POST UTME UNIOSUN 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality $|2x - 3| > 5$.
A. x < -4 or x > 4
B. x < -4 or x > 2
C. x < 2 or x > 4
D. x < -2 or x > 4
Question 2
Solve the inequality $|x - 2| > 3$.
A. x < -1 or x > 5
B. x < -1 or x > 2
C. x < 2 or x > 5
D. x < 5 or x > 2
Question 3
A survey of 100 students found that 60 students preferred Mathematics, 30 preferred Science, and 10 preferred both. What is the probability that a randomly selected student prefers Mathematics or Science?
A. 0.7
B. 0.8
C. 0.9
D. 1.0
Question 4
Solve the system of equations $\begin{cases} x + y = 2 \ x - y = 1 \end{cases}$.
A. x = 1, y = 1
B. x = 1, y = -1
C. x = -1, y = 1
D. x = -1, y = -1
Question 5
Find the area under the curve \( y = x^2 + 2x + 1 \) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 20
C. 30
D. 40
Question 6
Solve the equation \( 2^x + 2^{x+1} = 2^{x+2} + 2^{x+3} \).
A. x = -1
B. x = 0
C. x = 1
D. x = 2
Question 7
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 8
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If a new score of 90 is added to the set, what is the new mean?
A. 80
B. 85
C. 90
D. 95
Question 9
Solve the inequality $\frac{x^2 - 4}{x + 2} > 0$.
A. $\( -\infty, -2 \) \cup \( 2, \infty \)$
B. $\( -\infty, -2 \) \cup \( -2, 2 \) \cup \( 2, \infty \)$
C. $\( -\infty, -2 \) \cup \( 2, \infty \)$
D. $\( -\infty, 2 \) \cup \( 2, \infty \)$
Question 10
Find the value of $\int_0^1 x^2 dx$.
A. \frac{1}{3}
B. \frac{1}{2}
C. \frac{2}{3}
D. \frac{1}{4}
Question 11
Solve the system of linear equations \( 2x + 3y = 7 \) and \( x - 2y = -3 \).
A. \left\( \frac{13}{7}, \frac{5}{7} \right \)
B. \left\( \frac{5}{7}, \frac{13}{7} \right \)
C. \left\( \frac{13}{7}, -\frac{5}{7} \right \)
D. \left\( -\frac{5}{7}, \frac{13}{7} \right \)
Question 12
Solve the system of equations $\begin{cases} x + y = 2 \ x - 2y = -3 \end{cases}$.
A. $\left\{ \left\( -1, \frac{5}{2} \right \) \right\}$
B. $\left\{ \left\( 1, \frac{1}{2} \right \) \right\}$
C. $\left\{ \left\( -1, \frac{1}{2} \right \) \right\}$
D. $\left\{ \left\( 1, \frac{5}{2} \right \) \right\}$
Question 13
Find the equation of the line pas\sing through the points $\( -2, 3 \)$ and $\( 1, -2 \)$.
A. y = -\\frac{5}{3}x - \\frac{13}{3}
B. y = \frac{5}{3}x + \frac{13}{3}
C. y = -\\frac{3}{5}x + \\frac{13}{5}
D. y = \\frac{3}{5}x - \\frac{13}{5}
Question 14
Find the value of \( \frac{1}{2} \int_{0}^{\pi} \sin x \, dx \).
A. \frac{1}{2}
B. \frac{1}{4}
C. \frac{3}{4}
D. \frac{1}{3}
Question 15
Find the value of $\frac{d^2}{dx^2} \left\( x^3 - 3x^2 + 2x - 1 \right \)$.
A. 6
B. -6
C. 12
D. -12

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