POST UTME COAL CITY UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the first 10 terms of the geometric series 2, 6, 18, ...
A. 104
B. 106
C. 108
D. 110
Question 2
A binary operation $\star$ is defined as $a \star b = a^2 + b^2$. Find the value of $2 \star 3$.
A. 5
B. 7
C. 9
D. 11
Question 3
A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?
A. 18
B. 19
C. 20
D. 21
Question 4
Find the area under the curve $y = x^2$ from $x = 0$ to $x = 2$.
A. 2
B. 4
C. 6
D. 8
Question 5
Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is 6, what is the sum of the data set?
A. 20
B. 30
C. 40
D. 50
Question 6
A cylindrical \tank with a radius of 4m and a height of 6m is filled with water. Find the volume of water in the \tank.
A. ( 96pi ) cubic meters
B. ( 192pi ) cubic meters
C. ( 384pi ) cubic meters
D. ( 576pi ) cubic meters
Question 7
In the set A = {1, 2, 3, 4, 5}, find the number of subsets with exactly 3 elements.
A. 5
B. 10
C. 15
D. 20
Question 8
Solve the differential equation \( \frac{dy}{dx} = \frac{y}{x} \) with the initial condition y(1) = 1.
A. y = \( ln|x| \)
B. y = \( \frac{1}{x} \)
C. y = \( \frac{1}{x^2} \)
D. y = \( \frac{1}{x^3} \)
Question 9
Find the area under the curve y = \( \sin^2\( x \ \)) from 0 to \( \frac{pi}{2} \) u\sing integration by substitution.
A. \( \frac{pi}{4} \)
B. \( \frac{pi}{2} \)
C. \( \frac{3pi}{4} \)
D. \( \frac{5pi}{4} \)
Question 10
A polynomial function has a degree of 4 and has zeros at \( x = -2, 1, 3 \). Find the polynomial function.
A. \( x + 2 \)\( x - 1 \)\( x - 3 \)\( x + 1 \ \) )
B. \( x - 2 \)\( x + 1 \)\( x - 3 \)\( x + 3 \ \) )
C. \( x + 2 \)\( x - 1 \)\( x + 3 \)\( x - 3 \ \) )
D. \( x - 2 \)\( x + 1 \)\( x - 3 \)\( x + 1 \ \) )
Question 11
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( \frac{2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{-2}{\( x^2 + 1 \ \)^2} )
Question 12
The equation of a circle is given by \( x^2 + y^2 + 2gx + 2fy + c = 0 \). Find the equation of the circle with center \( -2, 3 \ \) ) and radius 4.
A. \( x^2 + y^2 - 4x + 6y - 12 = 0 \)
B. \( x^2 + y^2 + 4x - 6y - 12 = 0 \)
C. \( x^2 + y^2 - 4x - 6y - 12 = 0 \)
D. \( x^2 + y^2 + 4x + 6y - 12 = 0 \)
Question 13
Find the value of ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 14
Solve the inequality 2x^2 + 5x - 3 > 0.
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -2 \) ∪ (2, ∞)
D. \( -∞, -4 \) ∪ (4, ∞)
Question 15
Solve the inequality \( \log_{10} \( x^2 - 4 \ \) > 2 ).
A. \( x > 2 \)
B. \( x < -2 \)
C. \( x > 4 \)
D. \( x < -4 \)

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: