8th grade math remote learning work€¦ · 17/3/2020 · 3) show all work. no work = no credit....
TRANSCRIPT
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
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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 = ______________________________________
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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
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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 _____________________________
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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: ___________________________________________
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5)
Equation: ___________________________________________
6)
Equation: ___________________________________________
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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
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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(#
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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 _________________________________