Final Exam Mixed Review

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20 questions

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What is the difference between \frac{7}{12} and \frac{1}{3}?

\frac{1}{5}

\frac{2}{5}

\frac{1}{3}

\frac{1}{4}

Which graph best represents a line with an x-intercept of -2 and a y-intercept of 5?

A

B

C

D

Which is the solution to the following equation: 7-4(x+2)=\frac{1}{3}(8x-12)?

x=\frac{14}{5}

x=\frac{4}{15}

x=-\frac{7}{12}

x=\frac{9}{20}

Use the given numbers to create a true equation.

Which is equivalent to \frac{x^{6}y^{5}z^{4}}{(xy)^{-5}}?

\frac{1}{xz^{4}}

x^{11}y^{10}z^{4}

xz^{4}

\frac{-x^{3}y^{2}z^{4}}{3}

Which is a factored form of the following expression: 5x^{2}-20x?

5(x-2)^{2}

(5x+4)(x+5)

5(x^{2}-4)

5x(x-4)

When completely factored, 2x^{2}+20x+48 is equivalent to:

2(x+4)(x+6)

2(x-4)(x-6)

2(x-10)(x+2)

2(x+10)(x-2)

Factor x^{2}-64y^{2}.

(x-8y)(x+16y)

(x-8y)^{2}

(x-8y)(x+8y)

(x+8y)(x-16y)

Which is equivalent to (2+\sqrt{5})(3+\sqrt{5})?

5+2\sqrt{5}

5+6\sqrt{5}

6+\sqrt{10}

11+5\sqrt{5}

Which function of x would have zeros of 1 and -5?

f(x)=2x^{2}+8x+10

f(x)=2x^{2}-8x-10

f(x)=2x^{2}+8x-9

f(x)=2x^{2}+8x-10

The graph of a function is shown. Identify three transformations applied to the parent function y=x^{2} to obtain the graph below.

Which set of ordered pairs is the solution to the system of equations shown?

{(0,-2),(6,10)}

{(0,3),(-1,2)}

{(-2,0),(10,-6)}

{(6,-0.5),(3,0)}

Which is the factored form of 8y^{3}-1?

(2y-1)(4y^{2}+2y-1)

(2y-1)(4y^{2}-2y-1)

(2y-1)(4y^{2}-2y+1)

(2y-1)(4y^{2}+2y+1)

The following is the graph of a function of x. Which is the interval(s) on which the function is increasing?

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

(-\infty,8)\cup(-4,\infty)

(2,\infty)

(-1,2)

Which function is the inverse of f(x)=x^{3}+17?

f^{-1}=\sqrt[3]{x+17}

f^{-1}=x+\sqrt[3]{17}

f^{-1}=x-\sqrt[3]{17}

f^{-1}=\sqrt[3]{x-17}

Simplify \frac{x^{2}}{x+2}\div\frac{x^{2}-3x}{x^{2}+4x+4}.

\frac{1}{x-3}

\frac{x-3}{x+2}

\frac{x^{3}+2x^{2}}{x^{2}3x}

\frac{x^{2}+2x}{x-3}

Which of the following states the solution to the following rational equation: \frac{3x+4}{2x}+\frac{2x+5}{3x}=\frac{21}{2x}.

x=\frac{41}{13}

x=-7

x=7

x=\frac{32}{5}

Which is expression is equivalent to x^{\frac{3}{5}}y^{4\frac{40}{5}}?

y^{8}\sqrt[5]{x^{3}}

x^{3}y^{6}\sqrt[5]{y}

\frac{1}{5}y^{8}\sqrt{x^{3}}

\frac{1}{5}\sqrt{x^{3}y^{40}}

Which expression is equivalent to\sqrt[3]{a^{4}b^{12}}

a^{\frac{4}{3}}b^{4}

\frac{1}{3}a^{4}b^{12}

a^{3}b^{\frac{1}{2}}

a^{\frac{1}{2}}b^{4}

Which is the simplest radical form for \sqrt{8}+5\sqrt{32}-\sqrt{2}?

21\sqrt{2}

18\sqrt{2}

4\sqrt{2}

22\sqrt{2}

What is the difference between \frac{7}{12} and \frac{1}{3}?

