POST UTME ELIZADE UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the trigonometric equation \( 2 \sin^2 x + 3 \cos x - 1 = 0 \) for ( x ) in the interval \( [0, 2 \pi] \).
A. \frac{\pi}{6}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{2}
Question 2
Solve for x in the equation \( 2x^2 + 5x - 3 = 0 \).
A. -1
B. -3
C. 1
D. 3
Question 3
A set of 5 consecutive integers has a median of 10. What is the sum of the integers?
A. 250
B. 260
C. 270
D. 280
Question 4
Solve the inequality 3^x + 2^x > 5.
A. x > 1
B. x < 1
C. x > 2
D. x < 2
Question 5
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. -1
B. 1
C. 2
D. 3
Question 6
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{-2x}{x^2 + 1}
C. \frac{2x}{\( x^2 + 1 \)^2}
D. \frac{2x}{x^2 + 1}
Question 7
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 29524
B. 29524.5
C. 29525
D. 29526
Question 8
Find the magnitude of the vector \( egin{pmatrix} 3 \ 4 \end{pmatrix} \).
A. 5
B. \sqrt{5}
C. \sqrt{25}
D. \sqrt{50}
Question 9
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for x.
A. 0
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. \frac{3\pi}{4}
Question 10
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \left\( -\frac{5}{4}, \frac{3}{2} \right \)
B. \left\( -\frac{3}{2}, \frac{5}{4} \right \)
C. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{5}{4}, \infty \right \)
D. \left\( -\infty, \frac{5}{4} \right \) \cup \left\( -\frac{3}{2}, \infty \right \)
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. 0.1587
B. 0.3413
C. 0.5
D. 0.8413
Question 12
Find the derivative of the function f(x) = \\frac{1}{2x^2 + 1} u\sing the chain rule.
A. -\\frac{2x}{\( 2x^2 + 1 \)^2}
B. \\frac{2x}{\( 2x^2 + 1 \)^2}
C. -\\frac{1}{\( 2x^2 + 1 \)^2}
D. \\frac{1}{\( 2x^2 + 1 \)^2}
Question 13
A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } X = 1 \ 0.3 & \text{if } X = 2 \ 0.5 & \text{if } X = 3 \end{cases} ). Find the expected value of X.
A. 1.5
B. 2
C. 2.5
D. 3
Question 14
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 1/3
C. 2/5
D. 3/5
Question 15
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If 80% of the scores are above 60, what is the value of the lower limit of the interval?
A. 50
B. 55
C. 60
D. 65

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