MRWC Spring Final Review (Units 3-7)

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3-E-2: State the system of equations you can use to find the number. Sketch the system by hand. Use your graph to determine whether the value of the logarithm is positive or negative. \log_{\sqrt{3}}{\frac{1}{5}}. Write positive or negative in the answer space. Show all of your work in the Show Your Work space for credit.

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3-E-2: State the system of equations you can use to find the number. Sketch the system by hand. Use your graph to determine whether the value of the logarithm is positive or negative. \log_{0.75}{\frac{2}{5}}. Write positive or negative in the answer space. Show all of your work in the Show Your Work space for credit.

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3-E-2: Use properties to evaluate the logarithm: \log_{81}{27} . Show all of your work in the Show Your Work space for credit.

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3-E-2: Let \log_3{25}=a and \log_3{6}=b. Rewrite \log_6{9} in terms of a and b. Show all of your work in the Show Your Work space for credit.

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3-F-1: What do the terms in the nested radical sequence b_{n}=\sqrt{42+b_{n-1}}: \sqrt{42+\sqrt{42+\sqrt{42+b_{n-1}}}} equal for large values of n? Find the result algebraically. Show all of your work in the Show Your Work space for credit.

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3-F-2: Select all the sets of numbers to which the number belongs. \sqrt{\sqrt{625}} Show all of your work in the Show Your Work space for credit.

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3-F-2: Select all the sets of numbers to which the number belongs. \frac{cos\hspace{1mm}30^{\circ}}{sin\hspace{1mm}30^{\circ}} Show all of your work in the Show Your Work space for credit.

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3-F-3: Select the correct conclusion of the following conjecture. You can use the following numbers to test it out: 5,\hspace{1mm}log\hspace{0.5mm}5,\hspace{1mm}\frac{1}{2},\hspace{1mm}0,\hspace{1mm}\sqrt{2},\hspace{1mm}\frac{1}{\sqrt{2}},\hspace{1mm}\pi,\hspace{1mm}log\hspace{0.5mm}2
The product of a rational number and an irrational number is irrational.

Justify your selection in the Show Your Work space for credit.

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3-F-4: Without using a calculator or doing calculations, state whether the inequality is true or false. \log_{3}\sqrt{5}<1. Justify your response in the Show Your Work space for credit.

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3-F-4: Without using a calculator or doing calculations, state whether the inequality is true or false. cos^2(\frac{\pi}{3})<cos(\frac{\pi}{3}). Justify your response in the Show Your Work space for credit.

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Intro to Unit 4: Select all the real numbers that can be described as an even number. Justify your choices in the Show Your Work space.

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4-B-1: Show that the first number is a factor of the second number: -\frac{3}{16} and -\frac{3}{28}

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4-B-1: Show that the first number is a factor of the second number: \frac{8\pi}{e} and -12e.

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4-C-1: Place r, the reciprocal of y in the proper location on the real number line. Explain why you placed r where you did.

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4-C-1: Place p, the product of x and y in the proper location on the real number line. Explain why you placed p where you did.

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4-C-1: Place p, the product of x and y in the proper location on the real number line. Explain why you placed p where you did.

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4-C-1: Place q, the quotient of \frac{x}{y} in the proper location on the real number line. Explain why you placed \frac{x}{y} where you did.

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4-C-2: Select the correct conclusion of the following conjecture.

The absolute value of a number is larger than the number.

Justify your selection in the Show Your Work space for credit.

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4-D: Drag the numbers to the correct category on the right. Justify your selection in the Show Your Work space for credit.

(\sqrt[4]{(-9)})^{2}
\sqrt[3]{(-2)^{3}}
\sqrt[4]{(-16)^{3}}
\sqrt[4]{(-9)^{2}}

Real Number
Not a real number

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5-C-1: Rewrite the complex number \frac{3-5i}{2+i} in a+bi form. Simplify your answer to receive full credit.

