Study Guide 9 Weeks Test :2) -...
Transcript of Study Guide 9 Weeks Test :2) -...
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Name_______________________________ Date______________ Period_______
Study Guide – 9 Weeks Test
Solve each equation. Show all work.
1) 𝟏
𝟔(𝒙 − 𝟒) =
𝟐
𝟑𝒙 +
𝟒
𝟑 2) −𝟓(𝒙 − 𝟒) = 𝟏𝟎𝒙 + 𝟏𝟎
3) −𝟑𝒚 + 𝟏 = 𝒚 + 𝟗 − 𝟒𝒚 4) 𝟖 − 𝟕(𝟒𝒙 − 𝟐) = −𝟐𝟖𝒙 + 𝟐𝟐
5) 𝟏. 𝟓𝒎 − 𝟏 = −𝟓 + 𝟏. 𝟕𝒎 6) 𝟐(𝒚 − 𝟒) + 𝟖 =𝟏
𝟐(𝟔𝒚 + 𝟐𝟎)
8th Grade
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7) Determine if each equation has no solution, one solution, or infinite many solutions. 𝟑(𝒙 + 𝟕) = 𝟐(𝒙 + 𝟕) + 𝒙 𝟑(𝒙 + 𝟕) = 𝟒𝒙 − 𝒙 + 𝟐𝟏 𝟑𝒙 + 𝟕 = 𝟓𝒙 + 𝟕 − 𝟑𝒙 8) The equation below has infinite many solutions. 𝒂𝒙 + 𝒃 = 𝟒(𝟐𝒙 + 𝟑) − 𝟏𝟎𝒙 For this to be true, what must be the value of a? What must be the value of b? Solve and graph each inequality. Show all work.
9) −𝟐𝒚 − 𝟑 ≤ −𝟓 10) 𝟔 − 𝒙 > 𝟑
11) 𝟑(𝒙 − 𝟒) ≥ −𝟓𝒙 + 𝟒
![Page 3: Study Guide 9 Weeks Test :2) - PC\|MACimages.pcmac.org/.../Uploads/Forms/8th_Grade_Study_Guide.pdf · 2017. 9. 27. · Study Guide – 9 Weeks Test Solve each equation. Show all work.](https://reader036.fdocuments.us/reader036/viewer/2022071214/604286bdea127645e55ecd29/html5/thumbnails/3.jpg)
12) CIRCLE the numbers that could be solutions to the inequality listed.
𝒙 < 𝟓
𝒙 > −𝟐
𝒙 ≥ 𝟗
𝒙 ≤ −𝟕𝟎 13) Complete the input/output table using the given function rule. 𝒚 = 𝟑𝒙 – 𝟐
14) Label each with either a Function or Not a Function.
-15 0 5 6 18
-4 -2 -1 8 30
-9 8.9 9 10 21
-80 -70 -50 -1 10
x -2 -1 4 0 7 5
y
![Page 4: Study Guide 9 Weeks Test :2) - PC\|MACimages.pcmac.org/.../Uploads/Forms/8th_Grade_Study_Guide.pdf · 2017. 9. 27. · Study Guide – 9 Weeks Test Solve each equation. Show all work.](https://reader036.fdocuments.us/reader036/viewer/2022071214/604286bdea127645e55ecd29/html5/thumbnails/4.jpg)
15) Which table creates the graph shown. 16) Create a model for the equation 𝒚 = 𝟐𝒙 − 𝟑 by making a table of order pairs and graphing.
What is the y-intercept? What is the slope? 17)
X Y
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18) Write an equation that represents the table. 19) Name the slope and y-intercept for each equation or table below.
SLOPE Y-Intercept 𝒚 = 𝟐𝒙 𝒚 = 𝟒𝒙 − 𝟓 𝒚 = 𝟑 − 𝟔𝒙
20) What other word means SLOPE? What other word means Y-Intercept? A. x-intercept A. x-intercept C. initial value B. initial value B. rate of change C. rate of change
![Page 6: Study Guide 9 Weeks Test :2) - PC\|MACimages.pcmac.org/.../Uploads/Forms/8th_Grade_Study_Guide.pdf · 2017. 9. 27. · Study Guide – 9 Weeks Test Solve each equation. Show all work.](https://reader036.fdocuments.us/reader036/viewer/2022071214/604286bdea127645e55ecd29/html5/thumbnails/6.jpg)
21) 22) Label each as either linear or nonlinear.
𝒚 = 𝒙𝟐 − 𝟓 𝒚 = 𝒙 − 𝟒 𝒚 = 𝟐𝒙 + 𝟏 23) Sunset Splash and Spa charges their customers a fee for entering plus an amount per hour of stay.
What is the initial fee for entering the Spa?
What is the rate of change?
What would a person be charged for spending 𝟖 hours at the spa?
