POST UTME SUMMIT UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of \( \log_{10} \( 1000 \ \) ).
A. ( 3 )
B. ( 4 )
C. ( 5 )
D. ( 6 )
Question 2
Determine the value of $x$ in the equation $2^x + 5^x = 7^x$.
A. 1
B. 2
C. 3
D. 4
Question 3
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 4
A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, and P\( X = 3 \) = 0.3. Find the expected value of X.
A. 1.1
B. 1.2
C. 1.3
D. 1.4
Question 5
Solve the inequality \( x^2 + 4x - 5 \geq 0 \).
A. \( x \leq -5 \) or \( x \geq 1 \)
B. \( x \leq -1 \) or \( x \geq 5 \)
C. \( x \leq -5 \) or \( x \geq -1 \)
D. \( x \leq 1 \) or \( x \geq 5 \)
Question 6
Find the equation of the circle pas\sing through the points ((2,3)) and ((4,5)) with center on the line \( y=2x+1 \).
A. \( x^2+y^2-4x-6y+13=0 \)
B. \( x^2+y^2+2x-4y+5=0 \)
C. \( x^2+y^2-2x+6y-11=0 \)
D. \( x^2+y^2+4x+2y-9=0 \)
Question 7
Solve the inequality \( \frac{x^2-4x-3}{x^2+2x-3}>0 \).
A. \( x<-1 \text{ or } x>3 \)
B. \( x<-1 \text{ or } x<3 \)
C. \( x>1 \text{ or } x>3 \)
D. \( x<1 \text{ or } x<3 \)
Question 8
A set of numbers is defined as \( S = \{ x \in \mathbb{R} : x^2 - 4x + 3 = 0 \} \). Find the elements of the set S.
A. \( \{ 1, 3 \} \)
B. \( \{ -1, -3 \} \)
C. \( \{ 1, -3 \} \)
D. \( \{ -1, 3 \} \)
Question 9
A circle with center ( C ) and radius ( r ) passes through the points ( A ) and ( B ). If \( CA = 3 \) and \( CB = 4 \), find the area of the circle.
A. \pi r^2
B. \frac{1}{2} \pi r^2
C. \frac{1}{4} \pi r^2
D. \frac{1}{8} \pi r^2
Question 10
Find the value of \( \log_{10} \( 1000 \ \) ).
A. ( 3 )
B. ( 4 )
C. ( 5 )
D. ( 6 )
Question 11
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the quotient rule.
A. \( f'(x) = \frac{2x^2 - 4}{\( x - 2 \)^2} \)
B. \( f'(x) = \frac{2x}{x - 2} \)
C. \( f'(x) = \frac{x^2 - 4}{\( x - 2 \)^2} \)
D. \( f'(x) = \frac{2x^2 - 4x}{\( x - 2 \)^2} \)
Question 12
Solve the differential equation \( \frac{dy}{dx} = \frac{x^2}{y} \).
A. y = \frac{x^3}{3} + C
B. y = \frac{x^3}{3} - C
C. y = \frac{x^3}{3} + 3C
D. y = \frac{x^3}{3} - 3C
Question 13
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. -\frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. -\frac{1}{\( x^2 + 1 \)^2}
D. \frac{1}{\( x^2 + 1 \)^2}
Question 14
A fair six-sided die is rolled. What is the probability that the number appearing is greater than 4?
A. \( \frac{1}{6} \)
B. \( \frac{2}{6} \)
C. \( \frac{3}{6} \)
D. \( \frac{4}{6} \)
Question 15
Find the mean of the numbers 2, 4, 6, 8, 10.
A. ( 6 )
B. ( 7 )
C. ( 8 )
D. ( 9 )

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