POST UTME AAUA 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
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 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \ \) or \( x > \frac{3}{2} \ \)
B. \( x < -1 \ \) or \( x < \frac{3}{2} \ \)
C. \( x > -1 \ \) or \( x < \frac{3}{2} \ \)
D. \( x > -1 \ \) or \( x > \frac{3}{2} \ \)
Question 4
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. -2
B. -3
C. -4
D. -5
Question 5
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{3}x^3 + \frac{3}{2}x^2 - 2x \)
B. \( \frac{1}{2}x^3 + \frac{3}{2}x^2 - 2x \)
C. \( \frac{1}{2}x^3 + \frac{3}{2}x^2 - 2x + 8 \)
D. \( \frac{1}{3}x^3 + \frac{3}{2}x^2 - 2x + 8 \)
Question 6
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.8413
B. 0.6915
C. 0.6827
D. 0.9332
Question 7
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. \( x = \frac{pi}{6} \)
Question 8
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 90?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 9
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 10
Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 2 \).
A. 5
B. 7
C. 9
D. 11
Question 11
Find the sum of the first 5 terms of the geometric series \( 2x + 3x^2 + 4x^3 + \cdots \).
A. 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5
B. 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6
C. 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7
D. 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 + 9x^8
Question 12
In a triangle ABC, angle A = 30°, angle B = 90°, and side AB = 5 cm. Find the area of the triangle.
A. 10 cm²
B. 15 cm²
C. 20 cm²
D. 25 cm²
Question 13
A histogram of exam scores is shown below. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 14
A binary operation ∗ on the set of integers is defined as \( a ∗ b = a^2 + b^2 \). Find the value of ( 2 ∗ 3 ).
A. 13
B. 19
C. 25
D. 37
Question 15
Find the sum of the first 10 terms of the geometric series: 2, 6, 18, 54, ...
A. 104
B. 106
C. 108
D. 110

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