POST UTME UNIOSUN 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Find the value of \( \frac{1}{2} \int_{0}^{\pi} \cos^2 x \, dx \).
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{5}
Question 3
Find the probability of drawing two hearts from a s\tandard deck of 52 cards.
A. \frac{1}{221}
B. \frac{1}{13}
C. \frac{1}{17}
D. \frac{1}{25}
Question 4
Let ( X ) and ( Y ) be indep\endent random variables with probability density functions \( f_X\( x \ \) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ) and \( f_Y\( y \ \) = egin{cases} 3y^2, & 0 leq y leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that \( X + Y leq 1 \).
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 5
Find the derivative of the function ( f(x) = \frac{1}{x^2} ) u\sing the power rule.
A. -\frac{2}{x^3}
B. \frac{2}{x^3}
C. -\frac{1}{x^3}
D. \frac{1}{x^3}
Question 6
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 7
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 8
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 9
Let ( f(x) = x^2 + 2x - 3 ). Find the value of \( f\( -2 \ \) + f(1) ).
A. -3
B. -1
C. 1
D. 3
Question 10
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 11
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 12
Let ( f(x) = \frac{1}{1 + x^2} ). Find the value of \( int_{-1}^{1} f\( x \ \) , dx ).
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{5}
Question 13
Find the value of ( x ) that satisfies the equation \( 2^x = 16 \).
A. 2
B. 3
C. 4
D. 5
Question 14
Solve the equation \( x^2 + 4x - 5 = 0 \).
A. x = -5, x = 1
B. x = -1, x = 5
C. x = -1, x = -5
D. x = 1, x = 5
Question 15
Let ( f(x) = x^2 + 2x - 3 ). Find the value of ( f(1) + f\( -2 \) ).
A. -3
B. -1
C. 1
D. 3

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