POST UTME CRAWFORD UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
In the diagram below, find the value of x.
A. 30
B. 60
C. 90
D. 120
Question 3
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 4
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
Question 5
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 6
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16
C. \left\( x + 3 \right \)^2 + \left\( y - 2 \right \)^2 = 16
D. \left\( x - 3 \right \)^2 + \left\( y + 2 \right \)^2 = 16
Question 7
In the diagram below, if the length of the hypotenuse is 10 units, and the length of the shorter leg is 6 units, find the length of the longer leg.
A. 8
B. 6
C. 12
D. 4
Question 8
In the diagram below, if the length of the longer leg is 8 units, and the length of the shorter leg is 6 units, find the length of the hypotenuse.
A. 10
B. 12
C. 8
D. 6
Question 9
Find the value of x in the equation \( \sin \( 2x \ \) = \frac{1}{2} ).
A. 30
B. 60
C. 90
D. 120
Question 10
Solve the inequality \frac{x-2}{x+1} > 0.
A. x < -1 \text{ or } x > 2
B. x < 2 \text{ or } x > -1
C. x < -1 \text{ or } x < 2
D. x > -1 \text{ or } x < 2
Question 11
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 1.854
B. 2.354
C. 3.654
D. 4.854
Question 12
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 13
Find the area of the triangle with vertices ( (0, 0), (3, 0), (0, 4) ).
A. 12
B. 16
C. 20
D. 24
Question 14
Simplify the expression \( \sqrt[3]{64x^3y^3} \).
A. \( 4x^1y^1 \)
B. \( 4x^3y^3 \)
C. \( 4x^1y^3 \)
D. \( 4x^3y^1 \)
Question 15
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

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