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Algebra 1 TeachersWeekly Assessment Package #1

Units 1 - 3

Created by: Jeanette Stein

©2014 Algebra 1 Teachers

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SEMESTER 1 SKILLS 3

UNIT 1 5

WEEK #1 6WEEK #2 7WEEK #3 9WEEK #4 11

UNIT 1 - KEYS 13

WEEK #1 - KEY 14WEEK #2 - KEY 15WEEK #3 - KEY 17WEEK #4 -KEY 19

UNIT 2 21

WEEK #5 22WEEK #6 24WEEK #7 26

UNIT 2 - KEYS 28

WEEK #5 - KEY 29WEEK #6 - KEY 31WEEK #7 - KEY 33

UNIT 3 35

WEEK #8 36WEEK #9 37

UNIT 3 - KEYS 39

WEEK #8 KEY 40WEEK #9 KEY 41

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Algebra 1 Common Core

Semester 1 SkillsSkill

NumberAlgebra 1

Unit CCSS Skill

1 1 A.REI.3 Solve two step equations (including proportions)

2 1 Order of Operations

3 1 Create a table from a situation

4 1 A.REI.10 Create a graph from a situation

5 1 F.BF.1 Create an equation from a situation

6 1 F.IF.1 Identify a function

7 1 F.IF.2 Evaluate a function

8 1 A.REI.6 Basic Systems with a table and graph

9 1 F.LE.1 Identify linear, exponential, quadratic, and absolute value functions

10 2 F.IF.6 Calculate Slope

11 2 S.ID.7 Interpret meaning of the slope and intercepts

12 2 F.BF.2 Construct an arithmetic sequence

13 2 F.BF.4 Find the inverse of a function

14 2 F.BF.3 Translate a graph in function notation

15 3 S.ID.6 Find the line of best fit

16 3 S.ID.6 Predict future events given data

17 3 S.ID.8 Calculate Correlation Coefficient with technology

18 3 S.ID.9 Understand the difference between Causation and Correlation

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19 4 S.ID.1 Create box plots

20 4 S.ID.2 Calculate and compare measures of central tendencies

21 4 S.ID.2 Calculate standard deviation

22 4 S.ID.3 Understand the effects of outliers

23 4 S.ID.5 Use two way frequency tables to make predictions

24 5 A.REI.3 Solve advanced linear equations

25 5 A.REI.1 A.CED.4 Solve literal equations and justify the steps

26 5 A.REI.3 Solve inequalities

27 5 A.REI.12 Graph inequalities

28 6 A.REI.6 Solve a system of equations by graphing

29 6 A.REI.6 Solve a system of equations by substitution

30 6 A.REI.5 Solve a system of equations by elimination

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Unit 1Weekly Assessments

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Week #1

1. The carnival charges $15 for admissions and $2 per ride. (x = number of rides, y = cost)

Write an equation for the situation.

___________________________

Fill in the table.

x y

4. Are the following expressions equivalent to 10? Circle yes or no

(−8)+6 (8−5) yes / no

3+6 (5+4 )÷3−7yes / no

(−4)(−3)÷6−2[5−(−8)+(6÷2)] yes / no

2. Which equations are equivalent to 10=4 x? Circle yes or no.

a. 8 x=20 yes / no

b. 12=4 x+2 yes / no

c. 12=6 x yes / no

5. Solve for x

3 x+4=10 2+12x=4

3. Graph: y=2x+1 6. Graph: 2 x+3 y=12

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Week #2

1. The admission for the class to go to Michigan’s Adventure is $24 per person. The cost of the busses for the entire 9th grade will be $450.a. Write an equation or rule that represents the function.

___________________________________b. Make a table that show how much a trip will cost for 50 students, 100 students, 150 students, and 200 students.

c. Graph.

2. a. Which point shows the heaviest bag? _________

b. Which point shows the cheapest bag? ________

c. Which bag is the best value? ___________

Why? _____________________________________

__________________________________________

___________________________________________

3. Does this graph represent a function? _______Why or why not?

______________________

______________________

______________________

______________________

_______________________________________________

4. Every student earns a grade on the last test. Please define the domain and range of this function.

Domain _________________________________

Range __________________________________

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Week #2 Continued

5. Evaluate the function for the given values.

f (x)=3x−2 x+1

f (3)=¿________________

f (−1)=¿_________________

f (⅖)=¿__________________

6. Deshawn’s Bikes rents bikes for $11 plus $5 per hour. Maria paid $51 to rent a bike. For how many hours did she rent the bike?

