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POST UTME UNIBEN 2022 Mathematics | Objective

Are you preparing for POST UTME UNIBEN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, P\( X = 3 \) = 0.3. If Y is another random variable such that Y = 2X - 1, find the probability that Y is greater than 3.

A. 0.2

B. 0.4

Correct C. 0.6

D. 0.8

Correct Answer: C

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Question 2

Solve for x in the equation \( 2x^3 - 5x^2 + 3x - 1 = 0 \).

A. x = 1

B. x = -1

Correct C. x = \frac{1}{2}

D. x = -\frac{1}{2}

Correct Answer: C

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Question 3

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

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

B. \( x - 2 \)^2 + \( y - 3 \)^2 = 4

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

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 25

Correct Answer: A

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Question 4

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 5

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \) with initial term \( a_1 = 3 \). Find the sum of the first 5 terms of the sequence.

Correct A. 65

B. 75

C. 85

D. 95

Correct Answer: A

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Question 6

Given that \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \), find the vector \( mathbf{a} \times mathbf{b} \).

Correct A. \( egin{pmatrix} 7 \ -6 \end{pmatrix} \)

B. \( egin{pmatrix} -6 \ 7 \end{pmatrix} \)

C. \( egin{pmatrix} 6 \ -7 \end{pmatrix} \)

D. \( egin{pmatrix} -7 \ 6 \end{pmatrix} \)

Correct Answer: A

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Question 7

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 - 2

D. y = x + 2

Correct Answer: A

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Question 8

Find the sum of the first 5 terms of the geometric series with first term \( a = 2 \) and common ratio \( r = 3 \).

Correct A. \( 2\( 3^5 - 1 \ \) )

B. \( 2\( 3^5 + 1 \ \) )

C. \( 2\( 3^5 - 2 \ \) )

D. \( 2\( 3^5 + 2 \ \) )

Correct Answer: A

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Question 9

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

Correct A. \( x = -2 \)

B. \( x = 2 \)

C. \( x = -1 \)

D. \( x = 1 \)

Correct Answer: A

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Question 10

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).

Correct A. ( 6 )

B. ( 12 )

C. ( 18 )

D. ( 24 )

Correct Answer: A

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Question 11

Find the volume of the frustum of a cone with radii 6 cm and 3 cm and height 8 cm.

A. \( \frac{1}{3} pi \( 6^2 + 3^2 + 6 cdot 3 \ \) cdot 8 )

B. \( \frac{1}{3} pi \( 6^2 + 3^2 - 6 cdot 3 \ \) cdot 8 )

Correct C. \( \frac{1}{3} pi \( 6^2 + 3^2 + 6 cdot 3 \ \) cdot 8 )

D. \( \frac{1}{3} pi \( 6^2 + 3^2 - 6 cdot 3 \ \) cdot 8 )

Correct Answer: C

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Question 12

Solve for x in the equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} \).

Correct A. \( x = 3 \)

B. \( x = 4 \)

C. \( x = 5 \)

D. \( x = 6 \)

Correct Answer: A

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Question 13

A random variable X has a probability distribution given by \( P\( X = 1 \ \) = \frac{1}{3} ) and \( P\( X = 2 \ \) = \frac{2}{3} ). Find the probability that X is greater than 1.

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

Correct B. \( \frac{2}{3} \)

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

D. \( \frac{2}{5} \)

Correct Answer: B

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Question 14

Find the mean and s\tandard deviation of the data set { 2, 4, 6, 8, 10 }.

Correct A. \( ar{x} = 6, sigma = 2 \)

B. \( ar{x} = 5, sigma = 1 \)

C. \( ar{x} = 6, sigma = 1 \)

D. \( ar{x} = 5, sigma = 2 \)

Correct Answer: A

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Question 15

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the histogram is symmetric, what is the probability that a randomly selected score is greater than 70?

A. \( \frac{1}{4} \)

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

Correct C. \( \frac{3}{4} \)

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

Correct Answer: C

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Question 16

Given that \( \sin^2 x + \cos^2 x = 1 \), find \( \tan^2 x \) in terms of \( \sin^2 x \) and \( \cos^2 x \).

Correct A. \( \frac{\sin^2 x}{\cos^2 x} \)

B. \( \sin^2 x + \cos^2 x \)

C. \( \frac{\cos^2 x}{\sin^2 x} \)

D. \( \sin^2 x \cos^2 x \)

Correct Answer: A

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Question 17

Solve for ( x ) in the equation \( 2^{2x} = 8 \).

A. \( x = 2 \)

B. \( x = 3 \)

Correct C. \( x = \frac{3}{2} \)

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

Correct Answer: C

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Question 18

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25 \)

B. \( x - 4 \)^2 + \( y - 3 \)^2 = 25 \)

C. \( x - 3 \)^2 + \( y - 4 \)^2 = 30 \)

D. \( x - 4 \)^2 + \( y - 3 \)^2 = 30 \)

Correct Answer: A

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Question 19

Find the vector ( mathbf{a} ) given that \( mathbf{a} cdot mathbf{b} = 6 \) and \( mathbf{a} cdot mathbf{c} = 3 \), where \( mathbf{b} = 2mathbf{i} + 3mathbf{j} \) and \( mathbf{c} = mathbf{i} - 2mathbf{j} \).

Correct A. \( 3mathbf{i} + 2mathbf{j} \)

B. \( 2mathbf{i} + 3mathbf{j} \)

C. \( mathbf{i} - 2mathbf{j} \)

D. \( 4mathbf{i} - mathbf{j} \)

Correct Answer: A

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Question 20

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

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 21

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 6 cm.

A. 256\pi cm^3

B. 512\pi cm^3

Correct C. 768\pi cm^3

D. 1024\pi cm^3

Correct Answer: C

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Question 22

Solve the equation \( \frac{1}{x+1} + \frac{1}{x-1} = \frac{1}{2} \) for x.

Correct A. x = 2

B. x = -2

C. x = 1

D. x = -1

Correct Answer: A

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Question 23

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

A. 4/3

B. 8/3

Correct C. 16/3

D. 32/3

Correct Answer: C

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Question 24

Solve the matrix equation \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix} \) for x and y.

Correct A. x = 1, y = 2

B. x = 2, y = 1

C. x = 1, y = 1

D. x = 2, y = 2

Correct Answer: A

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Question 25

Find the derivative of the function f(x) = x^3 + 2x^2 - 5x + 1.

Correct A. 3x^2 + 4x - 5

B. 3x^2 + 4x + 5

C. 3x^2 - 4x - 5

D. 3x^2 - 4x + 5

Correct Answer: A

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