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POST UTME COVENANT UNIVERSITY 2018 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 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Determine the value of $x$ in the equation [ egin{pmatrix} 2 & 1 \ 3 & 2 \end{pmatrix} egin{pmatrix} x \ 1 \end{pmatrix} = egin{pmatrix} 5 \ 8 \end{pmatrix} ].

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 2

A set $S$ contains the elements $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$. If $T$ is a subset of $S$ such that $T$ contains the elements of $S$ that are greater than $5$, what is the number of elements in $T$?

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 3

The sequence $\{a_n\}$ is defined by $a_n = 2n + 1$ for $n = 1, 2, 3, \dots$. Find the sum of the first five terms of the sequence.

A. 30

B. 35

Correct C. 40

D. 45

Correct Answer: C

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Question 4

Solve the inequality $\frac{x}{2} + 3 > 7$.

Correct A. x > 8

B. x < 8

C. x > 2

D. x < 2

Correct Answer: A

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Question 5

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

A. 2

B. 4

Correct C. 8

D. 16

Correct Answer: C

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Question 6

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

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

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

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

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

Correct Answer: A

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Question 7

Solve the equation $ x^2 + 4x + 4 = 0 $ u\sing the quadratic formula.

A. \frac{-4 \pm \sqrt{16 - 16}}{2}

B. \frac{-4 \pm \sqrt{16 + 16}}{2}

Correct C. \frac{-4 \pm \sqrt{16 - 4}}{2}

D. \frac{-4 \pm \sqrt{16 + 4}}{2}

Correct Answer: C

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Question 8

Find the area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 2 $ u\sing integration.

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 9

Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ) u\sing the s\tandard form.

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

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

C. $ x - 2 $^2 + $ y - 3 $^2 = 9

D. $ x - 2 $^2 + $ y - 3 $^2 = 25

Correct Answer: A

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Question 10

Find the derivative of the function ( f(x) = \sin$ x^2 $ ) u\sing the chain rule.

Correct A. f'(x) = 2x \cos$ x^2 $

B. f'(x) = -2x \cos$ x^2 $

C. f'(x) = x^2 \cos$ x^2 $

D. f'(x) = -x^2 \cos$ x^2 $

Correct Answer: A

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Question 11

Find the area under the curve $ y = \frac{1}{2}x^2 + 2x - 3 $ from $ x = 0 $ to $ x = 4 $.

A. 24

B. 36

Correct C. 48

D. 60

Correct Answer: C

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Question 12

Solve the system of linear equations u\sing matrices: $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} $.

Correct A. [1, 2]

B. [2, 3]

C. [3, 4]

D. [4, 5]

Correct Answer: A

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Question 13

Find the probability of drawing two cards from a deck of 52 cards such that the second card drawn is a heart given that the first card drawn is a heart.

Correct A. 1/3

B. 1/4

C. 1/5

D. 1/6

Correct Answer: A

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Question 14

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

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = 3x - 2

D. y = 3x + 2

Correct Answer: A

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Question 15

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 16

Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 17

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

A. 10

B. 100

Correct C. 1000

D. 10000

Correct Answer: C

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Question 18

A particle moves along the curve $y = x^3 - 6x^2 + 9x + 2$ with a velocity of $\frac{dy}{dt} = 6x^2 - 12x + 9$. Find the acceleration of the particle at the point where $x = 1$.

A. 18

B. 36

Correct C. 54

D. 72

Correct Answer: C

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Question 19

Find the area of the region bounded by the curves $y = x^2$ and $y = 4 - x^2$.

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 20

Solve the equation $\frac{dy}{dx} = \frac{x^2 + 1}{x^2 - 1}$ for $y$.

Correct A. y = \frac{1}{2} \log $ x^2 - 1 $ + C

B. y = \frac{1}{2} \log $ x^2 + 1 $ + C

C. y = \frac{1}{2} \log $ x^2 - 1 $ - C

D. y = \frac{1}{2} \log $ x^2 + 1 $ - C

Correct Answer: A

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Question 21

Let A be a 3x3 matrix with determinant 6. If A is multiplied by a scalar k, what is the determinant of kA?

Correct A. 6k^3

B. 6k

C. 6

D. 6k^2

Correct Answer: A

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Question 22

A polynomial P(x) has roots at x = -2, x = 1, and x = 3. What is the polynomial P(x) in factored form?

Correct A. $ x + 2 $$ x - 1 $$ x - 3 $

B. $ x - 2 $$ x + 1 $$ x - 3 $

C. $ x + 2 $$ x + 1 $$ x - 3 $

D. $ x - 2 $$ x - 1 $$ x + 3 $

Correct Answer: A

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Question 23

A set A contains the elements {1, 2, 3, 4, 5}. What is the number of subsets of A that contain exactly 3 elements?

Correct A. 10

B. 20

C. 30

D. 40

Correct Answer: A

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Question 24

A sequence is defined by the formula a_n = 2n + 1. What is the sum of the first 5 terms of the sequence?

Correct A. 15

B. 20

C. 25

D. 30

Correct Answer: A

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Question 25

A histogram is shown below. What is the mean of the data represented by the histogram?

A. 20

Correct B. 25

C. 30

D. 35

Correct Answer: B

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