Exam Body

Year

Subject

Paper Type

POST UTME CALEB UNIVERSITY 2022 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 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the value of x in the equation \( \sin\( 2x \ \) = \frac{1}{2} ) given that ( 0 leq x leq 2pi ).

Correct A. \( \frac{pi}{6} \)

B. \( \frac{pi}{4} \)

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

D. \( \frac{pi}{2} \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 2

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

Correct A. \( \frac{64}{3} \)

B. \( \frac{32}{3} \)

C. \( \frac{16}{3} \)

D. \( \frac{8}{3} \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 3

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

Correct A. \( x = 1, y = 2 \)

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

C. \( x = 3, y = 4 \)

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

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 4

Find the derivative of the function ( f(x) = \sin\( x^2 \) ).

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

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

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

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

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 5

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. \( x-4 \ \)^2 + \( y-5 \)^2 = 16 )

D. \( x-5 \ \)^2 + \( y-4 \)^2 = 16 )

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 6

In the diagram below, the graph of \( y = \frac{1}{2} \sin 2x \) is shown. What is the amplitude of the function?

A. 1

Correct B. 0.5

C. 2

D. 4

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 7

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

Correct A. \( x < -3 \) or \( x > 1 \)

B. \( x < -3 \) or \( x < 1 \)

C. \( x > -3 \) or \( x > 1 \)

D. \( x < -3 \) or \( x < 1 \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 8

A bag contains 5 red marbles, 8 blue marbles, and 12 green marbles. If a marble is drawn at random, what is the probability that it is not blue?

A. \( \frac{1}{3} \)

B. \( \frac{2}{5} \)

Correct C. \( \frac{3}{5} \)

D. \( \frac{4}{5} \)

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 9

Solve the equation \( x^2 + 4x - 5 = 0 \).

Correct A. \( x = -5 \) or \( x = 1 \)

B. \( x = -1 \) or \( x = 5 \)

C. \( x = -5 \) or \( x = -1 \)

D. \( x = 1 \) or \( x = 5 \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 10

A company produces 200 units of a product per day. If the production rate is increased by 20%, what is the new production rate?

Correct A. 240 units/day

B. 220 units/day

C. 200 units/day

D. 180 units/day

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 11

Find the equation of the circle with center at ((2,3)) and radius (5).

Correct A. \( x^2 + y^2 - 4x + 6y + 9 = 0 \)

B. \( x^2 + y^2 + 4x - 6y + 9 = 0 \)

C. \( x^2 + y^2 - 4x - 6y + 9 = 0 \)

D. \( x^2 + y^2 + 4x + 6y + 9 = 0 \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 12

Solve the inequality \( |x - 2| > 3 \).

Correct A. \( x < -1 \text{ or } x > 5 \)

B. \( x < 1 \text{ or } x > 5 \)

C. \( x < -1 \text{ or } x > 2 \)

D. \( x < 1 \text{ or } x > 2 \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 13

Find the value of (x) in the equation \( x^2 + 2x - 6 = 0 \).

Correct A. \( x = -3 \)

B. \( x = 2 \)

C. \( x = -2 \)

D. \( x = 3 \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 14

A survey of 50 students found that 30 students preferred Mathematics, 20 students preferred Science, and 10 students preferred both subjects. What is the probability that a randomly selected student prefers Mathematics?

Correct A. \( \frac{3}{5} \)

B. \( \frac{2}{5} \)

C. \( \frac{1}{5} \)

D. \( \frac{4}{5} \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 15

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

Correct A. \( y = \frac{1}{2}x + \frac{1}{2} \)

B. \( y = \frac{1}{2}x - \frac{1}{2} \)

C. \( y = 2x - 1 \)

D. \( y = 2x + 1 \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 16

Determine the value of the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].

A. -1

B. 1

Correct C. 0

D. 2

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 17

A sequence is defined as [ a_n = 2n + 1 \] for [ n = 1, 2, 3, \ldots \]. Find the sum of the first five terms of the sequence.

A. 55

Correct B. 60

C. 65

D. 70

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 18

A set of three vectors is given by [ \mathbf{a} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}, \mathbf{b} = \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}, \mathbf{c} = \begin{pmatrix} 7 \ 8 \ 9 \end{pmatrix}. \] Find the cross product of vectors [ \mathbf{a} \times \mathbf{b} \].

Correct A. \begin{pmatrix} -3 \\ 6 \\ -3 \end{pmatrix}

B. \begin{pmatrix} 3 \\ -6 \\ 3 \end{pmatrix}

C. \begin{pmatrix} 6 \\ -3 \\ -6 \end{pmatrix}

D. \begin{pmatrix} -6 \\ 3 \\ 6 \end{pmatrix}

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 19

A histogram is given below. Find the mean of the data set.

A. 30

B. 35

Correct C. 40

D. 45

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 20

Two events are indep\endent if the occurrence or non-occurrence of one does not affect the probability of the occurrence of the other. Which of the following events are indep\endent?

Correct A. Event A and Event B

B. Event A and Event C

C. Event B and Event C

D. Event A, Event B, and Event C

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 21

Find the value of x in the equation \( 2x^2 + 5x - 3 = 0 \).

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 22

A circle with center (0, 0) and radius 4 passes through which of the following points?

Correct A. (3, 4)

B. (4, 3)

C. \( -3, -4 \)

D. \( -4, -3 \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 23

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 24

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

Correct A. 72

B. 48

C. 24

D. 12

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 25

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

Correct A. x > 4

B. x < 4

C. x > 2

D. x < 2

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows

Help others prepare! Share this practice hub:

Chat with Support