POST UTME BELLS UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Evaluate the definite integral \( int_{0}^{1} x^2 \sin x , dx \) u\sing integration by parts.
A. \( -\cos x + x^2 \sin x \)
B. \( \cos x - x^2 \sin x \)
C. \( -\sin x - x^2 \cos x \)
D. \( \sin x + x^2 \cos x \)
Question 2
Find the area of the triangle with vertices $(0, 0)$, $(3, 0)$, and $(0, 2)$.
A. 6
B. 12
C. 18
D. 24
Question 3
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.
A. \( \frac{-x}{\( 1 - x^2 \ \)^{3/2}} )
B. \( \frac{x}{\( 1 - x^2 \ \)^{3/2}} )
C. \( \frac{1}{\( 1 - x^2 \ \)^{3/2}} )
D. \( \frac{-1}{\( 1 - x^2 \ \)^{3/2}} )
Question 4
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 5
A circle has a radius of 4 cm. Find the area of the circle u\sing the formula \( A = pi r^2 \).
A. ( 16pi ) cm^2
B. ( 32pi ) cm^2
C. ( 64pi ) cm^2
D. ( 128pi ) cm^2
Question 6
Find the derivative of the function ( f(x) = x^3 \sin x ) u\sing the product rule.
A. ( f'(x) = 3x^2 \sin x + x^3 \cos x )
B. ( f'(x) = 3x^2 \cos x - x^3 \sin x )
C. ( f'(x) = 3x^2 \sin x - x^3 \cos x )
D. ( f'(x) = 3x^2 \cos x + x^3 \sin x )
Question 7
Solve the inequality $|x - 2| > 3$.
A. x < -1 \text{ or } x > 5
B. x > -1 \text{ or } x < 5
C. x < 1 \text{ or } x > 5
D. x > 1 \text{ or } x < 5
Question 8
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 2 \cdot \frac{3^{10} - 1}{3 - 1}
B. 2 \cdot \frac{3^{11} - 1}{3 - 1}
C. 2 \cdot \frac{3^{12} - 1}{3 - 1}
D. 2 \cdot \frac{3^{13} - 1}{3 - 1}
Question 9
Determine the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 2x$ about the x-axis.
A. \frac{32\pi}{15}
B. \frac{16\pi}{3}
C. \frac{32\pi}{5}
D. \frac{64\pi}{3}
Question 10
Solve for x in the equation \( \frac{x}{2} + 5 = 11 \).
A. 6
B. 12
C. 18
D. 24
Question 11
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = 1x + 1
B. y = 2x + 2
C. y = 3x + 3
D. y = 4x + 4
Question 12
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 1/3
C. 2/5
D. 3/8
Question 13
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of the students.
A. 169.4 cm, 181.6 cm
B. 170.5 cm, 180.5 cm
C. 168.5 cm, 182.5 cm
D. 171.5 cm, 179.5 cm
Question 14
Solve for x in the equation \( 2x^2 + 5x - 3 = 0 \).
A. x = -1.5, x = 2
B. x = -2, x = 1.5
C. x = 1, x = -3
D. x = 2, x = -1
Question 15
Solve the inequality \( 2x - 5 > 3x + 2 \).
A. x < -1
B. x > -1
C. x < 1
D. x > 1

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