POST UTME REDEEMERS UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = \frac{1}{2}x^2 - 3x + 5 \) from \( x = 0 \) to \( x = 4 \).
A. \( 4 \ \)
B. \( 8 \ \)
C. \( 16 \ \)
D. \( 32 \ \)
Question 2
A set of numbers has a mean of 20 and a s\tandard deviation of 5. If the set contains 10 numbers, what is the sum of the numbers?
A. 200
B. 250
C. 300
D. 350
Question 3
A random experiment has two possible outcomes: A and B. The probability of outcome A is 0.4, and the probability of outcome B is 0.6. If the experiment is repeated 100 times, how many times can we expect outcome A to occur?
A. 40
B. 50
C. 60
D. 70
Question 4
A fair six-sided die is rolled. What is the probability that the number obtained is greater than 4, given that the number obtained is an even number?
A. \frac{1}{3}
B. \frac{2}{3}
C. \frac{1}{2}
D. \frac{2}{5}
Question 5
Determine the value of x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \).
A. -2
B. 2
C. 4
D. 6
Question 6
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \left\( - \frac{5}{4}, \frac{3}{2} \right \)
B. \left\( - \infty, - \frac{3}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
C. \left\( - \frac{3}{2}, \frac{3}{2} \right \)
D. \left\( - \infty, \frac{3}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
Question 8
A circle with center ( C(2, 3) ) and radius \( r = 4 \) is drawn on a coordinate plane. What is the equation of the circle?
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
C. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
Question 9
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. x = -2, x = -3
B. x = 2, x = 3
C. x = -1, x = -6
D. x = 1, x = 6
Question 10
Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = 2x$ for $0 < x < 1$ and $f_Y(y) = 3y^2$ for $0 < y < 1$. Find $P\( X > Y \)$.
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{5}{8}
Question 11
Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).
A. \( x = -1 \ \)
B. \( x = 3 \ \)
C. \( x = -3 \ \)
D. \( x = 1 \ \)
Question 12
Solve for y in the equation \( y = \frac{1}{2} \log_{10} \( x^2 \ \) + 3 ).
A. \frac{1}{2} \log_{10} \( x^2 \) + 3
B. \frac{1}{2} \log_{10} \( x^2 \) - 3
C. \frac{1}{2} \log_{10} \( x^2 \) + 5
D. \frac{1}{2} \log_{10} \( x^2 \) - 5
Question 13
Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} \).
A. 0
B. 4
C. -4
D. 8
Question 14
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 15
A company produces two products, A and B. Product A requires 2 hours of labor and 3 hours of machine time, while product B requires 3 hours of labor and 2 hours of machine time. If the company has 120 hours of labor and 180 hours of machine time available, how many units of product A and product B should be produced to maximize profit?
A. 20 units of A, 30 units of B
B. 30 units of A, 20 units of B
C. 40 units of A, 10 units of B
D. 10 units of A, 40 units of B

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