POST UTME NILE UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Simplify the expression \( \frac{\sqrt[3]{64} + \sqrt[3]{216}}{\sqrt[3]{8} - \sqrt[3]{27}} \).
A. 4
B. 2
C. 3
D. 1
Question 2
In the diagram below, the equation of the circle is given by \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 ). Find the equation of the \tangent line to the circle at the point ( (5, 7) ).
A. y = -x + 12
B. y = x + 5
C. y = -x - 3
D. y = x - 2
Question 3
Solve the inequality: \( \frac{x}{x + 1} > 0 \ \)
A. x < -1
B. x > -1
C. x < 0
D. x > 0
Question 4
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. 16/3
B. 32/3
C. 64/3
D. 128/3
Question 5
A function ( f(x) = \frac{1}{x^2 + 1} ) has a local maximum at \( x = a \). Find the value of ( a ).
A. 0
B. 1
C. -1
D. 2
Question 6
Find the derivative of the function f(x) = \frac{\log x}{x^2} u\sing the quotient rule.
A. \frac{1}{x^3} - \frac{2\log x}{x^3}
B. \frac{2\log x}{x^3} - \frac{1}{x^3}
C. \frac{1}{x^3} + \frac{2\log x}{x^3}
D. \frac{2}{x^3} - \frac{\log x}{x^3}
Question 7
Solve for x in the equation \( x^3 + 2x^2 - 7x - 12 = 0 \).
A. -3
B. -2
C. 3
D. 4
Question 8
Find the vector ( mathbf{v} ) such that \( mathbf{v} cdot mathbf{i} = 3 \) and \( mathbf{v} cdot mathbf{j} = -2 \).
A. \mathbf{v} = \langle 3, -2 \rangle
B. \mathbf{v} = \langle -3, 2 \rangle
C. \mathbf{v} = \langle 3, 2 \rangle
D. \mathbf{v} = \langle -3, -2 \rangle
Question 9
Solve the system of equations: \( \begin{cases} x + y = 4 \ 2x - 3y = -1 \end{cases} \).
A. x = 1, y = 3
B. x = 2, y = 2
C. x = 3, y = 1
D. x = 4, y = 0
Question 10
Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \).
A. x \in \left[ -\frac{3}{2}, \frac{1}{2} \right]
B. x \in \left[ -\infty, -\frac{3}{2} \right] \cup \left[ \frac{1}{2}, \infty \right]
C. x \in \left[ -\infty, \frac{1}{2} \right]
D. x \in \left[ -\frac{3}{2}, \infty \right]
Question 11
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 12
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. \( x - 3 \)^2 + \( y - 4 \)^2 = 16
Question 13
Solve the system of equations: \[ \begin{align*} x^2 + y^2 + z^2 &= 4 \ x + y + z &= 0 \ x^2y^2z^2 &= 1 \end{align*} \]
A. \[ (x, y, z) = \( -1, 1, 0 \) \]
B. \[ (x, y, z) = (0, 0, 2) \]
C. \[ (x, y, z) = \( -2, 1, 1 \) \]
D. \[ (x, y, z) = \( 1, -1, 0 \) \]
Question 14
Solve the trigonometric equation: \( \sin^2 x + \cos^2 x = 1 \ \)
A. x = \frac{\pi}{4}
B. x = \frac{\pi}{2}
C. x = \frac{\pi}{3}
D. x = \frac{\pi}{6}
Question 15
Find the derivative of the function \[ f(x) = \frac{x^2 + 3x + 2}{x^2 - 4x + 3} \]
A. \[ f'(x) = \frac{\( x^2 - 4x + 3 \)\( 2x + 3 \) - \( x^2 + 3x + 2 \)\( 2x - 4 \)}{\( x^2 - 4x + 3 \)^2} \]
B. \[ f'(x) = \frac{\( x^2 - 4x + 3 \)\( 2x + 3 \) + \( x^2 + 3x + 2 \)\( 2x - 4 \)}{\( x^2 - 4x + 3 \)^2} \]
C. \[ f'(x) = \frac{\( x^2 - 4x + 3 \)\( 2x + 3 \) - \( x^2 + 3x + 2 \)\( 2x + 4 \)}{\( x^2 - 4x + 3 \)^2} \]
D. \[ f'(x) = \frac{\( x^2 - 4x + 3 \)\( 2x + 3 \) + \( x^2 + 3x + 2 \)\( 2x + 4 \)}{\( x^2 - 4x + 3 \)^2} \]

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