Exam Body

Year

Subject

Paper Type

POST UTME REDEEMERS UNIVERSITY 2023 Mathematics | Objective

Are you preparing for POST UTME REDEEMERS UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 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. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \)

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. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)

B. \( x < -\frac{3}{2} \) or \( x > \frac{5}{4} \)

C. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)

D. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)

Correct Answer: A

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

Question 3

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

Correct A. \( \frac{32}{3} pi \)

B. \( \frac{16}{3} pi \)

C. \( \frac{64}{3} pi \)

D. \( \frac{128}{3} pi \)

Correct Answer: A

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

Question 4

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 5

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

Correct A. ( 16pi )

B. ( 32pi )

C. ( 64pi )

D. ( 128pi )

Correct Answer: A

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

Question 6

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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

Question 7

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

Correct A. x = -2

B. x = -1

C. x = 0

D. x = 1

Correct Answer: A

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

Question 8

Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).

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 9

Find the mean of the data set: 2, 4, 6, 8, 10.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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

Question 10

Find the area of the circle with radius 4 cm.

Correct A. 16π

B. 32π

C. 64π

D. 128π

Correct Answer: A

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

Question 11

Let X be a random variable with probability density function (pdf) given by f(x) = \( \frac{1}{2}e^{-|x|} \) for -∞ < x < ∞. Find the probability that X lies between -1 and 1.

Correct A. 0.6321

B. 0.6065

C. 0.1353

D. 0.2389

Correct Answer: A

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

Question 12

Solve the inequality \( |x^2 - 4| geq 3 \).

Correct A. \( -∞, -1] ∪ [1, ∞ \)

B. \( -∞, -2] ∪ [2, ∞ \)

C. \( -∞, -3] ∪ [3, ∞ \)

D. \( -∞, -4] ∪ [4, ∞ \)

Correct Answer: A

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

Question 13

A sequence is defined by \( a_n = \frac{2n + 1}{3n - 2} \). Find the sum of the first five terms of the sequence.

Correct A. 1.6667

B. 2.3333

C. 3.0000

D. 3.6667

Correct Answer: A

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

Question 14

A function f(x) is defined as (f(x) = \frac{1}{x^2 + 1}). Find the derivative of f(x) 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 15

Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).

Correct A. 1, 2, 3

B. 1, 2, 4

C. 1, 3, 4

D. 2, 3, 4

Correct Answer: A

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

Question 16

Find the value of 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 17

A survey of 100 students found that 60 students preferred Mathematics, 30 students preferred Science, and 10 students preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?

Correct A. 0.7

B. 0.8

C. 0.9

D. 0.95

Correct Answer: A

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

Question 18

In the diagram below, what is the value of x?

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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

Question 19

Find the volume of the cylinder with radius 4 cm and height 10 cm.

A. 400\pi

Correct B. 500\pi

C. 600\pi

D. 800\pi

Correct Answer: B

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

Question 20

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

A. x = -2

Correct B. x = -3

C. x = -6

D. x = -8

Correct Answer: B

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

Question 21

In a set of consecutive integers, the sum of the first n terms is given by the formula \( S_n = \frac{n}{2} \( 2a + (n - 1 \ \)d) ), where a is the first term and d is the common difference. If the sum of the first 10 terms is 210, and the common difference is 2, find the value of a.

Correct A. 98

B. 100

C. 102

D. 104

Correct Answer: A

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

Question 22

A binary operation \( * \) on the set of real numbers is defined as \( a * b = ab + 2 \). Find the value of \( 2 * 3 * 4 \).

A. 38

B. 40

Correct C. 42

D. 44

Correct Answer: C

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

Question 23

A geometric sequence has a first term of 2 and a common ratio of 3. Find the sum of the first 5 terms.

A. 731

B. 733

Correct C. 735

D. 737

Correct Answer: C

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

Question 24

A vector \( \vec{a} \) has a magnitude of 5 and is directed at an angle of 30° to the positive x-axis. Find the x and y components of the vector.

Correct A. 4.33, 4.33

B. 4.33, 2.67

C. 2.67, 4.33

D. 2.67, 2.67

Correct Answer: A

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

Question 25

A probability experiment consists of rolling a fair six-sided die. If the outcome is an even number, the player wins a prize. Find the probability of winning the prize.

Correct A. 1/2

B. 1/3

C. 2/3

D. 1/6

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