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POST UTME UNN 2021 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 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the value of $\int_{0}^{\pi} \frac{\sin^2 x}{\sin^2 x + 1} dx$.

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{3}

D. \frac{\pi}{6}

Correct Answer: A

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Question 2

Solve the system of equations: $\begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases}$.

Correct A. \begin{cases} x = 1 \ y = 2 \end{cases}

B. \begin{cases} x = 2 \ y = 1 \end{cases}

C. \begin{cases} x = 3 \ y = 4 \end{cases}

D. \begin{cases} x = 4 \ y = 3 \end{cases}

Correct Answer: A

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Question 3

Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$.

Correct A. f'(x) = \frac{-2x}{$ x^2 + 1 $^2}

B. f'(x) = \frac{2x}{$ x^2 + 1 $^2}

C. f'(x) = \frac{1}{$ x^2 + 1 $^2}

D. f'(x) = \frac{-1}{$ x^2 + 1 $^2}

Correct Answer: A

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Question 4

Solve the inequality $|2x - 3| > 5$.

Correct A. x < -1 \text{ or } x > 4

B. x < 1 \text{ or } x > 4

C. x < -1 \text{ or } x < 4

D. x > 1 \text{ or } x > 4

Correct Answer: A

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Question 5

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 6

Find the value of $ int_{0}^{1} \frac{1}{x^2 + 1} dx $ u\sing the method of substitution.

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{6}

D. \frac{\pi}{8}

Correct Answer: A

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Question 7

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

Correct A. \left$ -\infty, \frac{3}{2} \right $ \cup \left$ 1, \infty \right $

B. \left$ -\infty, -1 \right $ \cup \left$ 2, \infty \right $

C. \left$ -\infty, -2 \right $ \cup \left$ 3, \infty \right $

D. \left$ -\infty, -3 \right $ \cup \left$ 4, \infty \right $

Correct Answer: A

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Question 8

Find the equation of the \tangent line to the curve $ y = x^2 + 2x - 3 $ at the point ( (1, 2) ).

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 9

Solve the system of equations $ x + y = 2 $ and $ xy = 1 $.

Correct A. \left$ 1, 1 \right $

B. \left$ -1, -1 \right $

C. \left$ 1, -1 \right $

D. \left$ -1, 1 \right $

Correct Answer: A

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Question 10

Find the area under the curve $ y = x^3 - 6x^2 + 9x + 2 $ from $ x = 0 $ to $ x = 2 $.

A. 14

B. 16

Correct C. 18

D. 20

Correct Answer: C

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Question 11

Find the derivative of ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.

A. $ \frac{-1}{2}x^{-\frac{3}{2}} $

B. $ \frac{1}{2}x^{-\frac{1}{2}} $

Correct C. $ -\frac{1}{2}x^{-\frac{3}{2}} $

D. $ \frac{1}{2}x^{-\frac{3}{2}} $

Correct Answer: C

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Question 12

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 between 60 and 90?

Correct A. 0.8413

B. 0.8413

C. 0.8413

D. 0.8413

Correct Answer: A

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Question 13

Find the vector ( mathbf{v} ) such that $ mathbf{v} cdot mathbf{i} = 3 $, $ mathbf{v} cdot mathbf{j} = -4 $, and $ mathbf{v} cdot mathbf{k} = 5 $.

Correct A. $ mathbf{v} = 3mathbf{i} - 4mathbf{j} + 5mathbf{k} $

B. $ mathbf{v} = 3mathbf{i} + 4mathbf{j} - 5mathbf{k} $

C. $ mathbf{v} = -3mathbf{i} - 4mathbf{j} + 5mathbf{k} $

D. $ mathbf{v} = 3mathbf{i} - 4mathbf{j} - 5mathbf{k} $

Correct Answer: A

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Question 14

Solve the equation $ 2^x + 2^{-x} = 12 $ for ( x ).

Correct A. $ x = \log_2 3 $

B. $ x = \log_2 4 $

C. $ x = \log_2 6 $

D. $ x = \log_2 8 $

Correct Answer: A

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Question 15

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

A. $ \frac{1}{2} $

B. $ \frac{1}{3} $

C. $ \frac{2}{3} $

Correct D. $ \frac{1}{6} $

Correct Answer: D

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Question 16

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

A. 12143

Correct B. 12145

C. 12147

D. 12149

Correct Answer: B

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Question 17

A solid sphere of radius 4 cm is inscribed in a cube. Find the volume of the sphere.

Correct A. 268.08

B. 268.1

C. 268.12

D. 268.14

Correct Answer: A

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Question 18

Solve the matrix equation AX = B, where A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}, X = \begin{bmatrix} x \ y \end{bmatrix}, and B = \begin{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 19

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

A. 10

B. 100

Correct C. 1000

D. 10000

Correct Answer: C

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Question 20

A circle has a diameter of 10 cm. Find the area of the circle.

Correct A. 78.5

B. 78.55

C. 78.6

D. 78.65

Correct Answer: A

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Question 21

A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of the university students.

Correct A. 170.5 cm, 179.5 cm

B. 172.5 cm, 177.5 cm

C. 174.5 cm, 175.5 cm

D. 176.5 cm, 173.5 cm

Correct Answer: A

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Question 22

In the diagram below, the circle with center O passes through points A, B, and C. If the radius of the circle is 10 cm, calculate the area of triangle ABC.

A. 50 cm^2

B. 75 cm^2

Correct C. 100 cm^2

D. 125 cm^2

Correct Answer: C

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Question 23

Solve the inequality $x^2 + 4x - 5 > 0$.

Correct A. $x < -5$ or $x > 1$

B. $x < -1$ or $x > 5$

C. $x < 1$ or $x > 5$

D. $x < -5$ or $x < 1$

Correct Answer: A

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Question 24

A rec\tangular garden measures 15 m by 8 m. If a path that is 2 m wide is built around the garden, what is the area of the path?

A. 48 m^2

B. 64 m^2

Correct C. 80 m^2

D. 96 m^2

Correct Answer: C

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Question 25

If $x^2 - 6x + 8 = 0$, solve for x.

Correct A. $x = 2$ or $x = 4$

B. $x = 1$ or $x = 8$

C. $x = 3$ or $x = 5$

D. $x = 6$ or $x = 9$

Correct Answer: A

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