POST UTME RHEMA UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In a triangle with sides of length 5, 12, and 13, what is the measure of the angle opposite the side of length 12?
A. 30\circ
B. 60\circ
C. 90\circ
D. 120\circ
Question 2
A random sample of 16 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the population mean.
A. 173.2 cm, 177.8 cm
B. 174.1 cm, 176.9 cm
C. 172.9 cm, 178.1 cm
D. 173.5 cm, 177.5 cm
Question 3
Find the equation of the line pas\sing through the points (A(2, 3)) and (B(4, 5)).
A. \( y = \frac{5-3}{4-2}x + \frac{3 \cdot 4 - 5 \cdot 2}{4 - 2} \)
B. \( y = \frac{5-3}{4-2}x + \frac{3 \cdot 2 - 5 \cdot 4}{4 - 2} \)
C. \( y = \frac{5-3}{4-2}x + \frac{3 \cdot 4 - 5 \cdot 2}{2 - 4} \)
D. \( y = \frac{5-3}{2-4}x + \frac{3 \cdot 4 - 5 \cdot 2}{4 - 2} \)
Question 4
A bakery sells 250 loaves of bread per day at ₦120 per loaf. If the \cost price per loaf is ₦80, calculate the profit per loaf and the total profit per day.
A. ₦40, ₦10,000
B. ₦30, ₦8,000
C. ₦20, ₦6,000
D. ₦10, ₦4,000
Question 5
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, -2 \) \cup \( 2, \infty \)
D. \( -\infty, 1 \) \cup \( 3, \infty \)
Question 6
Find the value of x in the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. 2
B. -3
C. -2
D. 1
Question 7
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) for ( x in mathbb{R} ).
A. \( x = 1 \)
B. \( x = 2 \)
C. \( x = 3 \)
D. \( x = 6 \)
Question 8
Let \( S = {x in mathbb{R} : x^2 + 2x + 1 = 0} \). Find \( lim_{x \to 2} \frac{x^2 - 4}{x - 2} \) if it exists.
A. 4
B. 2
C. \frac{1}{2}
D. \frac{1}{4}
Question 9
Find the area under the curve \( y = x^2 + 2x + 1 \) from \( x = 0 \) to \( x = 2 \).
A. 7
B. 6
C. 5
D. 4
Question 10
A set of 10 numbers has a mean of 20. If 5 is added to each number, what is the new mean?
A. 22.5
B. 25
C. 20
D. 22
Question 11
Solve the equation \( 2^x + 2^{x+1} = 3 cdot 2^{x+1} \) for ( x ).
A. \( x = -1 \)
B. \( x = 0 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 12
Solve for x in the equation \(\log_{10} \( x^2 \) = 4\).
A. 10^4
B. 10^8
C. 10^12
D. 10^16
Question 13
Solve for (x) in the equation \( 2^x + 5^x = 7^x \).
A. \( x = 1 \)
B. \( x = 2 \)
C. \( x = 3 \)
D. \( x = 4 \)
Question 14
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \( \frac{-x}{\( x^2 + 1 \ \)^{3/2}} )
B. \( \frac{x}{\( x^2 + 1 \ \)^{3/2}} )
C. \( \frac{1}{\( x^2 + 1 \ \)^{3/2}} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^{3/2}} )
Question 15
Find the area of the triangle with vertices ( A(0, 0) ), ( B(2, 0) ), and ( C(1, 3) ).
A. ( 3 )
B. ( 6 )
C. ( 9 )
D. ( 12 )

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