POST UTME MOUNTAIN TOP UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A set of numbers has a mean of 10 and a s\tandard deviation of 2. What is the probability that a randomly selected number from this set is greater than 12?
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 2
A vector \vec{a} has components a_1=2, a_2=3, a_3=4. Find the magnitude of \vec{a}.
A. 5
B. \sqrt{29}
C. \sqrt{30}
D. \sqrt{31}
Question 3
Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).
A. \( \frac{pi}{4} \)
B. \( \frac{pi}{2} \)
C. \( \frac{pi}{3} \)
D. \( \frac{pi}{6} \)
Question 4
Determine the volume of the frustum of a cone with radii 6 cm and 4 cm, and height 10 cm, given that the slant height is 8 cm. Express your answer in terms of π.
A. \frac{1}{3}\pi(6^2+4^2+6\cdot4)\cdot10
B. \frac{1}{3}\pi(6^2+4^2-6\cdot4)\cdot10
C. \frac{1}{3}\pi(6^2+4^2+6\cdot4)\cdot8
D. \frac{1}{3}\pi(6^2+4^2-6\cdot4)\cdot8
Question 5
Find the surface area of a sphere with a radius of 4 cm.
A. 201.06
B. 202.06
C. 203.06
D. 204.06
Question 6
Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 7
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the highest score is 95, find the lowest score.
A. 55
B. 60
C. 65
D. 70
Question 8
A number is divisible by 3 if the sum of its digits is divisible by 3. Find the smallest number greater than 1000 that is divisible by 3.
A. 1002
B. 1005
C. 1008
D. 1011
Question 9
Find the derivative of ( 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{x^2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{1}{\( x^2 + 1 \ \)^2} )
Question 10
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. 24π cm³
B. 48π cm³
C. 96π cm³
D. 192π cm³
Question 11
A circle with center ( C(2, 3) ) and radius 4 passes through the point ( P(6, 5) ). Find the equation of the circle.
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 20 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 24 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 28 )
Question 12
A random variable X has a probability distribution given by P\( X=1 \)=0.3, P\( X=2 \)=0.4, P\( X=3 \)=0.3. Find the expected value of X.
A. 1
B. 2
C. 3
D. 4
Question 13
A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that both balls are blue?
A. \( \frac{1}{14} \)
B. \( \frac{1}{7} \)
C. \( \frac{3}{14} \)
D. \( \frac{1}{2} \)
Question 14
Simplify the expression \( \frac{1}{2} \times \frac{3}{4} \) u\sing binary operations.
A. \( \frac{3}{8} \)
B. \( \frac{1}{8} \)
C. \( \frac{3}{4} \)
D. \( \frac{1}{4} \)
Question 15
In the complex plane, let \( z = x + yi \) be a point on the circle \( x^2 + y^2 = 4 \). If ( z ) is rotated 90° counterclockwise about the origin, what is the equation of the new circle?
A. \( x^2 + y^2 = 4 \)
B. \( x^2 + y^2 = 16 \)
C. \( x^2 + y^2 = 2 \)
D. \( x^2 + y^2 = 1 \)

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