POST UTME BSU 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of $\int_0^1 \frac{1}{1+x^2} dx$.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 2
A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.
A. 8 cm
B. 6 cm
C. 4 cm
D. 2 cm
Question 3
Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A. 6x + 2
B. 6x - 2
C. 3x^2 + 2
D. 3x^2 - 2
Question 4
A set of 5 consecutive integers has a median of 8. What is the sum of the integers?
A. 40
B. 50
C. 60
D. 70
Question 5
Solve for $x$: $\log_2 x + \log_2 \( x-1 \) = 2$.
A. 3
B. 4
C. 5
D. 6
Question 6
Solve for x in the equation: \( \sin^2\( x \ \) + \cos^2(x) = 1 ). What is the value of x?
A. 0
B. π/2
C. π
D. 3π/2
Question 7
Find the equation of the circle with center ( (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 8
Find the equation of the circle with center \( -2, 3 \) 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 9
The mean of a set of numbers is 25. If the set is increased by 10% and then decreased by 5%, what is the new mean?
A. 24.5
B. 25.5
C. 26.5
D. 27.5
Question 10
Find the volume of the solid formed by rotating the region bounded by \( y = x^2 \) and \( y = 2x \) about the x-axis.
A. 16\pi
B. 32\pi
C. 48\pi
D. 64\pi
Question 11
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = \frac{\pi}{4}
B. x = \frac{\pi}{2}
C. x = \frac{3\pi}{4}
D. x = \pi
Question 12
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x > -1 \) or \( x < \frac{3}{2} \)
C. \( x < -1 \) or \( x < \frac{3}{2} \)
D. \( x > -1 \) or \( x > \frac{3}{2} \)
Question 13
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. \frac{-1}{2x^{3/2}}
B. \frac{1}{2x^{3/2}}
C. \frac{1}{x^{3/2}}
D. \frac{-1}{x^{3/2}}
Question 14
Solve for x in the equation \( \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2} \).
A. x = 2
B. x = -1
C. x = 1
D. x = -2
Question 15
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. 0.68
B. 0.85
C. 0.95
D. 0.99

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