Exam Body

Year

Subject

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POST UTME UNIBEN 2019 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 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.

A. 30π cm³

Correct B. 60π cm³

C. 90π cm³

D. 120π cm³

Correct Answer: B

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Question 2

Solve for x in the equation \( \log_{2} \( x^2 \ \) = 4 ).

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 3

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 4

A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.

A. 20

B. 30

C. 40

Correct D. 50

Correct Answer: D

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Question 5

In the diagram below, ( AB ) is a diameter of the circle with center ( O ). If \( ∠AOB = 60^{circ} \), find the measure of ( ∠ACB ).

A. 30^{circ}

B. 45^{circ}

Correct C. 60^{circ}

D. 90^{circ}

Correct Answer: C

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Question 6

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 probability that X is greater than 2.

Correct A. 0.7

B. 0.4

C. 0.3

D. 0.2

Correct Answer: A

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Question 7

Find the vector projection of vector \vec{a} = 2\hat{i} + 3\hat{j} onto vector \vec{b} = \hat{i} + \hat{j}.

Correct A. \frac{5}{6}\hat{i} + \frac{5}{6}\hat{j}

B. \frac{1}{6}\hat{i} + \frac{1}{6}\hat{j}

C. \frac{3}{4}\hat{i} + \frac{3}{4}\hat{j}

D. \frac{1}{2}\hat{i} + \frac{1}{2}\hat{j}

Correct Answer: A

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Question 8

Solve the quadratic equation \frac{x^2 + 2x - 3}{x + 1} = 0.

Correct A. x = -3

B. x = 1

C. x = -1

D. x = 2

Correct Answer: A

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Question 9

Find the value of x in the equation \log_{10}\( x^2 \) = 4.

Correct A. 10^8

B. 10^4

C. 10^2

D. 10^6

Correct Answer: A

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Question 10

A set A contains the elements {1, 2, 3, 4, 5}. Find the number of subsets of A that contain exactly two elements.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 11

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

A. -2

Correct B. -3

C. 1

D. 2

Correct Answer: B

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Question 12

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 13

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 14

Find the value of \( \log_{10} \( x^2 \ \) ) given that \( x = 10^4 \).

A. 8

B. 10

Correct C. 12

D. 16

Correct Answer: C

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Question 15

Solve for x in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 16

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

A. \( x = -10 \)

Correct B. \( x = 1 \)

C. \( x = -1 \)

D. \( x = 2 \)

Correct Answer: B

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Question 17

A circle with center (0, 0) and radius 5 passes through which of the following points?

A. (3, 4)

B. (4, 3)

Correct C. (5, 0)

D. (0, 5)

Correct Answer: C

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Question 18

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

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

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

C. \( x < -1 \) or \( x < 3 \)

D. \( x > 1 \) or \( x > 3 \)

Correct Answer: A

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Question 19

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. \( y = -2x + 1 \)

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

Correct Answer: A

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Question 20

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

A. \( x = -2 \)

Correct B. \( x = -3 \)

C. \( x = 2 \)

D. \( x = 3 \)

Correct Answer: B

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Question 21

Find the value of x in the equation \( \frac{x}{2} + 5 = 11 \).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 22

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

Correct A. x < -1 or x > 3

B. x < 1 or x > 3

C. x < -3 or x > 1

D. x < 3 or x > 1

Correct Answer: A

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Question 23

Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, 54, ... ).

Correct A. 120

B. 150

C. 180

D. 200

Correct Answer: A

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Question 24

Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).

Correct A. x = 3, y = 1

B. x = 1, y = 3

C. x = 2, y = 2

D. x = 4, y = 0

Correct Answer: A

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Question 25

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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