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POST UTME FUTA 2018 Mathematics | Objective

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Question 1

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

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

Solve the system of equations u\sing 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

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

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{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

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

Correct A. $ x > 3 \ $

B. $ x < 3 \ $

C. $ x = 3 \ $

D. $ x = 2 \ $

Correct Answer: A

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Question 7

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

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

Correct A. $ x = \frac{pi}{4} \ $

B. $ x = \frac{pi}{2} \ $

C. $ x = \frac{3pi}{4} \ $

D. $ x = \frac{5pi}{4} \ $

Correct Answer: A

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Question 9

Find the derivative of the function ( f(x) = x^3 - 2x^2 + 3x - 1 ) u\sing 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

Solve the quadratic equation $ x^2 + 4x + 4 = 0 $ u\sing 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

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

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

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

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

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 = - \frac{1}{2}x + 1

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

Correct Answer: A

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Question 16

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

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

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

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

Correct A. 64\pi

B. 128\pi

C. 256\pi

D. 512\pi

Correct Answer: A

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Question 20

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

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

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

A. 12

Correct B. 16

C. 24

D. 32

Correct Answer: B

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Question 23

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

Find the equation of the line pas\sing 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

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

A. 16

Correct B. 32

C. 64

D. 128

Correct Answer: B

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