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POST UTME WELLSPRING UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details

Find the equation of the circle with center \(-2,3\) and radius 4.

Correct 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 + \(y-3\)^\(2 = 16\) )

Correct Answer: A

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Question 2 View Details

Find the derivative of ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using the chain rule.

Correct A. ( f'\((x) =\)\(\frac{-2x}{x^2 + 1\) ^2}\)\) )

B. ( f'\((x) =\)\(\frac{2x}{x^2 + 1\) ^2}\)\) )

C. ( f'\((x) =\)\(\frac{2}{x^2 + 1\) ^2}\)\) )

D. ( f'\((x) =\)\(\frac{-2}{x^2 + 1\) ^2}\)\) )

Correct Answer: A

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Question 3 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.

Correct A. ( 72 ) \(cm^3\)

B. ( 48 ) \(cm^3\)

C. ( 36 ) \(cm^3\)

D. ( 24 ) \(cm^3\)

Correct Answer: A

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Question 4 View Details

Solve the matrix equation \(egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix}\).

Correct A. \(x = 1, y = 2\)

B. \(x = 2, y = 1\)

C. \(x = 1, y = 1\)

D. \(x = 2, y = 2\)

Correct Answer: A

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Question 5 View Details

Find the area of the triangle with vertices ( A(1,2) ), ( B(3,4) ), and ( C(2,1) ).

Correct A. ( 6 )

B. ( 8 )

C. ( 10 )

D. ( 12 )

Correct Answer: A

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Question 6 View Details

A random sample of 25 students from a university had an average height of 175 cm with a standard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?

Correct A. 0.1587

B. 0.3413

C. 0.4772

D. 0.6179

Correct Answer: A

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Question 7 View Details

In the diagram below, the circle with center O has a radius of 4 cm. The point P lies on the circle. If the angle POQ measures 60°, what is the length of the chord PQ?

A. 4 cm

Correct B. 6 cm

C. 8 cm

D. 10 cm

Correct Answer: B

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Question 8 View Details

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. \(1/2\)

B. \(1/3\)

Correct C. \(2/5\)

D. \(3/8\)

Correct Answer: C

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Question 9 View Details

If f(x) = \(3x^2 + 2x - 5\), find the derivative of f(x) using the chain rule.

Correct A. 6x + 2

B. \(3x^2 + 2x - 5\)

C. 12x + 4

D. \(9x^2 + 4x - 10\)

Correct Answer: A

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Question 10 View Details

In the diagram below, the triangle ABC has a base of 6 cm and a height of 8 cm. If the angle B measures 60°, what is the area of the triangle?

A. 24 \(cm^2\)

B. 30 \(cm^2\)

Correct C. 36 \(cm^2\)

D. 40 \(cm^2\)

Correct Answer: C

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Question 11 View Details

In a survey of 100 students, 60 students preferred Mathematics, 30 students preferred Science, and 10 students preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?

Correct A. \(\frac{80}{100}\)

B. \(\frac{70}{100}\)

C. \(\frac{90}{100}\)

D. \(\frac{95}{100}\)

Correct Answer: A

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Question 12 View Details

Find the mean of the following data set: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

A. \(\frac{180}{10}\)

Correct B. \(\frac{200}{10}\)

C. \(\frac{220}{10}\)

D. \(\frac{240}{10}\)

Correct Answer: B

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Question 13 View Details

Solve for x in the equation \(2^x + 2^x = 64\).

A. \(x = 5\)

Correct B. \(x = 6\)

C. \(x = 7\)

D. \(x = 8\)

Correct Answer: B

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Question 14 View Details

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. ( pi \((4)^2\) )

B. ( 2pi \((4)^2\) )

C. ( 4pi \((4)^2\) )

D. ( 16pi \((4)^2\) )

Correct Answer: A

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Question 15 View Details

A line passes through the points (2, 3) and (4, 5). Find the equation of the line in slope-intercept form.

Correct A. \(y = \frac{2}{3}x + \frac{1}{3}\)

B. \(y = \frac{2}{3}x - \frac{1}{3}\)

C. \(y = \frac{3}{2}x + \frac{1}{2}\)

D. \(y = \frac{3}{2}x - \frac{1}{2}\)

Correct Answer: A

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Question 16 View Details

In a binary number system, what is the value of the digit in the \((2^3\)\) place in the number \(110101_2\\((2^3) place in the number\)?

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 17 View Details

A circle with center \(C\) and radius \(r\) passes through points \(A\) and \(B\). If (AB = 2r\), what is the measure of angle \(\\((AB = 2r), what is the measure of angle \angle ACB\)?

A. 30\degree

B. 60\degree

Correct C. 90\degree

D. 120\degree

Correct Answer: C

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Question 18 View Details

A vector \(\vec{a}\) has magnitude \(5\) and direction \(\theta = 30\degree). What is the \(x\)-component of \\(). What is the (x\(\vec{a}\)?

A. 2.5

Correct B. 3.75

C. 4.33

D. 5.00

Correct Answer: B

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Question 19 View Details

A histogram with (5\) classes has a mean of \(20\\((5) classes has a mean of\) and a standard deviation of \(5\). What is the value of the class width?

A. 2

B. 4

Correct C. 6

D. 8

Correct Answer: C

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Question 20 View Details

A line passes through points \(-2, 3\)\) and \(4, -1\)\). What is the equation of the line in slope-intercept form?

Correct A. \(y = -x + 5\)

B. \(y = x + 2\)

C. \(y = -x - 3\)

D. \(y = x - 1\)

Correct Answer: A

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Question 21 View Details

A right triangle has legs of length \(3\) and \(4\). What is the length of the hypotenuse?

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 22 View Details

A function (f(x)\) is defined as \(f(x) = 2x^2 + 3x - 1\\((f(x)) is defined as\). What is the value of \(f -2\)\)?

A. -11

B. -9

C. -7

D. -5

Correct Answer: VIEW ANSWER

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Question 23 View Details

Find the volume of the solid formed by revolving the region bounded by the curves \(y = x\^2\), \(y = 0\), and \(x = 2\) about the x-axis.

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 24 View Details

A random variable X has a probability density function f(x) = \(\frac{1}{2}\)\) for \(0 < x\) < 2. Find the probability that X is greater than 1.

A. \(\frac{1}{4}\)\)

Correct B. \(\frac{1}{2}\)\)

C. \(\frac{3}{4}\)\)

D. \(\frac{5}{8}\)\)

Correct Answer: B

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Question 25 View Details

Find the derivative of the function f(x) = \(\frac{1}{x^2 + 1}\)\)\) using the chain rule.

Correct A. \(\frac{-2x}{x^2 + 1\) ^2}\)\)

B. \(\frac{2x}{x^2 + 1\) ^2}\)\)

C. \(\frac{-x}{x^2 + 1\) ^2}\)\)

D. \(\frac{x}{x^2 + 1\) ^2}\)\)

Correct Answer: A

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