POST UTME MOUNTAIN TOP UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In the diagram below, $ABCD$ is a rec\tangle with $AB = 6$ and $BC = 8$. Find the area of the shaded region.
A. 24
B. 32
C. 40
D. 48
Question 2
Solve the inequality $\frac{1}{x+1} + \frac{1}{x-1} \geq \frac{1}{2}$.
A. $x \in \( -\infty, -2 \) \cup \( 1, \infty \)$
B. $x \in \( -\infty, -2 \) \cup [1, \infty)$
C. $x \in \( -\infty, -1 \) \cup \( 1, \infty \)$
D. $x \in \( -\infty, -1 \) \cup [1, \infty)$
Question 3
A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).
A. 13
B. 17
C. 19
D. 25
Question 4
A sequence is defined by $a_n = 2n + 1$. Find the sum of the first $5$ terms.
A. 2 + 5 + 8 + 11 + 14
B. 1 + 3 + 5 + 7 + 9
C. 2 + 4 + 6 + 8 + 10
D. 1 + 2 + 3 + 4 + 5
Question 5
A geometric progression has first term $a = 2$ and common ratio $r = 3$. Find the sum of the first $5$ terms.
A. 2 + 6 + 18 + 54 + 162
B. 2 + 6 + 18 + 54 + 162 + 486
C. 2 + 6 + 18 + 54 + 162 + 486 + 1458
D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374
Question 6
Find the volume of the frustum of a cone with height $h$ and radii $r_1$ and $r_2$.
A. \frac{1}{3}\pi h \( r_1^2 + r_2^2 + r_1 r_2 \)
B. \frac{1}{3}\pi h \( r_1^2 - r_2^2 \)
C. \frac{1}{3}\pi h \( r_1^2 + r_2^2 - r_1 r_2 \)
D. \frac{1}{3}\pi h \( r_1^2 - r_2^2 + r_1 r_2 \)
Question 7
In the circuit below, find the equivalent resis\tance.
A. ( 2 Omega )
B. ( 4 Omega )
C. ( 6 Omega )
D. ( 8 Omega )
Question 8
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) for ( x ) in the interval \( -infty, infty \ \) ).
A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)
C. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{5}{4} \) or \( x > \frac{3}{2} \)
Question 9
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 10
Find the derivative of the function ( f(x) = \tan x ) u\sing the chain rule.
A. \( sec^2 x \)
B. \( \tan^2 x \)
C. ( sec x )
D. \( \tan x \)
Question 11
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 12
Find the sum of the first 5 terms of the geometric series \( 2x^2 + 3x + 4 \).
A. \( 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 \)
B. \( 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 \)
C. \( 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 \)
D. \( 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 \)
Question 13
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 4 \)^2 = 16
Question 14
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. \( 2 \sin x \cos x \)
B. \( 2 \sin x \)
C. \( 2 \cos x \)
D. \( 2 \sin^2 x \)
Question 15
A company produces 500 units of a product per day. If the demand for the product increases by 10% per day, how many units will the company produce after 3 days?
A. 1500
B. 1600
C. 1700
D. 1800

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