POST UTME CALEB UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A particle moves along the x-axis with a velocity given by $v(t) = 2t^2 - 5t + 1$. Find the acceleration of the particle at $t = 2s$.
A. -3m/s^2
B. -2m/s^2
C. -1m/s^2
D. 1m/s^2
Question 2
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 3
Find the sum of the first 10 terms of the geometric series 2, 6, 18, ...
A. 1023
B. 1024
C. 1025
D. 1026
Question 4
Solve the equation \( x^2 + 4x - 5 = 0 \).
A. \( x = -5 \) or \( x = 1 \)
B. \( x = -1 \) or \( x = 5 \)
C. \( x = -5 \) or \( x = -1 \)
D. \( x = 1 \) or \( x = 5 \)
Question 5
Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$ u\sing the quotient rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{-2}{\( x^2 + 1 \)^2}
C. \frac{2x}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 6
Solve the inequality \( 2x - 5 > 3 \).
A. x > 4
B. x < 4
C. x > 2
D. x < 2
Question 7
A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the number on the die is even, the coin is flipped twice. If the number on the die is odd, the coin is flipped once. What is the probability that the number of heads obtained is odd?
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{2}{3}
Question 8
Determine the value of $\lim_{x\to 0} \frac{\sin^2 x}{x^2}$ u\sing L'Hopital's rule.
A. 1
B. 0
C. \frac{1}{2}
D. \frac{2}{3}
Question 9
Find the value of x in the equation \( 2x^2 + 5x - 3 = 0 \).
A. 1
B. -1
C. 2
D. -2
Question 10
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?
A. 72
B. 48
C. 24
D. 12
Question 11
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 12
Solve the inequality $|x - 2| > 3$.
A. \( -\infty, -1 \) \cup \( 4, \infty \)
B. \( -\infty, 1 \) \cup \( 2, \infty \)
C. \( -\infty, 4 \) \cup \( 2, \infty \)
D. \( -\infty, 1 \) \cup \( 4, \infty \)
Question 13
Find the area under the curve \( y = x^2 \) from x = 0 to x = 4.
A. 64
B. 32
C. 16
D. 8
Question 14
Determine the value of $x$ in the equation $2^x + 5^x = 3^x + 7^x$.
A. 1
B. 2
C. 3
D. 4
Question 15
A circle with center (0, 0) and radius 4 passes through which of the following points?
A. (3, 4)
B. (4, 3)
C. \( -3, -4 \)
D. \( -4, -3 \)

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