POST UTME LAUTECH 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = \frac{2}{2} x + \frac{1}{2}
B. y = \frac{2}{2} x + \frac{1}{2}
C. y = \frac{2}{2} x + \frac{1}{2}
D. y = \frac{2}{2} x + \frac{1}{2}
Question 2
Solve the inequality \frac{x - 2}{x + 1} < 0.
A. \( -\\infty, -1 \) \\cup \( 2, \\infty \)
B. \( -\\infty, -1 \) \\cup \( 2, \\infty \)
C. \( -\\infty, -1 \) \\cup \( 2, \\infty \)
D. \( -\\infty, -1 \) \\cup \( 2, \\infty \)
Question 3
Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1, and f_Y(y) = 3y^2, 0 < y < 1. Find the probability that X + Y < 1.
A. 1/4
B. 1/2
C. 3/4
D. 1
Question 4
Solve for x in the equation \( \frac{1}{2} \log_{10} \( x^2 \ \) = 4 )
A. 10
B. 100
C. 1000
D. 10000
Question 5
Solve the system of linear equations \begin{align*} x + y &= 4 \ x - y &= 2 \end{align*}.
A. \{ (2, 2) \}
B. \{ (2, 2) \}
C. \{ (2, 2) \}
D. \{ (2, 2) \}
Question 6
Simplify the expression: \frac{2x^2 - 5x + 3}{x^2 - 2x - 3}
A. \frac{\( 2x - 3 \)\( x - 1 \)}{\( x - 3 \)\( x + 1 \)}
B. \frac{\( 2x - 1 \)\( x - 3 \)}{\( x - 3 \)\( x + 1 \)}
C. \frac{\( 2x - 3 \)\( x + 1 \)}{\( x - 3 \)\( x - 1 \)}
D. \frac{\( 2x - 1 \)\( x + 3 \)}{\( x - 3 \)\( x + 1 \)}
Question 7
Solve for x in the equation \( x^3 + 2x^2 - 7x + 12 = 0 \).
A. -3
B. -2
C. 1
D. 4
Question 8
A survey of 100 students revealed that 60% of them preferred Mathematics, 20% preferred English, and 20% preferred neither. If 5 students who preferred Mathematics were randomly selected, what is the probability that at least 3 of them preferred English?
A. 0.25
B. 0.30
C. 0.35
D. 0.40
Question 9
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. What is the probability that a randomly selected score will be between 60 and 90?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 10
A circle with center ( C ) and radius 4 passes through the point ( P(3, 4) ). Find the equation of the circle.
A. \( x - 3 \)^2 + \( y - 4 \)^2 = 16
B. \( x + 3 \)^2 + \( y - 4 \)^2 = 16
C. \( x - 3 \)^2 + \( y + 4 \)^2 = 16
D. \( x + 3 \)^2 + \( y + 4 \)^2 = 16
Question 11
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. Calculate the coefficient of variation (CV) of the sample.
A. 12.5%
B. 15%
C. 17.5%
D. 20%
Question 12
In the diagram below, the volume of the rec\tangular prism is 240 cm^3. If the length and width are doubled, what is the new volume?
A. 960 cm^3
B. 480 cm^3
C. 240 cm^3
D. 120 cm^3
Question 13
Find 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 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 14
A rec\tangular box has a length of 10 cm, a width of 5 cm, and a height of 8 cm. What is the volume of the box in cubic centimeters?
A. 400
B. 500
C. 600
D. 800
Question 15
Find the mean deviation of the data set: { 2, 4, 6, 8, 10 }.
A. 2
B. 4
C. 6
D. 8

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