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POST UTME GREENFIELD UNIVERSITY 2021 Mathematics | Objective

Are you preparing for POST UTME GREENFIELD UNIVERSITY exams? Reviewing past 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.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the value of $\frac{d}{dx}\left$ \frac{1}{x^2}\right $$ u\sing 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

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 s\tandard deviation of the scores.

Correct A. mean = 86.5, s\tandard deviation = 5.5

B. mean = 87.5, s\tandard deviation = 5.2

C. mean = 88.5, s\tandard deviation = 5.8

D. mean = 89.5, s\tandard deviation = 6.2

Correct Answer: A

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Question 3

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

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

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

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 perp\endicular 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

Find the equation of the line pas\sing 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

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

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

Find the volume of the solid formed by revolving the region bounded by the parabola $ y = x^2 $ and the line $ y = 2x $ 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

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

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

A rec\tangular 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

A sequence is defined as $ a_n = 2n + 1 $ for $ n = 1, 2, 3, ldots $. 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

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

Let $ mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} $ and $ mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} $. Find the vector $ mathbf{a} \times mathbf{b} $ u\sing 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

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

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

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing 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

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

Find the value of x in the equation $ 2x^2 + 5x - 3 = 0 $ u\sing 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

Solve the system of equations $ \begin{cases} x + 2y = 4 \ 3x - 2y = 5 \end{cases} $ u\sing 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

Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing 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

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

Solve the inequality $ 2x^2 + 5x - 3 > 0 $ u\sing the quadratic formula.

A. \[ x < -1 \]

Correct B. \[ x > 3 \]

C. \[ x < 3 \]

D. \[ x > -3 \]

Correct Answer: B

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