Exam Body

Year

Subject

Paper Type

POST UTME PAN-ATLANTIC UNIVERSITY 2021 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 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the value of x in the equation \( \frac{x}{2} + 5 = 11 \).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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

Question 2

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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

Question 3

A cylindrical \tank has a height of 10m and a radius of 4m. If the \tank is filled with water to a height of 6m, calculate the volume of water in the \tank.

A. 480π

Correct B. 600π

C. 720π

D. 960π

Correct Answer: B

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

Question 4

A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:4, how many loaves of whole wheat bread are sold per day?

Correct A. 200

B. 250

C. 300

D. 350

Correct Answer: A

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

Question 5

A car travels from city A to city B at an average speed of 60 km/h. On the return trip, the car travels at an average speed of 40 km/h. What is the average speed of the car for the entire trip?

A. 48 km/h

B. 50 km/h

Correct C. 52 km/h

D. 54 km/h

Correct Answer: C

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

Question 6

Find the value of x in the equation \( \frac{x}{2} + \frac{3}{4} = \frac{7}{8} \).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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

Question 7

Solve for y in the equation \( y^2 - 6y + 8 = 0 \).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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

Question 8

A circle with center (0, 0) and radius 4 passes through the point (12, 16). Find the equation of the circle.

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

B. \( x^2 + y^2 = 64 \)

C. \( x^2 + y^2 = 32 \)

D. \( x^2 + y^2 = 48 \)

Correct Answer: A

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

Question 9

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

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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

Question 10

A set A has 5 elements and a set B has 3 elements. Find the number of elements in the union of sets A and B.

A. 6

Correct B. 7

C. 8

D. 9

Correct Answer: B

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

Question 11

In a survey of 50 students, the heights of the students were recorded in centimeters. The mean height was 170 cm, and the s\tandard deviation was 5 cm. If the heights of the students were normally distributed, what is the probability that a randomly selected student has a height between 165 cm and 175 cm?

Correct A. 0.9772

B. 0.6827

C. 0.3413

D. 0.1587

Correct Answer: A

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

Question 12

Solve the inequality \frac{x^2-4x-3}{x^2-6x+8} > 0.

Correct A. \left\( -\infty, 3 \right \) \cup \left\( 4, \infty \right \)

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

C. \left\( -\infty, 2 \right \) \cup \left\( 4, \infty \right \)

D. \left\( -\infty, 1 \right \) \cup \left\( 2, \infty \right \)

Correct Answer: A

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

Question 13

A rec\tangular box has a length of 6 cm, a width of 4 cm, and a height of 2 cm. What is the volume of the box in cubic centimeters?

Correct A. 48

B. 64

C. 72

D. 96

Correct Answer: A

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

Question 14

A circle has a radius of 4 cm. What is the area of the circle in square centimeters?

A. 50.24

B. 100.48

C. 200.96

Correct D. 314.16

Correct Answer: D

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

Question 15

A right triangle has a hypotenuse of 10 cm and one leg of 6 cm. What is the length of the other leg in centimeters?

Correct A. 8

B. 6

C. 4

D. 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 \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{16}{3} \)

B. ( 8 )

C. ( 4 )

D. ( 2 )

Correct Answer: A

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

Question 17

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

A. \( x = 10^2 \)

Correct B. \( x = 10^4 \)

C. \( x = 10^{-2} \)

D. \( x = 10^{-4} \)

Correct Answer: B

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

Question 18

Find the value of \( \sin \( 2\theta \ \) ) given that \( \sin \( \theta \ \) = \frac{3}{5} ) and \( \cos \( \theta \ \) = \frac{4}{5} ).

Correct A. \( \frac{24}{25} \)

B. \( \frac{16}{25} \)

C. \( \frac{12}{25} \)

D. \( \frac{8}{25} \)

Correct Answer: A

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

Question 19

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

A. \( \frac{1}{6} \)

B. \( \frac{1}{3} \)

C. \( \frac{2}{3} \)

Correct D. \( \frac{5}{6} \)

Correct Answer: D

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

Question 20

Find the vector ( mathbf{v} ) that satisfies the equation \( mathbf{v} cdot mathbf{i} = 3 \) and \( mathbf{v} cdot mathbf{j} = 4 \).

Correct A. \( mathbf{v} = 3mathbf{i} + 4mathbf{j} \)

B. \( mathbf{v} = 4mathbf{i} + 3mathbf{j} \)

C. \( mathbf{v} = 3mathbf{i} - 4mathbf{j} \)

D. \( mathbf{v} = 4mathbf{i} - 3mathbf{j} \)

Correct Answer: A

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

Question 21

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

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

Question 22

Solve for x in the equation \(\tan x = \frac{1}{\sqrt{3}}\).

Correct A. \frac{\pi}{6}

B. \frac{\pi}{3}

C. \frac{\pi}{2}

D. \frac{5\pi}{6}

Correct Answer: A

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

Question 23

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

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

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

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

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

Correct Answer: B

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

Question 24

Evaluate the definite integral \(\int_0^1 x^2 dx\).

A. \frac{1}{3}

B. \frac{1}{2}

Correct C. 1

D. \frac{2}{3}

Correct Answer: C

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

Question 25

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

Correct A. \boxed{-2}

B. \boxed{-1}

C. \boxed{2}

D. \boxed{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