POST UTME PAN-ATLANTIC UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A random variable ( X ) has a probability density function ( f(x) = \begin{cases} 2x & 0 < x < 1 \ 0 & \text{otherwise} \end{cases} ). Find \( P\( 0.2 < X < 0.8 \ \) ).
A. 0.3
B. 0.4
C. 0.5
D. 0.6
Question 2
Find the value of ( x ) in the matrix equation \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 7 \ 10 \end{bmatrix} \).
A. x = 3
B. x = 4
C. x = 5
D. x = 6
Question 3
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 4
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 5
A circle with center (2, 3) and radius 4 passes through the point (1, 1). Find the equation of the circle.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 4
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 9
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
Question 6
If ( f(x) = \frac{x^2 - 4}{x - 2} ), find \( f\( -2 \ \) ).
A. 0
B. 1
C. 2
D. 3
Question 7
Solve for x in the equation \( \log_{10} \( x^2 \) = 4 \).
A. 10
B. 100
C. 1000
D. 10000
Question 8
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 9
Find the sum of the infinite geometric series \( 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots \).
A. 2
B. 4
C. 8
D. 16
Question 10
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 11
Solve for x in the equation \( \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2} \).
A. x = -2
B. x = 1
C. x = 2
D. x = -1
Question 12
Solve for x in the equation \( \frac{1}{x+2} + \frac{1}{x-3} = \frac{1}{2} \).
A. x = -1
B. x = 2
C. x = 5
D. x = -5
Question 13
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \ \)
B. \( x = 2 \ \)
C. \( x = -1 \ \)
D. \( x = 1 \ \)
Question 14
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x in [0, 2pi] ).
A. [0, \frac{pi}{2}] cup [\frac{3pi}{2}, 2pi]
B. [0, \frac{pi}{2}] cup [\frac{pi}{2}, pi]
C. [0, \frac{pi}{2}] cup [pi, \frac{3pi}{2}]
D. [0, \frac{pi}{2}] cup [\frac{3pi}{2}, 2pi]
Question 15
In the diagram below, find the value of x.
A. 3
B. 4
C. 5
D. 6

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