POST UTME UNN 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \( \frac{1}{2} \log_{10} \( x^2 \) = 4 \).
A. x = 10^8
B. x = 10^4
C. x = 10^2
D. x = 10^6
Question 2
If \( \vec{a} = \begin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( \vec{b} = \begin{pmatrix} 4 \ 5 \end{pmatrix} \), find the magnitude of the cross product \( \vec{a} \times \vec{b} \).
A. 10
B. 12
C. 15
D. 20
Question 3
Solve the inequality $\frac{x-2}{x+1} > 0$.
A. \( -\infty, -1 \) \cup \( 2, \infty \)
B. \( -\infty, -1 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 2, \infty \)
D. \( -\infty, 1 \) \cup \( 2, \infty \)
Question 4
Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \).
A. x \leq -3 \text{ or } x \geq \frac{1}{2}
B. x \leq -3 \text{ or } x \leq \frac{1}{2}
C. x \geq -3 \text{ or } x \geq \frac{1}{2}
D. x \geq -3 \text{ or } x \leq \frac{1}{2}
Question 5
Solve for x in the linear equation \( 2x + 5 = 11 \ \).
A. 3
B. 4
C. 5
D. 6
Question 6
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 7
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. 0
B. -2
C. -1
D. 1
Question 8
Find the value of ( x ) in the equation \( 2^x = 16 \).
A. 2
B. 3
C. 4
D. 5
Question 9
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. x^2 + y^2 + 4x - 6y + 13 = 0
B. x^2 + y^2 - 4x + 6y + 13 = 0
C. x^2 + y^2 + 4x + 6y + 13 = 0
D. x^2 + y^2 - 4x - 6y + 13 = 0
Question 10
Find the equation of the line pas\sing through the points [ (2, 3) \] and [ (4, 5) \].
A. y = 2x + 1
B. y = 2x - 1
C. y = -2x + 1
D. y = -2x - 1
Question 11
A histogram represents the distribution of exam scores. If the mean score is 60 and the s\tandard deviation is 10, what is the probability that a randomly selected score is between 50 and 70?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 12
Find the determinant of the 3x3 matrix \( \begin{bmatrix} 2 & 3 & 1 \\ 4 & 2 & 3 \\ 1 & 1 & 2 \end{bmatrix} \ \).
A. -1
B. 1
C. 2
D. 3
Question 13
Find the derivative of the function \( f(x) = 3x^2 + 2x - 5 \) u\sing the power rule.
A. 6x + 2
B. 3x + 2
C. 2x + 5
D. x^2 + 2
Question 14
A box contains 12 red balls and 8 blue balls. If 2 balls are drawn at random, what is the probability that both balls are blue?
A. \frac{1}{5}
B. \frac{1}{10}
C. \frac{1}{15}
D. \frac{1}{20}
Question 15
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = -1
C. x = 0
D. x = 1

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