POST UTME RSU 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{1}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-1}{\( x^2 + 1 \)^2} )
Question 2
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 3
Find the volume of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the y-axis.
A. 32\pi/5
B. 48\pi/5
C. 64\pi/5
D. 80\pi/5
Question 4
Find the area under the curve y = 2x^2 + 3x - 4 from x = 0 to x = 2.
A. 20
B. 30
C. 40
D. 50
Question 5
A random variable X has a probability distribution given by P(X) = \( 1/2 \)^\( X-1 \) for X = 1, 2, 3, ... . Find the expected value of X.
A. 2
B. 3
C. 4
D. 5
Question 6
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 7
In a normal distribution, the mean is 10 and the s\tandard deviation is 2. What is the probability that a value is between 8 and 12?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 8
A set of 5 consecutive integers has a median of 8. What is the sum of the squares of these integers?
A. 400
B. 420
C. 440
D. 460
Question 9
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( 22.5 + 24 - 8 = 38.5 \)
B. \( 8 + 24 - 2 = 30 \)
C. \( 8 + 24 - 8 = 24 \)
D. \( 22.5 + 24 - 8 = 38.5 \)
Question 10
Find the surface area of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 32\pi/5
B. 48\pi/5
C. 64\pi/5
D. 80\pi/5
Question 11
A solid is formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis. Find the volume of the solid.
A. 16\pi/5
B. 32\pi/5
C. 48\pi/5
D. 64\pi/5
Question 12
Solve the quadratic equation: \(x^2+4x+4=0\)
A. x=-2
B. x=2
C. x=-1
D. x=1
Question 13
Determine the volume of the frustum of a cone with a height of 10 cm, a lower base radius of 4 cm, and an upper base radius of 2 cm.
A. 50\pi cm^3
B. 75\pi cm^3
C. 100\pi cm^3
D. 125\pi cm^3
Question 14
A histogram has a mean of 25 and a s\tandard deviation of 5. What is the probability that a randomly selected value from this histogram is greater than 30?
A. 0.25
B. 0.30
C. 0.35
D. 0.40
Question 15
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 2.
A. 13/3
B. 14/3
C. 15/3
D. 16/3

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