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POST UTME AFE BABALOLA UNIVERSITY 2024 Mathematics | Objective

Are you preparing for POST UTME AFE BABALOLA 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

A random variable X has a probability distribution given by P(X) = \( 1/2 \)^\( X-1 \) for X = 1, 2, 3, ... . Find the probability that X is greater than 2.

A. 1/2

B. 1/4

Correct C. 1/8

D. 3/4

Correct Answer: C

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Question 2

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

A. 32\pi/5

B. 64\pi/5

Correct C. 128\pi/5

D. 256\pi/5

Correct Answer: C

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Question 3

Solve the inequality |x - 2| > 3.

Correct A. x < -1 or x > 5

B. x < 1 or x > 5

C. x < 1 or x > 3

D. x < 3 or x > 5

Correct Answer: A

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Question 4

A right circular cone has a height of 12 cm and a base radius of 6 cm. Find the volume of the cone.

Correct A. 288\pi

B. 288\pi/3

C. 288\pi/2

D. 288\pi/5

Correct Answer: A

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Question 5

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

A. 64\pi/5

B. 128\pi/5

Correct C. 256\pi/5

D. 512\pi/5

Correct Answer: C

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Question 6

Solve for x in the equation \( \sqrt[3]{x^2} = 4 \).

Correct A. 64

B. 16

C. 256

D. 1024

Correct Answer: A

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Question 7

Find the value of \( \log_{10} \( x^2 \ \) ) given that \( \log_{10} \( x \ \) = 2 ).

A. 4

Correct B. 8

C. 16

D. 32

Correct Answer: B

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Question 8

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).

Correct A. -2

B. -1

C. 0

D. 2

Correct Answer: A

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Question 9

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 10

Solve the system of linear equations \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).

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

B. \begin{bmatrix} 2 \ 3 \end{bmatrix}

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

D. \begin{bmatrix} 4 \ 5 \end{bmatrix}

Correct Answer: A

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Question 11

In the diagram below, a circle with center O and radius 6cm is \tangent to the x-axis at point P. If the line OP is ext\ended to meet the y-axis at point Q, what is the length of OQ?

Correct A. 12cm

B. 8cm

C. 10cm

D. 6cm

Correct Answer: A

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Question 12

A binary operation \(*\) on the set \{0, 1\} is defined as follows: \begin{align*} 0*0&=0,\ 0*1=1,\ 1*0=1,\ 1*1=0. \end{align*} Find the value of \(\( 1*0 \)*\( 1*0)\ \).

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 13

In the diagram below, a line passes through points A(2, 3) and B(4, 5). If the line has a slope of 2, what is the equation of the line in slope-intercept form?

Correct A. y = 2x + 1

B. y = 2x - 1

C. y = 2x + 2

D. y = 2x - 2

Correct Answer: A

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Question 14

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experimenter wins a prize. If the number rolled is odd, the experimenter loses a prize. What is the probability that the experimenter wins a prize?

Correct A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 15

Solve the equation \(x^2 + 5x + 6 = 0\).

Correct A. -2

B. -3

C. -1

D. 1

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.

Correct A. ( f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

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

C. ( f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

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

Correct Answer: A

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Question 17

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

Correct A. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)

B. \( x > \frac{3}{2} \) or \( x < -\frac{5}{4} \)

C. \( x > -\frac{5}{4} \) and \( x < \frac{3}{2} \)

D. \( x < -\frac{5}{4} \) and \( x > \frac{3}{2} \)

Correct Answer: A

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Question 18

Find the value of \( \sin\( 2x \ \) ) given that \( \sin\( x \ \) = \frac{1}{2} ) and \( \cos\( x \ \) = \frac{\sqrt{3}}{2} ).

Correct A. \( \frac{\sqrt{3}}{2} \)

B. \( \frac{1}{2} \)

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

D. \( \frac{1}{2} \)

Correct Answer: A

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Question 19

Solve the system of equations \( egin{cases} x + y = 2 \ 2x - y = 3 \end{cases} \) u\sing matrices.

Correct A. \( x = 1, y = 1 \)

B. \( x = 2, y = 0 \)

C. \( x = 0, y = 2 \)

D. \( x = 1, y = 2 \)

Correct Answer: A

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Question 20

Find the derivative of the function ( f(x) = x^3 - 2x^2 + 3x - 1 ) u\sing the power rule.

Correct A. ( f'(x) = 3x^2 - 4x + 3 )

B. ( f'(x) = 3x^2 - 4x + 3 )

C. ( f'(x) = 3x^2 - 4x + 3 )

D. ( f'(x) = 3x^2 - 4x + 3 )

Correct Answer: A

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Question 21

Solve the inequality \( x^2 - 4x + 3 > 0 \) u\sing the quadratic formula.

Correct A. \( x < 1 \) or \( x > 3 \)

B. \( x > 1 \) or \( x < 3 \)

C. \( x < 1 \) and \( x > 3 \)

D. \( x > 1 \) and \( x < 3 \)

Correct Answer: A

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Question 22

Find the value of \( \cos\( 2x \ \) ) given that \( \sin\( x \ \) = \frac{1}{2} ) and \( \cos\( x \ \) = \frac{\sqrt{3}}{2} ).

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

B. \( \frac{1}{2} \)

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

D. \( -\frac{\sqrt{3}}{2} \)

Correct Answer: A

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Question 23

Solve the system of equations \( egin{cases} x + y = 2 \ 2x - y = 3 \end{cases} \) u\sing substitution.

A. \( x = 1, y = 1 \)

B. \( x = 2, y = 0 \)

C. \( x = 0, y = 2 \)

D. \( x = 1, y = 2 \)

Correct Answer: VIEW ANSWER

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Question 24

A histogram of exam scores is shown below. If the mean score is 75 and the s\tandard deviation is 10, what is the probability that a randomly selected student scored above 85?

Correct A. 0.5

B. 0.25

C. 0.75

D. 0.1

Correct Answer: A

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Question 25

Find the sum of the first 10 terms of the geometric series 2x + 3x^2 + 4x^3 + ...

A. 1040x^10

Correct B. 1050x^10

C. 1060x^10

D. 1070x^10

Correct Answer: B

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