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

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Question 1

Determine 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

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Question 2

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 3

Solve for x in the inequality \( 2x - 5 > 3 \).

Correct A. \( x > 4 \)

B. \( x < 4 \)

C. \( x > 2 \)

D. \( x < 2 \)

Correct Answer: A

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Question 4

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?

Correct A. ₦1250

B. ₦12500

C. ₦125000

D. ₦1250000

Correct Answer: A

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Question 5

Find the volume of the cylinder with radius 6 cm and height 10 cm.

A. \( 180 \pi \) cm³

B. \( 360 \pi \) cm³

Correct C. \( 600 \pi \) cm³

D. \( 1200 \pi \) cm³

Correct Answer: C

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Question 6

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

Correct A. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )

B. \( x-3 \ \)^2 + \( y-2 \)^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 7

Solve for (x) in the equation \( 2^x + 2^{x+1} = 3 cdot 2^x \).

Correct A. \( x = 2 \)

B. \( x = 1 \)

C. \( x = 0 \)

D. \( x = -1 \)

Correct Answer: A

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Question 8

Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = x^3 \) about the x-axis.

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

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

C. \( \frac{1}{2} pi \)

D. \( \frac{2}{3} pi \)

Correct Answer: A

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Question 9

A circle with center at ((0,0)) and radius 5 passes through the point ((3,4)). Find the equation of the circle.

Correct A. \( x^2 + y^2 = 25 \)

B. \( x^2 + y^2 = 9 \)

C. \( x^2 + y^2 = 16 \)

D. \( x^2 + y^2 = 36 \)

Correct Answer: A

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Question 10

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

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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 matrix equation \( \begin{bmatrix} 2 & 1 \ 1 & 3 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix} \).

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ 1 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 13

Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 14

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

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

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

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

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

Correct Answer: A

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Question 15

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

Correct A. \( -\infty, -1 \) \cup \( 3, \infty \)

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

C. \( -\infty, 1 \) \cup \( 3, \infty \)

D. \( -\infty, -3 \) \cup \( 1, \infty \)

Correct Answer: A

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Question 16

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

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 17

Solve the inequality \( |x - 2| > 3 \).

Correct A. \( x < -1 \) or \( x > 5 \)

B. \( x < -1 \) or \( x > 4 \)

C. \( x < -5 \) or \( x > 1 \)

D. \( x < 1 \) or \( x > 5 \)

Correct Answer: A

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Question 18

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

Correct A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )

B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )

C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )

D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 9 )

Correct Answer: A

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Question 19

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

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 20

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

A. \( \sin x = 1 \)

B. \( \cos x = 1 \)

Correct C. \( \sin x = 0 \)

D. \( \cos x = 0 \)

Correct Answer: C

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Question 21

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

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 22

A firm produces two products, A and B. Product A requires 2 hours of labor and 3 hours of capital, while product B requires 3 hours of labor and 2 hours of capital. If the firm has 120 hours of labor and 180 hours of capital available, how many units of product A and product B should the firm produce to maximize profit?

Correct A. 10 units of A and 15 units of B

B. 15 units of A and 10 units of B

C. 20 units of A and 5 units of B

D. 5 units of A and 20 units of B

Correct Answer: A

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Question 23

Find the area under the curve y = 2x^3 - 5x^2 + x + 1 from x = 0 to x = 2.

A. 14

B. 28

Correct C. 42

D. 56

Correct Answer: C

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Question 24

A right circular cone has a height of 10 cm and a base radius of 5 cm. Find the volume of the cone.

A. 250\pi

B. 500\pi

Correct C. 750\pi

D. 1000\pi

Correct Answer: C

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Question 25

Find the derivative of the function y = x^4 - 2x^2 + 1.

Correct A. 4x^3 - 4x

B. 2x^3 - 2x

C. x^3 - x

D. x^2 - 1

Correct Answer: A

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