POST UTME AAUA 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \( \tan x = \frac{1}{\sqrt{3}} \) and \( 0 leq x leq \frac{pi}{2} \).
A. π/6
B. π/4
C. π/3
D. π/2
Question 2
In a probability experiment, two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 3
A histogram of exam scores is shown below. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 4
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 + 2
D. y = x - 2
Question 5
Solve the inequality \( x^2 - 4x - 5 > 0 \).
A. \( -\infty, -1 \) \cup \( 5, \infty \)
B. \( -\infty, 1 \) \cup \( 5, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, 1 \) \cup \( 5, \infty \)
Question 6
Let ( f(x) = \frac{x^2 - 4}{x + 2} ). Find the value of \( f\( -2 \ \) ) if it exists.
A. undefined
B. -4
C. 0
D. 2
Question 7
A vector \( \vec{a} \) has a magnitude of 5 and makes an angle of 30° with the positive x-axis. Find the x and y components of \( \vec{a} \).
A. x = 4, y = 3
B. x = 3, y = 4
C. x = 4, y = 4
D. x = 3, y = 3
Question 8
In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the sample is normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?
A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6179
Question 9
The mean of 5 numbers is 15. If one of the numbers is 10, what is the sum of the other 4 numbers?
A. 50
B. 60
C. 70
D. 80
Question 10
Find the value of k in the matrix equation \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} k & 0 \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 3 & 2 \ 9 & 6 \end{bmatrix} \).
A. 3
B. 4
C. 5
D. 6
Question 11
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{5}{6} \)
Question 12
A random experiment consists of two indep\endent events, A and B. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?
A. 0.2
B. 0.4
C. 0.6
D. 0.8
Question 13
Solve the inequality: 2x^2 + 5x - 3 > 0.
A. x < -1 or x > 3/2
B. x > -1 or x < 3/2
C. x < 3/2 or x > -1
D. x > 3/2 or x < -1
Question 14
Find the derivative of ( f(x) = x^2 \sin x ) u\sing the product rule.
A. ( f'(x) = 2x \sin x + x^2 \cos x \)
B. ( f'(x) = x^2 \cos x - 2x \sin x \)
C. ( f'(x) = 2x \cos x + x^2 \sin x \)
D. ( f'(x) = x^2 \sin x - 2x \cos x \)
Question 15
Solve for ( x ) in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ).
A. \( x = \frac{pi}{4} \)
B. \( x = \frac{pi}{2} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{pi}{6} \)

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: