POST UTME IMS U 2021 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. 400\pi
B. 800\pi
C. 1600\pi
D. 3200\pi
Question 2
In the diagram below, if the area of the triangle is 24 cm², and the base is 8 cm, what is the height of the triangle?
A. 3 cm
B. 4 cm
C. 6 cm
D. 8 cm
Question 3
Find the area of the triangle with base 5 cm and height 6 cm.
A. 10
B. 15
C. 20
D. 25
Question 4
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. \frac{-1}{2x^{3/2}}
B. \frac{1}{2x^{3/2}}
C. \frac{1}{x^{3/2}}
D. \frac{-1}{x^{3/2}}
Question 5
Solve the system of equations \( x + y = 2 \) and \( 2x - 3y = - 5 \).
A. 1
B. 2
C. 3
D. 4
Question 6
Solve the system of equations \( x + y = 2 \) and \( xy = 1 \).
A. \( x = 1, y = 1 \)
B. \( x = 1, y = -1 \)
C. \( x = -1, y = 1 \)
D. \( x = -1, y = -1 \)
Question 7
Find the derivative of the function ( f(x) = x^2 \sin x ) u\sing the product rule.
A. x^2 \cos x + 2x \sin x
B. x^2 \cos x - 2x \sin x
C. x^2 \sin x + 2x \cos x
D. x^2 \sin x - 2x \cos x
Question 8
Solve the inequality $\frac{x^2-4}{x^2-9} > 0$.
A. \( -3,-2 \) \cup (2,3)
B. \( -3,-2 \) \cup \( 2,\infty \)
C. \( -\infty,-3 \) \cup \( -2,2 \) \cup \( 3,\infty \)
D. \( -\infty,-3 \) \cup \( -2,2 \) \cup \( 3,\infty \)
Question 9
A box contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that they are of different colors?
A. \frac{1}{2}
B. \frac{2}{5}
C. \frac{3}{5}
D. \frac{4}{5}
Question 10
Find the sum of the first 10 terms of the geometric series \( 2x^2 + 4x^4 + 8x^6 + ldots \).
A. 1023
B. 1024
C. 1025
D. 1026
Question 11
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
A. \( x < -3 \) or \( x > \frac{1}{2} \)
B. \( x < -3 \) or \( x < \frac{1}{2} \)
C. \( x > -3 \) or \( x > \frac{1}{2} \)
D. \( x > -3 \) or \( x < \frac{1}{2} \)
Question 12
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \( \frac{-x}{\( x^2 + 1 \ \)^{3/2}} )
B. \( \frac{x}{\( x^2 + 1 \ \)^{3/2}} )
C. \( \frac{1}{\( x^2 + 1 \ \)^{3/2}} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^{3/2}} )
Question 13
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 14
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. ( 1 )
B. \( -1 \)
C. ( 0 )
D. ( 2 )
Question 15
In the diagram below, if the volume of the rec\tangular prism is 240 cm³, and the area of the base is 12 cm², what is the height of the prism?
A. 6 cm
B. 8 cm
C. 10 cm
D. 12 cm

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