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POST UTME UNN 2021 Mathematics | Objective

Prepare for your exams with POST UTME UNN questions? Reviewing past/model 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.

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Question 1 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the value of \(int_{0}^{1} \frac{1}{x^2 + 1} dx\) using 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 View Details

Solve the inequality \(2x^2 - 5x - 3 > 0\) using 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 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of ( f(x) = \(\frac{1}\){\(\sqrt{x}\)}\) ) using 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 View Details

A histogram of exam scores has a mean of 75 and a standard 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 View Details

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. \(\mathbf{v} = 3\mathbf{i} - 4\mathbf{j} + 5\mathbf{k}\)

B. \(\mathbf{v} = 3\mathbf{i} + 4\mathbf{j} - 5\mathbf{k}\)

C. \(\mathbf{v} = -3\mathbf{i} - 4\mathbf{j} + 5\mathbf{k}\)

D. \(\mathbf{v} = 3\mathbf{i} - 4\mathbf{j} - 5\mathbf{k}\)

Correct Answer: A

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Question 14 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Solve the matrix equation (AX = B\), where A = \begin{bmatrix} 1 & 2 \\\(((AX = B)\), where A = \ 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 View Details

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 View Details

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 View Details

A random sample of 25 students from a university had a mean height of 175 cm with a standard deviation of 5 cm. If the population standard 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 View Details

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 View Details

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 View Details

A rectangular 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 View Details

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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