POST UTME LEAD CITY UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation $\frac{x}{x+1} + \frac{x}{x-1} = 2$.
A. x = -1
B. x = 1
C. x = -2
D. x = 2
Question 2
A set $A$ is defined as $A = \{x \in \mathbb{R} : x^2 + 2x + 1 > 0\}$. Find the value of $\cup A$.
A. \mathbb{R}
B. \( -\infty, 0 \)
C. \( 0, \infty \)
D. \( -1, 1 \)
Question 3
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the power rule.
A. 6x + 2
B. 6x - 2
C. 3x^2 + 2
D. 3x^2 - 2
Question 4
Solve the equation [ 2x^2 + 3x - 1 = 0 ].
A. x = -1/2
B. x = 1/2
C. x = -1
D. x = 1
Question 5
A sequence is defined by the recurrence relation [ a_n = 2a_{n-1} + 3 ] with initial term [ a_1 = 2 ]. Find the sum of the first five terms of the sequence.
A. 55
B. 65
C. 75
D. 85
Question 6
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula. What is the value of ( x )?
A. 0
B. -2
C. 2
D. -1
Question 7
A sphere has a radius of 5 cm. What is the volume of the sphere?
A. 32.67
B. 50.24
C. 100.48
D. 200.96
Question 8
Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{1}{2^n} \).
A. 1
B. \( \frac{1}{2} \)
C. \( \frac{2}{3} \)
D. \( \frac{3}{4} \)
Question 9
Evaluate the definite integral \( int_{0}^{1} x^2 dx \).
A. \( \frac{1}{3} \)
B. \( \frac{1}{2} \)
C. \( \frac{2}{3} \)
D. \( \frac{3}{4} \)
Question 10
A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 60 and 80?
A. 0.25
B. 0.5
C. 0.75
D. 0.9
Question 11
A circle has a radius of 4 cm. What is the area of the circle?
A. 16
B. 25.12
C. 50.24
D. 100.48
Question 12
Solve the inequality $\frac{1}{x-2} + \frac{1}{x+2} \leq \frac{1}{2}$.
A. x \in \( -\infty, -2 \) \cup \( 2, \infty \)
B. x \in \( -\infty, -2 \) \cup (2, 4]
C. x \in \( -\infty, -2 \) \cup (2, \infty]
D. x \in \( -\infty, -2] \cup \( 2, \infty \ \)
Question 13
Find the value of $\int_{0}^{\pi} \sin^2(x) \cos^2(x) dx$.
A. 0
B. \frac{\pi}{4}
C. \frac{\pi}{2}
D. \frac{3\pi}{4}
Question 14
Find the value of $\sum_{n=1}^{\infty} \frac{1}{n^2}$.
A. 1
B. \frac{1}{2}
C. \frac{1}{3}
D. \frac{1}{4}
Question 15
A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, and P\( X = 3 \) = 0.3. What is the expected value of X?
A. 1.1
B. 1.2
C. 1.3
D. 1.4

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