POST UTME ABU 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the Pythagorean identity.
A. \( \sin x = pm 1 \)
B. \( \cos x = pm 1 \)
C. \( \tan x = pm 1 \)
D. \( cot x = pm 1 \)
Question 2
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \frac{1}{3}
B. \frac{1}{2}
C. \frac{2}{3}
D. \frac{5}{6}
Question 3
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ) u\sing the s\tandard form of a circle.
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. \( x - 2 \ \)^2 + \( y - 4 \)^2 = 16 )
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > \frac{3}{2}
B. x < -1 or x < \frac{3}{2}
C. x > -1 or x > \frac{3}{2}
D. x > -1 or x < \frac{3}{2}
Question 5
Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{1}{2^n} \) u\sing the formula for the sum of an infinite geometric series.
A. \( \frac{1}{2} \)
B. \( \frac{1}{3} \)
C. \( \frac{1}{4} \)
D. \( \frac{1}{5} \)
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > -\frac{5}{4} \)
C. \( x < \frac{3}{2} \) or \( x > -\frac{5}{4} \)
D. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)
Question 7
A particle moves in a straight line with a velocity of ( v(t) = 2t + 5 ) m/s. Find the acceleration of the particle at time t = 2 s.
A. a(2) = 4 m/s^2
B. a(2) = 6 m/s^2
C. a(2) = 8 m/s^2
D. a(2) = 10 m/s^2
Question 8
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) if ( 0 leq x leq 2pi ).
A. x = \frac{\pi}{4}
B. x = \frac{3\pi}{4}
C. x = \frac{5\pi}{4}
D. x = \frac{7\pi}{4}
Question 9
A binary operation ( ast ) is defined as \( a ast b = ab + 2 \). Find the value of ( 3 ast 4 ).
A. 3 \ast 4 = 14
B. 3 \ast 4 = 16
C. 3 \ast 4 = 18
D. 3 \ast 4 = 20
Question 10
Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 3x - 1} ) u\sing the quotient rule.
A. \( \frac{-2x + 3}{\( 2x^2 + 3x - 1 \ \)^2} )
B. \( \frac{2x + 3}{\( 2x^2 + 3x - 1 \ \)^2} )
C. \( \frac{2x^2 + 3x - 1}{\( 2x^2 + 3x - 1 \ \)^2} )
D. \( \frac{-2x^2 - 3x + 1}{\( 2x^2 + 3x - 1 \ \)^2} )

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