Time (hours)
Cost $
2 41
6 73 10 105
![Page 7: Study Guide 9 Weeks Test :2) - PC\|MACimages.pcmac.org/.../Uploads/Forms/8th_Grade_Study_Guide.pdf · 2017. 9. 27. · Study Guide – 9 Weeks Test Solve each equation. Show all work.](https://reader036.fdocuments.us/reader036/viewer/2022071214/604286bdea127645e55ecd29/html5/thumbnails/7.jpg)
24) 25) Randy is shopping for CD’s to give as gifts to his friends. He is considering two stores. The pricing for each store is shown below.
CD Express Music Place 𝟔 CD’s for $𝟕𝟓
Which store is cheaper per CD?
How much will Randy save per CD at this store?
Number of CD’s
Cost $
3 45 5 75
8 120 10 150
![Page 8: Study Guide 9 Weeks Test :2) - PC\|MACimages.pcmac.org/.../Uploads/Forms/8th_Grade_Study_Guide.pdf · 2017. 9. 27. · Study Guide – 9 Weeks Test Solve each equation. Show all work.](https://reader036.fdocuments.us/reader036/viewer/2022071214/604286bdea127645e55ecd29/html5/thumbnails/8.jpg)
26) State if each represents a proportional or non-proportional relationship.
Every 3 out of 12 people
live in a rural area. The City Pool costs $8 per
day to visit during the
summer. There is also a $25
yearly registration fee.
![Page 9: Study Guide 9 Weeks Test :2) - PC\|MACimages.pcmac.org/.../Uploads/Forms/8th_Grade_Study_Guide.pdf · 2017. 9. 27. · Study Guide – 9 Weeks Test Solve each equation. Show all work.](https://reader036.fdocuments.us/reader036/viewer/2022071214/604286bdea127645e55ecd29/html5/thumbnails/9.jpg)
ANSWER KEY
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Name_______________________________ Date______________ Period_______
Study Guide – 9 Weeks Test
Solve each equation. Show all work.
1) 𝟏
𝟔(𝒙 − 𝟒) =
𝟐
𝟑𝒙 +
𝟒
𝟑 2) −𝟓(𝒙 − 𝟒) = 𝟏𝟎𝒙 + 𝟏𝟎
Answer: −𝟒 Answer: 𝟐
𝟑
3) −𝟑𝒚 + 𝟏 = 𝒚 + 𝟗 − 𝟒𝒚 4) 𝟖 − 𝟕(𝟒𝒙 − 𝟐) = −𝟐𝟖𝒙 + 𝟐𝟐 Answer: No solution Answer: Infinite Many Solutions
5) 𝟏. 𝟓𝒎 − 𝟏 = −𝟓 + 𝟏. 𝟕𝒎 6) 𝟐(𝒚 − 𝟒) + 𝟖 =𝟏
𝟐(𝟔𝒚 + 𝟐𝟎)
Answer: 20 Answer: -10
Answer Key
8th Grade
![Page 11: Study Guide 9 Weeks Test :2) - PC\|MACimages.pcmac.org/.../Uploads/Forms/8th_Grade_Study_Guide.pdf · 2017. 9. 27. · Study Guide – 9 Weeks Test Solve each equation. Show all work.](https://reader036.fdocuments.us/reader036/viewer/2022071214/604286bdea127645e55ecd29/html5/thumbnails/11.jpg)
7) Determine if each equation has no solution, one solution, or infinite many solutions. 𝟑(𝒙 + 𝟕) = 𝟐(𝒙 + 𝟕) + 𝒙 Answer: no solution 𝟑(𝒙 + 𝟕) = 𝟒𝒙 − 𝒙 + 𝟐𝟏 Answer: Infinite Many Solutions 𝟑𝒙 + 𝟕 = 𝟓𝒙 + 𝟕 − 𝟑𝒙 Answer: 1 solution 8) The equation below has infinite many solutions. 𝒂𝒙 + 𝒃 = 𝟒(𝟐𝒙 + 𝟑) − 𝟏𝟎𝒙 For this to be true, what must be the value of a? What must be the value of b? a must be -2 b must be 12 Solve and graph each inequality. Show all work.
9) −𝟐𝒚 − 𝟑 ≤ −𝟓 Symbol Flip! 𝒚 ≥ 𝟏 10) 𝟔 − 𝒙 > 𝟑 Symbol Flip! 𝒙 < 𝟑
11) 𝟑(𝒙 − 𝟒) ≥ −𝟓𝒙 + 𝟒 𝒙 ≥ 𝟐
![Page 12: Study Guide 9 Weeks Test :2) - PC\|MACimages.pcmac.org/.../Uploads/Forms/8th_Grade_Study_Guide.pdf · 2017. 9. 27. · Study Guide – 9 Weeks Test Solve each equation. Show all work.](https://reader036.fdocuments.us/reader036/viewer/2022071214/604286bdea127645e55ecd29/html5/thumbnails/12.jpg)
12) CIRCLE the numbers that could be solutions to the inequality listed.
