POST UTME NOUN 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for x in the interval \( [0, 2\pi] \).
A. \( x = \frac{\pi}{4}, \frac{3\pi}{4} \)
B. \( x = \frac{\pi}{2}, \frac{3\pi}{2} \)
C. \( x = \frac{\pi}{4}, \frac{5\pi}{4} \)
D. \( x = \frac{\pi}{2}, \frac{7\pi}{4} \)
Question 2
Find the value of \( \frac{d}{dx} \left\( \frac{1}{x} \right \ \) ).
A. -\frac{1}{x^2}
B. \frac{1}{x^2}
C. -\frac{1}{x}
D. \frac{1}{x}
Question 3
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 4
Find the value of x in the equation \frac{x}{x + 1} = \frac{3}{4}.
A. \frac{3}{5}
B. \frac{4}{5}
C. \frac{5}{6}
D. \frac{6}{7}
Question 5
Find the area of the triangle with vertices ( A(0, 0), B(2, 0), C(1, 2) ).
A. ( 2 )
B. ( 4 )
C. ( 6 )
D. ( 8 )
Question 6
Solve the equation x^2 - 4x - 5 = 0.
A. x = -1 \pm \sqrt{6}
B. x = 1 \pm \sqrt{6}
C. x = -1 \pm \sqrt{5}
D. x = 1 \pm \sqrt{5}
Question 7
Let f(x) = 3x^2 + 2x - 5 and g(x) = 2x^2 - 3x + 1. Find the value of \( f + g \)(2).
A. 25
B. 30
C. 35
D. 40
Question 8
Find the value of x in the equation \log_{10} \( x^2 \) = 4.
A. 10^4
B. 10^8
C. 10^{4/2}
D. 10^{4/3}
Question 9
Find the value of \( \sin \left\( \frac{\pi}{4} \right \ \) \cos \left\( \frac{\pi}{3} \right \) - \cos \left\( \frac{\pi}{4} \right \) \sin \left\( \frac{\pi}{3} \right \) ).
A. \frac{1}{2}
B. \frac{\sqrt{3}}{2}
C. \frac{1}{\sqrt{2}}
D. \\frac{\\sqrt{3}}{\\sqrt{2}}
Question 10
Find the area of the triangle formed by the points ( A(2, 3) ), ( B(4, 5) ), and ( C(6, 2) ).
A. \( \frac{1}{2} \times 4 \times 3 \)
B. \( \frac{1}{2} \times 4 \times 2 \)
C. \( \frac{1}{2} \times 3 \times 2 \)
D. \( \frac{1}{2} \times 3 \times 4 \)
Question 11
Find the quadratic equation in the form \( ax^2 + bx + c = 0 \) whose roots are 2 and 3.
A. x^2 - 5x + 6 = 0
B. x^2 + 5x + 6 = 0
C. x^2 - 5x - 6 = 0
D. x^2 + 5x - 6 = 0
Question 12
Solve the equation \( x^2 - 4x + 3 = 0 \).
A. \left\( 1, 3 \right \)
B. \left\( 1, 2 \right \)
C. \left\( 2, 3 \right \)
D. \left\( 1, 1 \right \)
Question 13
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. 24\pi cm^3
B. 32\pi cm^3
C. 48\pi cm^3
D. 64\pi cm^3
Question 14
A polynomial ( p(x) ) is defined as ( p(x) = x^3 - 2x^2 + x - 1 ). Find the value of \( p\( -1 \ \) ).
A. 1
B. -1
C. 0
D. 2
Question 15
Find the derivative of the function ( f(x) = \frac{1}{x^2} ) u\sing the chain rule.
A. \( -\frac{2}{x^3} \)
B. \( \frac{2}{x^3} \)
C. \( -\frac{1}{x^3} \)
D. \( \frac{1}{x^3} \)

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