POST UTME LAUTECH 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find its volume.
A. 400 \text{ cm}^3
B. 500 \text{ cm}^3
C. 600 \text{ cm}^3
D. 800 \text{ cm}^3
Question 2
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 3
Solve the inequality \frac{x^2 - 4}{x + 2} > 0.
A. \( -\\infty, -2 \) \\cup \( 0, \\infty \)
B. \( -\\infty, -2 \) \\cup \( 0, \\infty \)
C. \( -\\infty, -2 \) \\cup \( 0, \\infty \)
D. \( -\\infty, -2 \) \\cup \( 0, \\infty \)
Question 4
Solve for x in the equation \( x^3 + 2x^2 - 7x + 12 = 0 \).
A. -3
B. -2
C. 1
D. 4
Question 5
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16
C. \left\( x + 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16
D. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
Question 6
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 7
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 8
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \)
A. 0
B. 1
C. 2
D. 3
Question 9
Solve the equation \frac{x}{x + 1} = \frac{2}{3}.
A. \{ 4 \}
B. \{ 4 \}
C. \{ 4 \}
D. \{ 4 \}
Question 10
Solve the equation: \frac{x}{2} + 3 = 7
A. 8
B. 10
C. 12
D. 14
Question 11
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.9544
B. 0.9772
C. 0.9987
D. 0.9999
Question 12
Find the value of \( \sin\( 2x \ \) ) given that \( \cos\( x \ \) = \frac{3}{5} ) and \( \sin\( x \ \) = \frac{4}{5} )
A. \frac{24}{25}
B. \frac{16}{25}
C. \frac{12}{25}
D. \frac{8}{25}
Question 13
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 14
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 15
In the circle shown, find the length of the arc intercepted by the central angle of 60°.
A. 3π cm
B. 6π cm
C. 9π cm
D. 12π cm

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