POST UTME ACHIEVERS UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the cylinder with radius 4 cm and height 10 cm
A. 160π
B. 200π
C. 240π
D. 280π
Question 2
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 all students in the university.
A. 170.3 cm, 180.7 cm
B. 168.1 cm, 182.9 cm
C. 169.5 cm, 181.5 cm
D. 171.1 cm, 179.9 cm
Question 3
A circle has a radius of 5 cm. Find the area of the circle.
A. 25\pi
B. 50\pi
C. 75\pi
D. 100\pi
Question 4
Solve the system of equations $x + y = 2$ and $xy = 1$.
A. (1, 1)
B. \( 1, -1 \)
C. \( -1, 1 \)
D. \( -1, -1 \)
Question 5
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. x = -2
B. x = -1
C. x = 1
D. x = 2
Question 6
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) u\sing the factor theorem.
A. \( x = 1 \)
B. \( x = 2 \)
C. \( x = 3 \)
D. \( x = 4 \)
Question 7
A linear equation is defined as \( 2x + 3y = 6 \). If x = 2, what is the value of y?
A. 1
B. 2
C. 3
D. 4
Question 8
Find the value of $\int_0^1 x^2 \ln(x) dx$.
A. 1/3
B. 1/2
C. 2/3
D. 1
Question 9
Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?
A. 10
B. 12
C. 14
D. 16
Question 10
Solve for x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \).
A. \( x = -10 \)
B. \( x = 3 \)
C. \( x = -3 \)
D. \( x = 10 \)
Question 11
Find the area under the curve [ y = x^2 + 2x - 3 ] from x = 0 to x = 4.
A. 20
B. 30
C. 40
D. 50
Question 12
A histogram of exam scores is shown below. If the mean score is 75 and the s\tandard deviation is 10, find the area under the curve between 60 and 80.
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 13
Find the derivative of the function [ f(x) = 3x^2 + 2x - 5 ].
A. f'(x) = 6x + 2
B. f'(x) = 6x - 2
C. f'(x) = 3x^2 + 2
D. f'(x) = 3x^2 - 2
Question 14
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 15
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).
A. ( 6 )
B. ( 8 )
C. ( 10 )
D. ( 12 )

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