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Week #3

1. Are the following functions? Circle yes or no.

y+2=4 x−2 yes / no

yes / no

{(2, 3), (5, -2), (5, 6), (3, 3), (4, 1)} yes / no

3. Find the domain and range of the function.

f (x)=x2+2

Domain: __________________________

Range: ___________________________

2. The Red bus company charges $100 plus $50 per hour to rent a bus. The Blue bus company charges $200 plus $25 per hour.

After how many hours do the bus companies charge the same amount? _________________

Hours rented

RedBus $

Blue bus $

0

1

2

3

4

5

6

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Week #3 Continued

4. Write a story that fits the graph.

___________________________________________

___________________________________________

___________________________________________

___________________________________________

___________________________________________

___________________________________________

___________________________________________

___________________________________________

_____________________________________________________________________________________________

_____________________________________________________________________________________________

_____________________________________________________________________________________________

5. Write a function for the pattern

7, 12, 17, 22, 27, …

f (x)=¿___________________________

What is the value of f (14)? ____________________

6. Willie spent half of his weekly allowance on clothes. To earn more money his parents let him weed the garden for $5. What is his weekly allowance if he ended with $12?

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Week #4

1. The original line is solid. What is the translation to the dotted line written in function notation?

_______________________________________

4. Oakland Coliseum, home of the Oakland Raiders, is capable of seating 63,026 fans. For each game, the amount of money that the Raiders' organization brings in as revenue is a function of the number of people, n, in attendance. If each ticket costs $30.00, find the domain and range of this function.

Domain: ____________________________

Range: _____________________________

2. Given f(x)below, please graph (Be sure to label)

a. f(x-2)

b. f(x)+3

5. A certain business keeps a database of information about its customers.

Let C be the rule which assigns to each customer

shown in the table his or her home phone number. Is C a function? _________________

Customer Name Home Phone Number

Heather Baker 3105100091

Mike London 3105200256

Sue Green 3234132598

Bruce Swift 3234132598

Michelle Metz 2138061124

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Week #4 Continued

3. You are going to a water park. You can buy a wrist band for $10 and go on the slides all day long, or you can pay $0.75 for every slide.

Which is the better buy? How do you know?

____________________________________________

____________________________________________

____________________________________________

____________________________________________

____________________________________________

____________________________________________

____________________________________________

____________________________________________

6. For a field trip 26 students rode in cars and the rest filled nine buses.

How many students were in each bus if 332 students were on the trip?

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Unit 1 - KEYSWeekly Assessments

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Week #1 - KEY

1. The carnival charges $15 for admissions and $2 per ride. (x = number of rides, y = cost)

Write an equation for the situation.

Y = 15 + 2xFill in the table.

x y

0 15

1 17

2 19

3 21

4. Are the following expressions equivalent to 10? Circle yes or no

(−8)+6 (8−5) yes / no

3+6 (5+4 )÷3−7yes / no

(−4)(−3)÷6−2[5−(−8)+(6÷2)] yes / no

2. Which equations are equivalent to 10=4 x? Circle yes or no.

a. 8 x=20 yes / no

b. 12=4 x+2 yes / no

c. 12=6 x yes / no

5. Solve for x

3 x+4=10 2+12x=4

X = 2 x = 4

3. Graph: y=2x+1 6. Graph: 2 x+3 y=12

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Week #2 - KEY

1. The admission for the class to go to Michigan’s Adventure is $24 per person. The cost of the busses for the entire 9th grade will be $450.a. Write an equation or rule that represents the function.

Y = 450 + 24 xb. Make a table that show how much a trip will cost for 50 students, 100 students, 150 students, and 200 students.

students 50 100 150 200

Cost ($) 1650 2850 4050 5250

c. Graph.

0 50 100 150 200

2. a. Which point shows the heaviest bag? G

b. Which point shows the cheapest bag? C

c. Which bag is the best value? ANSWERS WILL VARY

Why? _____________________________________

__________________________________________

___________________________________________

3. Does this graph represent a function? NOWhy or why not?

Using the vertical line test, the line will hit two points at several different x values.

