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POST UTME BELLS UNIVERSITY 2024 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 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Given that \( \sin^2 x + \cos^2 x = 1 \), find the value of \( \tan x \) when \( \sin x = \frac{3}{5} \).

A. 0.6

Correct B. 0.8

C. 1.2

D. 1.5

Correct Answer: B

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Question 2

Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).

Correct A. 1.5

B. -2

C. 3

D. -1

Correct Answer: A

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Question 3

Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 4

A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that both balls are red?

Correct A. 0.25

B. 0.5

C. 0.75

D. 1

Correct Answer: A

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Question 5

Find the value of ( x ) in the equation \( x^2 + 4x + 4 = 0 \).

Correct A. -2

B. 0

C. 2

D. 4

Correct Answer: A

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Question 6

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).

Correct A. 4/5

B. 3/5

C. 5/4

D. 2/3

Correct Answer: A

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Question 7

A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3 or 5?

A. 1/3

Correct B. 1/2

C. 2/3

D. 5/6

Correct Answer: B

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Question 8

The equation of a circle is \( x^2 + y^2 = 16 \). Find the equation of the line pas\sing through the point ( (4, 0) ) that is \tangent to the circle.

Correct A. y = 4x + 16

B. y = 4x - 16

C. y = 4x + 4

D. y = 4x - 4

Correct Answer: A

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Question 9

Simplify the expression \( \frac{\log_2 x - \log_2 3}{\log_2 x + \log_2 3} \).

Correct A. 1/3

B. 1/2

C. 2/3

D. 3/4

Correct Answer: A

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Question 10

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side.

Correct A. 8 cm

B. 6 cm

C. 10 cm

D. 12 cm

Correct Answer: A

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Question 11

A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, and P\( X = 3 \) = 0.3. Find the expected value of X.

Correct A. 1.1

B. 1.2

C. 1.3

D. 1.4

Correct Answer: A

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Question 12

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

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

B. \frac{\pi}{2}

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

D. \frac{\pi}{6}

Correct Answer: A

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Question 13

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 is greater than 85?

A. 0.1587

B. 0.3413

C. 0.4772

Correct D. 0.6915

Correct Answer: D

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Question 14

Find the vector \[ \vec{a} \times \vec{b} \] given that \[ \vec{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} \] and \[ \vec{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \].

Correct A. \begin{pmatrix} -1 \ 8 \ -5 \end{pmatrix}

B. \begin{pmatrix} 1 \ -8 \ 5 \end{pmatrix}

C. \begin{pmatrix} -1 \ -8 \ 5 \end{pmatrix}

D. \begin{pmatrix} 1 \ 8 \ -5 \end{pmatrix}

Correct Answer: A

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Question 15

Solve the equation \[ x^2 + 5x + 6 = 0 \] u\sing the quadratic formula.

Correct A. \begin{pmatrix} -2 \ 3 \end{pmatrix}

B. \begin{pmatrix} -3 \ 2 \end{pmatrix}

C. \begin{pmatrix} 2 \ -3 \end{pmatrix}

D. \begin{pmatrix} 3 \ -2 \end{pmatrix}

Correct Answer: A

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Question 16

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

A. \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

B. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

Correct C. \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

D. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

Correct Answer: C

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Question 17

Solve the system of linear equations u\sing matrices:

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

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

C. \begin{bmatrix} 5 \ 6 \end{bmatrix}

D. \begin{bmatrix} 7 \ 8 \end{bmatrix}

Correct Answer: A

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Question 18

Find the determinant of the matrix \begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19

A particle moves in a straight line with a velocity of 5 m/s. If the acceleration is 2 m/s^2, find the dis\tance traveled in 3 seconds.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 20

Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...

A. 62

Correct B. 64

C. 66

D. 68

Correct Answer: B

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Question 21

Find the equation of the circle pas\sing through the points (2,3), (4,5), and \( -1,2 \).

Correct A. \( x^2 + y^2 - 4x + 10y + 25 = 0 \)

B. \( x^2 + y^2 + 4x - 10y - 25 = 0 \)

C. \( x^2 + y^2 - 2x - 6y + 9 = 0 \)

D. \( x^2 + y^2 + 2x + 6y - 9 = 0 \)

Correct Answer: A

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Question 22

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

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

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

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

D. \( x < -\frac{3}{2} \) or \( x > 1 \)

Correct Answer: A

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Question 23

Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix} \).

Correct A. ( 10 )

B. ( 20 )

C. ( 30 )

D. ( 40 )

Correct Answer: A

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Question 24

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

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

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

C. \( \frac{2}{3} \)

Correct D. \( \frac{5}{6} \)

Correct Answer: D

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Question 25

The mean of five numbers is 20. If one of the numbers is 15, what is the sum of the other four numbers?

Correct A. ( 80 )

B. ( 90 )

C. ( 100 )

D. ( 110 )

Correct Answer: A

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