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POST UTME GREENFIELD UNIVERSITY 2021 Mathematics | Objective

Prepare for your exams with POST UTME GREENFIELD UNIVERSITY questions? Reviewing past/model questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1 View Details

Determine the value of \(\frac{d}{dx}\left \frac{1}{x^2}\right\)\) using the chain rule.

Correct A. \(\frac{2}{x^3}\)\)\)

B. -\(\frac{2}{x^3}\)\)\)

C. \(\frac{1}{x^3}\)\)\)

D. -\(\frac{1}{x^3}\)\)\)

Correct Answer: A

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Question 2 View Details

A set of 10 students scored the following marks in a mathematics test: 85, 90, 78, 92, 88, 76, 95, 89, 91, 84. Calculate the mean and standard deviation of the scores.

Correct A. \(mean = 86.5\), standard \(deviation = 5.5\)

B. \(mean = 87.5\), standard \(deviation = 5.2\)

C. \(mean = 88.5\), standard \(deviation = 5.8\)

D. \(mean = 89.5\), standard \(deviation = 6.2\)

Correct Answer: A

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Question 3 View Details

Solve the inequality \(x^2 - 6x + 8 > 0\).

Correct A. \(x < 2\) or \(x > 4\)

B. \(x > 2\) or \(x < 4\)

C. \(x < 4\) or \(x > 2\)

D. \(x > 4\) or \(x < 2\)

Correct Answer: A

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Question 4 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). Find the sum of the first 10 terms of the sequence.

Correct A. \(1 + 3 + 5 + ... + 21 = 110\)

B. \(1 + 3 + 5 + ... + 21 = 120\)

C. \(1 + 3 + 5 + ... + 21 = 130\)

D. \(1 + 3 + 5 + ... + 21 = 140\)

Correct Answer: A

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Question 5 View Details

A histogram is shown below. What is the value of the area of the shaded region?

A. 10

Correct B. 20

C. 30

D. 40

Correct Answer: B

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Question 6 View Details

Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 1 \ -1 \end{pmatrix}\). Find the vector ( mathbf{c} ) such that ( mathbf{c} ) is perpendicular to both ( mathbf{a} ) and ( mathbf{b} ).

Correct A. \(egin{pmatrix} -3 \ 2 \end{pmatrix}\)

B. \(egin{pmatrix} 3 \ -2 \end{pmatrix}\)

C. \(egin{pmatrix} 2 \ -3 \end{pmatrix}\)

D. \(egin{pmatrix} -2 \ 3 \end{pmatrix}\)

Correct Answer: A

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Question 7 View Details

Find the equation of the line passing through the points ( (2,3) ) and ( (4,5) ).

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

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

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

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

Correct Answer: A

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Question 8 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 + \(y-3\)^\(2 = 4\) )

C. \(x-2 \\)^2 + \(y-3\)^\(2 = 64\) )

D. \(x-2 \\)^2 + \(y-3\)^\(2 = 25\) )

Correct Answer: A

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Question 9 View Details

Solve the inequality \(2x^2 + 3x - 1 > 0\).

Correct A. \(x < -\frac{1}{2}\) or \(x > \frac{1}{2}\)

B. \(x < -\frac{1}{2}\) or \(x < \frac{1}{2}\)

C. \(x > -\frac{1}{2}\) or \(x < \frac{1}{2}\)

D. \(x > -\frac{1}{2}\) or \(x > \frac{1}{2}\)

Correct Answer: A

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Question 10 View Details

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

Correct A. \(\frac{4}{3} \pi\)

B. \(\frac{2}{3} \pi\)

C. \(\frac{1}{3} \pi\)

D. \(\frac{1}{2} \pi\)

Correct Answer: A

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Question 11 View Details

In a certain number base, the value of the digit 5 is represented as ( overline{101} ). If the number base is denoted by ( b ), determine the value of ( b ) if the number ( overline{101} ) represents the decimal value 5.

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 12 View Details

A set of 5 cards numbered 1 to 5 is randomly drawn from a deck of 20 cards numbered 1 to 20. If the sum of the numbers on the 5 cards is 25, what is the probability that the number 5 is among the 5 cards drawn?

A. \(1/6\)

Correct B. \(1/5\)

C. \(1/4\)

D. \(1/3\)

Correct Answer: B

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Question 13 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Determine the volume of the prism in cubic centimeters.

Correct A. 72

B. 80

C. 90

D. 100

Correct Answer: A

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Question 14 View Details

A sequence is defined as (a_\(n = 2n + 1\)\) for \(n = 1, 2, 3, ldots\\((a_n = 2n + 1) for\). Determine the sum of the first 5 terms of the sequence.

A. 15

B. 20

C. 25

Correct D. 30

Correct Answer: D

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Question 15 View Details

A geometric progression has a first term of 2 and a common ratio of 3. Determine the sum of the first 5 terms of the progression.

Correct A. 243

B. 256

C. 270

D. 300

Correct Answer: A

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Question 16 View Details

Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 4 \ 5 end{pmatrix}\). Find the vector \(\\(end{pmatrix}). Find the vector \mathbf{a} \times \mathbf{b}\) using the cross product formula.

Correct A. \begin{pmatrix} -13 \ 8 \end{pmatrix}

B. \begin{pmatrix} 13 \ -8 \end{pmatrix}

C. \begin{pmatrix} 8 \ -13 \end{pmatrix}

D. \begin{pmatrix} -8 \ 13 \end{pmatrix}

Correct Answer: A

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Question 17 View Details

Consider the sequence \(a_n = 2n^2 + 3n - 1\). Find the sum of the first 5 terms of the sequence.

Correct A. 120

B. 130

C. 140

D. 150

Correct Answer: A

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Question 18 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \(\frac{1}{3}\)\)

Correct B. \(\frac{2}{3}\)\)

C. \(\frac{1}{2}\)\)

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

Correct Answer: B

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Question 19 View Details

Find the derivative of the function ( f(x) = \(3x^2 + 2x - 5\) ) using the power rule.

Correct A. 6x + 2

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

C. 6x - 2

D. \(3x^2 - 2\)

Correct Answer: A

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Question 20 View Details

Simplify the expression \(\sqrt{16} + \sqrt{9}\).

A. 5

Correct B. 7

C. 9

D. 11

Correct Answer: B

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Question 21 View Details

Find the value of x in the equation \(2x^2 + 5x - 3 = 0\) using the quadratic formula.

A. \(x = -1\)

Correct B. \(x = 3\)

C. \(x = -3\)

D. \(x = 1\)

Correct Answer: B

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Question 22 View Details

Solve the system of equations \(\begin{cases} x + 2y = 4 \ 3x - 2y = 5 \end{cases}\) using matrices.

Correct A. \(\begin{pmatrix} 2 \ 1 \end{pmatrix}\)

B. \(\begin{pmatrix} 1 \ 2 \end{pmatrix}\)

C. \(\begin{pmatrix} 3 \ -1 \end{pmatrix}\)

D. \(\begin{pmatrix} -1 \ 3 \end{pmatrix}\)

Correct Answer: A

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Question 23 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. \(f'(x) = \frac{1}{x^2 + 1 ^2}\)

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

Correct Answer: A

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Question 24 View Details

Determine the sum of the first 5 terms of the geometric series \(2 + 6 + 18 + \cdots\).

Correct A. 124

B. 126

C. 128

D. 130

Correct Answer: A

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Question 25 View Details

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

A. \(x < -1\)

Correct B. \(x > 3\)

C. \(x < 3\)

D. \(x > -3\)

Correct Answer: B

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