4. Every student earns a grade on the last test. Please define the domain and range of this function.

Domain STUDENTS

Range SCORES

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1000

2000

3000

4000

5000

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Week #2 Continued

5. Evaluate the function for the given values.

f (x)=3x−2 x+1

f (3)=¿ 4

f (−1)=¿ 0

f (⅖)=¿ 1.4

6. Deshawn’s Bikes rents bikes for $11 plus $5 per hour. Maria paid $51 to rent a bike. For how many hours did she rent the bike?

11 + 5x = 51 X = 8

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Week #3 - KEY

1. Are the following functions? Circle yes or no.

y+2=4 x−2 yes / no

yes / no

{(2, 3), (5, -2), (5, 6), (3, 3), (4, 1)} yes / no

3. Find the domain and range of the function.

f (x)=x2+2

Domain: all real numbers

Range: f(x) is greater than or equal to 2

2. The Red bus company charges $100 plus $50 per hour to rent a bus. The Blue bus company charges $200 plus $25 per hour.

After how many hours do the bus companies charge the same amount? 4 hours

Hours rented

RedBus $

Blue bus $

0 100 200

1 150 225

2 200 250

3 250 275

4 300 300

5 350 325

6 400 350

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Week #3 Continued

4. Write a story that fits the graph.

VARY

___________________________________________

___________________________________________

___________________________________________

___________________________________________

___________________________________________

___________________________________________

___________________________________________

_____________________________________________________________________________________________

_____________________________________________________________________________________________

_____________________________________________________________________________________________

5. Write a function for the pattern

7, 12, 17, 22, 27, …

f (x)=¿ 5x + 2

What is the value of f (14)? 72

6. Willie spent half of his weekly allowance on clothes. To earn more money his parents let him weed the garden for $5. What is his weekly allowance if he ended with $12?

x/2 + 5 = 12

x = 14

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Week #4 -KEY

1. The original line is solid. What is the translation to the dotted line written in function notation?

(x, y+4)

4. Oakland Coliseum, home of the Oakland Raiders, is capable of seating 63,026 fans. For each game, the amount of money that the Raiders' organization brings in as revenue is a function of the number of people, n, in attendance. If each ticket costs $30.00, find the domain and range of this function.

Domain: Number of People

Range: Amount of Money

2. Given f(x)below, please graph (Be sure to label)

a. f(x-2)

b. f(x)+3

5. A certain business keeps a database of information about its customers.

Let C be the rule which assigns to each customer shown in

the table his or her home phone number. Is C a function?

YES

Customer Name Home Phone Number

Heather Baker 3105100091

Mike London 3105200256

Sue Green 3234132598

Bruce Swift 3234132598

Michelle Metz 2138061124

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Week #4 Continued

3. You are going to a water park. You can buy a wrist band for $10 and go on the slides all day long, or you can pay $0.75 for every slide.

Which is the better buy? How do you know?

VARY

____________________________________________

____________________________________________

____________________________________________

____________________________________________

____________________________________________

____________________________________________

____________________________________________

6. For a field trip 26 students rode in cars and the rest filled nine buses.

How many students were in each bus if 332 students were on the trip?

26 + 9x = 332

X = 34

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Unit 2Weekly Assessments

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Week #5

1. Given f (x)=x2−2x+9, find:

a. f (2)=¿

b. f (−3)=¿

c. f (1/2)=¿

2. Find the slope of the graph between the two points.

a. (4, 3), (8, -5)

b. (3/4, 5/2), (2/3, -1/4)

c. (5, 8), (5, 10)

3.  You have $22.50 in your piggy bank. You choose to buy two cookies every day at lunch for yourself and your sweetheart. They cost $.75 for both cookies. Create an equation, table, and graph for this situation.

Equation: _________________________

Table: Graph:

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Week #5 Continued

4. The below table provides some U.S. Population data from 1982 to 1988:Year Population

(thousands)Change in Population (thousands)

1982 231,664 ---1983 233,792 21281984 235,825 20331985 237,924 20991986 240,133 22091987 242,289 21561987 244,499 2210

If we were to model the relationship between the U.S. population and the year, would a linear function be appropriate? Explain why or why not.

Mike decides to use a linear function to model the relationship. He chooses 2139, the average of the values in the 3rd column, for the slope. What meaning does this value have in the context of this model?

