POST UTME BABCOCK UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.
A. f'(x) = \frac{x}{\( 1 - x^2 \)^{3/2}}
B. f'(x) = \frac{-x}{\( 1 - x^2 \)^{3/2}}
C. f'(x) = \frac{1}{\( 1 - x^2 \)^{3/2}}
D. f'(x) = \frac{-1}{\( 1 - x^2 \)^{3/2}}
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{1}{2}, \infty \right \)
B. \left\( -\infty, \frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
C. \left\( -\infty, -\frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
D. \left\( -\infty, \frac{1}{2} \right \) \cup \left\( -\frac{3}{2}, \infty \right \)
Question 3
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \left\( -2, 2 \right \)
B. \left\( -2 \right \)
C. \left\( 2 \right \)
D. \left\( -2, -1 \right \)
Question 4
Find the area under the curve \( y = \frac{1}{2}x^2 - 3x + 5 \) from \( x = 0 \) to \( x = 4 \).
A. 20
B. 25
C. 30
D. 35
Question 5
Find the volume of the solid formed by rotating the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.
A. \( \frac{2}{3} pi \)
B. \( \frac{4}{3} pi \)
C. \( \frac{8}{3} pi \)
D. \( \frac{16}{3} pi \)
Question 6
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 7
A circle has a radius of 4 cm. Find the area of the circle.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 8
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 blue ball is drawn?
A. \frac{3}{8}
B. \frac{5}{8}
C. \frac{1}{2}
D. \frac{3}{4}
Question 9
A bakery sells a total of 480 loaves of bread per day. They make a profit of ₦5 per loaf of bread. If they sell a total of ₦2400 per day, what is the ratio of the number of loaves of bread they sell to the number of loaves of bread they do not sell?
A. 1:239
B. 1:239
C. 1:239
D. 1:239
Question 10
A car travels from point A to point B at an average speed of 60 km/h. If the dis\tance between the two points is 240 km, how long does the journey take?
A. 4 hours
B. 6 hours
C. 8 hours
D. 10 hours
Question 11
A group of fri\ends want to share some money in the ratio 2:3:5. If they have ₦1200 to share, how much will each person get?
A. ₦400
B. ₦600
C. ₦800
D. ₦1000
Question 12
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} \) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 13
A sequence is defined as [ a_n = \frac{1}{n} \]. Find the sum of the first 5 terms of the sequence.
A. \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5}
B. \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}
C. \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5}
D. \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{6}
Question 14
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 12
B. 16
C. 20
D. 24
Question 15
Determine the value of x in the equation [ \sin^2(x) + \cos^2(x) = 1 ].
A. \pi/2
B. \pi/4
C. \pi/6
D. \pi/8

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