Exam Body

Year

Subject

Paper Type

POST UTME SKYLINE UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME SKYLINE 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

A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is 6 cm, calculate the 95% confidence interval for the mean height of all students in the university.

Correct A. 170.35 cm, 179.65 cm

B. 168.35 cm, 181.65 cm

C. 169.35 cm, 180.65 cm

D. 171.35 cm, 178.65 cm

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 2

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

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

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

C. \( f'(x) = \frac{x}{\( x^2 + 1 \)^2} \)

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

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 3

A histogram of exam scores for a class of 50 students is shown below. If the mean score is 75 and the s\tandard deviation is 10, find the area under the curve between 60 and 80.

Correct A. 0.4

B. 0.5

C. 0.6

D. 0.7

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 4

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 = 16 \)

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

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

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 5

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \) with initial term \( a_1 = 3 \). Find the first five terms of the sequence.

Correct A. [3, 7, 15, 31, 63]

B. [3, 5, 7, 9, 11]

C. [3, 6, 12, 24, 48]

D. [3, 8, 16, 32, 64]

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 6

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 7

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 8

Solve the inequality \( x^2 - 4x + 4 geq 0 \).

Correct A. x \leq 2

B. x \geq 2

C. x < 2

D. x > 2

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 9

Find the derivative of the function ( f(x) = x^3 - 6x^2 + 9x + 2 ).

Correct A. 3x^2 - 12x + 9

B. 3x^2 - 12x + 10

C. 3x^2 - 12x + 9 + 2

D. 3x^2 - 12x + 9 - 2

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 10

Solve the trigonometric equation \( 2 \sin^2 x + 3 \cos x - 1 = 0 \).

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

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

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

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

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 11

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

Correct A. f'(x) = -\frac{1}{2x^{3/2}}

B. f'(x) = \frac{1}{2x^{3/2}}

C. f'(x) = -\frac{1}{x^{3/2}}

D. f'(x) = \frac{1}{x^{3/2}}

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 12

A circle with center (0, 0) and radius 4 passes through the point (3, 4). Find the equation of the circle.

Correct A. \( x - 0 \)^2 + \( y - 0 \)^2 = 16

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

C. \( x - 0 \)^2 + \( y - 0 \)^2 = 9

D. \( x - 3 \)^2 + \( y - 4 \)^2 = 9

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 13

Find the area under the curve \( y = x^2 \) from x = 0 to x = 4.

Correct A. \frac{64}{3}

B. \frac{32}{3}

C. \frac{16}{3}

D. \frac{8}{3}

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 14

Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...

Correct A. 312

B. 3120

C. 31200

D. 312000

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 15

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

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

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

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

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

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 16

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

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 17

Let \( S = \{ 1, 2, 3, 4, 5 \} \). Find the number of subsets of ( S ) that contain exactly two elements.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 18

Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).

A. 1210

B. 1230

Correct C. 1250

D. 1270

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 19

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

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 20

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. 16/15

Correct B. 32/15

C. 64/15

D. 128/15

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 21

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) u\sing the formula \( mathrm{proj}_{mathbf{a}} mathbf{b} = \frac{mathbf{a} cdot mathbf{b}}{| mathbf{a} |^2} mathbf{a} \).

Correct A. \\begin{pmatrix} \\frac{4}{13} \\frac{6}{13} \\end{pmatrix}

B. \\begin{pmatrix} \\frac{2}{13} \\frac{3}{13} \\end{pmatrix}

C. \\begin{pmatrix} \\frac{1}{13} \\frac{2}{13} \\end{pmatrix}

D. \\begin{pmatrix} \\frac{3}{13} \\frac{4}{13} \\end{pmatrix}

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 22

Solve the inequality \( \log_{10} \( x^2 + 1 \ \) > 3 ).

Correct A. \left\( -\infty, -\frac{1}{10} \right \) \cup \left\( \frac{1}{10}, \infty \right \)

B. \left\( -\infty, -\frac{1}{10} \right \) \cup \left\( \frac{1}{10}, 0 \right \) \cup \left\( 0, \infty \right \)

C. \left\( -\infty, -\frac{1}{10} \right \) \cup \left\( \frac{1}{10}, 0 \right \)

D. \left\( -\infty, -\frac{1}{10} \right \) \cup \left\( 0, \infty \right \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 23

Find the value of ( x ) in the equation \( 2^x + 3^x = 5^x \).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 24

A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?

A. \frac{1}{2}

Correct B. \frac{1}{3}

C. \frac{2}{3}

D. \frac{4}{5}

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 25

Solve the equation \( x^2 + 4x + 4 = 0 \).

A. \\left\( -2, \\infty \\right \)

Correct B. \\left\( -\\infty, -2 \\right \)

C. \\left\( -\\infty, 2 \\right \)

D. \\left\( 2, \\infty \\right \)

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows

Help others prepare! Share this practice hub:

Chat with Support