POST UTME WELLSPRING UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the mean of the data set { 2, 4, 6, 8, 10 }.
A. 5
B. 6
C. 7
D. 8
Question 2
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) by factoring.
A. \left\( x-1\right)\left\( x-2\right)\left(x-3\right \ \)=0
B. \left\( x-1\right)\left\( x-2\right)\left(x+3\right \ \)=0
C. \left\( x-1\right)\left\( x-2\right)\left(x-6\right \ \)=0
D. \left\( x-1\right)\left\( x-2\right)\left(x-9\right \ \)=0
Question 3
A company has two factories, A and B, producing a total of 1000 units of a product per day. Factory A produces 60% of the total units, while factory B produces the remaining 40%. If factory A produces x units per day, how many units does factory B produce per day?
A. 400
B. 600
C. 800
D. 1000
Question 4
Solve the inequality \( |x - 2| > 3 \).
A. x < -1 \text{ or } x > 5
B. x < 1 \text{ or } x > 5
C. x < -1 \text{ or } x > 2
D. x < 1 \text{ or } x > 2
Question 5
Find the determinant of the matrix \( egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} \).
A. 1
B. 2
C. 3
D. 4
Question 6
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, 30)
B. (30, 20)
C. (25, 25)
D. (35, 15)
Question 7
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 5. If the scores are normally distributed, what is the probability that a randomly selected score is between 70 and 80?
A. 0.3413
B. 0.3415
C. 0.3417
D. 0.3419
Question 8
Find the derivative of the function $f(x) = \frac{x^2 + 1}{x^2 - 1}$.
A. \frac{2x}{\( x^2 - 1 \)^2}
B. \frac{2x^3 + 2x}{\( x^2 - 1 \)^2}
C. \frac{2x^3 - 2x}{\( x^2 - 1 \)^2}
D. \frac{2x^3 + 2}{\( x^2 - 1 \)^2}
Question 9
Find the value of x in the equation \( \frac{1}{x} + \frac{1}{3} = \frac{1}{2} \).
A. 1
B. 2
C. 3
D. 4
Question 10
Solve the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) for (x).
A. 0
B. π/2
C. π
D. 3π/2
Question 11
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 12
Determine the area under the curve of the function ( f(x) = \frac{1}{x^2 + 1} ) from \( x = 0 \) to \( x = 1 \).
A. \( \frac{pi}{2} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{6} \)
D. \( \frac{pi}{8} \)
Question 13
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. 0.68
B. 0.85
C. 0.95
D. 0.99
Question 14
A random variable X has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} \) for \( x = 1, 2, 3 \). Find the probability that X is greater than 2.
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{5}{8}
Question 15
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 3.
A. 27
B. 30
C. 33
D. 36

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