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POST UTME RHEMA UNIVERSITY 2024 Mathematics | Objective

Are you preparing for POST UTME RHEMA 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 volume of the solid formed by rotating the region bounded by $y=x^2$ and $y=4$ about the x-axis.

Correct A. \frac{64\pi}{3}

B. \frac{32\pi}{3}

C. \frac{16\pi}{3}

D. \frac{8\pi}{3}

Correct Answer: A

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Question 2

Solve for x in the equation $\log_{2}$ x-1 $ + \log_{2}$ x+1 $ = 2$.

Correct A. x=3

B. x=2

C. x=1

D. x=-1

Correct Answer: A

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Question 3

A right circular cylinder has a height of 10 cm and a radius of 4 cm. Find the surface area of the cylinder.

A. 160\pi

Correct B. 200\pi

C. 240\pi

D. 280\pi

Correct Answer: B

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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

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Question 5

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the volume of the prism.

Correct A. 72

B. 80

C. 84

D. 90

Correct Answer: A

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Question 6

Find the area under the curve y = 2x^2 + 3x - 4 from x = 0 to x = 2.

Correct A. \frac{8}{3}

B. \frac{16}{3}

C. \frac{32}{3}

D. \frac{64}{3}

Correct Answer: A

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Question 7

Solve for x in the equation \frac{1}{2} \log_{10} $ x^2 $ = 4.

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 8

A binary operation \ast is defined as a \ast b = ab + 2. Find the value of 3 \ast 4.

A. 14

B. 16

Correct C. 18

D. 20

Correct Answer: C

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Question 9

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experiment is repeated. If the number rolled is odd, the experiment stops. What is the probability that the experiment will stop after exactly two rolls?

A. \frac{1}{6}

B. \frac{1}{3}

C. \frac{1}{2}

Correct D. \frac{2}{3}

Correct Answer: D

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Question 10

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 will be between 60 and 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 11

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

Correct A. \boxed{$ x - 2 $^2 + $ y - 3 $^2 = 16}

B. $ x - 2 $^2 + $ y - 3 $^2 = 20

C. $ x - 2 $^2 + $ y - 3 $^2 = 12

D. $ x - 2 $^2 + $ y - 3 $^2 = 8

Correct Answer: A

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Question 12

Solve the inequality \frac{x + 2}{x - 1} > 0.

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

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

C. x > -2 \text{ or } x > 1

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

Correct Answer: A

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Question 13

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

Correct A. \boxed{-\frac{2x}{$ x^2 + 1 $^2}}

B. \frac{2x}{$ x^2 + 1 $^2}

C. \frac{2}{$ x^2 + 1 $^2}

D. \frac{2x^2}{$ x^2 + 1 $^2}

Correct Answer: A

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Question 14

Solve the equation x^2 + 4x - 5 = 0 u\sing the quadratic formula.

Correct A. \boxed{x = -5 \text{ or } x = 1}

B. x = -1 \text{ or } x = 5

C. x = -2 \text{ or } x = 2

D. x = -3 \text{ or } x = 3

Correct Answer: A

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Question 15

Find the sum of the first 5 terms of the geometric series with first term 2 and common ratio 3.

Correct A. \boxed{2 + 6 + 18 + 54 + 162}

B. 2 + 6 + 18 + 54 + 162 + 486

C. 2 + 6 + 18 + 54 + 162 - 486

D. 2 + 6 + 18 + 54 + 162 + 243

Correct Answer: A

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Question 16

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

A. 2x

B. -2x

Correct C. \frac{-2x}{$ x^2 + 1 $^2}

D. \frac{2x}{$ x^2 + 1 $^2}

Correct Answer: C

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Question 17

A vector $ \vec{a} $ has components $ a_x = 3 $ and $ a_y = 4 $. Find the magnitude of the vector.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 18

A solid cylinder has a radius of 4 cm and a height of 10 cm. Find the volume of the cylinder.

A. 800\pi

Correct B. 1600\pi

C. 3200\pi

D. 6400\pi

Correct Answer: B

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Question 19

A polynomial function is defined as ( f(x) = x^3 - 6x^2 + 9x + 2 ). Find the derivative of the function.

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

B. 3x^2 - 12x + 10

C. 3x^2 - 12x + 11

D. 3x^2 - 12x + 12

Correct Answer: A

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Question 20

A sequence is defined as $ a_n = 2n + 1 $. Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

C. 25

Correct D. 30

Correct Answer: D

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Question 21

Solve for x in the quadratic equation $ x^2 + 5x + 6 = 0 $.

A. 2

Correct B. -3

C. -2

D. 1

Correct Answer: B

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Question 22

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?

Correct A. 0.4

B. 0.6

C. 0.8

D. 0.2

Correct Answer: A

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Question 23

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 + 2 $^2 + $ y + 3 $^2 = 16 \)

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

Correct Answer: A

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Question 24

Solve the trigonometric 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

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Question 25

A company produces x units of a product and incurs a \cost of ( C(x) = 2x^2 + 10x + 5 \) naira. Find the marginal \cost when x = 10.

A. 20

Correct B. 30

C. 40

D. 50

Correct Answer: B

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