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POST UTME CALEB UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details

Find the value of x in the equation $$12x \$ = $\frac{1}{2}$\) ) 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

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Question 2 View Details

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

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Question 3 View Details

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

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Question 4 View Details

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

Correct A. ( f'$(x) = 2xcos$$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

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Question 5 View Details

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

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Question 6 View Details

In the diagram below, the graph of $y = \frac{1}{2} $12x$ is shown. What is the amplitude of the function?

A. 1

Correct B. 0.5

C. 2

D. 4

Correct Answer: B

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Question 7 View Details

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

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Question 8 View Details

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

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Question 9 View Details

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

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Question 10 View Details

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

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Question 11 View Details

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

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Question 12 View Details

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

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Question 13 View Details

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

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Question 14 View Details

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

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Question 15 View Details

Find the equation of the line passing 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

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Question 16 View Details

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

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Question 17 View Details

A sequence is defined as [ (a_$n = 2n + 1$\) \] for [ \$(a_n = 2n + 1) \(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

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Question 18 View Details

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

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Question 19 View Details

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

A. 30

B. 35

Correct C. 40

D. 45

Correct Answer: C

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Question 20 View Details

Two events are independent 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 independent?

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

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Question 21 View Details

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

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Question 22 View Details

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

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Question 23 View Details

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 24 View Details

A rectangular 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

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Question 25 View Details

Solve the inequality $2x - 5 > 3$.

Correct A. $x > 4$

B. $x < 4$

C. $x > 2$

D. $x < 2$

Correct Answer: A

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