POST UTME AFE BABALOLA UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( x^2 - 4x + 4 > 0 \).
A. x < 2
B. x > 2
C. x < 1
D. x > 1
Question 2
A die is rolled. What is the probability that the number obtained is greater than 4?
A. 1/6
B. 1/3
C. 1/2
D. 2/3
Question 3
Find the area of the triangle with vertices ( (0, 0), (3, 0), (0, 2) ).
A. ( 6 )
B. ( 8 )
C. ( 10 )
D. ( 12 )
Question 4
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. x = -2
B. x = -3
C. x = 2
D. x = 3
Question 5
A set of 10 numbers has a mean of 20. If 5 is added to each number, what is the new mean?
A. 22
B. 25
C. 28
D. 30
Question 6
A histogram has a mean of 25 and a s\tandard deviation of 5. If the data is normally distributed, what is the probability that a randomly selected value is greater than 30?
A. 0.1587
B. 0.3413
C. 0.5000
D. 0.8413
Question 7
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} )
C. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2x}{x^2 + 1} )
Question 8
In the diagram below, the graph of \( y = \frac{1}{2} \tan 2x \) is shown. What is the value of ( x ) at the point where the graph intersects the line \( y = 0 \)?
A. \( \frac{pi}{4} \)
B. \( \frac{pi}{6} \)
C. \( \frac{pi}{3} \)
D. \( \frac{pi}{2} \)
Question 9
A vector ( mathbf{a} ) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of ( mathbf{a} ).
A. x = 4.33, y = 2.5
B. x = 2.5, y = 4.33
C. x = 3.54, y = 2.5
D. x = 2.5, y = 3.54
Question 10
In the diagram below, ( ABC ) is a right-angled triangle with \( angle B = 90^circ \). If \( AB = 6 \) cm and \( BC = 8 \) cm, find the length of ( AC ).
A. 10
B. 12
C. 15
D. 20
Question 11
Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for ( x in mathbb{R} ).
A. \( -infty, -2 \ \) cup (2, infty) )
B. \( -infty, -2 \ \) cup (2, infty) ) and \( x = -2 \)
C. \( -infty, -2 \ \) cup (2, infty) ) and \( x = 2 \)
D. \( -infty, -2 \ \) cup (2, infty) )
Question 12
A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that at least one of the balls drawn is blue?
A. \frac{3}{8}
B. \frac{5}{8}
C. \frac{1}{2}
D. \frac{3}{4}
Question 13
A company produces two products, A and B. The profit on each unit of A is ₦100 and the profit on each unit of B is ₦120. If the company produces 200 units of A and 300 units of B, what is the total profit?
A. ₦42,000
B. ₦48,000
C. ₦50,000
D. ₦60,000
Question 14
Solve the inequality x^2 - 4x - 5 > 0.
A. \( -\infty, -1 \) \cup \( 5, \infty \)
B. \( -\infty, 1 \) \cup \( 5, \infty \)
C. \( -\infty, -1 \) \cup (1, 5)
D. \( -\infty, 1 \) \cup \( -5, \infty \)
Question 15
Find the volume of the frustum of a cone with radii 6 cm and 3 cm and height 8 cm.
A. 120\pi
B. 150\pi
C. 180\pi
D. 200\pi

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