -2 \rangle

B. \mathbf{v} = \langle -3, 2 \rangle

C. \mathbf{v} = \langle 3, 2 \rangle

D. \mathbf{v} = \langle -3, -2 \rangle

Correct Answer: A

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Question 11

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 12

Solve the system of equations: \[ \begin{align*} x^2 + y^2 + z^2 &= 4 \ x + y + z &= 0 \ x^2y^2z^2 &= 1 \end{align*} \]

Correct A. \[ (x, y, z) = \( -1, 1, 0 \) \]

B. \[ (x, y, z) = (0, 0, 2) \]

C. \[ (x, y, z) = \( -2, 1, 1 \) \]

D. \[ (x, y, z) = \( 1, -1, 0 \) \]

Correct Answer: A

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Question 13

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?

Correct A. 0.1587

B. 0.3413

C. 0.4772

D. 0.6915

Correct Answer: A

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Question 14

Find the derivative of the function \[ f(x) = \frac{x^2 + 3x + 2}{x^2 - 4x + 3} \]

Correct A. \[ f'(x) = \frac{\( x^2 - 4x + 3 \)\( 2x + 3 \) - \( x^2 + 3x + 2 \)\( 2x - 4 \)}{\( x^2 - 4x + 3 \)^2} \]

B. \[ f'(x) = \frac{\( x^2 - 4x + 3 \)\( 2x + 3 \) + \( x^2 + 3x + 2 \)\( 2x - 4 \)}{\( x^2 - 4x + 3 \)^2} \]

C. \[ f'(x) = \frac{\( x^2 - 4x + 3 \)\( 2x + 3 \) - \( x^2 + 3x + 2 \)\( 2x + 4 \)}{\( x^2 - 4x + 3 \)^2} \]

D. \[ f'(x) = \frac{\( x^2 - 4x + 3 \)\( 2x + 3 \) + \( x^2 + 3x + 2 \)\( 2x + 4 \)}{\( x^2 - 4x + 3 \)^2} \]

Correct Answer: A

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Question 15

A 3x3 matrix A has the following elements: \[ A = \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \]

Correct A. \[ |A| = 0 \]

B. \[ |A| = 1 \]

C. \[ |A| = -1 \]

D. \[ |A| = 2 \]

Correct Answer: A

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Question 16

Find the sum of the infinite geometric series: \( sum_{n=1}^{infty} \frac{1}{2^n} \)

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 17

Solve the trigonometric equation: \( \sin^2 x + \cos^2 x = 1 \ \)

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

B. x = \frac{\pi}{2}

C. x = \frac{\pi}{3}

D. x = \frac{\pi}{6}

Correct Answer: A

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Question 18

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

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

Correct Answer: A

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Question 19

Solve the inequality: \( \frac{x}{x + 1} > 0 \ \)

A. x < -1

Correct B. x > -1

C. x < 0

D. x > 0

Correct Answer: B

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Question 20

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

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

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

C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16

D. \( x - 3 \)^2 + \( y - 4 \)^2 = 16

Correct Answer: A

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Question 21

In the diagram below, the equation of the circle is given by \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 ). Find the equation of the \tangent line to the circle at the point ( (5, 7) ).

Correct A. y = -x + 12

B. y = x + 5

C. y = -x - 3

D. y = x - 2

Correct Answer: A

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Question 22

A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} ) for \( x = 1, 2, 3 \). Find the probability that ( X ) is greater than 2.

A. 0.5

Correct B. 0.75

C. 0.25

D. 0.33

Correct Answer: B

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Question 23

Simplify the expression \( \frac{\sqrt[3]{64} + \sqrt[3]{216}}{\sqrt[3]{8} - \sqrt[3]{27}} \).

Correct A. 4

B. 2

C. 3

D. 1

Correct Answer: A

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Question 24

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

A. 16/3

Correct B. 32/3

C. 64/3

D. 128/3

Correct Answer: B

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Question 25

A function ( f(x) = \frac{1}{x^2 + 1} ) has a local maximum at \( x = a \). Find the value of ( a ).

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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