POST UTME AL-HIKMAH UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A circle has a radius of 4 cm. Find its area.
A. \( pi r^2 = pi \( 4 \ \)^2 = 16pi ) cm^2
B. \( pi r^2 = pi \( 4 \ \)^2 = 64pi ) cm^2
C. \( pi r^2 = pi \( 4 \ \)^2 = 16pi ) cm^2
D. \( pi r^2 = pi \( 4 \ \)^2 = 64pi ) cm^2
Question 2
Find the area of the triangle with vertices ( (0, 0) ), ( (2, 0) ), and ( (0, 2) ).
A. ( 2 )
B. ( 4 )
C. ( 6 )
D. ( 8 )
Question 3
A particle moves along the curve \( y = x^2 + 2x + 1 \) with a velocity of 2 m/s. Find the acceleration at the point where the particle is at \( x = 1 \).
A. 4 m/s^2
B. 2 m/s^2
C. -2 m/s^2
D. 6 m/s^2
Question 4
Solve the equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = 0
B. x = π/2
C. x = π
D. x = 2π
Question 5
In the triangle below, find the length of side AC.
A. 5
B. 10
C. 15
D. 20
Question 6
Solve the equation \( x^2 + 4x - 5 = 0 \) u\sing the quadratic formula.
A. \( x = \frac{-4 pm \sqrt{16 + 20}}{2} = \frac{-4 pm \sqrt{36}}{2} = \frac{-4 pm 6}{2} \)
B. \( x = \frac{-4 pm \sqrt{16 - 20}}{2} = \frac{-4 pm \sqrt{-4}}{2} \)
C. \( x = \frac{-4 pm \sqrt{16 + 20}}{2} = \frac{-4 pm \sqrt{36}}{2} = \frac{-4 pm 6}{2} \)
D. \( x = \frac{-4 pm \sqrt{16 - 20}}{2} = \frac{-4 pm \sqrt{-4}}{2} \)
Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -3 \) ∪ (1, ∞)
B. \( -∞, -1 \) ∪ (3, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, 3)
Question 8
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, find the probability that it is blue.
A. 1/2
B. 2/7
C. 3/8
D. 5/8
Question 9
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5 cm
B. 7.07 cm
C. 8 cm
D. 9 cm
Question 10
Find the area under the curve y = x^2 from x = 0 to x = 4.
A. 16
B. 32
C. 64
D. 128
Question 11
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. -\frac{1}{2}x^{-\frac{3}{2}}
B. \frac{1}{2}x^{-\frac{3}{2}}
C. -\frac{1}{2}x^{-\frac{1}{2}}
D. \frac{1}{2}x^{-\frac{1}{2}}
Question 12
Solve the equation \( x^2 + 2x - 3 = 0 \).
A. \( x = -3 \) or \( x = 1 \)
B. \( x = -1 \) or \( x = 3 \)
C. \( x = 1 \) or \( x = -3 \)
D. \( x = -3 \) or \( x = -1 \)
Question 13
A random variable X has a probability distribution given by P\( X = 1 \) = 0.2, P\( X = 2 \) = 0.3, P\( X = 3 \) = 0.5. Find E(X).
A. 1.5
B. 2.0
C. 2.5
D. 3.0
Question 14
Find the equation of the circle with centre \( -2, 3 \) and radius 4.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 15
A solid right circular cone has a height of 20 cm and a base radius of 10 cm. Find the volume of the cone in cubic centimeters.
A. 1000\pi
B. 2000\pi
C. 3000\pi
D. 4000\pi

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