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POST UTME BABCOCK UNIVERSITY 2023 Mathematics | Objective

Are you preparing for POST UTME BABCOCK 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.

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Question 1

Find the determinant of the matrix $ egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} $.

A. 1

Correct B. -1

C. 2

D. 3

Correct Answer: B

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Question 2

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 50.24 cm^2

B. 100.48 cm^2

C. 50.24 cm^3

D. 100.48 cm^3

Correct Answer: A

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Question 3

Find the area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 4 $.

Correct A. 32

B. 64

C. 16

D. 128

Correct Answer: A

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Question 4

Solve the equation $ 2x + 5 = 11 $.

Correct A. 3

B. 2

C. 4

D. 5

Correct Answer: A

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Question 5

Find the value of ( x ) in the equation $ x^2 - 4x - 5 = 0 $.

Correct A. 5

B. -1

C. 2

D. 3

Correct Answer: A

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Question 6

Find the value of $\frac{d}{dx} \left$ \frac{1}{x^2 + 1} \right $$ u\sing the quotient 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 7

Solve the inequality $\left| x - 2 \right| > 3$.

Correct A. $x < -1$ or $x > 5$

B. $x < 1$ or $x > 5$

C. $x < -1$ or $x > 2$

D. $x < 1$ or $x > 2$

Correct Answer: A

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Question 8

Find the sum of the first 5 terms of the geometric series $\sum_{n=1}^5 \frac{2}{3^n}$.

Correct A. \frac{2}{3} + \frac{2}{9} + \frac{2}{27} + \frac{2}{81} + \frac{2}{243}

B. \frac{2}{3} + \frac{2}{9} + \frac{2}{27} + \frac{2}{81} + \frac{2}{243}

C. \frac{2}{3} + \frac{2}{9} + \frac{2}{27} + \frac{2}{81}

D. \frac{2}{3} + \frac{2}{9} + \frac{2}{27}

Correct Answer: A

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Question 9

Solve the matrix equation $\begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 3 \end{bmatrix}$.

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

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

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

D. \begin{bmatrix} 2 \ 2 \end{bmatrix}

Correct Answer: A

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Question 10

A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?

Correct A. 12

B. 13

C. 14

D. 15

Correct Answer: A

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Question 11

A random sample of 25 students from a population of 1000 students had a mean height of 175 cm with a s\tandard deviation of 5 cm. Calculate the 95% confidence interval for the population mean.

Correct A. 170.4 cm, 179.6 cm

B. 172.5 cm, 177.5 cm

C. 174.5 cm, 175.5 cm

D. 171.2 cm, 178.8 cm

Correct Answer: A

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Question 12

Solve the inequality $ 2x^2 + 5x - 3 \geq 0 $ u\sing the quadratic formula.

Correct A. $ x \leq -1.5 $ or $ x \geq 1 $

B. $ x \leq -1 $ or $ x \geq 1.5 $

C. $ x \leq -1.5 $ or $ x \geq 1.5 $

D. $ x \leq 1 $ or $ x \geq 1.5 $

Correct Answer: A

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Question 13

Find the determinant of the matrix \[ \begin{bmatrix} 2 & 3 & 1 \\ 4 & 1 & 2 \\ 3 & 2 & 1 \end{bmatrix} \].

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 14

A company produces two products, A and B. The profit from the sale of product A is ₦200 per unit, while the profit from the sale of product B is ₦150 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. ₦25000

Correct B. ₦30000

C. ₦35000

D. ₦40000

Correct Answer: B

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Question 15

A histogram of the heights of 100 students is shown below. If the mean height of the students is 175 cm, what is the s\tandard deviation?

Correct A. 5 cm

B. 10 cm

C. 15 cm

D. 20 cm

Correct Answer: A

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Question 16

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

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Question 17

A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. 1/6

B. 1/3

C. 1/2

Correct D. 2/3

Correct Answer: D

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Question 18

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. 16/3

Correct B. 32/3

C. 64/3

D. 128/3

Correct Answer: B

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Question 19

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

Correct A. $ -∞, -3 $ ∪ (1, ∞)

B. $ -∞, -1 $ ∪ (3, ∞)

C. $ -∞, 1 $ ∪ (3, ∞)

D. $ -∞, -3 $ ∪ $ -1, ∞ $

Correct Answer: A

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Question 20

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

Correct A. 24/25

B. 16/25

C. 20/25

D. 12/25

Correct Answer: A

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Question 21

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

Correct A. ( f'(x) = \frac{-x}{$ x^2 + 1 $^{\frac{3}{2}}} )

B. ( f'(x) = \frac{x}{$ x^2 + 1 $^{\frac{3}{2}}} )

C. ( f'(x) = \frac{1}{$ x^2 + 1 $^{\frac{3}{2}}} )

D. ( f'(x) = \frac{x^2}{$ x^2 + 1 $^{\frac{3}{2}}} )

Correct Answer: A

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Question 22

A binary operation ( odot ) is defined as $ a odot b = ab + 2 $. Find the value of ( 3 odot 4 ).

A. 14

Correct B. 16

C. 18

D. 20

Correct Answer: B

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Question 23

Solve the trigonometric equation $ \sin^2 x + \cos^2 x = 1 $ for ( x ) in the interval ( [0, 2pi] ).

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

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

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

D. $ x = \frac{5pi}{4} $

Correct Answer: A

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Question 24

A random experiment consists of rolling a fair six-sided die. Find the probability that the sum of the numbers on the two dice is 7.

A. \frac{1}{6}

Correct B. \frac{1}{3}

C. \frac{1}{2}

D. \frac{2}{3}

Correct Answer: B

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Question 25

Convert the decimal number 0.000123 to a binary number.

A. 0.000123

Correct B. 0.00011011

C. 0.00010101

D. 0.00011101

Correct Answer: B

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