POST UTME CALEB UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A matrix ( A ) is defined as \( A = egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} \). Find the determinant of ( A ).
A. 5
B. 3
C. 2
D. 1
Question 2
A histogram of exam scores is shown below. What is the mean score of the exam?
A. 60
B. 70
C. 80
D. 90
Question 3
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x + 2
D. y = x - 2
Question 4
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.
A. 72
B. 48
C. 24
D. 12
Question 5
Find the area of the triangle with vertices ( A(1, 2), B(3, 4), C(2, 1) ).
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. \( \frac{1}{2} \times 3 \times 4 \)
Question 6
Find the derivative of the function [ f(x) = \frac{1}{x^2 + 1} \].
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}
Question 7
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. \( 2 \sin x \cos x \)
B. \( \cos x \)
C. \( \sin x \)
D. \( \cos^2 x \)
Question 8
Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A. 6x + 2
B. 3x^2 + 2
C. 6x - 2
D. 3x^2 - 2
Question 9
Solve the system of equations u\sing matrices:\n\n\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \( x = 2, y = 3 \)
B. \( x = 3, y = 2 \)
C. \( x = 4, y = 5 \)
D. \( x = 5, y = 4 \)
Question 10
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the Chain Rule.
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} )
Question 11
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
D. 0.5
Question 12
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 6
B. 8
C. 10
D. 12
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
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. \( \frac{1}{2} \times 4^3 + 3 \times 4 - 2 \times 4 \)
Question 14
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x^2 + y^2 + 4x - 6y + 5 = 0 \)
B. \( x^2 + y^2 - 4x + 6y + 5 = 0 \)
C. \( x^2 + y^2 + 4x + 6y + 5 = 0 \)
D. \( x^2 + y^2 - 4x - 6y + 5 = 0 \)
Question 15
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for \( x \).
A. \( x = \frac{\pi}{2} \)
B. \( x = \frac{\pi}{4} \)
C. \( x = \frac{3\pi}{4} \)
D. \( x = \frac{5\pi}{4} \)

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: