POST UTME RSU 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, -3 \) ∪ (3, ∞)
Question 2
If $x^2 + 2x + 1 = 0$, find the value of $x^3 + 2x^2 + x + 1$.
A. -1
B. 0
C. 1
D. 2
Question 3
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 12
C. 14
D. 16
Question 4
A right circular cone has a height of 15 cm and a base radius of 8 cm. Find its volume.
A. 1000π cm^3
B. 1200π cm^3
C. 1500π cm^3
D. 1800π cm^3
Question 5
A random variable $X$ has a probability distribution given by $P\( X=x \)=\frac{1}{2}$. Find the expected value of $X$.
A. 0
B. 1
C. 2
D. 3
Question 6
A solid cylinder has a height of 10 cm and a radius of 4 cm. Find the volume of the cylinder.
A. 800π cm^3
B. 1000π cm^3
C. 1200π cm^3
D. 1600π cm^3
Question 7
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16
C. \left\( x + 3 \right \)^2 + \left\( y - 2 \right \)^2 = 16
D. \left\( x - 3 \right \)^2 + \left\( y + 2 \right \)^2 = 16
Question 8
If ( f(x) = \frac{1}{x^2 + 1} ), find ( f'(x) ).
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )
Question 9
A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.
A. 8 cm
B. 6 cm
C. 10 cm
D. 12 cm
Question 10
Solve the inequality \( 2x^2 + 5x - 3 \ge 0 \).
A. \( x \le -\frac{3}{2} \) or \( x \ge \frac{1}{2} \)
B. \( x \le -\frac{1}{2} \) or \( x \ge \frac{3}{2} \)
C. \( x \le -\frac{1}{2} \) or \( x \ge \frac{1}{2} \)
D. \( x \le -\frac{3}{2} \) or \( x \ge -\frac{1}{2} \)
Question 11
A binary operation ∗ is defined as a ∗ b = a^2 + b^2. Find the value of 2 ∗ 3.
A. 13
B. 17
C. 19
D. 21
Question 12
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \ \).
A. \( 2 + 6 + 18 + \cdots + 12288 \)
B. \( 2 + 6 + 18 + \cdots + 12288 \)
C. \( 2 + 6 + 18 + \cdots + 12288 \)
D. \( 2 + 6 + 18 + \cdots + 12288 \)
Question 13
Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...
A. 10496
B. 10504
C. 10512
D. 10520
Question 14
A sequence is defined by the recurrence relation a_n = 2a_{n-1} + 1, with a_1 = 3. Find the sum of the first 5 terms of the sequence.
A. 3 + 7 + 15 + 31 + 63
B. 3 + 5 + 11 + 23 + 47
C. 3 + 6 + 12 + 24 + 48
D. 3 + 8 + 16 + 32 + 64
Question 15
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find \( lim_{x \to 2} f\( x \ \) ) u\sing the chain rule.
A. \( \lim_{x \to 2} f(x) = \frac{0}{0} \)
B. \( \lim_{x \to 2} f(x) = \frac{4}{0} \)
C. \( \lim_{x \to 2} f(x) = \frac{0}{0} \)
D. \( \lim_{x \to 2} f(x) = \frac{4}{2} \)

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