POST UTME PAN-ATLANTIC UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. Find the range of the set.
A. 16
B. 18
C. 20
D. 22
Question 2
A function f(x) is defined as ( f(x) = \frac{x^2 - 4x + 3}{x^2 + 2x + 1} ). Find the domain of the function.
A. \( -\infty, -1 \) \cup \( -1, \infty \)
B. \( -\infty, 1 \) \cup \( 1, \infty \)
C. \( -\infty, -2 \) \cup \( -2, \infty \)
D. \( -\infty, 2 \) \cup \( 2, \infty \)
Question 3
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 12
C. 14
D. 16
Question 4
A random variable X has a probability distribution given by the following histogram. What is the expected value of X?
A. 2
B. 3
C. 4
D. 5
Question 5
Find the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \tan\( x \ \) = \frac{3}{4} ).
A. 0
B. \frac{\pi}{4}
C. \frac{3\pi}{4}
D. \frac{5\pi}{4}
Question 6
Find the sum of the first 10 terms of the geometric series \( 2x^2 + 4x^3 + 8x^4 + ldots \).
A. 2x^2 \( 1 - x^2 \)^{-1} \( 1 - x^{10} \)
B. 2x^2 \( 1 - x^2 \)^{-1}
C. 2x^2 \( 1 - x^{10} \)
D. 2x^2 \( 1 - x^2 \)^{-1} \( 1 - x^{10} \)^{-1}
Question 7
In the diagram below, find the value of x.
A. 3
B. 4
C. 5
D. 6
Question 8
Find the area under the curve \( y = x^2 - 4x + 3 \) from \( x = 1 \) to \( x = 3 \).
A. \( 4 \ \)
B. \( 6 \ \)
C. \( 8 \ \)
D. \( 10 \ \)
Question 9
If ( f(x) = \frac{x^2 - 4}{x - 2} ), find \( f\( -2 \ \) ).
A. 0
B. 1
C. 2
D. 3
Question 10
Solve the inequality \( \frac{x}{x+1} > \frac{1}{x+1} \) for \( x in mathbb{R} setminus { -1 } \).
A. \( -1, 0 \) ∪ (1, ∞)
B. \( -1, 0 \) ∪ (0, ∞)
C. \( -1, 0 \) ∪ \( -∞, -1 \)
D. \( -1, 0 \) ∪ (0, 1)
Question 11
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.
A. 0.2
B. 0.3
C. 0.4
D. 0.5
Question 12
Solve for x in the equation \( \log_{10} \( x^2 \) = 4 \).
A. 10
B. 100
C. 1000
D. 10000
Question 13
Find the value of \( \sin 2x \) if \( \cos x = \frac{3}{5} \) and \( \sin x = \frac{4}{5} \).
A. \frac{24}{25}
B. \frac{16}{25}
C. \frac{20}{25}
D. \frac{12}{25}
Question 14
Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 15
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 3, \infty \)
D. \( -\infty, -3 \) \cup \( 1, \infty \)

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