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5-C-1: Rewrite the complex number \frac{2-3i}{-2i} in a+bi form. Simplify your answer to receive full credit.

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5-C-1: Rewrite the complex number \frac{2}{2+i}-\frac{2}{2-i} in a+bi form. Simplify your answer to receive full credit.

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Post 5-C-4: Evaluate the power of i. i^{603}

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5-D-1: Write the complex number \sqrt{2}-\sqrt{2}i in Trigonometric form. Write the argument in Degrees. Show your work.

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5-D-1: Write the complex number -2-2\sqrt{3}i in polar form. Write the argument in radians. Show your work.

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5-D-1: Given z=-6-4i, state the value of |z|. Show your work and give the exact value (no decimal approximation).

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5-E-3: Find the quotient of \frac{18\sqrt{15}\left(\cos315+\sin315\right)}{3\sqrt{3}\left(\cos135+\sin135\right)}. Write the complex number in Cartesian form. Show your work.

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5-E-4: Find the power (\sqrt{2}+\sqrt{2}i)^{6} Write the complex number in Cartesian form. Show your work.

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5-F-1: Choose all the operations under which the set is closed.
Multiples of 4

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5-F-1: Choose all the operations under which the set is closed.
Nonnegative Integers

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6-A-1: A local basketball tournament is played in round-robin format where every team plays every other team. Assuming that every team plays every other team exactly once, how many games will be played among 18 teams? Show two ways to get your answer.

1

6-B-1: What relationship does this describe?
Five kids were asked to choose two ice cream flavors from chocolate, vanilla and strawberry.
Draw a mapping to justify your answer.

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6-B-1: Which of the following relations are functions?
Draw mappings to justify your answer.

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7-A-1:Describe the points on the number line using interval notation

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7-A-1:State the domain of the graph of the function in interval notation.

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7-A-1: State the range of the graph of the function in interval notation.

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7-A-1: State the domain of the graph of the function in interval notation.

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7-A-1: State the range of the graph of the function in interval notation.

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7-A-1: Given the symbolic notation, graph it on the number line.
-5\leq{x}<4, x\in \Re

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7-A-3: Graph y=\sqrt{x+3}, x<3

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7-A-3: Graph y=\pi, -2<x\leq{8}

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7-A-3: Graph
f(x)=\left\{ \begin{array}{cc} \sqrt{x+3}, & \hspace{5mm} x>-3\\-|x+2|+1, & \hspace{5mm} x\leq-3\\ \end{array} \right.

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7-A-3: Write an equation for the given graph.

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7-A-2: State the domain of the function in interval notation f(x)=\frac{x-3}{x-6}.

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7-A-2: State the domain of the function in interval notation f(x)=log(x-6).

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7-A-2: State the domain of the function in interval notation f(x)=\sqrt{x-6}.

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7-A-3: Write a piecewise function for the following situation. A tour guide charges the following:
1 - 8 people cost $10 per person
9 - 15 people cost $9 per person
16 or more people costs a flat rate of $120

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7-A-4: Determine by factoring whether the rational function has a hole or a vertical asymptote at x = 3.
f(x)=\frac{3x^{2}+20x-7}{x+7}. Justify your answer in the Show Your Work space.

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7-A-4: Determine by factoring whether the rational function has a hole or a vertical asymptote at x = 3.
f(x)=\frac{x^{2}-6x-7}{x+7}. Justify your answer in the Show Your Work space.

