POST UTME PAN-ATLANTIC UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...
A. 312
B. 3120
C. 31200
D. 312000
Question 2
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 3
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
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \left\( -\frac{5}{4}, \frac{3}{2} \right \)
B. \left\( -\infty, -\frac{5}{4} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
C. \left\( -\infty, -\frac{5}{4} \right \) \cup \left\( -\frac{3}{2}, \infty \right \)
D. \left\( -\infty, \frac{3}{2} \right \)
Question 5
Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, ... ).
A. ( 62 )
B. ( 64 )
C. ( 66 )
D. ( 68 )
Question 6
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 7
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 8
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 9
Solve for y in the equation \( 2y^2 + 5y - 3 = 0 \).
A. -1
B. 1
C. 3
D. -3
Question 10
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 11
Solve the matrix equation \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 3 \ 4 \end{bmatrix}
C. \begin{bmatrix} 5 \ 6 \end{bmatrix}
D. \begin{bmatrix} 7 \ 8 \end{bmatrix}
Question 12
Solve the system of linear equations \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 13
A set A contains 3 elements. Find the number of subsets of A.
A. 8
B. 16
C. 32
D. 64
Question 14
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \)
B. ( 3 )
C. ( 4 )
D. ( 6 )
Question 15
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

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