POST UTME LEAD CITY UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).
Question 2
Solve the inequality \frac{x^2 - 4x - 5}{x - 5} > 0.
A. \( -\infty, -1 \) \cup \( 5, \infty \)
B. \( -\infty, 1 \) \cup \( 5, \infty \)
C. \( -\infty, -5 \) \cup \( 5, \infty \)
D. \( -\infty, 5 \) \cup \( 5, \infty \)
Question 3
Solve the equation $\log_{10}\( x^2 \) = 4$ for $x$.
A. \pm 10
B. \pm 20
C. \pm 40
D. \pm 80
Question 4
A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If 80% of the scores fall below 90, what is the value of the score that corresponds to the 80th percentile?
A. 80
B. 85
C. 90
D. 95
Question 5
Solve the quadratic equation $x^2 + 5x + 6 = 0$.
A. x = -2, x = -3
B. x = -1, x = -6
C. x = 2, x = 3
D. x = 1, x = 6
Question 6
Solve the system of equations \( egin{cases} x + y + z = 6 \ 2x + 3y - z = 2 \ x - 2y + 3z = -3 \end{cases} \) u\sing matrices.
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 7
Find the area under the curve $y = x^2$ from $x = 0$ to $x = 4$.
A. 64
B. 32
C. 16
D. 8
Question 8
Solve the inequality $|x-2| > 3$.
A. \( -\infty, -1 \) \cup \( 5, \infty \)
B. \( -\infty, -1 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 5, \infty \)
D. \( -\infty, 5 \) \cup \( 1, \infty \)
Question 9
A circle has a radius of 4 cm. Find the area of the circle.
A. 16\pi cm^2
B. 32\pi cm^2
C. 64\pi cm^2
D. 80\pi cm^2
Question 10
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = \frac{1}{2}x + 1
B. y = \frac{1}{2}x - 1
C. y = 2x - 3
D. y = 2x + 3
Question 11
Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).
A. \( x - 3 \)^2 + \( y - 4 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 9
C. \( x - 1 \)^2 + \( y - 2 \)^2 = 4
D. \( x - 4 \)^2 + \( y - 5 \)^2 = 25
Question 12
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. \cos^2 x
B. -\cos^2 x
C. \sin^2 x
D. -\sin^2 x
Question 13
In a probability experiment, two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?
A. 0.24
B. 0.48
C. 0.64
D. 0.76
Question 14
Find the volume of the solid formed by revolving the region bounded by the curve $y = \frac{1}{2}x^2 + 1$, the $x$-axis, and the line $x = 2$ about the $x$-axis.
A. \frac{8\pi}{3}
B. \frac{16\pi}{3}
C. \frac{32\pi}{3}
D. \frac{64\pi}{3}
Question 15
A number is chosen at random from the set {1, 2, 3, 4, 5, 6}. What is the probability that the number is even?
A. 0.5
B. 0.6
C. 0.7
D. 0.8

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