POST UTME RHEMA UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A histogram of exam scores is shown below. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 2
Find 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. 16/3
B. 32/3
C. 64/3
D. 128/3
Question 3
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).
A. \( 2\( 1 - 2^{10} \ \) )
B. \( 2\( 1 + 2^{10} \ \) )
C. \( 2\( 1 - 2^{10} \ \) )
D. \( 2\( 1 + 2^{10} \ \) )
Question 4
The mean of five numbers is 10. If one of the numbers is 5, find the sum of the other four numbers.
A. 25
B. 30
C. 35
D. 40
Question 5
A histogram is constructed with 5 classes of equal width. The frequency of the classes are 10, 15, 20, 15, and 10. What is the mean of the histogram?
A. 12
B. 15
C. 18
D. 20
Question 6
A cylindrical \tank with a radius of 4m and a height of 10m is filled with water. If the water level is at 6m, what is the volume of the water in the \tank?
A. ( 800pi ) m³
B. ( 1600pi ) m³
C. ( 2400pi ) m³
D. ( 3200pi ) m³
Question 7
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. ( f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}} )
B. ( f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}} )
C. ( f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}} )
D. ( f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}} )
Question 8
A sequence is defined by $a_n = \frac{\( -1 \)^n}{n}$. Find the sum of the first 5 terms of the sequence.
A. -1.366
B. -1.366
C. -1.366
D. -1.366
Question 9
Find the derivative of the function $f(x) = \frac{1}{x^2+1}$ u\sing the quotient rule.
A. \frac{-2x}{\( x^2+1 \)^2}
B. \frac{2x}{\( x^2+1 \)^2}
C. \frac{x}{\( x^2+1 \)^2}
D. \frac{-x}{\( x^2+1 \)^2}
Question 10
Find the value of $\frac{d}{dx}\left\( \frac{1}{x^2}\right \)$ u\sing the chain rule.
A. -\frac{2}{x^3}
B. \frac{2}{x^3}
C. -\frac{1}{x^3}
D. \frac{1}{x^3}
Question 11
Find the value of $x$ in the equation $2^x = 64$.
A. 4
B. 5
C. 6
D. 7
Question 12
Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is P(A and B)?
A. 0.2
B. 0.24
C. 0.3
D. 0.36
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
B. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)
C. \( x < -\frac{3}{2} \) or \( x < \frac{1}{2} \)
D. \( x > -\frac{3}{2} \) or \( x < \frac{1}{2} \)
Question 14
A set of 5 numbers has a mean of 10 and a median of 8. If the largest number is 15, find the sum of the remaining 3 numbers.
A. 20
B. 30
C. 40
D. 50
Question 15
A histogram has a mean of 20 and a s\tandard deviation of 5. Find the value of the highest bar.
A. 25
B. 30
C. 35
D. 40

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