Exam Body

Year

Subject

Paper Type

POST UTME PAN-ATLANTIC UNIVERSITY 2024 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 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the derivative of the function ( f(x) = \frac{1}{2} \log_{10} $ x^2 + 1 $ ) u\sing the chain rule.

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

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

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

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

Correct Answer: A

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

Question 2

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 cdot 3 + 3 cdot 2 + 5 cdot 2 $

B. 2$ 5 cdot 3 + 3 cdot 2 + 5 cdot 2 $ + 2$ 5 cdot 2 + 3 cdot 2 + 5 cdot 3 $

C. 2$ 5 cdot 3 + 3 cdot 2 + 5 cdot 2 $ - 2$ 5 cdot 2 + 3 cdot 2 + 5 cdot 3 $

D. 2$ 5 cdot 3 + 3 cdot 2 + 5 cdot 2 $ + 2$ 5 cdot 2 + 3 cdot 2 + 5 cdot 3 $ + 2$ 5 cdot 2 + 3 cdot 2 + 5 cdot 3 $

Correct Answer: A

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

Question 3

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

Correct A. \int_0^1 \frac{1}{x^2 + 1} dx

B. \int_0^1 \frac{1}{x^2 + 1} dx + \int_0^1 \frac{1}{x^2 + 1} dx

C. \int_0^1 \frac{1}{x^2 + 1} dx - \int_0^1 \frac{1}{x^2 + 1} dx

D. \int_0^1 \frac{1}{x^2 + 1} dx + \int_0^1 \frac{1}{x^2 + 1} dx + \int_0^1 \frac{1}{x^2 + 1} dx

Correct Answer: A

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

Question 4

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

Correct A. \pi r^2

B. \pi r^2 + \pi r^2

C. \pi r^2 - \pi r^2

D. \pi r^2 + \pi r^2 + \pi r^2

Correct Answer: A

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

Question 5

Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.

Correct A. f'(x) = 2 \sin x \cos x

B. f'(x) = 2 \sin x \cos x + 2 \cos x \sin x

C. f'(x) = 2 \sin x \cos x - 2 \cos x \sin x

D. f'(x) = 2 \sin x \cos x + 2 \cos x \sin x

Correct Answer: A

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

Question 6

A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of all students in the university.

Correct A. 169.3 cm, 181.7 cm

B. 170.5 cm, 180.5 cm

C. 171.5 cm, 179.5 cm

D. 172.5 cm, 178.5 cm

Correct Answer: A

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

Question 7

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

Correct A. $x < -3$ or $x > 2$

B. $-3 < x < 2$

C. $x < -3$ or $2 < x < 3$

D. $x > 3$

Correct Answer: A

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

Question 8

Find the sum of the first 10 terms of the geometric series $\sum_{n=1}^{10} 2^n$.

Correct A. 2047

B. 2048

C. 2049

D. 2050

Correct Answer: A

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

Question 9

A vector $\vec{a}$ has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of $\vec{a}$.

Correct A. $\vec{a} = 4.33\hat{i} + 2.5\hat{j}$

B. $\vec{a} = 4.33\hat{i} - 2.5\hat{j}$

C. $\vec{a} = -4.33\hat{i} + 2.5\hat{j}$

D. $\vec{a} = -4.33\hat{i} - 2.5\hat{j}$

Correct Answer: A

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

Question 10

Solve the equation $\sin^2(x) + \cos^2(x) = 1$.

A. $x = \frac{\pi}{2}$

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

C. $x = \frac{3\pi}{4}$

D. $x = \frac{5\pi}{4}$

Correct Answer: B

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

Question 11

Find the value of x in the equation $ \log_{10} \( x^2 \ $ = 4 ).

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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

Question 12

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

Correct A. 50.24

B. 100.48

C. 200.96

D. 400.96

Correct Answer: A

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

Question 13

A particle moves in a straight line with an initial velocity of 5 m/s. If the acceleration is 2 m/s^2, find the velocity after 3 seconds.

A. 13

B. 15

Correct C. 17

D. 19

Correct Answer: C

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

Question 14

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \frac{1}{3}

Correct B. \frac{2}{3}

C. \frac{1}{2}

D. \frac{2}{5}

Correct Answer: B

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

Question 15

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

A. x \leq 2

Correct B. x \geq 2

C. x < 2

D. x > 2

Correct Answer: B

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

Question 16

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 2 \cdot \frac{3^{10} - 1}{3 - 1}

B. 2 \cdot \frac{3^{11} - 1}{3 - 1}

C. 2 \cdot \frac{3^{9} - 1}{3 - 1}

D. 2 \cdot \frac{3^{8} - 1}{3 - 1}

Correct Answer: A

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

Question 17

A circle has equation $ x - 1 \ $^2 + $ y - 2 $^2 = 4 ). Find the equation of the \tangent line at point ( (3, 5) ).

Correct A. y - 5 = -\frac{1}{2}$ x - 3 $

B. y - 5 = \frac{1}{2}$ x - 3 $

C. y - 5 = $ x - 3 $

D. y - 5 = -$ x - 3 $

Correct Answer: A

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

Question 18

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 19

Solve the system of equations: $ \begin{cases} x + y = 4 \ x - 2y = -3 \end{cases} $.

Correct A. \begin{cases} x = 7 \ y = -3 \end{cases}

B. \begin{cases} x = 1 \ y = 3 \end{cases}

C. \begin{cases} x = 3 \ y = 1 \end{cases}

D. \begin{cases} x = -1 \ y = 5 \end{cases}

Correct Answer: A

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

Question 20

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

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

Question 21

Find the value of $\int_0^1 $ 2x^3 - 5x^2 + 3x - 1 $ dx$.

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 22

Solve the inequality $|x - 2| > 3$.

Correct A. $ -∞, -1 $ ∪ (4, ∞)

B. $ -∞, 1 $ ∪ (4, ∞)

C. $ -∞, -1 $ ∪ (1, ∞)

D. $ -∞, 4 $ ∪ (1, ∞)

Correct Answer: A

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

Question 23

Find the equation of the \tangent line to the curve $y = x^2 + 2x - 3$ at the point $(1, 2)$.

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

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

Question 24

Find the area of the region bounded by the curves $y = x^2$ and $y = 2x$.

Correct A. 4/3

B. 2/3

C. 1/3

D. 1/2

Correct Answer: A

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

Question 25

Solve the system of equations $x + y = 2$ and $xy = 1$.

Correct A. (1, 1)

B. $ 1, -1 $

C. $ -1, 1 $

D. $ -1, -1 $

Correct Answer: A

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