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Unit Circle: Drag the trig function expressions to their exact value.

cos\hspace{1mm}\pi
sin\hspace{1mm}\frac{\pi}{4}
tan\hspace{1mm}0
sin\hspace{1mm}\frac{\pi}{6}
cos\hspace{1mm}\frac{11\pi}{6}
tan\hspace{1mm}\frac{\pi}{2}
cos\hspace{1mm}\frac{2\pi}{3}
tan\hspace{1mm}\frac{5\pi}{4}
sin\hspace{1mm}\frac{2\pi}{3}
sin\hspace{1mm}\frac{5\pi}{3}
cos\hspace{1mm}\frac{5\pi}{4}
tan\hspace{1mm}\frac{7\pi}{6}

0
undefined
1
-1
1/2
-\frac{1}{2}
\frac{\sqrt{3}}{2}
-\frac{\sqrt{3}}{2}
\frac{\sqrt{2}}{2}
-\frac{\sqrt{2}}{2}
\frac{\sqrt{3}}{3}
-\frac{\sqrt{3}}{3}
\sqrt{3}
-\sqrt{3}

3-E-2: Use properties to evaluate the logarithm: \log_{81}{27} . Show all of your work in the Show Your Work space for credit.

3-E-2: Let \log_3{25}=a and \log_3{6}=b. Rewrite \log_6{9} in terms of a and b. Show all of your work in the Show Your Work space for credit.

3-F-1: What do the terms in the nested radical sequence b_{n}=\sqrt{42+b_{n-1}}: \sqrt{42+\sqrt{42+\sqrt{42+b_{n-1}}}} equal for large values of n? Find the result algebraically. Show all of your work in the Show Your Work space for credit.

3-F-2: Select all the sets of numbers to which the number belongs. \sqrt{\sqrt{625}} Show all of your work in the Show Your Work space for credit.

3-F-2: Select all the sets of numbers to which the number belongs. \frac{cos\hspace{1mm}30^{\circ}}{sin\hspace{1mm}30^{\circ}} Show all of your work in the Show Your Work space for credit.

3-F-4: Without using a calculator or doing calculations, state whether the inequality is true or false. \log_{3}\sqrt{5}<1. Justify your response in the Show Your Work space for credit.

3-F-4: Without using a calculator or doing calculations, state whether the inequality is true or false. cos^2(\frac{\pi}{3})<cos(\frac{\pi}{3}). Justify your response in the Show Your Work space for credit.

Intro to Unit 4: Select all the real numbers that can be described as an even number. Justify your choices in the Show Your Work space.

4-B-1: Show that the first number is a factor of the second number: -\frac{3}{16} and -\frac{3}{28}

4-B-1: Show that the first number is a factor of the second number: \frac{8\pi}{e} and -12e.

4-C-1: Place r, the reciprocal of y in the proper location on the real number line. Explain why you placed r where you did.

4-C-1: Place p, the product of x and y in the proper location on the real number line. Explain why you placed p where you did.

4-C-1: Place p, the product of x and y in the proper location on the real number line. Explain why you placed p where you did.

4-C-1: Place q, the quotient of \frac{x}{y} in the proper location on the real number line. Explain why you placed \frac{x}{y} where you did.

4-C-2: Select the correct conclusion of the following conjecture. The absolute value of a number is larger than the number.Justify your selection in the Show Your Work space for credit.

4-D: Drag the numbers to the correct category on the right. Justify your selection in the Show Your Work space for credit.

5-C-1: Rewrite the complex number \frac{3-5i}{2+i} in a+bi form. Simplify your answer to receive full credit.

5-C-1: Rewrite the complex number \frac{2-3i}{-2i} in a+bi form. Simplify your answer to receive full credit.

5-C-1: Rewrite the complex number \frac{2}{2+i}-\frac{2}{2-i} in a+bi form. Simplify your answer to receive full credit.

Post 5-C-4: Evaluate the power of i. i^{603}

5-D-1: Write the complex number \sqrt{2}-\sqrt{2}i in Trigonometric form. Write the argument in Degrees. Show your work.

5-D-1: Write the complex number -2-2\sqrt{3}i in polar form. Write the argument in radians. Show your work.

5-D-1: Given z=-6-4i, state the value of |z|. Show your work and give the exact value (no decimal approximation).

5-E-3: Find the quotient of \frac{18\sqrt{15}\left(\cos315+\sin315\right)}{3\sqrt{3}\left(\cos135+\sin135\right)}. Write the complex number in Cartesian form. Show your work.

