POST UTME MOUNTAIN TOP UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
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 3
A set of exam scores has a mean of 80 and a s\tandard deviation of 5. If the scores are normally distributed, what is the probability that a randomly selected score will be greater than 90?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 4
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 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 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 7
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 8
Find the value of $x$ in the equation $2^x + 2^{x+1} = 3 cdot 2^{x+1}$.
A. -1
B. 0
C. 1
D. 2
Question 9
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 10
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 11
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 12
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \).
A. -2
B. 2
C. 4
D. 6
Question 13
A random sample of 16 students from a population of 100 students has a mean height of 170 cm with a s\tandard deviation of 5 cm. Calculate the probability that a randomly selected student from the population has a height greater than 175 cm.
A. 0.25
B. 0.375
C. 0.5
D. 0.625
Question 14
A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 2 cm. Calculate its surface area.
A. 120
B. 150
C. 180
D. 200
Question 15
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 48\pi cm^3
B. 64\pi cm^3
C. 80\pi cm^3
D. 96\pi cm^3

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