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POST UTME BSU 2024 Mathematics | Objective

Are you preparing for POST UTME BSU 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 derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.

Correct A. \frac{-1}{2x^{3/2}}

B. \frac{1}{2x^{3/2}}

C. \frac{1}{x^{3/2}}

D. \frac{-1}{x^{3/2}}

Correct Answer: A

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Question 2

A box contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that they are of different colors?

Correct A. \frac{5}{14}

B. \frac{3}{14}

C. \frac{2}{7}

D. \frac{1}{2}

Correct Answer: A

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Question 3

The volume of a cylinder is given by $ V = \pi r^2 h $. If the radius of the cylinder is increased by 20% and the height is decreased by 15%, what is the new volume?

Correct A. \frac{21}{16} \pi r^2 h

B. \frac{25}{16} \pi r^2 h

C. \frac{27}{16} \pi r^2 h

D. \frac{29}{16} \pi r^2 h

Correct Answer: A

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Question 4

The mean of a set of numbers is 25. If the set is increased by 10% and then decreased by 5%, what is the new mean?

Correct A. 24.5

B. 25.5

C. 26.5

D. 27.5

Correct Answer: A

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Question 5

A histogram of exam scores has a mean of 80 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 70 and 90?

Correct A. 0.68

B. 0.69

C. 0.70

D. 0.71

Correct Answer: A

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Question 6

Find the value of $\int_0^1 \frac{1}{1+x^2} dx$.

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 7

Solve for $x$: $\log_2 x + \log_2 $ x-1 $ = 2$.

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 8

Find the area of the region bounded by the curves $y = x^2$ and $y = 2x$.

A. \frac{1}{3}

Correct B. \frac{2}{3}

C. 1

D. 2

Correct Answer: B

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Question 9

Solve for $x$: $\sin^2 x + \cos^2 x = 1$.

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

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

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

D. x = \pi

Correct Answer: A

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Question 10

Find the value of $\frac{d}{dx} \left$ \frac{1}{x} \right $$.

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

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

C. -\frac{1}{x}

D. \frac{1}{x}

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. 40

B. 50

Correct C. 60

D. 70

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} 5 \ 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

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?

A. 0.68

Correct B. 0.85

C. 0.95

D. 0.99

Correct Answer: B

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Question 14

A right circular cone has a radius of 6 cm and a height of 8 cm. Find the volume of the cone.

A. 288\pi

Correct B. 384\pi

C. 480\pi

D. 576\pi

Correct Answer: B

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Question 15

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

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

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

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

D. x = \pi

Correct Answer: A

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Question 16

In the diagram below, the graph of $ y = \frac{1}{2} \sin \( 2x \ $ ) is shown. What is the amplitude of the graph?

A. 1

Correct B. 0.5

C. 2

D. 0.25

Correct Answer: B

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Question 17

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

Correct A. $ x < -1 $ or $ x > \frac{3}{2} $

B. $ x > -1 $ or $ x < \frac{3}{2} $

C. $ x < -1 $ or $ x < \frac{3}{2} $

D. $ x > -1 $ or $ x > \frac{3}{2} $

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 + 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 19

A right-angled triangle has sides of length ( 3 ), ( 4 ), and ( 5 ). Find the area of the triangle.

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 20

Solve the equation $ x^2 - 4x + 4 = 0 $.

Correct A. $ x = 2 $

B. $ x = 1 $

C. $ x = 3 $

D. $ x = 4 $

Correct Answer: A

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Question 21

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

A. x = 2

B. x = -1

Correct C. x = 1

D. x = -2

Correct Answer: C

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Question 22

Find the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. V = 100\pi cm^3

B. V = 200\pi cm^3

Correct C. V = 300\pi cm^3

D. V = 400\pi cm^3

Correct Answer: C

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Question 23

A set of 5 consecutive integers has a median of 8. What is the sum of the integers?

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 24

A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

Correct A. 8 cm

B. 6 cm

C. 4 cm

D. 2 cm

Correct Answer: A

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Question 25

A sequence is defined recursively as $ a_n = 2a_{n-1} + 1 $, where $ a_1 = 3 $. Find the value of $ a_{10} $.

A. 1023

Correct B. 1025

C. 1027

D. 1029

Correct Answer: B

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