Use Mike's model to predict the U.S. population in 1992.

5.  As I fill the following beaker with water at a constant rate, graph the height of the water in relation to time.

     

6. Suppose f  is a function.

a. If12=f (−9), give the coordinates of a point on the graph of f.

b. If 16 is a solution of the equationf (w)=6, give a point on the graph of f.

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Week #6

1. Emma understands that the function, f ( x )=3.5 x+10 gives her the price for the bands t-shirts given the $10 set up fee and the price of $3.50 per shirt.

She also knows that there are 88 band members.

What is the total cost for the shirts?

2. Lauren keeps records of the distances she travels in a taxi and what she pays:

Distance, d, in miles

Fare, F, in dollars

3 8.25

5 12.75

11 26.25

a. If you graph the ordered pairs(d , F)from the table, they lie on a line. How can you tell this without graphing them?

b. Show that the linear function in part (a) has equation F=2.25d+1.5.

c. What do the 2.25 and the 1.5 in the equation represent in terms of taxi rides?

3. Solve the following equations and justify the steps.

a. 13

(4 x+1 )=9 b. 10=5 x−34

Week #6 Continued

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4. If you have $10, you can buy 4 cookies and no brownies or you can buy 5 brownies and no cookies. There are several other options as well. Graph the situation.

If you have $10 and you buy 1 cookie a day you will run out of money after 5 days. Graph the situation.

Which situation has the cheaper cookie? (Circle one)

1st 2nd Not enough information

a. 5.b. a. Let F assign to each student in your math class

his/her locker number. Explain why F is a function.

c. b. Describe conditions on the class that would have to be true in order for F to have an inverse.

6. Candy bars cost $1.50 each. What is the total bill?

What is the domain? _____________________

What is the range? _____________________

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Week #7

1. A souvenir shop in Niagara Falls sells picture postcards priced as follows:

a. Graph the price of buying postcards as a function of the number of cards purchased.

b. Is there something wrong with this pricing scheme? Explain.

a. 2.b. a. Suppose P1¿(0,5) and P2¿(3 ,−3). Sketch P1 and

P2.

For which real numbers m and b does the graph of a linear function described by the equation f (x)=mx+b contain P1 and P2? Explain.

Do any of these graphs also contain P2? Explain.

b. Suppose P1¿(0,5) and P2¿(0,7). Sketch P1 and P2.

Are there real numbers m and b for which the graph of a linear function described by the equation f (x)=mx+b contains P1 and P2? Explain.

c. Now suppose P1¿(c ,d ) and P2¿(g ,h) and c is not equal to g. Show that there is only one real number m and only one real number b for which the graph of f (x)=mx+bcontains the points P1 and P2.

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Postcards15 cents each

Six for $1

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Week #7 Continued

3. Given f ( x )=2x+1 and g ( x )= x2−1

2 . Show that the

two functions are inverses.

4. Graph f ( x )=2x+4 and the inverse of f (x).

Where do they intersect? _____________________

5. Translate the functions so that they intersect at (3,4) . (Feel free to use the graph if you like.)

f ( x )=13x+1

g ( x )=−12x+7

f ( x )=¿_____________________________________

g ( x )=¿_____________________________________

6. The three graphs show the functions

f ( x )=2x

g ( x )=2(x+1)

h ( x )=2 x+1

Label the three graphs below.

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Unit 2 - KEYSWeekly Assessments

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Week #5 - KEY

1. Given f (x)=x2−2x+9, find:

a. f (2)=¿ 9

b. f (−3)=¿ 24

c. f (1/2)=¿ 8.25

2. Find the slope of the graph between the two points.

a. (4, 3), (8, -5) -1/2

b. (3/4, 5/2), (1/2, -1/4) 11

c. (5, 8), (5, 10) undefined

3.  You have $22.50 in your piggy bank. You choose to buy two cookies every day at lunch for yourself and your sweetheart. They cost $.75 for both cookies. Create an equation, table, and graph for this situation.

Equation: y = 22.5 - 0.75x

Table: Graph: Money in Piggy Bank

X 0 5 10 15y 22.50 18.75 15.00 11.25

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Days

Dollars Remaining

0 5

5

10

10

15

20

15 20 x

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Week #5 Key Continued

4. The below table provides some U.S. Population data from 1982 to 1988:Year Population

(thousands)Change in Population (thousands)

1982 231,664 ---1983 233,792 21281984 235,825 20331985 237,924 20991986 240,133 22091987 242,289 21561987 244,499 2210

If we were to model the relationship between the U.S. population and the year, would a linear function be appropriate? Explain why or why not.

