POST UTME UNILORIN 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 not blue?
A. \( \frac{1}{3} \)
B. \( \frac{2}{5} \)
C. \( \frac{3}{5} \)
D. \( \frac{4}{5} \)
Question 2
Find the value of x in the equation \( \frac{x}{2} + 3 = 7 \).
A. 8
B. 10
C. 12
D. 14
Question 3
Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?
A. 12
B. 14
C. 16
D. 18
Question 4
A survey of 100 students found that 60% of them preferred pizza, 20% preferred burgers, and 20% preferred sandwiches. What is the probability that a randomly selected student prefers pizza?
A. 0.3
B. 0.4
C. 0.5
D. 0.6
Question 5
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 6
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{2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 7
Solve the inequality $x^2 + 4x + 4 > 0$.
A. \( -\infty, -2 \) \cup \( 2, \infty \)
B. \( -\infty, 2 \) \cup \( 2, \infty \)
C. \( -\infty, -2 \) \cup \( -2, 2 \) \cup \( 2, \infty \)
D. \( -\infty, -2 \) \cup \( 2, \infty \)
Question 8
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the power rule.
A. ( f'(x) = 6x + 2 )
B. ( f'(x) = 3x^2 + 2x - 5 )
C. ( f'(x) = 6x - 2 )
D. ( f'(x) = 3x^2 - 2x + 5 )
Question 9
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -3 \) ∪ \( -1, ∞ \)
D. \( -∞, 1 \) ∪ (3, ∞)
Question 10
Solve for $x$: $\log_{10}\( x^2 \) = 4$.
A. 10
B. 100
C. 1000
D. 10000
Question 11
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 12
A circle has a radius of 4 cm. What is its circumference?
A. 8π
B. 10π
C. 12π
D. 16π
Question 13
In the diagram below, $ABCD$ is a square with side length $s$. If $E$ is the midpoint of $AD$, find the length of $BE$.
A. \frac{s}{2}
B. s
C. \frac{\sqrt{2}s}{2}
D. s\sqrt{2}
Question 14
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. -2
B. -3
C. -1
D. 1
Question 15
Solve the system of equations: x + y = 4 and x - y = 2
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0

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