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POST UTME BELLS UNIVERSITY 2023 Mathematics | Objective

Are you preparing for POST UTME BELLS 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 $ from $ x = 0 $ to $ x = 4 $.

Correct A. ( 8 )

B. ( 16 )

C. ( 32 )

D. ( 64 )

Correct Answer: A

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Question 2

A random variable ( X ) has a probability distribution given by $ P\( X = x \ $ = \frac{1}{2} ) for $ x = 1, 2, 3 $. Find the probability that ( X ) is greater than 2.

A. $ \frac{1}{4} $

B. $ \frac{1}{2} $

Correct C. $ \frac{3}{4} $

D. $ \frac{1}{2} $

Correct Answer: C

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Question 3

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.

A. ( 0.1587 )

B. ( 0.3413 )

C. ( 0.5 )

Correct D. ( 0.8413 )

Correct Answer: D

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Question 4

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

A. $ \cos^2\( x \ $ )

Correct B. $ 2\sin\( x $\cos(x \) )

C. $ 2\sin\( x $\cos(x \) )

D. $ 2\sin^2\( x $\cos(x \) )

Correct Answer: B

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Question 5

A surd $ \sqrt[3]{27} $ can be expressed in the form $ a + b\sqrt[3]{c} $. Find the values of ( a ), ( b ), and ( c ).

Correct A. $ a = 3, b = 1, c = 3 $

B. $ a = 3, b = 2, c = 3 $

C. $ a = 2, b = 1, c = 3 $

D. $ a = 1, b = 2, c = 3 $

Correct Answer: A

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Question 6

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

A. $ x = -2 \ $

Correct B. $ x = 2 \ $

C. $ x = -1 \ $

D. $ x = 1 \ $

Correct Answer: B

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Question 7

A histogram of exam scores is shown below. What is the mean score?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 8

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

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

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

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

D. $ x = \frac{\pi}{6} \ $

Correct Answer: A

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Question 9

A vector $ \vec{a} $ is represented by the diagram below. What is the magnitude of $ \vec{a} $?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 10

A polynomial function ( f(x) = x^3 - 6x^2 + 11x - 6 ) is shown below. What is the value of $ f\( -1 \ $ )?

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 11

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

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 12

Solve the inequality $ 2x^2 + 5x - 3 > 0 $.

Correct A. \left$ -\infty, -\frac{3}{2} \right $ \cup \left$ \frac{1}{2}, \infty \right $

B. \left$ -\infty, -\frac{1}{2} \right $ \cup \left$ \frac{3}{2}, \infty \right $

C. \left$ -\infty, \frac{1}{2} \right $ \cup \left$ \frac{3}{2}, \infty \right $

D. \left$ -\infty, -\frac{3}{2} \right $ \cup \left$ \frac{1}{2}, \infty \right $

Correct Answer: A

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Question 13

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

Correct A. \left$ x - 2 \right $^2 + \left$ y - 3 \right $^2 = 16

B. \left$ x - 3 \right $^2 + \left$ y - 2 \right $^2 = 16

C. \left$ x - 4 \right $^2 + \left$ y - 3 \right $^2 = 16

D. \left$ x - 2 \right $^2 + \left$ y - 4 \right $^2 = 16

Correct Answer: A

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Question 14

Find the vector ( mathbf{a} ) such that $ mathbf{a} cdot mathbf{b} = 10 $ and $ mathbf{a} cdot mathbf{c} = 5 $, where $ mathbf{b} = 2mathbf{i} + 3mathbf{j} $ and $ mathbf{c} = mathbf{i} - mathbf{j} $.

Correct A. \mathbf{a} = 3mathbf{i} + 2mathbf{j}

B. \mathbf{a} = 2mathbf{i} + 3mathbf{j}

C. \mathbf{a} = mathbf{i} + 2mathbf{j}

D. \mathbf{a} = 4mathbf{i} + mathbf{j}

Correct Answer: A

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Question 15

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. \frac{8}{3}

Correct B. \frac{16}{3}

C. \frac{32}{3}

D. \frac{64}{3}

Correct Answer: B

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Question 16

Determine the value of $\int_{0}^{\pi} \sin^2 x \cos^2 x \, dx$.

A. \frac{\pi}{4}

B. \frac{\pi}{2}

C. \frac{3\pi}{4}

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

Correct Answer: D

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Question 17

Let $A = \begin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix}$. Find the eigenvalues of $A^2$.

Correct A. -3

B. -1

C. 1

D. 3

Correct Answer: A

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Question 18

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

Correct A. \frac{\pi}{4}

B. \frac{\pi}{2}

C. \frac{\pi}{3}

D. \frac{\pi}{6}

Correct Answer: A

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Question 19

Determine the value of $\sum_{n=1}^{\infty} \frac{1}{n^2 + 1}$.

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{6}

D. \frac{\pi}{8}

Correct Answer: A

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Question 20

Let $f(x) = \frac{x^2 - 4}{x - 2}$. Find the domain of $f(x)$.

Correct A. $ -\infty, 2 $ \cup $ 2, \infty $

B. $ -\infty, 2 $ \cup (2, 4]

C. $ -\infty, 2 $ \cup $ 4, \infty $

D. (2, 4]

Correct Answer: A

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Question 21

Find the value of $\int_{0}^{\pi} \frac{1}{1+\sin^2x} dx$.

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{3}

D. \frac{\pi}{6}

Correct Answer: A

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Question 22

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

Correct A. $ -\infty, -1 $ \cup $ 5, \infty $

B. $ -\infty, 1 $ \cup $ 3, \infty $

C. $ -\infty, -5 $ \cup $ 1, \infty $

D. $ -\infty, 5 $ \cup $ 1, \infty $

Correct Answer: A

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Question 23

Find the equation of the line pas\sing through the points $$ -2, 3 $$ and $$ 1, -2 $$.

Correct A. y = -\frac{5}{3}x + \frac{11}{3}

B. y = \frac{5}{3}x - \frac{11}{3}

C. y = -\frac{3}{5}x + \frac{11}{5}

D. y = \frac{3}{5}x - \frac{11}{5}

Correct Answer: A

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Question 24

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

A. 8

Correct B. 10

C. 12

D. 14

Correct Answer: B

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Question 25

Find the value of $\sum_{n=1}^{5} \frac{1}{n^2}$.

Correct A. \frac{25}{12}

B. \frac{27}{12}

C. \frac{29}{12}

D. \frac{31}{12}

Correct Answer: A

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