POST UTME LEAD CITY UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Solve the system of linear equations u\sing matrices: \begin{align*} 2x + 3y &= 7 \ 4x - 2y &= -2 \end{align*}
A. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 1 \ 1 \end{pmatrix}
B. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 2 \ 3 \end{pmatrix}
C. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 3 \ 2 \end{pmatrix}
D. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 4 \ 1 \end{pmatrix}
Question 3
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 4
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 5
Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.
A. \( \frac{1}{3} pi \)
B. \( \frac{2}{3} pi \)
C. \( \frac{4}{3} pi \)
D. \( \frac{8}{3} pi \)
Question 6
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 7
Solve the equation \log_{10} \( x^2 \) = 4.
A. 10^4
B. 10^8
C. 10^{-4}
D. 10^{-8}
Question 8
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
Question 9
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.
A. \( \frac{1}{2} \( 1 - x^2 \ \)^{-\frac{3}{2}} )
B. \( \frac{1}{2} \( 1 - x^2 \ \)^{-\frac{1}{2}} )
C. \( \frac{x}{\( 1 - x^2 \ \)^{\frac{3}{2}}} )
D. \( \frac{x}{\( 1 - x^2 \ \)^{\frac{1}{2}}} )
Question 10
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 11
Find the value of $\int_0^1 \frac{1}{1+x^2} dx$.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 12
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x + 1} ) u\sing the quotient rule.
A. \frac{2x + 2}{\( x + 1 \)^2}
B. \frac{2x + 2}{\( x + 1 \)^2} + \frac{1}{x + 1}
C. \frac{2x + 2}{\( x + 1 \)^2} - \frac{1}{x + 1}
D. \frac{2x + 2}{\( x + 1 \)^2} - \frac{2}{x + 1}
Question 13
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If 75% of the scores fall below 85, what is the z-score corresponding to 85?
A. 0.5
B. 1
C. 1.5
D. 2
Question 14
Find the area under the curve y = 3x^2 + 2x - 5 from x = 0 to x = 2.
A. 22
B. 24
C. 26
D. 28
Question 15
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

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