𝒙 < 𝟓
𝒙 > −𝟐
𝒙 ≥ 𝟗
𝒙 ≤ −𝟕𝟎 13) Complete the input/output table using the given function rule. 𝒚 = 𝟑𝒙 – 𝟐
14) Label each with either a Function or Not a Function. Function Not a Function
-15 0 5 6 18
-4 -2 -1 8 30
-9 8.9 9 10 21
-80 -70 -50 -1 10
x -2 -1 4 0 7 5
y -8 -5 10 -2 19 13
![Page 13: Study Guide 9 Weeks Test :2) - PC\|MACimages.pcmac.org/.../Uploads/Forms/8th_Grade_Study_Guide.pdf · 2017. 9. 27. · Study Guide – 9 Weeks Test Solve each equation. Show all work.](https://reader036.fdocuments.us/reader036/viewer/2022071214/604286bdea127645e55ecd29/html5/thumbnails/13.jpg)
15) Which table creates the graph shown. 16) Create a model for the equation 𝒚 = 𝟐𝒙 − 𝟑 by making a table of order pairs and graphing.
What is the y-intercept? -3 What is the slope? 2 17)
X Y
-1 -5
0 -3
1 -1
2 1
3 3
![Page 14: Study Guide 9 Weeks Test :2) - PC\|MACimages.pcmac.org/.../Uploads/Forms/8th_Grade_Study_Guide.pdf · 2017. 9. 27. · Study Guide – 9 Weeks Test Solve each equation. Show all work.](https://reader036.fdocuments.us/reader036/viewer/2022071214/604286bdea127645e55ecd29/html5/thumbnails/14.jpg)
18) Write an equation that represents the table. 𝒚 = 𝒙 – 𝟓 19) Name the slope and y-intercept for each equation or table below.
SLOPE Y-Intercept
𝒚 = 𝟐𝒙 2 0
𝒚 = 𝟒𝒙 − 𝟓 4 -5 𝒚 = 𝟑 − 𝟔𝒙 -6 3
-1 3
3 6 20) What other word means SLOPE? What other word means Y-Intercept? A. x-intercept A. x-intercept C. initial value B. initial value B. rate of change C. rate of change
![Page 15: Study Guide 9 Weeks Test :2) - PC\|MACimages.pcmac.org/.../Uploads/Forms/8th_Grade_Study_Guide.pdf · 2017. 9. 27. · Study Guide – 9 Weeks Test Solve each equation. Show all work.](https://reader036.fdocuments.us/reader036/viewer/2022071214/604286bdea127645e55ecd29/html5/thumbnails/15.jpg)
21) $200 22) Label each as either linear or nonlinear.
𝒚 = 𝒙𝟐 − 𝟓 𝒚 = 𝒙 − 𝟒 𝒚 = 𝟐𝒙 + 𝟏 nonlinear linear linear nonlinear 23) Sunset Splash and Spa charges their customers a fee for entering plus an amount per hour of stay.
What is the initial fee for entering the Spa? Answer: $25
What is the rate of change? Answer: $8
What would a person be charged for spending 𝟖 hours at the spa? Answer: $89
Time (hours)
Cost $
2 41
6 73 10 105
![Page 16: Study Guide 9 Weeks Test :2) - PC\|MACimages.pcmac.org/.../Uploads/Forms/8th_Grade_Study_Guide.pdf · 2017. 9. 27. · Study Guide – 9 Weeks Test Solve each equation. Show all work.](https://reader036.fdocuments.us/reader036/viewer/2022071214/604286bdea127645e55ecd29/html5/thumbnails/16.jpg)
24) 25) Randy is shopping for CD’s to give as gifts to his friends. He is considering two stores. The pricing for each store is shown below.
CD Express Music Place 𝟔 CD’s for $𝟕𝟓
Which store is cheaper per CD? Answer: Music Place
How much will Randy save per CD at this store? Answer: $15 – $12.50 = $2.50
Number of CD’s
Cost $
3 45
5 75 8 120
10 150
![Page 17: Study Guide 9 Weeks Test :2) - PC\|MACimages.pcmac.org/.../Uploads/Forms/8th_Grade_Study_Guide.pdf · 2017. 9. 27. · Study Guide – 9 Weeks Test Solve each equation. Show all work.](https://reader036.fdocuments.us/reader036/viewer/2022071214/604286bdea127645e55ecd29/html5/thumbnails/17.jpg)
26) State if each represents a proportional or non-proportional relationship. Non-proportional Proportional Proportional Non-Proportional Non-Proportional Proportional
Every 3 out of 12 people
live in a rural area. The City Pool costs $8 per
day to visit during the
summer. There is also a $25
yearly registration fee.