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POST UTME FUTA 2018 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation \(\frac{1}{2}x^2 + 5x - 3 = 0\).

Correct A. \(\frac{-5 + \sqrt{109}\)}{2}\)

B. \(\frac{-5 - \sqrt{109}\)}{2}\)

C. \(\frac{5 + \sqrt{109}\)}{2}\)

D. \(\frac{5 - \sqrt{109}\)}{2}\)

Correct Answer: A

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Question 2 View Details

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

Correct A. -\(\frac{2x}{x^2 + 1\) ^2}\)\)

B. \(\frac{2x}{x^2 + 1\) ^2}\)\)

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

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

Correct Answer: A

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Question 3 View Details

Solve the system of equations using matrices: \(\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ 11 \end{bmatrix}\).

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

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

C. \(x = 3\), \(y = 4\)

D. \(x = 4\), \(y = 3\)

Correct Answer: A

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Question 4 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 5 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. \(\frac{16}{15}\)\)\pi

B. \(\frac{32}{15}\)\)\pi

C. \(\frac{64}{15}\)\)\pi

D. \(\frac{128}{15}\)\)\pi

Correct Answer: A

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Question 6 View Details

Solve the inequality (\(\frac{x}{x-2}\(> 1\)\) for \\((frac{x}{x-2} > 1\(x > 2\)\).

Correct A. \(x > 3 \\)

B. \(x < 3 \\)

C. \(x = 3 \\)

D. \(x = 2 \\)

Correct Answer: A

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Question 7 View Details

Find the equation of the circle with center at ( (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 + \(y-3\)^\(2 = 9\) \)

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

Correct Answer: A

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Question 8 View Details

Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\) for \(0 < x < 2\pi\).

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

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

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

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

Correct Answer: A

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Question 9 View Details

Find the derivative of the function ( f(x) = \(x^3 - 2x^2 + 3x - 1\) ) using the power rule.

Correct A. ( f'\((x) =\)\(3x^2 - 4x + 3\) \)

B. ( f'\((x) =\)\(x^2 - 2x + 1\) \)

C. ( f'\((x) =\)\(3x^2 - 4x + 1\) \)

D. ( f'\((x) =\)\(x^2 - 2x - 1\) \)

Correct Answer: A

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Question 10 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\) using the quadratic formula.

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

B. \(x = 0 \\)

C. \(x = -1 \\)

D. \(x = 1 \\)

Correct Answer: A

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Question 11 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 48\pi

B. 64\pi

Correct C. 80\pi

D. 96\pi

Correct Answer: C

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Question 12 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9}\)\)\\() > 0.\)

A. \(-3, -1\) \cup (1, 3)

Correct B. \(-3, -1\) \cup (1, 3) \cup \(4, \infty\)

C. \(-3, -1\) \cup (1, 3) \cup \(-\infty, -4\)

D. \(-3, -1\) \cup (1, 3) \cup \(-\infty, -4\) \cup \(4, \infty\)

Correct Answer: B

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Question 13 View Details

Find the area of the triangle with vertices (2, 3), (4, 5), and (6, 7).

Correct A. 10

B. 15

C. 20

D. 25

Correct Answer: A

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Question 14 View Details

Solve the system of equations \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}.

Correct A. \left\{ \left\(- \frac{5}{7}, \frac{27}{7} \right\) \right\}

B. \left\{ \left\(- \frac{5}{7}, - \frac{27}{7} \right\) \right\}

C. \left\{ \left\(\frac{5}{7}, - \frac{27}{7} \right\) \right\}

D. \left\{ \left\(\frac{5}{7}, \frac{27}{7} \right\) \right\}

Correct Answer: A

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Question 15 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. \(y = -\)\(\frac{1}{2}\)\) x + 1

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

Correct Answer: A

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Question 16 View Details

Find the area of the circle with radius 4 cm.

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 17 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9}\)\)\\() < 0.\)

A. \(-3, -1\) \cup (1, 3)

Correct B. \(-3, -1\) \cup (1, 3) \cup \(-\infty, -4\)

C. \(-3, -1\) \cup (1, 3) \cup \(4, \infty\)

D. \(-3, -1\) \cup (1, 3) \cup \(-\infty, -4\) \cup \(4, \infty\)

Correct Answer: B

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Question 18 View Details

Find the equation of the circle with center (2, 3) and radius 4.

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

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

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 9\)

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

Correct Answer: VIEW ANSWER

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Question 19 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = \(\sqrt{x}\)\), the \\((y = sqrt{x}\(x)-axis, and the line \(x = 4\) about the \\()-axis, and the line (x = 4\(x\)-axis.

Correct A. 64\pi

B. 128\pi

C. 256\pi

D. 512\pi

Correct Answer: A

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Question 20 View Details

Solve the equation \(\log_{2}(x) + \log_{2} x - 2\)\(= 3\)\) for \(x\).

A. 8

B. 10

C. 12

Correct D. 14

Correct Answer: D

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Question 21 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 + \(y - 3\)^\(2 = 32\)

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

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 128\)

Correct Answer: A

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Question 22 View Details

In the diagram below, (ABCD\) is a rectangle and \(E\\((ABCD) is a rectangle and\) is the midpoint of (AD\). If \(AB = 6\\((AD). If\) and (BC = 8\), find the area of triangle \(ADE\\((BC = 8), find the area of triangle\).

A. 12

Correct B. 16

C. 24

D. 32

Correct Answer: B

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Question 23 View Details

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

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

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

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

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

Correct Answer: A

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Question 24 View Details

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

Correct A. \(y = x + 1\)

B. \(y = x - 1\)

C. \(y = x + 2\)

D. \(y = x - 2\)

Correct Answer: A

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Question 25 View Details

In the diagram below, (ABCD\) is a square and \(E\\((ABCD) is a square and\) is the midpoint of (AD\). If \(AB = 8\\((AD). If\), find the area of triangle \(ADE\).

A. 16

Correct B. 32

C. 64

D. 128

Correct Answer: B

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