POST UTME SUMMIT UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations \( x + y = 3 \) and \( xy = 2 \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 1, y = -2 \)
D. \( x = -2, y = 1 \)
Question 2
Find the equation of the circle with centre (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 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
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. ( 12 )
B. ( 14 )
C. ( 16 )
D. ( 18 )
Question 5
A histogram represents the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a different score range. If the height of each bar is proportional to the number of students in that score range, and the total number of students is 50, find the mean score of the class.
A. 60
B. 70
C. 80
D. 90
Question 6
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \).
A. \( \frac{8}{3} \)
B. \( \frac{16}{3} \)
C. \( \frac{32}{3} \)
D. \( \frac{64}{3} \)
Question 7
Find the value of \( \log_{10} \( 1000 \ \) ).
A. ( 3 )
B. ( 4 )
C. ( 5 )
D. ( 6 )
Question 8
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 9
Determine the value of $x$ in the equation $2^x + 5^x = 7^x$.
A. 1
B. 2
C. 3
D. 4
Question 10
A particle moves in a straight line with its velocity given by (v(t)=2t^2-5t+3). Find the acceleration of the particle at time \( t=2 \) seconds.
A. (a(2)=4)
B. (a(2)=-3)
C. (a(2)=0)
D. (a(2)=1)
Question 11
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 12
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 13
A bag contains 5 red marbles, 8 blue marbles, and 12 green marbles. If a marble is drawn at random, what is the probability that it is either red or blue?
A. \frac{13}{25}
B. \frac{15}{25}
C. \frac{17}{25}
D. \frac{19}{25}
Question 14
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = 2 \)
C. \( x = -1 \)
D. \( x = 1 \)
Question 15
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. \( \{ -1, 3 \} \)

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