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POST UTME COVENANT UNIVERSITY 2017 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 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

In a certain number base, the number 1011 is equivalent to 11 in base 10. What is the value of the number base?

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 2

Solve for x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ).

Correct A. \( x = \frac{pi}{4} \)

B. \( x = \frac{pi}{2} \)

C. \( x = \frac{pi}{3} \)

D. \( x = \frac{pi}{6} \)

Correct Answer: A

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Question 3

A polynomial function f(x) has a degree of 3 and a leading coefficient of 2. If f\( -2 \) = -23, find the value of f(1).

Correct A. -5

B. -3

C. -1

D. 1

Correct Answer: A

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Question 4

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is drawn at random, what is the probability that it is not blue?

Correct A. \frac{1}{2}

B. \frac{2}{3}

C. \frac{3}{4}

D. \frac{4}{5}

Correct Answer: A

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Question 5

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is the volume of the prism?

Correct A. 30 cm^3

B. 40 cm^3

C. 50 cm^3

D. 60 cm^3

Correct Answer: A

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Question 6

Determine the volume of the frustum of a cone with a height of 15 cm, a lower base radius of 4 cm, and an upper base radius of 6 cm.

A. 300\pi\text{ cm}^3

B. 400\pi\text{ cm}^3

Correct C. 500\pi\text{ cm}^3

D. 600\pi\text{ cm}^3

Correct Answer: C

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Question 7

Find the area under the curve of the function f(x) = 2x^2 + 3x - 1 from x = 0 to x = 2.

A. 17

Correct B. 19

C. 21

D. 23

Correct Answer: B

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Question 8

A set of 10 consecutive integers has a mean of 12. Find the sum of the integers.

A. 120

B. 130

Correct C. 140

D. 150

Correct Answer: C

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Question 9

Find the surface area of the sphere with a radius of 5 cm.

A. 50\pi\text{ cm}^2

Correct B. 100\pi\text{ cm}^2

C. 150\pi\text{ cm}^2

D. 200\pi\text{ cm}^2

Correct Answer: B

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Question 10

A number is 5 times the sum of its digits. If the number is divisible by 3, what is the sum of its digits?

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 11

Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.

Correct A. \frac{32\pi}{5}

B. \frac{64\pi}{5}

C. \frac{128\pi}{5}

D. \frac{256\pi}{5}

Correct Answer: A

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Question 12

If f(x) = \frac{1}{x^2 + 1}, find f'(x) u\sing the chain rule.

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

B. \frac{2x}{\( x^2 + 1 \)^2}

C. \frac{x}{\( x^2 + 1 \)^2}

D. \frac{2}{\( x^2 + 1 \)^2}

Correct Answer: A

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Question 13

Solve the equation \sin^2 x + \cos^2 x = 1 for x in the interval [0, 2\pi].

Correct A. x = \frac{\pi}{4}

B. x = \frac{3\pi}{4}

C. x = \frac{5\pi}{4}

D. x = \frac{7\pi}{4}

Correct Answer: A

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Question 14

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 = 9

C. \( x - 2 \)^2 + \( y - 3 \)^2 = 25

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 36

Correct Answer: A

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Question 15

A circle has equation x^2 + y^2 = 25. Find the length of the arc intercepted by the line y = x.

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 16

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 17

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 18

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 19

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 20

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

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

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

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

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

Correct Answer: A

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Question 21

Find the area under the curve of ( f(x) = \frac{1}{x^2} ) from \( x = 1 \) to \( x = 2 \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 22

Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 23

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

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 24

A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 25

A matrix is given by \( A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \). Find the determinant of the matrix.

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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