POST UTME CRAWFORD UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10^4
B. 10^8
C. 10^2
D. 10^6
Question 2
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = -1
C. x = 0
D. x = 1
Question 3
Find the value of x in the equation \( \sin \( 2x \ \) = \frac{1}{2} ).
A. 30
B. 60
C. 90
D. 120
Question 4
Solve the inequality \( 2x - 5 > 3 \).
A. x > 4
B. x < 4
C. x > 2
D. x < 2
Question 5
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 25
C. 35
D. 45
Question 6
Find the value of x in the equation \( \log_{2} \( x^2 \ \) = 8 ).
A. 256
B. 512
C. 1024
D. 2048
Question 7
In the diagram below, if the area of the triangle is 12 square units, and the length of the base is 4 units, find the height.
A. 3
B. 4
C. 6
D. 8
Question 8
A circle has a radius of 5 units. Find the area of the circle.
A. 25\pi
B. 50\pi
C. 100\pi
D. 200\pi
Question 9
Find the determinant of the matrix \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}
A. 0
B. 1
C. 2
D. 3
Question 10
Solve the matrix equation \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 7 \ 10 \end{bmatrix} \).
A. x = 3, y = 2
B. x = 2, y = 3
C. x = 1, y = 4
D. x = 4, y = 1
Question 11
If $y = \frac{1}{2}x^2 + 3x - 4$, find the value of $y$ when $x = 2$.
A. 1
B. 2
C. 3
D. 4
Question 12
Find the value of k such that the equation \( x^2 + kx + 16 = 0 \) has roots that are reciprocals of each other.
A. 4
B. -4
C. -8
D. 8
Question 13
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{x}{\( x^2 + 1 \)^2}
D. f'(x) = \frac{-x}{\( x^2 + 1 \)^2}
Question 14
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. 2x
B. -2x
C. \frac{-2x}{\( x^2 + 1 \)^2}
D. \frac{2x}{\( x^2 + 1 \)^2}
Question 15
Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).
A. x^2 + y^2 - 4x - 6y + 5 = 0
B. x^2 + y^2 - 3x - 4y + 3 = 0
C. x^2 + y^2 - 2x - 3y + 2 = 0
D. x^2 + y^2 - x - 2y + 1 = 0

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