POST UTME LEAD CITY UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
B. \( x < \frac{1}{2} \) or \( x > -\frac{3}{2} \)
C. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)
D. \( x < \frac{3}{2} \) or \( x > -\frac{1}{2} \)
Question 3
Find the derivative of the function \( y = \frac{1}{x^2 + 1} \ \) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-x}{\( x^2 + 1 \)^2}
D. \frac{x}{\( x^2 + 1 \)^2}
Question 4
Find the area under the curve $y = x^2 + 2x - 3$ from $x = 0$ to $x = 2$.
A. 10
B. 12
C. 14
D. 16
Question 5
Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 6
Determine 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 = 4 )
D. \( x-2 \ \)^2 + \( y+3 \)^2 = 4 )
Question 7
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi\text{ cm}^3
B. 48\pi\text{ cm}^3
C. 96\pi\text{ cm}^3
D. 192\pi\text{ cm}^3
Question 8
A circle has a radius of 4 cm. What is the area of the circle?
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 9
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 10
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. \( \frac{1}{4} \)
B. \( \frac{3}{8} \)
C. \( \frac{1}{2} \)
D. \( \frac{3}{4} \)
Question 11
Solve the inequality $\log_2\( x^2 - 4 \) > 2$.
A. \( 4, \infty \)
B. \( 2, \infty \)
C. \( -\infty, -2 \) \cup \( 2, \infty \)
D. \( -\infty, -2 \) \cup \( 4, \infty \)
Question 12
Simplify the expression \( \sqrt[3]{64x^3y^3} \).
A. \( 4x^1y^1 \)
B. \( 4x^3y^3 \)
C. \( 64x^3y^3 \)
D. \( 4x^3y^1 \)
Question 13
Solve the system of equations \( egin{cases} x + y + z = 6 \ 2x + 2y + 3z = 12 \ 3x + 2y + z = 9 \end{cases} \).
A. \( x = 1, y = 2, z = 3 \)
B. \( x = 2, y = 1, z = 3 \)
C. \( x = 3, y = 2, z = 1 \)
D. \( x = 1, y = 3, z = 2 \)
Question 14
A curve is defined by the equation $y = \frac{1}{x^2 + 1}$. Find the area under the curve from $x = 0$ to $x = 1$.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{5}
Question 15
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4

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