POST UTME NILE UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \)
B. ( 3 )
C. ( 4 )
D. ( 6 )
Question 2
A right circular cylinder has a height of 10 cm and a radius of 5 cm. What is its volume?
A. 500\pi
B. 1000\pi
C. 2000\pi
D. 5000\pi
Question 3
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Question 4
A set 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 will be between 60 and 90?
A. 0.68
B. 0.84
C. 0.95
D. 0.99
Question 5
Solve the equation \( 2^x = 8 \) for ( x ).
A. \( x = 2 \)
B. \( x = 3 \)
C. \( x = 4 \)
D. \( x = 1 \)
Question 6
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 7
A circle has a radius of 4 cm. Find the area of the circle.
A. 50.24
B. 50.27
C. 50.30
D. 50.33
Question 8
A sequence is defined as: 1, 2, 4, 8, 16, ... . What is the next term in the sequence?
A. 32
B. 64
C. 128
D. 256
Question 9
Find the surface area of the sphere with radius 5 cm.
A. 100\pi cm^2
B. 150\pi cm^2
C. 200\pi cm^2
D. 250\pi cm^2
Question 10
Solve the inequality \( x^2 - 4x + 3 > 0 \) u\sing the quadratic formula.
A. x < 1 or x > 3
B. x < 1 or x < 3
C. x > 1 or x > 3
D. x > 1 or x < 3
Question 11
Find the area of the circle with radius \( r = 4 \) u\sing the formula for the area of a circle.
A. A = 16\pi
B. A = 32\pi
C. A = 64\pi
D. A = 128\pi
Question 12
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \).
A. \( \frac{8}{3} \)
B. \( \frac{4}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{1}{3} \)
Question 13
Solve the system of equations \( x + y = 3, x - y = 1 \) u\sing the method of substitution.
A. x = 2, y = 1
B. x = 2, y = 2
C. x = 1, y = 2
D. x = 1, y = 1
Question 14
A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 15
Solve the system of equations \( x + y = 2, x - y = 1 \) u\sing the method of substitution.
A. x = 1, y = 1
B. x = 1, y = 2
C. x = 2, y = 1
D. x = 2, y = 2

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