\frac{1}{5}

\frac{2}{5}

\frac{1}{3}

\frac{1}{4}

Which graph best represents a line with an x-intercept of -2 and a y-intercept of 5?

A

B

C

D

Which is the solution to the following equation: 7-4(x+2)=\frac{1}{3}(8x-12)?

x=\frac{14}{5}

x=\frac{4}{15}

x=-\frac{7}{12}

x=\frac{9}{20}

Which is equivalent to \frac{x^{6}y^{5}z^{4}}{(xy)^{-5}}?

\frac{1}{xz^{4}}

x^{11}y^{10}z^{4}

xz^{4}

\frac{-x^{3}y^{2}z^{4}}{3}

Which is a factored form of the following expression: 5x^{2}-20x?

5(x-2)^{2}

(5x+4)(x+5)

5(x^{2}-4)

5x(x-4)

When completely factored, 2x^{2}+20x+48 is equivalent to:

2(x+4)(x+6)

2(x-4)(x-6)

2(x-10)(x+2)

2(x+10)(x-2)

Factor x^{2}-64y^{2}.

(x-8y)(x+16y)

(x-8y)^{2}

(x-8y)(x+8y)

(x+8y)(x-16y)

Which is equivalent to (2+\sqrt{5})(3+\sqrt{5})?

5+2\sqrt{5}

5+6\sqrt{5}

6+\sqrt{10}

11+5\sqrt{5}

Which function of x would have zeros of 1 and -5?

f(x)=2x^{2}+8x+10

f(x)=2x^{2}-8x-10

f(x)=2x^{2}+8x-9

f(x)=2x^{2}+8x-10

The graph of a function is shown. Identify three transformations applied to the parent function y=x^{2} to obtain the graph below.

Reflection over x-axis

Reflection over the y-axis

Translate 2 units left

Translate 2 units right

Translate 3 units up

Translate 3 units down

Which set of ordered pairs is the solution to the system of equations shown?

{(0,-2),(6,10)}

{(0,3),(-1,2)}

{(-2,0),(10,-6)}

{(6,-0.5),(3,0)}

Which is the factored form of 8y^{3}-1?

(2y-1)(4y^{2}+2y-1)

(2y-1)(4y^{2}-2y-1)

(2y-1)(4y^{2}-2y+1)

(2y-1)(4y^{2}+2y+1)

The following is the graph of a function of x.  Which is the interval(s) on which the function is increasing?

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

(-\infty,8)\cup(-4,\infty)

(2,\infty)

(-1,2)

Which function is the inverse of f(x)=x^{3}+17?

f^{-1}=\sqrt[3]{x+17}

f^{-1}=x+\sqrt[3]{17}

f^{-1}=x-\sqrt[3]{17}

f^{-1}=\sqrt[3]{x-17}

Simplify \frac{x^{2}}{x+2}\div\frac{x^{2}-3x}{x^{2}+4x+4}.

\frac{1}{x-3}

\frac{x-3}{x+2}

\frac{x^{3}+2x^{2}}{x^{2}3x}

\frac{x^{2}+2x}{x-3}

Which of the following states the solution to the following rational equation: \frac{3x+4}{2x}+\frac{2x+5}{3x}=\frac{21}{2x}.

x=\frac{41}{13}

x=-7

x=7

x=\frac{32}{5}

Which is expression is equivalent to x^{\frac{3}{5}}y^{4\frac{40}{5}}?

y^{8}\sqrt[5]{x^{3}}

x^{3}y^{6}\sqrt[5]{y}

\frac{1}{5}y^{8}\sqrt{x^{3}}

\frac{1}{5}\sqrt{x^{3}y^{40}}

Which expression is equivalent to\sqrt[3]{a^{4}b^{12}}

a^{\frac{4}{3}}b^{4}

\frac{1}{3}a^{4}b^{12}

a^{3}b^{\frac{1}{2}}

a^{\frac{1}{2}}b^{4}

Which is the simplest radical form for \sqrt{8}+5\sqrt{32}-\sqrt{2}?

21\sqrt{2}

18\sqrt{2}

4\sqrt{2}

22\sqrt{2}