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POST UTME COVENANT UNIVERSITY 2022 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 2022 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 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 32\pi

Correct B. 48\pi

C. 64\pi

D. 80\pi

Correct Answer: B

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Question 2

If $ f(x) = 3x^2 + 2x - 5 $ and $ g(x) = 2x^2 - 3x + 1 $, find the derivative of $ f(g(x)) $ u\sing the chain rule.

Correct A. 6x^3 + 10x^2 - 13x + 3

B. 6x^3 + 10x^2 - 13x - 3

C. 6x^3 + 10x^2 + 13x + 3

D. 6x^3 + 10x^2 - 13x - 1

Correct Answer: A

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Question 3

Solve the system of equations u\sing matrices: \begin{align*} 2x + 3y &= 7 \ 4x - 2y &= -2 \end{align*}

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ 1 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 4

A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 7?

A. \frac{1}{6}

B. \frac{1}{12}

Correct C. \frac{1}{36}

D. \frac{1}{18}

Correct Answer: C

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Question 5

Convert the decimal number 0.375 to a \fraction in its simplest form.

A. \frac{1}{4}

B. \frac{1}{8}

Correct C. \frac{3}{8}

D. \frac{3}{4}

Correct Answer: C

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Question 6

Find the equation of the line pas\sing through the points ( P(2,3) ) and ( Q(4,5) ).

A. $ y = x + 1 $

B. $ y = x - 1 $

Correct C. $ y = 2x - 1 $

D. $ y = 2x + 1 $

Correct Answer: C

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Question 7

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 8

Find the derivative of the function ( f(x) = 3x^2 - 2x + 1 ) u\sing the chain rule.

Correct A. ( f'(x) = 6x - 2 )

B. ( f'(x) = 6x + 2 )

C. ( f'(x) = 6x^2 - 2 )

D. ( f'(x) = 6x^2 + 2 )

Correct Answer: A

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Question 9

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

Correct A. $ x = 2, y = 2 $

B. $ x = 2, y = 6 $

C. $ x = 6, y = 2 $

D. $ x = 6, y = 6 $

Correct Answer: A

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Question 10

Find the equation of the circle with center ( C(2,3) ) and radius $ r = 4 $.

Correct A. $ x - 2 \ $^2 + $ y - 3 $^2 = 16 )

B. $ x - 2 \ $^2 + $ y - 3 $^2 = 4 )

C. $ x - 3 \ $^2 + $ y - 2 $^2 = 16 )

D. $ x - 3 \ $^2 + $ y - 2 $^2 = 4 )

Correct Answer: A

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Question 11

In the diagram below, the vector µA = 2i + 3j and vector µB = i - 2j. What is the magnitude of the resul\tant vector µA + µB?

A. 1.0

B. 3.0

Correct C. 5.0

D. 7.0

Correct Answer: C

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Question 12

If the equation of a circle is x^2 + y^2 + 4x - 6y - 12 = 0, find the radius of the circle.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 13

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is the volume of the prism?

Correct A. 72

B. 80

C. 88

D. 96

Correct Answer: A

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Question 14

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

A. x < -1

B. x > -1

Correct C. x < 1

D. x > 1

Correct Answer: C

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Question 15

Find the equation of the line pas\sing through the points (2, 3) and (4, 5).

A. y = 2x - 1

Correct B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: B

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Question 16

In the polynomial $p(x) = 3x^4 - 2x^3 + 5x^2 - x + 1$, find the value of $p$ -1 $$ u\sing the Remainder Theorem.

Correct A. 11

B. 13

C. 15

D. 17

Correct Answer: A

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Question 17

A circle has equation $x^2 + y^2 + 4x - 6y - 12 = 0$. Find the coordinates of the center of the circle.

Correct A. $ 2, -3 $

B. $ -2, 3 $

C. (3, 2)

D. $ -3, -2 $

Correct Answer: A

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Question 18

Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 19

A number is represented in base 8 as 1234. What is the value of this number in base 10?

A. 512

B. 768

Correct C. 1024

D. 1280

Correct Answer: C

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Question 20

A rec\tangular prism has dimensions 5 cm, 6 cm, and 7 cm. Find the volume of the prism.

Correct A. 210

B. 240

C. 270

D. 300

Correct Answer: A

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Question 21

Determine the value of $\frac{1}{2} \log_{10} $ x^2 $ = 4$.

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 22

Solve for $x$ in the equation $\begin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = 0$.

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 23

Find the equation of the line pas\sing through the points $(2,3)$ and $(4,5)$.

A. y = 2x - 1

Correct B. y = 2x + 1

C. y = x + 1

D. y = x - 1

Correct Answer: B

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Question 24

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

Correct A. $ -∞, -1 $ ∪ (5, ∞)

B. $ -∞, 1 $ ∪ (5, ∞)

C. $ -∞, -1 $ ∪ (2, 5)

D. $ -∞, 1 $ ∪ (2, 5)

Correct Answer: A

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Question 25

Find the value of $\sin(2x)$ given that $\sin(x) = \frac{3}{5}$ and $\cos(x) = \frac{4}{5}$.

Correct A. \frac{24}{25}

B. \frac{24}{25}

C. \frac{24}{25}

D. \frac{24}{25}

Correct Answer: A

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