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POST UTME COVENANT UNIVERSITY 2021 Mathematics | Objective

Are you preparing for POST UTME COVENANT UNIVERSITY 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 $\int_{0}^{\pi} \frac{1}{1+\sin^2(x)} dx$.

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

A survey of 100 students found that 40 students preferred Mathematics, 30 preferred Science, and 30 preferred both. What is the probability that a randomly selected student prefers Mathematics or Science?

Correct A. 0.7

B. 0.6

C. 0.5

D. 0.4

Correct Answer: A

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Question 3

In a geometric sequence, the first term is 2 and the common ratio is 3. Find the sum of the first five terms.

Correct A. 2+6+18+54+162

B. 2+6+18+54+162+486

C. 2+6+18+54+162+486+1458

D. 2+6+18+54+162+486+1458+4374

Correct Answer: A

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Question 4

A right circular cone has a height of 10 cm and a base radius of 5 cm. Find the volume of the cone.

Correct A. 250\pi

B. 500\pi

C. 750\pi

D. 1000\pi

Correct Answer: A

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Question 5

Find the area under the curve $y = x^2$ from $x = 0$ to $x = 2$.

Correct A. \frac{8}{3}

B. \frac{16}{3}

C. \frac{32}{3}

D. \frac{64}{3}

Correct Answer: A

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Question 6

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.

Correct A. ( f'(x) = \frac{x}{$ 1 - x^2 $^{3/2}} )

B. ( f'(x) = \frac{-x}{$ 1 - x^2 $^{3/2}} )

C. ( f'(x) = \frac{1}{$ 1 - x^2 $^{3/2}} )

D. ( f'(x) = \frac{-1}{$ 1 - x^2 $^{3/2}} )

Correct Answer: A

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Question 7

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

A. $ \frac{1}{6} $

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

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

D. $ \frac{5}{6} $

Correct Answer: B

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Question 8

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 9

Find the area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 2 $.

Correct A. $ \frac{8}{3} $

B. $ \frac{16}{3} $

C. $ \frac{32}{3} $

D. $ \frac{64}{3} $

Correct Answer: A

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Question 10

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

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

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

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

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

Correct Answer: A

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Question 11

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{pmatrix} ].

A. 0

B. -1

Correct C. 1

D. 2

Correct Answer: C

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Question 12

Solve the system of linear equations [ egin{cases} x + 2y - 3z = 7 \ 2x - 3y + z = -2 \ 3x + y + 2z = 5 \end{cases} ].

Correct A. \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}

B. \begin{pmatrix} 2 \ -1 \ 1 \end{pmatrix}

C. \begin{pmatrix} 3 \ 1 \ -2 \end{pmatrix}

D. \begin{pmatrix} 4 \ 2 \ -1 \end{pmatrix}

Correct Answer: A

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Question 13

Find the derivative of the function [ f(x) = \frac{1}{x^2 + 1} \] u\sing the chain rule.

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

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

C. \frac{1}{$ x^2 + 1 $^2}

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

Correct Answer: A

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Question 14

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \frac{1}{6}

B. \frac{2}{6}

C. \frac{3}{6}

Correct D. \frac{4}{6}

Correct Answer: D

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Question 15

Solve the quadratic equation [ x^2 + 5x + 6 = 0 \].

Correct A. \begin{pmatrix} -2 \ -3 \end{pmatrix}

B. \begin{pmatrix} -3 \ -2 \end{pmatrix}

C. \begin{pmatrix} 2 \ 3 \end{pmatrix}

D. \begin{pmatrix} 3 \ 2 \end{pmatrix}

Correct Answer: A

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Question 16

Determine the value of $x$ in the equation $2^x + 5^x = 7^x$.

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 17

Find the area under the curve $y = x^2 + 2x + 1$ from $x = 0$ to $x = 2$.

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 18

A set of 10 numbers has a mean of 20 and a s\tandard deviation of 5. Find the probability that a randomly selected number from the set is greater than 25.

A. 0.05

Correct B. 0.10

C. 0.15

D. 0.20

Correct Answer: B

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Question 19

Find the volume of the solid formed by revolving the region bounded by the curve $y = x^2$ and the line $x = 2$ about the x-axis.

A. 32\pi

Correct B. 64\pi

C. 128\pi

D. 256\pi

Correct Answer: B

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Question 20

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

A. 25\pi

Correct B. 50\pi

C. 75\pi

D. 100\pi

Correct Answer: B

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Question 21

A survey of 1000 students revealed that 60% of them preferred Mathematics as their favorite subject, while 40% preferred English Language. If 10% of the students who preferred Mathematics also preferred English Language, what is the probability that a randomly selected student who prefers Mathematics also prefers English Language?

Correct A. 0.1

B. 0.2

C. 0.3

D. 0.4

Correct Answer: A

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Question 22

A cylindrical \tank has a height of 10m and a radius of 4m. If the \tank is filled with water to a height of 8m, what is the volume of water in the \tank?

A. 2000π

Correct B. 2500π

C. 3000π

D. 3500π

Correct Answer: B

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Question 23

A polynomial function f(x) = ax^3 + bx^2 + cx + d has roots at x = -2, x = 1, and x = 3. If f$ -1 $ = 10, find the value of f(2).

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 24

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected student scored above 70?

A. 0.1

B. 0.2

Correct C. 0.3

D. 0.4

Correct Answer: C

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Question 25

A circuit consists of a 12V battery, a 4Ω resistor, and a 6Ω resistor connected in series. If the current through the circuit is 2A, what is the voltage across the 6Ω resistor?

A. 8V

Correct B. 10V

C. 12V

D. 14V

Correct Answer: B

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