POST UTME MOUNTAIN TOP UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P\( A \cap B \).
A. 0.2
B. 0.24
C. 0.3
D. 0.36
Question 2
A histogram 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 greater than 80.
A. \( P\( X > 80 \ \) = 0.1587 \)
B. \( P\( X > 80 \ \) = 0.3413 \)
C. \( P\( X > 80 \ \) = 0.5 \)
D. \( P\( X > 80 \ \) = 0.8413 \)
Question 3
A rec\tangular solid has dimensions 5 cm, 8 cm, and 3 cm. Find its surface area.
A. 154 cm^2
B. 156 cm^2
C. 158 cm^2
D. 160 cm^2
Question 4
Find the area under the curve \( y = x^2 + 2x + 1 \) from \( x = 0 \) to \( x = 2 \).
A. 7
B. 9
C. 11
D. 13
Question 5
Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 6
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 7
Find the sum of the first 5 terms of the geometric progression ( 2, 6, 18, ... ).
A. 240
B. 242
C. 244
D. 246
Question 8
A survey of 100 students found that 60 students preferred coffee, 30 students preferred tea, and 10 students preferred both. What is the probability that a randomly selected student prefers coffee?
A. 0.6
B. 0.7
C. 0.8
D. 0.9
Question 9
The vector \( \vec{a} \) has a magnitude of 5 and is directed at an angle of 30° to the positive x-axis. Find the x-component of the vector.
A. 4.33
B. 4.65
C. 4.97
D. 5.29
Question 10
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 12
A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers rolled is greater than 7?
A. \frac{1}{3}
B. \frac{1}{2}
C. \frac{2}{3}
D. \frac{3}{4}
Question 13
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 14
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > 3
B. x < 1 or x > 3
C. x < -3 or x > 1
D. x < 3 or x > 1
Question 15
The line \( y = 2x + 1 \) intersects the circle \( x^2 + y^2 = 4 \) at two points. Find the coordinates of the point of intersection.

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