Yes the function is linear, because the change of population stays relatively the same each year.

Mike decides to use a linear function to model the relationship. He chooses 2139, the average of the values in the 3rd column, for the slope. What meaning does this value have in the context of this model?

The number 2139 tells us the amount that the population increases each year.

Use Mike's model to predict the U.S. population in 1992.

5*2139 + 244,499 = 255,194

http://illustrativemathematics.org/illustrations/353

5.  As I fill the following beaker with water at a constant rate, graph the height of the water in relation to time.

     

6. Suppose f  is a function.

c. If12=f (−9), give the coordinates of a point on the graph of f.

(-9, 12)

d. If 16 is a solution of the equationf (w)=6, give a point on the graph of f.

(16, 6)

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Week #6 - KEY

1. Emma understands that the function, f ( x )=3.5 x+10 gives her the price for the bands t-shirts given the $10 set up fee and the price of $3.50 per shirt.

She also knows that there are 88 band members.

What is the total cost for the shirts?

f (88 )=318

$318

2. Lauren keeps records of the distances she travels in a taxi and what she pays:

Distance, d, in miles

Fare, F, in dollars

3 8.25

5 12.75

11 26.25

a. If you graph the ordered pairs(d , F)from the table, they lie on a line. How can you tell this without graphing them?

Yes, finding the slopes tells us that they are the same for both intervals.

b. Show that the linear function in part (a) has equationF=2.25d+1.5.

c. What do the 2.25 and the 1.5 in the equation represent in terms of taxi rides?

a. The 2.25 represents the cost per mile for the ride. The 1.5 represents a fixed cost for every ride; it does not depend on the distance traveled.

http://illustrativemathematics.org/illustrations/243

3. Solve the following equations and justify the steps.

a. 13

(4 x+1 )=9 b. 10=5 x−34

4x + 1 = 27 (Mult prop of equality)4x = 26 (Add prop of equality)X = 6.5 (Div prop of equality)

Week #6 Continued

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a. There is only one possible line in part (a), since two points determine a line. The graph of F−2.25d+1.5 is a line, so if we show that each ordered pair satisfies it then we will know that it is the same line as in part (a).

(3,8.25)(5,12.75)(11,26.25):2.25(3)+1.5=8.25:2.25(5)+1.5=12.75:

2.25(11)+1.5=26.25

40 = 5x – 3 (Mult prop of equality)43 = 5x (Add prop of equality)8.6 = x (Division prop of equality)

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4. If you have $10, you can buy 4 cookies and no brownies or you can buy 5 brownies and no cookies. There are several other options as well. Graph the situation.

If you have $10 and you buy 1 cookie a day you will run out of money after 5 days. Graph the situation.

Which situation has the cheaper cookie? (Circle one)

1st 2nd Not enough information

d. 5.e. a. Let F assign to each student in your math class

his/her locker number. Explain why F is a function.

F is a function because it assigns to each student in the class exactly one element, his/her locker number.

f. b. Describe conditions on the class that would have to be true in order for F to have an inverse.

Students would not share lockers.

6. Candy bars cost $1.50 each. What is the total bill?

What is the domain? Number of Candy Bars

What is the range? Cost

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brownies

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Week #7 - KEY

1. A souvenir shop in Niagara Falls sells picture postcards priced as follows:

a. Graph the price of buying postcards as a function of the number of cards purchased.

b. Is there something wrong with this pricing scheme? Explain.

Six for $1 cost approximately $0.17 each which is higher than the initial $0.15 per postcard.

c. 2.d. a. Suppose P1¿(0,5) and P2¿(3 ,−3). Sketch P1 and P2

.

For which real numbers m and b does the graph of a linear function described by the equation f (x)=mx+b contain P1 and P2? Explain.

m = -8/3b = 5

b. Suppose P1¿(0,5) and P2¿(0,7). Sketch P1 and P2.

Are there real numbers m and b for which the graph of a linear function described by the equation f (x)=mx+b contains P1 and P2? Explain.

