POST UTME GREENFIELD UNIVERSITY 2018 Mathematics | Objective

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Question 1
Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.
A. \( -\infty, -3 \) \cup \( 3, \infty \)
B. \( -3, 0 \) \cup (0, 3)
C. \( -\infty, -3 \) \cup (0, 3)
D. \( -\infty, 0 \) \cup \( 3, \infty \)
Question 2
Find the value of \sin(2x) given that \sin(x) = \frac{3}{5} and \cos(x) = \frac{4}{5}.
A. \frac{24}{25}
B. \frac{28}{25}
C. \frac{32}{25}
D. \frac{36}{25}
Question 3
Find the sum of the first 10 terms of the arithmetic progression 3, 6, 9, ...
A. 150
B. 160
C. 170
D. 180
Question 4
Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A. 6x + 2
B. 6x + 2
C. 6x + 2
D. 6x + 2
Question 5
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, 1 \) \cup \( 3, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, 1 \) \cup \( 1, \infty \)
Question 6
Solve the system of equations \begin{align*} x + y &= 4 \ x - 2y &= -2 \end{align*}.
A. \left\{ (2, 2) \right\}
B. \left\{ (2, 2) \right\}
C. \left\{ (2, 2) \right\}
D. \left\{ (2, 2) \right\}
Question 7
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 2.
A. \frac{14}{3}
B. \frac{16}{3}
C. \frac{18}{3}
D. \frac{20}{3}
Question 8
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 3.999999999999999
B. 4.000000000000001
C. 4.0000000000000005
D. 4.000000000000001
Question 9
Solve the equation x^2 + 2x - 6 = 0 by completing the square.
A. x = -3 \pm \sqrt{13}
B. x = -3 \pm \sqrt{12}
C. x = -3 \pm \sqrt{11}
D. x = -3 \pm \sqrt{10}
Question 10
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
B. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
C. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
D. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
Question 11
Solve the inequality \frac{x+2}{x-1} > 0.
A. \( -\infty, -2 \) \cup \( 1, \infty \)
B. \( -\infty, -2 \) \cup \( 1, \infty \)
C. \( -\infty, -2 \) \cup \( 1, \infty \)
D. \( -\infty, -2 \) \cup \( 1, \infty \)
Question 12
Let a_n = 2n^2 + 3n - 1. Find the sum of the first 5 terms of the sequence.
A. 120
B. 130
C. 140
D. 150
Question 13
A die is rolled twice. What is the probability that the sum of the two numbers is 7?
A. 1/6
B. 1/6
C. 1/6
D. 1/6
Question 14
Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.
A. 14
B. 16
C. 18
D. 20
Question 15
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 2\( 3^{10}-1 \)/\( 3-1 \)
B. 2\( 3^{10}+1 \)/\( 3-1 \)
C. 2\( 3^{10}-1 \)/\( 3+1 \)
D. 2\( 3^{10}+1 \)/\( 3+1 \)

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