POST UTME CALEB UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( |x - 2| > 3 \).
A. \( x < -1 \text{ or } x > 5 \)
B. \( x < 1 \text{ or } x > 5 \)
C. \( x < -1 \text{ or } x > 2 \)
D. \( x < 1 \text{ or } x > 2 \)
Question 2
In the diagram below, the graph of \( y = \frac{1}{2} \sin 2x \) is shown. What is the amplitude of the function?
A. 1
B. 0.5
C. 2
D. 4
Question 3
A particle moves along the curve y = x^2 + 2x + 1. Find the equation of the \tangent line at the point where x = -1.
A. y = -2x + 3
B. y = -2x - 3
C. y = 2x + 3
D. y = 2x - 3
Question 4
Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.
A. 64\pi cm^3
B. 128\pi cm^3
C. 256\pi cm^3
D. 512\pi cm^3
Question 5
Find the equation of the circle with center ( (2,3) ) and radius ( 4 ).
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 )
Question 6
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?
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
Question 7
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} \].
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}
Question 8
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 90?
A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6915
Question 9
A cylindrical \tank has a height of 10m and a radius of 4m. Water is pumped into the \tank at a rate of 2m^3/min. Find the rate at which the water level is ri\sing when the water level is 6m.
A. 0.05m/min
B. 0.1m/min
C. 0.15m/min
D. 0.2m/min
Question 10
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -3 \) or \( x > 1 \)
B. \( x < -3 \) or \( x < 1 \)
C. \( x > -3 \) or \( x > 1 \)
D. \( x < -3 \) or \( x < 1 \)
Question 11
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. \( \frac{2}{5} \)
C. \( \frac{3}{5} \)
D. \( \frac{4}{5} \)
Question 12
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?
A. \( \frac{3}{5} \)
B. \( \frac{2}{5} \)
C. \( \frac{1}{5} \)
D. \( \frac{4}{5} \)
Question 13
A company produces two products, A and B. The profit from the sale of product A is $₦100 per unit, and the profit from the sale of product B is $₦150 per unit. If the company produces 500 units of product A and 300 units of product B, what is the total profit?
A. ₦150,000
B. ₦175,000
C. ₦200,000
D. ₦225,000
Question 14
Find the equation of the circle with center at ((2,3)) and radius (5).
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. \( x^2 + y^2 + 4x + 6y + 9 = 0 \)
Question 15
Solve the system of equations \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 3 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 5 \)

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