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POST UTME GREENFIELD UNIVERSITY 2018 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 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 2\( 3^{10}-1 \)/\( 3-1 \)

B. 2\( 3^{10}+1 \)/\( 3-1 \)

C. 2\( 3^{10}-1 \)/\( 3+1 \)

D. 2\( 3^{10}+1 \)/\( 3+1 \)

Correct Answer: A

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Question 2

Solve the inequality \frac{x}{x+1} > 1.

Correct A. x < -1 or x > 0

B. x > -1 or x < 0

C. x < 0 or x > 1

D. x > 0 or x < 1

Correct Answer: A

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Question 3

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

Correct A. \frac{14}{3}

B. \frac{16}{3}

C. \frac{18}{3}

D. \frac{20}{3}

Correct Answer: A

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Question 4

Solve the equation x^2 + 4x + 4 = 0.

Correct A. x = -2

B. x = 2

C. x = -1 or x = -3

D. x = 1 or x = 3

Correct Answer: A

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Question 5

Find the value of x in the equation \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2}.

A. x = -1

Correct B. x = 1

C. x = -2

D. x = 2

Correct Answer: B

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Question 6

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

A. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

B. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

Correct C. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

D. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

Correct Answer: C

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Question 7

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 8

Find the vector ( mathbf{v} ) such that \( mathbf{v} cdot mathbf{i} = 3 \) and \( mathbf{v} cdot mathbf{j} = -2 \).

A. \begin{pmatrix} 3 \ 2 \end{pmatrix}

B. \begin{pmatrix} -3 \ 2 \end{pmatrix}

Correct C. \begin{pmatrix} 3 \ -2 \end{pmatrix}

D. \begin{pmatrix} -3 \ -2 \end{pmatrix}

Correct Answer: C

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Question 9

A polynomial ( p(x) ) has roots at \( x = -2, 1, 3 \). Write the polynomial in factored form.

Correct A. \( x + 2 \)\( x - 1 \)\( x - 3 \)

B. \( x - 2 \)\( x + 1 \)\( x - 3 \)

C. \( x + 2 \)\( x - 1 \)\( x + 3 \)

D. \( x - 2 \)\( x + 1 \)\( x - 3 \)

Correct Answer: A

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Question 10

Two events ( A ) and ( B ) are indep\endent. If ( P(A) = 0.4 ) and ( P(B) = 0.6 ), find ( P(A cap B) ).

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 11

Let X and Y be indep\endent events with P(X) = 0.4 and P(Y) = 0.6. Find the probability that X occurs but Y does not.

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 12

Solve for x in the equation \[ \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ 1 \end{bmatrix} = \begin{bmatrix} 3 \\ 3 \end{bmatrix} \].

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 13

Find the value of \sin(2x) given that \sin(x) = \frac{3}{5} and \cos(x) = \frac{4}{5}.

A. \frac{24}{25}

B. \frac{28}{25}

Correct C. \frac{32}{25}

D. \frac{36}{25}

Correct Answer: C

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Question 14

Let a_n = 2n^2 + 3n - 1. Find the sum of the first 5 terms of the sequence.

A. 120

B. 130

Correct C. 140

D. 150

Correct Answer: C

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Question 15

Find the area of the triangle with vertices (1, 2), (3, 4), and (5, 6).

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 16

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 256\pi\text{ cm}^3

B. 512\pi\text{ cm}^3

Correct C. 768\pi\text{ cm}^3

D. 1024\pi\text{ cm}^3

Correct Answer: C

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Question 17

Solve the inequality \frac{x^2 - 4x - 5}{x^2 - 6x + 8} > 0.

Correct A. \left\( -\infty, -1\right \) \cup \left\( 2, \infty\right \)

B. \left\( -\infty, 2\right \) \cup \left\( 5, \infty\right \)

C. \left\( -\infty, -1\right \) \cup \left\( 2, 5\right \)

D. \left\( -\infty, 5\right \) \cup \left\( 8, \infty\right \)

Correct Answer: A

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Question 18

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 - 3

D. y = 2x + 3

Correct Answer: A

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Question 19

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

A. 12\text{ cm}^2

B. 18\text{ cm}^2

Correct C. 24\text{ cm}^2

D. 30\text{ cm}^2

Correct Answer: C

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Question 20

Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 9 \end{bmatrix}.

Correct A. \begin{bmatrix} 1 \ 3 \end{bmatrix}

B. \begin{bmatrix} 2 \ 4 \end{bmatrix}

C. \begin{bmatrix} 3 \ 5 \end{bmatrix}

D. \begin{bmatrix} 4 \ 6 \end{bmatrix}

Correct Answer: A

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Question 21

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

A. 3.999999999999999

Correct B. 4.000000000000001

C. 4.0000000000000005

D. 4.000000000000001

Correct Answer: B

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Question 22

Solve the inequality \frac{x+2}{x-1} > 0.

Correct A. \( -\infty, -2 \) \cup \( 1, \infty \)

B. \( -\infty, -2 \) \cup \( 1, \infty \)

C. \( -\infty, -2 \) \cup \( 1, \infty \)

D. \( -\infty, -2 \) \cup \( 1, \infty \)

Correct Answer: A

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Question 23

A die is rolled twice. What is the probability that the sum of the two numbers is 7?

Correct A. 1/6

B. 1/6

C. 1/6

D. 1/6

Correct Answer: A

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Question 24

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

Correct A. 6x + 2

B. 6x + 2

C. 6x + 2

D. 6x + 2

Correct Answer: A

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Question 25

Solve the system of equations \begin{align*} x + y &= 4 \ x - 2y &= -2 \end{align*}.

Correct A. \left\{ (2, 2) \right\}

B. \left\{ (2, 2) \right\}

C. \left\{ (2, 2) \right\}

D. \left\{ (2, 2) \right\}

Correct Answer: A

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