Exam Body

Year

Subject

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POST UTME CALEB UNIVERSITY 2021 Mathematics | Objective

Are you preparing for POST UTME CALEB 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

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

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)

D. \( \frac{1}{2} \times 4^3 + 3 \times 4 - 2 \times 4 \)

Correct Answer: A

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Question 2

Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) u\sing the Rational Root Theorem.

A. \( x = 1 \)

B. \( x = 2 \)

Correct C. \( x = 3 \)

D. \( x = 4 \)

Correct Answer: C

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Question 3

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

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

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

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

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

Correct Answer: A

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Question 4

Solve the system of equations u\sing matrices:\n\n\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).

Correct A. \( x = 2, y = 3 \)

B. \( x = 3, y = 2 \)

C. \( x = 4, y = 5 \)

D. \( x = 5, y = 4 \)

Correct Answer: A

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Question 5

Find the area of the triangle with vertices ( A(1, 2), B(3, 4), C(2, 1) ).

Correct A. \( \frac{1}{2} \times 2 \times 3 \)

B. \( \frac{1}{2} \times 3 \times 2 \)

C. \( \frac{1}{2} \times 2 \times 4 \)

D. \( \frac{1}{2} \times 3 \times 4 \)

Correct Answer: A

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Question 6

Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 7

Find the volume of the frustum of a cone with radii 6 cm and 4 cm and height 10 cm.

A. 120\pi

B. 150\pi

Correct C. 180\pi

D. 200\pi

Correct Answer: C

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Question 8

Solve the inequality \( x^2 - 6x + 8 > 0 \).

A. x < 2

Correct B. x > 2

C. x < 4

D. x > 4

Correct Answer: B

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Question 9

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 10

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

A. x = \frac{\pi}{2}

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

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

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

Correct Answer: B

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Question 11

Find the determinant of the matrix [ egin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{pmatrix} ].

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 12

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

Correct A. x = \frac{\pi}{2}

B. x = \frac{3\pi}{2}

C. x = \pi

D. x = 0

Correct Answer: A

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Question 13

A random experiment has two indep\endent events [ A \] and [ B \]. If [ P(A) = \frac{1}{2} \] and [ P(B) = \frac{1}{3} \], find [ P\( A \cap B \) \].

Correct A. \frac{1}{6}

B. \frac{1}{3}

C. \frac{1}{2}

D. 1

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

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

D. \( x - 3 \)^2 + \( y - 2 \)^2 = 9

Correct Answer: A

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Question 15

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 16

A random sample of 25 students from a population of 1000 students has a mean height of 170 cm with a s\tandard deviation of 5 cm. Calculate the probability that the sample mean height of a new random sample of 20 students will be less than 165 cm.

A. 0.001

B. 0.01

C. 0.1

Correct D. 0.5

Correct Answer: D

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Question 17

Solve the following system of linear equations u\sing matrices:

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

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

Correct C. \begin{bmatrix} 5 \\ 11 \end{bmatrix}

D. \begin{bmatrix} 7 \\ 13 \end{bmatrix}

Correct Answer: C

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Question 18

Find the area under the curve y = x^2 from x = 0 to x = 4.

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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Question 19

Find the derivative of the function f(x) = 3x^2 + 2x - 5.

Correct A. 6x + 2

B. 3x^2 + 2

C. 6x - 2

D. 3x^2 - 2

Correct Answer: A

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Question 20

A rec\tangular box has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the volume of the box.

Correct A. 72

B. 48

C. 24

D. 12

Correct Answer: A

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Question 21

Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for \( x in \( -infty, -2 \ \) cup \( -2, infty \) ).

A. \( -2, -1 \) ∪ (1, ∞)

Correct B. \( -∞, -2 \) ∪ \( -1, 1 \) ∪ (1, ∞)

C. \( -∞, -2 \) ∪ (1, ∞)

D. \( -2, -1 \) ∪ (1, ∞)

Correct Answer: B

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Question 22

A matrix ( A ) is defined as \( A = egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} \). Find the determinant of ( A ).

Correct A. 5

B. 3

C. 2

D. 1

Correct Answer: A

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Question 23

A histogram of exam scores is shown below. What is the mean score of the exam?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 24

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

Correct A. \( 2 \sin x \cos x \)

B. \( \cos x \)

C. \( \sin x \)

D. \( \cos^2 x \)

Correct Answer: A

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Question 25

A quadratic equation is defined as \( x^2 + 4x + 4 = 0 \). Find the roots of the equation.

Correct A. \( -2, 0 \)

B. \( -1, 1 \)

C. (0, 2)

D. \( -1, -1 \)

Correct Answer: A

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