POST UTME WELLSPRING UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for y in the equation \( y^2 + 4y + 4 = 0 \).
A. 0
B. -2
C. 2
D. -4
Question 2
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 3
Find the value of x in the equation \( x^2 - 4x + 4 = 0 \).
A. 2
B. -2
C. 1
D. -1
Question 4
Solve the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) for (x).
A. 0
B. π/2
C. π
D. 3π/2
Question 5
Find the determinant of the matrix $\begin{bmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{bmatrix}$.
A. 4
B. 6
C. 8
D. 10
Question 6
Find the derivative of ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( \frac{1}{\( x^2 + 1 \ \)^2} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^2} )
Question 7
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 8
A binary operation \* is defined as \( a \* b = ab + 2a + 2b \). Find the value of \( 2 \* 3 \).
A. 10
B. 12
C. 14
D. 16
Question 9
In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the distribution of heights is approximately normal, what is the probability that a randomly selected student will be taller than 180 cm?
A. 0.1587
B. 0.3413
C. 0.5
D. 0.8413
Question 10
A fair six-sided die is rolled. If the outcome is an even number, a second die is rolled. If the outcome is an odd number, a third die is rolled. What is the probability that the outcome is a 6?
A. 1/6
B. 1/12
C. 1/24
D. 1/36
Question 11
Find the determinant of the matrix \[\begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}\].
A. 0
B. 1
C. 2
D. 3
Question 12
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
Question 13
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 the probability that $X + Y < 1$.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 14
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. x = -2 \pm \sqrt{3}
B. x = -2 \pm \sqrt{2}
C. x = -2 \pm \sqrt{1}
D. x = -2 \pm \sqrt{0}
Question 15
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

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