POST UTME RHEMA UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Solve for y in the equation \( y = \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 3
A vector \( \vec{a} \) has components \( a_x = 3 \) and \( a_y = 4 \). Find the magnitude of the vector.
A. 5
B. 10
C. 15
D. 20
Question 4
Find the volume of the solid formed by revolving the region bounded by the parabola y = x^2, the x-axis, and the line x = 2 about the x-axis.
A. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi
Question 5
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 6
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}
Question 7
Solve for x in the equation $\log_{2}\( x-1 \) + \log_{2}\( x+1 \) = 2$.
A. x=3
B. x=2
C. x=1
D. x=-1
Question 8
A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:3, how many loaves of whole wheat bread are sold per day?
A. 150
B. 180
C. 200
D. 250
Question 9
Solve the equation x^2 + 4x - 5 = 0 u\sing the quadratic formula.
A. \boxed{x = -5 \text{ or } x = 1}
B. x = -1 \text{ or } x = 5
C. x = -2 \text{ or } x = 2
D. x = -3 \text{ or } x = 3
Question 10
Solve the inequality \frac{x+2}{x-1}>0.
A. \( -\infty,-2)\cup\( 1,\infty \ \)
B. \( -\infty,1)\cup\( 2,\infty \ \)
C. \( -\infty,-2)\cup\( 1,2 \ \)
D. \( -\infty,1)\cup\( -2,\infty \ \)
Question 11
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 12
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 13
Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 14
Solve the inequality \frac{x + 2}{x - 1} > 0.
A. \boxed{x < -2 \text{ or } x > 1}
B. x < -2 \text{ or } x < 1
C. x > -2 \text{ or } x > 1
D. x < -2 \text{ or } x < 1
Question 15
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

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