POST UTME LEAD CITY UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 2
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. 1
B. 2
C. 3
D. 4
Question 3
Find the value of \( \sqrt{\frac{16}{25}} \).
A. 2
B. 4
C. 8
D. 16
Question 4
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 5
A histogram of exam scores has a mean of 80 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 70 and 90?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
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
A random variable ( X ) has a probability distribution given by \( P\( X=x \ \) = \frac{1}{2^x} ) for \( x = 1, 2, 3, ldots \). Find ( P(X geq 3) ).
A. \( \frac{1}{4} \)
B. \( \frac{1}{2} \)
C. \( \frac{3}{4} \)
D. \( \frac{7}{8} \)
Question 8
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 9
Find the area under the curve y = x^2 from x = 0 to x = 4.
A. 16
B. 32
C. 48
D. 64
Question 10
A particle moves in a plane with position vector \( \vec{r}\( t \ \) = 2\cos t\hat{i} + 3\sin t\hat{j}). Find the velocity vector at time $t = \frac{\pi}{4}$.
A. \frac{3}{2}\sqrt{2}\hat{i} + \frac{4}{\sqrt{2}}\hat{j}
B. \frac{4}{\sqrt{2}}\hat{i} + \frac{3}{2}\sqrt{2}\hat{j}
C. \frac{3}{2}\sqrt{2}\hat{i} - \frac{4}{\sqrt{2}}\hat{j}
D. -\frac{4}{\sqrt{2}}\hat{i} + \frac{3}{2}\sqrt{2}\hat{j}
Question 11
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 12
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 13
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 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. \( \frac{1}{4} \)
B. \( \frac{3}{8} \)
C. \( \frac{1}{2} \)
D. \( \frac{3}{4} \)
Question 15
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

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: