POST UTME MOUNTAIN TOP UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases} \) u\sing substitution.
A. x = 2, y = 2
B. x = 3, y = 1
C. x = 1, y = 3
D. x = 4, y = 0
Question 2
Solve the equation \( \frac{1}{2} \sin^2 x + \frac{1}{4} \cos^2 x = \frac{1}{4} \)
A. \frac{\pi}{6}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{2}
Question 3
A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 7?
A. 1/6
B. 1/12
C. 1/36
D. 1/24
Question 4
The line $y = 2x + 3$ intersects the circle $x^2 + y^2 = 16$ at two points. Find the coordinates of the point where the line is \tangent to the circle.
A. \( 4, -1 \)
B. \( -4, -1 \)
C. (4, 1)
D. \( -4, 1 \)
Question 5
The polynomial $P(x) = x^3 - 6x^2 + 11x - 6$ has a root at $x = 1$. Find the value of $P(2)$.
A. 0
B. 2
C. 4
D. 6
Question 6
A set of data has a mean of 25 and a s\tandard deviation of 5. Find the probability that a randomly selected value from the set is greater than 30.
A. \( \frac{1}{4} \)
B. \( \frac{1}{2} \)
C. \( \frac{3}{4} \)
D. \( \frac{1}{3} \)
Question 7
Find the value of \( x \) in the equation \( 2^x + 2^{-x} = 10 \)
A. 2
B. 3
C. 4
D. 5
Question 8
Find the derivative of the function \( f(x) = \frac{1}{x^2 + 1} \)
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{1}{\( x^2 + 1 \)^2}
D. \frac{-1}{\( x^2 + 1 \)^2}
Question 9
The quadratic equation $x^2 + 4x + 4 = 0$ has two equal roots. Find the value of $x$.
A. -2
B. -1
C. 0
D. 1
Question 10
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} ) for \( x = 1, 2, 3 \). Find the probability that ( X ) is greater than 2.
A. \( \frac{1}{4} \)
B. \( \frac{1}{2} \)
C. \( \frac{3}{4} \)
D. \( \frac{1}{3} \)
Question 11
Find the derivative of the function \( f(x) = \frac{x^2}{x^2 + 1} \)
A. \frac{2x\( x^2 + 1 \) - 2x^3}{\( x^2 + 1 \)^2}
B. \frac{2x\( x^2 + 1 \) + 2x^3}{\( x^2 + 1 \)^2}
C. \frac{2x\( x^2 + 1 \) - 2x^3}{\( x^2 + 1 \)^2}
D. \frac{2x\( x^2 + 1 \) + 2x^3}{\( x^2 + 1 \)^2}
Question 12
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 13
Solve the equation \( \sin x + \cos x = \sqrt{2} \)
A. \frac{\pi}{4}
B. \frac{3\pi}{4}
C. \frac{5\pi}{4}
D. \frac{7\pi}{4}
Question 14
The mean of a set of 5 numbers is 10. If one of the numbers is 15, what is the sum of the other 4 numbers?
A. 40
B. 45
C. 50
D. 55
Question 15
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 2 \cdot \frac{3^{10} - 1}{3 - 1}
B. 2 \cdot \frac{3^{11} - 1}{3 - 1}
C. 2 \cdot \frac{3^{12} - 1}{3 - 1}
D. 2 \cdot \frac{3^{13} - 1}{3 - 1}

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: