Name: ________________________________

8th Grade Math Remote Learning Work

Directions:

1) Complete the packet in pencil.

2) Answer every question and box youranswer.

3) Show ALL work. No work = no credit.

Day 1: Pythagorean Theorem

Day 2: Estimating Non-Perfect Square Roots and Cube Roots

Day 3: Writing Equations in Slope-Intercept form

Day 4: Graphing Equations

Day 5: Exponents

Day 6: Scatter Plots

Day 7: Rational and Irrational Numbers and Terminating and Repeating Decimals

Day 8: Integers

Day 9: Solving Systems of Equations Algebraically

Day 10: Deciding How Many Solutions a System Has

2

Day 1: Pythagorean Theorem

Take a minute and jot down everything you already know about Pythagorean Theorem.

Practice

1) At what height is the ladder touching the wall?

Answer: _____________________________________

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2)

Answer: ______________________________

3) Which of the following side lengths would make a right triangle?

a) 12, 5, 14b) 8, 7, 15c) 4, 10, √84d) √1,2 √5

4)

c = ______________________________________

4

5)

a) 50 yardsb) 60 yardsc) 40 yardsd) 37 yards

6) Is the triangle below a right triangle? How do you know?

2"

8"

62

5

Day 2: Estimating Non-perfect square roots and cube roots.

For each of these problems, tell which two, consecutive whole numbers it is between and the whole number it is closest to.

1) √10 is between ________________________ and ______________________

Is closest to ______________________________

2) √9! is between ________________________ and ______________________

Is closest to ______________________________

3) √28 is between ________________________ and ______________________

Is closest to ______________________________

4) √3! is between ________________________ and ______________________

Is closest to ______________________________

5) √35! is between ________________________ and ______________________

Is closest to ______________________________

6) √95 is between ________________________ and ______________________

Is closest to ______________________________

7) √70 is between ________________________ and ______________________

Is closest to _____________________________

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8) √200 is between ________________________ and ______________________

Is closest to ______________________________

9) √120! is between ________________________ and ______________________

Is closest to ______________________________

10) √5! is between ________________________ and ______________________

Is closest to ______________________________

11) √52 is between ________________________ and ______________________

Is closest to ______________________________

12) √38 is between ________________________ and ______________________

Is closest to ______________________________

13) √4! is between ________________________ and ______________________

Is closest to ______________________________

14) √11! is between ________________________ and ______________________

Is closest to ______________________________

15) √90 is between ________________________ and ______________________

Is closest to _____________________________

7

Day 3: Writing equations in slope-intercept form

Slope-intercept form: y= mx + b

Look at the graphs and then write the equation of each line is slope-intercept form. Don’t forget to look at whether or not the slopes are negative or positive.

1)

Equation: _____________________________________________

2)

Equation: ___________________________________________

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3)

Equation: ___________________________________________

4)

Equation: ___________________________________________

9

5)

Equation: ___________________________________________

6)

Equation: ___________________________________________

10

Day 4: Graphing equations

Now, graph equations on the coordinate grid from their equation in slope-intercept form.

1) y = -2x + 4

2) y = x – 2

11

3) y = -x + 1

4) y = 2x + 2

12

5) y = 3x – 1

6) y = -2x - 3

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Day 5: Exponents

Use your exponent rules to simplify the following.

1) 10! ⋅ 10"

2) 10 ⋅ 10"

3) 10# ⋅ 10$

4) 10! ⋅ 10!

5) 10% ⋅ 10!

6) 10" ⋅ 10" ⋅ 10"

7) Which of the following are equivalent to 106? Select all that areequivalent.

a. 10# ∙ 10"

b. 10! ∙ 10!

c. (10!)!

d. (10#)!

e. 100,000

f. 1,000,000

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8) Write each expression as a single power of 10.

a. &&'⋅ &&'⋅ &&'

b. ( &&'⋅ &&'⋅ &&')(!

c. 10(! ⋅ 10(#

d. 10" ⋅ 10(&

e. &'"

&'#

f. (10(")%

9) Write each of the following with a single, POSITIVE exponent:a. !

!$%

b. (0.173)() ⋅ (0.173)#

c. '.+$"

'.+$&

d. 𝑎$ ÷ 𝑎(! ∙ 𝑎(#

15

Day 6: Scatter Plots

Use the following scatter plot for #1 and 2.

1. What kind of association is there between the age of the motorcycle andthe sale price of the motorcycle?

a. No associationb. A positive associationc. A negative associationd. A non-linear association

2. As the age of the motorcycle increases, the sale price of the motorcyclea. Decreasesb. Increasesc. Neither increases nor decreasesd. None of the above

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3. Use the scatter plot below to answer the following questions. For this data, the inputs are the horizontal values, and the outputs are the vertical values.

a. Draw a line that you think is a good fit for this data.

b. What kind of association is there between the input and output?How do you know?

c. Use your line of fit to estimate what you would expect the outputvalue to be when the input is 10.

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4. Elena said, “I think this line is a good fit because half of the points are onone side of the line and half of the points are on the other side.” Do youagree? Explain your reasoning.

5. Do you think this is a good line of best fit? Explain your reasoning.

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Day 7: Rational and Irrational Numbers and Terminating and Repeating Decimals

1) From the following numbers, select all that are rational.

a) ,$

b) 0.62c) 0.6d) 0.6π

2) From the following numbers, select all that are rational.

a) '.'"'.&#

b) 1.586c) √𝜋d) √3 + 6

3) Write this decimal as a fraction: 0. 787777

4) Decide whether each number in this list is rational or irrational.

(&!!, 0.1234,√37, − 77, − √100, − √12

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5) Write this decimal as a fraction: 0. 97

6) In your own words, say what an irrational number is. Give at least twoexamples.

7) Write this decimal as a fraction: 5.347

8) Give two examples of rational numbers.

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Day 8: Integers

Solve.

1) -8 – 10 = _________________________

2) 9 – 12 = _________________________

3) -8 + 7 = __________________________

4) 1 – (-12) = ________________________

5) -5 + 10 = _________________________

6) 3 + -7 = __________________________

7) -10 + - 10 = _______________________

8) -7 – 11 = __________________________

9) 12 – 15 = _________________________

10) 11 + - 12 = _______________________

11) -12 + -12 = ________________________

12) -1 + 3 = ___________________________

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13) 3 – 7 = _______________________

14) 10 – (-10) = ___________________

15) 25 – (-10) = ___________________

16) -4 – 9 = ______________________

17) -8 + 10 = _____________________

18) -11 + -12 = ___________________

19) 8 – 15 = ______________________

20) -1 + -6 = ______________________

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Day 9: Solving Systems Algebraically

Solve the following systems of equations and write your answer as a coordinate point.

1) 9𝑦 = 2𝑥 + 3𝑦 = 5𝑥 − 4

______________________

2)

9 𝑦 = 𝑥 + 3𝑦 = 2𝑥 − 4

_______________________

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3) 9𝑦 = 2𝑥 + 1𝑦 = 6𝑥 − 3

_______________________________

4)

9 𝑦 = 𝑥 − 3𝑦 = 3𝑥 + 1

______________________________

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5) 9𝑦 = 4𝑥 + 3𝑦 = 5𝑥 + 7

________________________________________

6)

9 𝑦 = 𝑥 − 8𝑦 = 3𝑥 + 12

________________________________________

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Day 10: Types of Solutions

State whether the system of equations has no solution, one solution, or infinite solutions.

1) 9𝑦 = 2𝑥 + 3𝑦 = 5𝑥 + 3

_____________________________________

2)

9𝑦 = 3𝑥 + 4𝑦 = 3𝑥 − 4

_____________________________________

3) 9𝑦 = 2𝑥 + 1𝑦 = 2𝑥 + 1

____________________________________

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4)

9 𝑦 = 𝑥 + 3𝑦 = 2𝑥 − 8

__________________________________

5) 9𝑦 = 𝑥 + 3𝑦 = 𝑥 − 4

___________________________________

6)

9𝑦 = 4𝑥 + 3𝑦 = 4𝑥 − 4

____________________________________

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Additional Practice

1) Write this decimal as a fraction: 2.817

2) Noah and Han are preparing for a jump rope contest. Noah can jump 40times in 0.5 minutes. Han can jump 𝑦 times in 𝑥 minutes, where 𝑦 = 78𝑥. Ifthey both jump for 2 minutes, who jumps more times? How many more?

3) A line contains the point (3,5). If the line has negative slope, which ofthese points could also be on the line?

a. (2,0)b. (4,7)c. (5,4)d. (6,5)

4) Solve for x.

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5) What fraction is equivalent to 0.4 ?

Categorize each of these as having one solution, no solution, or infinite solutions?

6) −8𝑥 + 3 = −8𝑥 − 4 _________________________________

7) 6 = 4(𝑥 − 3) − 4𝑥 _________________________________

8) −3𝑥 − 8 = 2𝑥 − 8 − 5𝑥 _________________________________

9) 2(𝑥 − 3) = −5 + 𝑥 _________________________________