POST UTME ABU 2019 Mathematics | Objective

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Question 1 View Details
Find the derivative of the function ( f(x) = \(\frac{1}{2x^2 + 3x - 1}\)\)\) ) using the quotient rule.
Correct 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}\)\) )

Correct Answer: A

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Question 2 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\) using the quadratic formula.
Correct 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 \(x < \frac{3}{2}\)

Correct Answer: A

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Question 3 View Details
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ) using the standard form of a circle.
Correct 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 + \(y - 4\)^\(2 = 16\) )

Correct Answer: A

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Question 4 View Details
Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\) using the Pythagorean identity.
Correct A. \($1x = \pm 1\)
B. \($1x = \pm 1\)
C. \($1x = \pm 1\)
D. \($1x = \pm 1\)

Correct Answer: A

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Question 5 View Details
Find the sum of the infinite geometric series \(sum_{n = 1}^{\infty} \frac{1}{2^n}\) using the formula for the sum of an infinite geometric series.
Correct A. \(\frac{1}{2}\)
B. \(\frac{1}{3}\)
C. \(\frac{1}{4}\)
D. \(\frac{1}{5}\)

Correct Answer: A

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Question 6 View Details
Solve for x in the equation \(\sin^2 x + \cos^2 x = 1\) if ( 0 leq x leq 2pi ).
Correct A. \(x =\)\(\frac{\pi}{4}\)\)
B. \(x =\)\(\frac{3\pi}{4}\)\)
C. \(x =\)\(\frac{5\pi}{4}\)\)
D. \(x =\)\(\frac{7\pi}{4}\)\)

Correct Answer: A

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Question 7 View Details
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 \(t = 2\\((m/s). Find the acceleration of the particle at time\) s.
Correct A. \(a(2) = 4\)\(m/s\^2\)
B. \(a(2) = 6\)\(m/s\^2\)
C. \(a(2) = 8\)\(m/s\^2\)
D. \(a(2) = 10\)\(m/s\^2\)

Correct Answer: A

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Question 8 View Details
A binary operation ( ast ) is defined as \(a ast b = ab + 2\). Find the value of ( 3 ast 4 ).
Correct A. 3 \ast \(4 = 14\)
B. 3 \ast \(4 = 16\)
C. 3 \ast \(4 = 18\)
D. 3 \ast \(4 = 20\)

Correct Answer: A

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Question 9 View Details
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \(\frac{1}{3}\)\)
B. \(\frac{1}{2}\)\)
Correct C. \(\frac{2}{3}\)\)
D. \(\frac{5}{6}\)\)

Correct Answer: C

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Question 10 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\).
Correct 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 < \(\frac{3}{2}\)\)

Correct Answer: A

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