POST UTME WELLSPRING UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details
Determine the area under the curve of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) from \(x = 0\) to \(x = 1\).
Correct A. \(\frac{\pi}{2}\)
B. \(\frac{\pi}{4}\)
C. \(\frac{\pi}{6}\)
D. \(\frac{\pi}{8}\)

Correct Answer: A

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Question 2 View Details
A histogram of exam scores has a mean of 75 and a standard deviation of 5. If the scores are normally distributed, what is the probability that a randomly selected score is between 70 and 80?
Correct A. 0.3413
B. 0.3415
C. 0.3417
D. 0.3419

Correct Answer: A

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Question 3 View Details
Solve for ( x ) in the equation \(\log_{10} x^2 \\)\(= 4 ).\)
A. 10
B. 100
Correct C. 1000
D. 10000

Correct Answer: C

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Question 4 View Details
Find the equation of the circle with center ( (3, 4) ) and radius 5.
Correct A. \(x - 3 \\)^2 + \(y - 4\)^\(2 = 25\) )
B. \(x - 4 \\)^2 + \(y - 3\)^\(2 = 25\) )
C. \(x - 3 \\)^2 + \(y - 4\)^\(2 = 30\) )
D. \(x - 4 \\)^2 + \(y - 3\)^\(2 = 30\) )

Correct Answer: A

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Question 5 View Details
In the circuit below, what is the equivalent resistance between points A and B?
Correct A. \(\frac{R1 \cdot R2}{R1 + R2}\)
B. \(R1 + R2\)
C. \(\frac{R1 + R2}{R1 \cdot R2}\)
D. \(\frac{R1 \cdot R2}{R1 - R2}\)

Correct Answer: A

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Question 6 View Details
Let \(X\) and \(Y\) be independent random variables with probability density functions (f_\(X(x) = 2x\)\) for \(0 < x < 1\\((f_X(x) = 2x) for\) and (f_\(Y(y) = \(3y^2\)\)\) for \(0 < y < 1\\((f_Y(y) = 3y^2) for\). Find the probability that \(X + Y < 1\).
Correct A. \(\frac{1}{2}\)\)
B. \(\frac{1}{3}\)\)
C. \(\frac{2}{3}\)\)
D. \(\frac{3}{4}\)\)

Correct Answer: A

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Question 7 View Details
Find the determinant of the matrix \(\begin{bmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{bmatrix}\).
Correct A. 4
B. 6
C. 8
D. 10

Correct Answer: A

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Question 8 View Details
Solve the inequality \(\log_2 x^2 + 1\)\(> 3\)\).
Correct A. \left\(\frac{1}{2}, \infty \right\)
B. \left\(-\infty, -\frac{1}{2} \right\)
C. \left\(-\frac{1}{2}, \frac{1}{2} \right\)
D. \left\(-\infty, \infty \right\)

Correct Answer: A

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Question 9 View Details
Find the equation of the circle with center \(\left \frac{3}{2}, \frac{1}{2} \right\)\) and radius \(\frac{1}{2}\).
Correct A. \left\(x - \frac{3}{2} \right\)^2 + \left\(y - \frac{1}{2} \right\)\\((^2\) =\)\(\frac{1}{4}\)\)
B. \left\(x - \frac{1}{2} \right\)^2 + \left\(y - \frac{3}{2} \right\)\\((^2\) =\)\(\frac{1}{4}\)\)
C. \left\(x - \frac{1}{2} \right\)^2 + \left\(y - \frac{1}{2} \right\)\\((^2\) =\)\(\frac{1}{4}\)\)
D. \left\(x - \frac{3}{2} \right\)^2 + \left\(y - \frac{3}{2} \right\)\\((^2\) =\)\(\frac{1}{4}\)\)

Correct Answer: A

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Question 10 View Details
Find the derivative of the function \(f(x) = \frac{x^2 + 1}{x^2 - 1}\).
A. \(\frac{2x}{x^2 - 1\) ^2}\)\)
Correct 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}\)\)

Correct Answer: B

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Question 11 View Details
Solve for x in the equation \(\sin^2 x \\) + \\(\cos^2(x)\)\(= 1 )\), given that \($1x \\) = \(\frac{3}{5}\)\) ).
A. \(x =\)\(\frac{\pi}{4}\)\)
Correct B. \(x =\)\(\frac{3\pi}{4}\)\)
C. \(x =\)\(\frac{5\pi}{4}\)\)
D. \(x =\)\(\frac{7\pi}{4}\)\)

Correct Answer: B

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Question 12 View Details
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. \(\frac{1}{2}\)\)
Correct C. \(\frac{3}{4}\)\)
D. \(\frac{5}{8}\)\)

Correct Answer: C

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Question 13 View Details
Solve the equation \(x^2 + 4x + 4 = 0\) using the quadratic formula.
Correct A. \(x = -2\)\pm \(\sqrt{3}\)
B. \(x = -2\)\pm \(\sqrt{2}\)
C. \(x = -2\)\pm \(\sqrt{1}\)
D. \(x = -2\)\pm \(\sqrt{0}\)

Correct Answer: A

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Question 14 View Details
A binary operation * is defined as \(a \* b = ab + 2a + 2b\\(* is defined as (a\). Find the value of \(2 \* 3\).
A. 10
Correct B. 12
C. 14
D. 16

Correct Answer: B

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Question 15 View Details
Solve the inequality \(|x - 2| > 3\).
Correct 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 } \(x > 2\)

Correct Answer: A

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Question 16 View Details
Find the value of x in the equation \(\frac{1}{x} + \frac{1}{3} = \frac{1}{2}\).
Correct A. 1
B. 2
C. 3
D. 4

Correct Answer: A

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Question 17 View Details
Solve for y in the equation \(y^2 + 4y + 4 = 0\).
A. 0
Correct B. -2
C. 2
D. -4

Correct Answer: B

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Question 18 View Details
Find the determinant of the matrix \(egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix}\).
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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Question 19 View Details
Find the mean of the data set { 2, 4, 6, 8, 10 }.
A. 5
Correct B. 6
C. 7
D. 8

Correct Answer: B

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Question 20 View Details
Find the value of x in the equation \(x^2 - 4x + 4 = 0\).
Correct A. 2
B. -2
C. 1
D. -1

Correct Answer: A

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Question 21 View Details
In a random sample of 100 students, the mean height is 175 cm with a standard 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
Correct D. 0.8413

Correct Answer: D

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Question 22 View Details
A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. What is the surface area of the prism?
A. 240
B. 260
Correct C. 280
D. 300

Correct Answer: C

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Question 23 View Details
Solve the equation \(x^3 - 6x^2 + 11x - 6 = 0\) by factoring.
Correct 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

Correct Answer: A

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Question 24 View Details
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?
Correct A. 400
B. 600
C. 800
D. 1000

Correct Answer: A

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Question 25 View Details
Find the determinant of the matrix \(\begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}\).
Correct A. 0
B. 1
C. 2
D. 3

Correct Answer: A

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