POST UTME SUMMIT UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. -1
C. 1
D. 2
Question 2
Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 64\pi cm^3
B. 128\pi cm^3
C. 256\pi cm^3
D. 512\pi cm^3
Question 3
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 1/3
C. 2/5
D. 3/5
Question 4
Find the sum of the first 5 terms of the geometric series \( 2x^2 - 3x + 1 \).
A. \( 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 \)
B. \( 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 \)
C. \( 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 1 \)
D. \( 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x \)
Question 5
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
B. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)
C. \( x < -\frac{3}{2} \) or \( x < \frac{1}{2} \)
D. \( x > -\frac{3}{2} \) or \( x < \frac{1}{2} \)
Question 6
Solve the inequality \( x^2 - 4x + 3 > 0 \).
A. \( x < 1 \) or \( x > 3 \)
B. \( x < 3 \) or \( x > 1 \)
C. \( x < 1 \) or \( x < 3 \)
D. \( x > 1 \) or \( x < 3 \)
Question 7
Let ( f(x) = \frac{1}{x^2 + 1} ). Find the derivative of ( f(x) ) u\sing the chain rule.
A. ( f'(x) = -\frac{2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = -\frac{1}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{1}{\( x^2 + 1 \)^2} )
Question 8
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, 1 \) \cup \( 3, \infty \)
C. \( -\infty, -3 \) \cup \( 1, \infty \)
D. \( -\infty, 3 \) \cup \( 1, \infty \)
Question 9
Solve the system of equations \n\begin{align*} \n 2x+y &= 4, \n 3x-2y &= 5. \n\end{align*}
A. (1, 2)
B. (2, 1)
C. (3, 4)
D. (4, 3)
Question 10
The sum of the first n terms of an arithmetic progression is given by \( S_n = \frac{n}{2} \( 2a + (n - 1 \ \)d) ). Find the value of d if a = 2 and S_n = 120.
A. 10
B. 20
C. 30
D. 40
Question 11
Find the equation of the \tangent line to the curve $y=x^2+2x-3$ at the point $(1, 2)$.
A. y = 3x - 1
B. y = 3x + 1
C. y = x + 1
D. y = x - 1
Question 12
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 16 )
C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
Question 13
Solve the inequality 2x^2 + 5x - 3 > 0.
A. x < -1 or x > 3/2
B. x > -1 or x < 3/2
C. x < -1 or x < 3/2
D. x > -1 or x > 3/2
Question 14
Find the value of $\frac{d}{dx}\left\( \frac{1}{x^2}\right \)$.
A. -\frac{2}{x^3}
B. \frac{2}{x^3}
C. -\frac{1}{x^3}
D. \frac{1}{x^3}
Question 15
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 3.
A. 9
B. 18
C. 27
D. 36

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