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POST UTME UNN 2020 Mathematics | Objective

Are you preparing for POST UTME UNN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

Correct A. -2

B. 2

C. 4

D. 6

Correct Answer: A

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Question 2

If the function [ f(x) = \frac{1}{x} ] has a horizontal asymptote at [ y = c ], find the value of [ c ].

A. 0

B. 1

C. -1

Correct D. ∞

Correct Answer: D

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Question 3

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 blue?

A. \frac{1}{14}

B. \frac{1}{7}

Correct C. \frac{3}{14}

D. \frac{1}{2}

Correct Answer: C

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Question 4

Solve the quadratic equation [ x^2 + 4x + 4 = 0 ].

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 5

A company produces two products, A and B. The profit from the sale of one unit of product A is ₦100, and the profit from the sale of one unit of product B is ₦120. If the company produces 20 units of product A and 15 units of product B, what is the total profit?

A. ₦2500

Correct B. ₦2800

C. ₦3000

D. ₦3200

Correct Answer: B

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Question 6

Let X be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.

A. 0.25

Correct B. 0.5

C. 0.75

D. 1

Correct Answer: B

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Question 7

A set of 10 students scored the following marks in a mathematics test: 85, 90, 78, 92, 88, 76, 95, 89, 91, 84. Calculate the mean and s\tandard deviation of the marks.

Correct A. {mean: 87.5, std_dev: 5.5}

B. {mean: 88.5, std_dev: 6.5}

C. {mean: 89.5, std_dev: 7.5}

D. {mean: 90.5, std_dev: 8.5}

Correct Answer: A

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Question 8

Solve the equation \( \log_{10} \( x^2 \ \) = 4 ) for x.

Correct A. 10

B. -10

C. 2

D. -2

Correct Answer: A

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Question 9

A circle with center (0, 0) and radius 5 passes through the point (3, 4). Find the equation of the circle.

Correct A. x^2 + y^2 = 25

B. x^2 + y^2 = 16

C. x^2 + y^2 = 9

D. x^2 + y^2 = 4

Correct Answer: A

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Question 10

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 2197

B. 2187

C. 2177

D. 2167

Correct Answer: A

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Question 11

Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the chain rule.

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

B. ( f'(x) = \frac{2x}{x - 2} \)

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

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

Correct Answer: A

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Question 12

A set ( A ) contains the elements ( { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } ). Find the number of subsets of ( A ) that contain exactly 3 elements.

Correct A. \( 2^3 \ \)

B. \( 3^3 \ \)

C. \( 10 \ \)

D. \( 5 \ \)

Correct Answer: A

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Question 13

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

A. \( 15 \ \)

B. \( 25 \ \)

C. \( 35 \ \)

Correct D. \( 45 \ \)

Correct Answer: D

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Question 14

A polynomial function is defined by ( f(x) = x^3 - 6x^2 + 11x - 6 ). Find the value of ( f(2) ).

Correct A. \( 0 \ \)

B. \( 2 \ \)

C. \( 4 \ \)

D. \( 6 \ \)

Correct Answer: A

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Question 15

A geometric progression is defined by \( a_n = 2a_{n-1} \) with \( a_1 = 2 \). Find the sum of the first 5 terms of the progression.

Correct A. \( 62 \ \)

B. \( 63 \ \)

C. \( 64 \ \)

D. \( 65 \ \)

Correct Answer: A

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Question 16

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

A. 48\pi cm^3

B. 64\pi cm^3

Correct C. 96\pi cm^3

D. 128\pi cm^3

Correct Answer: C

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Question 17

Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10^4

Correct B. 10^8

C. 10^12

D. 10^16

Correct Answer: B

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Question 18

Find the area under the curve \( y = x^2 + 2x - 3 \) from x = 0 to x = 2.

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 19

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

A. 35

B. 40

Correct C. 45

D. 50

Correct Answer: C

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Question 20

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

Correct A. \( -\infty, -1 \) \cup \( 3, \infty \)

B. \( -\infty, -3 \) \cup \( 1, \infty \)

C. \( -\infty, -2 \) \cup \( 2, \infty \)

D. \( -\infty, -4 \) \cup \( 4, \infty \)

Correct Answer: A

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Question 21

A histogram is a graphical representation of a frequency distribution. What is the primary advantage of u\sing a histogram over a bar chart?

Correct A. It allows for the visualization of continuous data

B. It is easier to read and unders\tand

C. It can be used to display both categorical and numerical data

D. It is more aesthetically plea\sing

Correct Answer: A

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Question 22

Solve for x in the equation \( \tan\( x \ \) = \frac{1}{\sqrt{3}} ).

A. 30°

Correct B. 60°

C. 45°

D. 90°

Correct Answer: B

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Question 23

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

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 24

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

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 25

A solid cylinder has a radius of 4 cm and a height of 10 cm. Find the volume of the cylinder.

A. 800π

Correct B. 1000π

C. 1200π

D. 1600π

Correct Answer: B

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