POST UTME PAN-ATLANTIC UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation [ 2^x + 3^x = 5^x ].
A. x = 1
B. x = 2
C. x = 3
D. x = 4
Question 2
A triangle has sides of length 5 cm, 12 cm, and 13 cm. Find the area of the triangle.
A. ( 30 ) cm²
B. ( 60 ) cm²
C. ( 90 ) cm²
D. ( 120 ) cm²
Question 3
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 4
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 5
A set of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is between 60 and 80.
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 6
Solve for y in the equation \( 2y^2 + 5y - 3 = 0 \).
A. -1
B. 1
C. 3
D. -3
Question 7
Solve the system of linear equations \( egin{cases} x + y + z = 6 \ x + 2y + 3z = 12 \ 2x + 3y + 4z = 20 \end{cases} \).
A. \( x = 1, y = 2, z = 3 \)
B. \( x = 2, y = 1, z = 3 \)
C. \( x = 1, y = 3, z = 2 \)
D. \( x = 2, y = 3, z = 1 \)
Question 8
A polynomial function f(x) has a degree of 4 and a leading coefficient of 2. If f\( -2 \) = 20 and f(1) = -3, find the value of f(0).
A. 10
B. 15
C. 20
D. 25
Question 9
Find the sum of the first 5 terms of the geometric series \( 2 + 6 + 18 + \cdots \).
A. 120
B. 150
C. 180
D. 200
Question 10
Solve the inequality \( \frac{x^2 - 4}{x + 2} geq 0 \) for ( x in mathbb{R} ).
A. \( -infty, -2 \ \) cup [0, infty) )
B. \( -infty, -2 \ \) cup \( -2, 0 \) cup (0, infty) )
C. \( -infty, -2 \ \) cup (0, infty) )
D. \( -infty, -2 \ \) cup [0, 2] )
Question 11
A 3x3 matrix A has the following elements: a11 = 2, a12 = -1, a13 = 3, a21 = 4, a22 = 1, a23 = -2, a31 = 5, a32 = 2, a33 = 1. Find the determinant of matrix A.
A. 0
B. 10
C. 20
D. 30
Question 12
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 6
B. 12
C. 18
D. 24
Question 13
Find the probability that at least one of the events A and B occurs, given that P(A) = 0.4, P(B) = 0.3, and P\( A \cap B \) = 0.1.
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 14
Solve the equation: \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = 2 \)
C. \( x = -1 \)
D. \( x = 1 \)
Question 15
A set of exam scores has a mean of 80 and a s\tandard deviation of 10. If a new score of 90 is added to the set, what is the new mean?
A. 79.5
B. 80.5
C. 81.5
D. 82.5

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