5-E-4: Find the power (\sqrt{2}+\sqrt{2}i)^{6} Write the complex number in Cartesian form. Show your work.

5-F-1: Choose all the operations under which the set is closed.Multiples of 4

5-F-1: Choose all the operations under which the set is closed.Nonnegative Integers

6-A-1: A local basketball tournament is played in round-robin format where every team plays every other team. Assuming that every team plays every other team exactly once, how many games will be played among 18 teams? Show two ways to get your answer.

6-B-1: What relationship does this describe?Five kids were asked to choose two ice cream flavors from chocolate, vanilla and strawberry.Draw a mapping to justify your answer.

6-B-1: Which of the following relations are functions? Draw mappings to justify your answer.

7-A-1:Describe the points on the number line using interval notation

7-A-1:State the domain of the graph of the function in interval notation.

7-A-1: State the range of the graph of the function in interval notation.

7-A-1: State the domain of the graph of the function in interval notation.

7-A-1: State the range of the graph of the function in interval notation.

7-A-1: Given the symbolic notation, graph it on the number line.-5\leq{x}<4, x\in \Re

7-A-3: Graph y=\sqrt{x+3}, x<3

7-A-3: Graph y=\pi, -2<x\leq{8}

7-A-3: Graphf(x)=\left\{ \begin{array}{cc} \sqrt{x+3}, & \hspace{5mm} x>-3\\-|x+2|+1, & \hspace{5mm} x\leq-3\\ \end{array} \right.

7-A-3: Write an equation for the given graph.

7-A-2: State the domain of the function in interval notation f(x)=\frac{x-3}{x-6}.

7-A-2: State the domain of the function in interval notation f(x)=log(x-6).

7-A-2: State the domain of the function in interval notation f(x)=\sqrt{x-6}.

7-A-3: Write a piecewise function for the following situation. A tour guide charges the following: 1 - 8 people cost $10 per person 9 - 15 people cost $9 per person 16 or more people costs a flat rate of $120

7-A-4: Determine by factoring whether the rational function has a hole or a vertical asymptote at x = 3.f(x)=\frac{3x^{2}+20x-7}{x+7}. Justify your answer in the Show Your Work space.

7-A-4: Determine by factoring whether the rational function has a hole or a vertical asymptote at x = 3.f(x)=\frac{x^{2}-6x-7}{x+7}. Justify your answer in the Show Your Work space.

Unit Circle: Drag the trig function expressions to their exact value.

4-C-2: Select the correct conclusion of the following conjecture.

The absolute value of a number is larger than the number.

Justify your selection in the Show Your Work space for credit.

5-F-1: Choose all the operations under which the set is closed.
Multiples of 4

5-F-1: Choose all the operations under which the set is closed.
Nonnegative Integers

6-B-1: What relationship does this describe?
Five kids were asked to choose two ice cream flavors from chocolate, vanilla and strawberry.
Draw a mapping to justify your answer.

6-B-1: Which of the following relations are functions?
Draw mappings to justify your answer.

7-A-1: Given the symbolic notation, graph it on the number line.
-5\leq{x}<4, x\in \Re

7-A-3: Graph
f(x)=\left\{ \begin{array}{cc} \sqrt{x+3}, & \hspace{5mm} x>-3\\-|x+2|+1, & \hspace{5mm} x\leq-3\\ \end{array} \right.

7-A-3: Write a piecewise function for the following situation. A tour guide charges the following:
1 - 8 people cost $10 per person
9 - 15 people cost $9 per person
16 or more people costs a flat rate of $120

7-A-4: Determine by factoring whether the rational function has a hole or a vertical asymptote at x = 3.
f(x)=\frac{3x^{2}+20x-7}{x+7}. Justify your answer in the Show Your Work space.

7-A-4: Determine by factoring whether the rational function has a hole or a vertical asymptote at x = 3.
f(x)=\frac{x^{2}-6x-7}{x+7}. Justify your answer in the Show Your Work space.