POST UTME UNN 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. 0.3413
B. 0.6827
C. 0.9544
D. 0.9973
Question 2
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 3
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 = 20
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 24
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 28
Question 4
A right circular cone has a height of 20 cm and a radius of 10 cm. Find the volume of the cone in cubic centimeters.
A. 1000\pi
B. 2000\pi
C. 3000\pi
D. 4000\pi
Question 5
Find the equation of the circle with center at (2, 3) and pas\sing through the point (4, 5).
A. \boxed{\( x - 2 \)^2 + \( y - 3 \)^2 = 5}
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 10
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 15
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 20
Question 6
In a set of consecutive integers, the sum of the first five terms is 15 more than the sum of the last five terms. If the middle term is 11, find the sum of all the terms in the set.
A. 150
B. 200
C. 250
D. 300
Question 7
A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms.
A. 15
B. 20
C. 25
D. 30
Question 8
Solve the equation \sin^2 x + \cos^2 x = 1 for x in the interval [0, 2\pi].
A. 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}
B. 0, \frac{\pi}{2}, \pi, \frac{5\pi}{2}
C. 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, \frac{5\pi}{2}
D. 0, \pi, 2\pi
Question 9
A vector \mathbf{a} has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. A vector \mathbf{b} has a magnitude of 3 units and makes an angle of 60° with the positive x-axis. Calculate the dot product of \mathbf{a} and \mathbf{b}.
A. 4.5
B. 5.5
C. 6.5
D. 7.5
Question 10
Solve the inequality \frac{x^2 - 4x - 5}{x^2 - 2x - 6} > 0.
A. \( -\infty, -3 \) \cup \( 1, \infty \)
B. \( -\infty, -2 \) \cup \( 1, \infty \)
C. \( -\infty, -3 \) \cup \( -2, \infty \)
D. \( -\infty, -2 \) \cup \( -3, \infty \)
Question 11
A polynomial f(x) = x^3 + 2x^2 - 7x + 12 has a root at x = -1. Calculate the value of f\( -1 \).
A. 1
B. 2
C. 3
D. 4
Question 12
Solve the system of equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix} \).
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} -1 \ 2 \end{bmatrix}
C. \begin{bmatrix} 1 \ -2 \end{bmatrix}
D. \begin{bmatrix} -1 \ -2 \end{bmatrix}
Question 13
Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.
A. \( -3, -1 \) \cup (1, 3)
B. \( -3, -1 \) \cup (1, 3) \cup (4, 6)
C. \( -3, -1 \) \cup (1, 3) \cup \( -6, -4 \)
D. \( -3, -1 \) \cup (1, 3) \cup (4, 6) \cup \( -6, -4 \)
Question 14
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. \frac{\pi}{6}
B. \frac{\pi}{12}
C. \frac{\pi}{18}
D. \frac{\pi}{24}
Question 15
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. 1/3
C. 1/2
D. 2/3

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