POST UTME RHEMA UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A histogram 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. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 2
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 3
Find the derivative of the function f(x) = \frac{1}{x^2 + 1} u\sing the chain rule.
A. \boxed{-\frac{2x}{\( x^2 + 1 \)^2}}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{2}{\( x^2 + 1 \)^2}
D. \frac{2x^2}{\( x^2 + 1 \)^2}
Question 4
Find the value of x in the equation \( x^2 - 4x + 4 = 0 \).
A. 2
B. -2
C. 1
D. -1
Question 5
Solve for x in the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. 2
B. -3
C. -2
D. 1
Question 6
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 7
A binary operation \ast is defined as a \ast b = ab + 2. Find the value of 3 \ast 4.
A. 14
B. 16
C. 18
D. 20
Question 8
Find the sum of the first 5 terms of the geometric series with first term 2 and common ratio 3.
A. \boxed{2 + 6 + 18 + 54 + 162}
B. 2 + 6 + 18 + 54 + 162 + 486
C. 2 + 6 + 18 + 54 + 162 - 486
D. 2 + 6 + 18 + 54 + 162 + 243
Question 9
Find the volume of the solid formed by rotating the region bounded by $y=x^2$ and $y=4$ about the x-axis.
A. \frac{64\pi}{3}
B. \frac{32\pi}{3}
C. \frac{16\pi}{3}
D. \frac{8\pi}{3}
Question 10
A right circular cylinder has a height of 10 cm and a radius of 4 cm. Find the surface area of the cylinder.
A. 160\pi
B. 200\pi
C. 240\pi
D. 280\pi
Question 11
If \( A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and \( B = \begin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \), find the product ( AB ).
A. \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}
B. \begin{bmatrix} 23 & 26 \ 47 & 54 \end{bmatrix}
C. \begin{bmatrix} 21 & 24 \ 45 & 52 \end{bmatrix}
D. \begin{bmatrix} 25 & 28 \ 49 & 56 \end{bmatrix}
Question 12
A solid cylinder has a radius of 4 cm and a height of 10 cm. Find the volume of the cylinder.
A. 800\pi
B. 1600\pi
C. 3200\pi
D. 6400\pi
Question 13
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. 2x
B. -2x
C. \frac{-2x}{\( x^2 + 1 \)^2}
D. \frac{2x}{\( x^2 + 1 \)^2}
Question 14
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. \frac{4}{3}\pi
B. \frac{2}{3}\pi
C. \frac{1}{3}\pi
D. \frac{1}{2}\pi
Question 15
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{-x}{\( x^2+1 \)^2}
D. f'(x) = \frac{x}{\( x^2+1 \)^2}

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