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POST UTME GREENFIELD UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

Find the value of \(sum_{n = 1}^{10} \frac{1}{n^2}\)

Correct A. 1.6449340668482264

B. 1.6449340668482265

C. 1.6449340668482266

D. 1.6449340668482267

Correct Answer: A

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Question 2 View Details

Solve for ( x ) in the equation \(2x^2 + 5x - 3 = 0\)

Correct A. -1.5

B. 1.5

C. -1

D. 2

Correct Answer: A

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Question 3 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 2\)

Correct A. 4

B. 2

C. 1

D. 3

Correct Answer: A

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Question 4 View Details

Solve the system of equations \(x + y = 2\) and \(x - y = 1\)

Correct A. (1, 1)

B. (2, 0)

C. (0, 2)

D. (1, 0)

Correct Answer: A

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Question 5 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. \(x - 3\)^2 + \(y - 2\)^\(2 = 16\)

C. \(x - 4\)^2 + \(y - 3\)^\(2 = 16\)

D. \(x - 2\)^2 + \(y - 4\)^\(2 = 16\)

Correct Answer: A

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Question 6 View Details

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

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

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

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

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

Correct Answer: B

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Question 7 View Details

A circle with center ( C(2, 3) ) and radius \(r = 4\) has a chord ( AB ) of length ( 6 ). Find the distance from the center of the circle to the chord.

Correct A. 2

B. 4

C. 6

D. 8

Correct Answer: A

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Question 8 View Details

The mean of a set of numbers is (\bar{x}\(= 10\)\). If the sum of the numbers is \\((bar{x} = 10\(S = 40\), find the variance.

A. 10

Correct B. 20

C. 30

D. 40

Correct Answer: B

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Question 9 View Details

Find the area under the curve \(y = x^2 + 2x - 3\) from \(x = 0\) to \(x = 2\).

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 10 View Details

A polynomial function has roots at \(x = -2, 0, 3\). Find the polynomial function in factored form.

Correct A. \(f(x) =\)\(x + 2\), x)\(x - 3 \\)

B. \(f(x) =\)\(x - 2\), x)\(x + 3 \\)

C. \(f(x) =\)\(x + 2\), x)\(x - 2 \\)

D. \(f(x) =\)\(x - 2\), x)\(x + 3 \\)

Correct Answer: A

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Question 11 View Details

Find the equation of the circle with centre at \(\left -2, 3 \right \\) ) and radius ( 4 ).

Correct A. \(x^2 + y^2 + 4x - 6y - 7 = 0\)

B. \(x^2 + y^2 - 4x + 6y - 7 = 0\)

C. \(x^2 + y^2 + 2x - 3y - 7 = 0\)

D. \(x^2 + y^2 - 2x + 3y - 7 = 0\)

Correct Answer: A

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Question 12 View Details

Solve the equation \(\frac{1}{2} \log_{10} x^2 \\)\(= 4 ).\)

Correct A. \(x = 10^{8}\)

B. \(x = 10^{4}\)

C. \(x = 10^{2}\)

D. \(x = 10^{6}\)

Correct Answer: A

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Question 13 View Details

Find the derivative of the function ( 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 14 View Details

Solve the equation \(\sin^2 x + \cos^2 x = 1\) for ( x ) in the interval ( [0, 2pi] ).

A. \(x = \frac{\pi}{2}\)

Correct B. \(x = \frac{\pi}{4}\)

C. \(x = \frac{3\pi}{4}\)

D. \(x = \frac{5\pi}{4}\)

Correct Answer: B

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Question 15 View Details

Find the equation of the line passing through the points ( (1, 2) ) and ( (3, 4) ).

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

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

C. \(y = -2x + 1\)

D. \(y = -2x - 1\)

Correct Answer: A

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Question 16 View Details

Find the value of x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 17 View Details

A circle has a radius of 5 cm. Find the area of the circle.

Correct A. 25π

B. 50π

C. 100π

D. 200π

Correct Answer: A

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Question 18 View Details

Find the mean of the following data set: 2, 4, 6, 8, 10.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 19 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, -1\) ∪ (1, ∞)

D. \(-∞, 1\) ∪ (3, ∞)

Correct Answer: A

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Question 20 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).

A. 32

Correct B. 64

C. 128

D. 256

Correct Answer: B

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Question 21 View Details

Determine the value of (\theta\) in the equation \\((theta\(\sin^2\theta + \cos^2\theta = 1\).

Correct A. 0

B. 90

C. 180

D. 270

Correct Answer: A

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Question 22 View Details

A set \(A\) contains \(5\) elements, and a set \(B\) contains \(3\) elements. If \(A \cap B = \emptyset\), what is the number of elements in \(A \cup B\)?

A. 8

Correct B. 7

C. 6

D. 5

Correct Answer: B

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Question 23 View Details

A sequence is defined by the formula (a_\(n =\)\(\frac{1}{n}\)\). What is the sum of the first \\((a_n = frac{1}{n}\(5\) terms of this sequence?

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 24 View Details

A polynomial \(p(x)\) has roots \(x = -2\) and (x = 3\). What is the product of the roots of the polynomial \(p(x) + 2\\((x = 3). What is the product of the roots of the polynomial\)?

Correct A. -6

B. -4

C. -2

D. 6

Correct Answer: A

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Question 25 View Details

A circle with center \(C\) and radius \(r\) passes through the point \(P\). What is the equation of the circle in standard form?

Correct A. \(x - h\)^2 + \(y - k\)^\(2 = r\^2\)

B. \(x^2\) + \\((y^2\)\(= r\)\\()^2\)

C. \(x^2\) + \\((y^2 - 2gx - 2fy\)\(= 0\)\)

D. \(x^2\) + \\((y^2 + 2gx + 2fy\)\(= 0\)\)

Correct Answer: A

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