No, because this is not a function.

c. Extension: Now suppose P1¿(c ,d ) and P2¿(g ,h) and c is not equal to g. Show that there is only one real number m and only one real number b for which the graph of f (x)=mx+bcontains the points P1 and P2.

See website for full explanation.

http://illustrativemathematics.org/illustrations/377

Week #7 Continued

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Postcards15 cents each

Six for $1

Number of Postcards

Price (Dollars)

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3. Given f ( x )=2x+1 and g ( x )= x2−1

2 . Show that the

two functions are inverses.

F(g(x)) = 2(x2−1

2 ) +1 = x

G(f(x)) = 2x+1

2−1

2 = x

4. Graph f ( x )=2x+4 and the inverse of f (x).

Where do they intersect? (-4, -4)

5. Translate the functions so that they intersect at (3,4) . (Feel free to use the graph if you like.)

f ( x )=13x+1

g ( x )=−12x+7

f ( x )=13(x+4)+1

g ( x )=−12

(x+4)+7

6. The three graphs show the functions

f ( x )=2x (Blue)

g ( x )=2(x+1) (Red)

h ( x )=2 x+1 (Green)

Label the three graphs below.

http://map.mathshell.org/materials/tasks.php?taskid=295&subpage=novice

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Unit 3Weekly Assessments

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Week #8

The table gives the number of hours spent studying for a science exam and the final exam grade.

Study hours

3 2 5 1 0 4 3

Grade 84 77 92 70 60 90 75

1 a. Draw a scatter plot of the data and draw in the line of best fit.

1 b. What is the equation for the line of best fit?

1 c. Predict the grade for a student who studied for 6 hours.

2. Solve two step equations5−3x=11

3. Write a story problem for the following equation.2 x+4=10

4. Evaluate the functionf (3 )=2 x2−4

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Week #9

1. The accompanying table shows the enrollment of a preschool from 1980 through 2000. Write a linear regression equation to model the data in the table.

2. Find the inverse of the function.y=3 x−7

3. Create a scatterplot and a table of the Average Cost Loaf of Bread. Use the graph to predict the cost in 2050. 1930, 9 cents, 1940, 10 cents, 1950, 12 cents, 1960, 22 cents, 1970, 25 cents, 1980, 50 cents, 1990, 70 cents, 2008, $2.79

Cost in 2020 = ____________________

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4. Match the following correlation coefficients with the approprite graph.

r=−.86r=.90r=.80r=−.10

_____________0

5

10

15

00

5

10

15

0 _____________

_____________0

5

10

15

00

5

10

15

0 _____________

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Unit 3 - KEYSWeekly Assessments

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Week #8 KEY

The table gives the number of hours spent studying for a science exam and the final exam grade.

Study hours

3 2 5 1 0 4 3

Grade 84 77 92 70 60 90 75

1 a. Draw a scatter plot of the data and draw in the line of best fit.

1 b. What is the equation for the line of best fit?

Answers may vary: y = 5x + 60

1 c. Predict the grade for a student who studied for 6 hours.

Answers may vary: 90

2. Solve two step equations5−3x=11

X = -2

3. Write a story problem for the following equation.2 x+4=10

Answers may vary: You have $4 and your grandma gives you $2 per week. How long will it take you to have $10?

4. Evaluate the functionf (3 )=2 x2−4

f(3) = 14

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0 1 2 3 4 5 6

60

100

80

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Week #9 KEY

1. The accompanying table shows the enrollment of a preschool from 1980 through 2000. Write a linear regression equation to model the data in the table.

Answers will vary: y = 1.15x + 14

2. Find the inverse of the function.y=3 x−7

y= x3+ 7

3

3. Create a scatterplot and a table of the Average Cost Loaf of Bread. Use the graph to predict the cost in 2050. 1930, 9 cents, 1940, 10 cents, 1950, 12 cents, 1960, 22 cents, 1970, 25 cents, 1980, 50 cents, 1990, 70 cents, 2008, $2.79

Year 1930 1940 1950 1960 1970 1980 1990 2008

Cost .09 .10 .12 .22 .25 .50 .70 2.79

Cost in 2020 = Answers will vary

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4. Match the following correlation coefficients with the approprite graph.r=−.86r=.90r=.80r=−.10

r = -.100

5

10

15

00

5

10

15

0 r = .90

r = -.860

5

10

15

00

5

10

15

0 r = .80

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