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POST UTME GREENFIELD UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of the function ( f(x) = \(\frac{x^2 + 2x - 3}{x^2 - 4}\)\)\) ) using 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 View Details

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 View Details

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 View Details

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 View Details

Two events ( A ) and ( B ) are independent. 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 View Details

Let X and Y be independent 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 View Details

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 View Details

Find the value of sin(2x) given that \\(sin(x) =\)\(\\(sin(2x) given that sin(x) = \frac{3}{5}\)\) 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 View Details

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 View Details

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 View Details

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\pitext{ cm}^3

B. 512\pitext{ cm}^3

Correct C. 768\pitext{ cm}^3

D. 1024\pitext{ cm}^3

Correct Answer: C

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Question 17 View Details

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 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. \(y = 2x - 3\)

D. \(y = 2x + 3\)

Correct Answer: A

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Question 19 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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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