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Algebra 1 TeachersWeekly Assessment Package

Units 1 - 12

Created by: Jeanette Stein

©2014 Algebra 1 Teachers

Show all work below. Name _________________________

SEMESTER 1 SKILLS 6

SEMESTER 2 SKILLS 8

UNIT 1 11

WEEK #1 12WEEK #2 13WEEK #3 15WEEK #4 17

UNIT 1 - KEYS 20

WEEK #1 - KEY 21WEEK #2 - KEY 22WEEK #3 - KEY 24WEEK #4 -KEY 26

UNIT 2 28

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

UNIT 2 - KEYS 35

WEEK #5 - KEY 36WEEK #6 - KEY 38WEEK #7 - KEY 40

UNIT 3 42

WEEK #8 43WEEK #9 44

UNIT 3 - KEYS 46

WEEK #8 KEY 47WEEK #9 KEY 48

UNIT 4 50

2 Unit 12 - KEYS | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers


WEEK #11 51WEEK #12 53WEEK #13 56

UNIT 4 - KEYS 58

WEEK #11 KEY 59WEEK #12 KEY 61WEEK #13 KEY 64

UNIT 5 66

WEEK #14 67WEEK #15 68

UNIT 5 - KEYS 70


UNIT 6 74

WEEK #16 75WEEK #17 77

UNIT 6 - KEYS 79


UNIT 7 84

WEEK #18 - UNDERSTANDING INTEREST 85WEEK #19 - SEQUENCES 86

UNIT 7 - KEYS 87

WEEK #18 - ANSWER KEY 88WEEK #19 - ANSWER KEY 89

UNIT 8 90

WEEK #20 - INTRODUCTION TO EXPONENTIAL FUNCTIONS 91



WEEK #21 - RADICAL FUNCTIONS 92WEEK #22 - MODELING EXPONENTIAL FUNCTIONS 93

UNIT 8 - KEYS 95

WEEK #20 - ANSWER KEY 96WEEK #21 - ANSWER KEY 97WEEK #22 - ANSWER KEY 98

UNIT 9 100

WEEK #23 - COMPARING LINEAR AND EXPONENTIAL FUNCTIONS 101WEEK #24 - COMBINING LINEAR AND EXPONENTIAL FUNCTIONS 102

UNIT 9 - KEYS 103

WEEK #23 - KEY 104WEEK #24 - KEY 105

UNIT 10 106

WEEK #25 - QUADRATICS AS FUNCTIONS 106WEEK #26 - GRAPHING QUADRATICS 107WEEK #27 - INTRODUCTION TO FACTORING 109

UNIT 10 - KEYS 110

WEEK #25 - QUADRATICS AS FUNCTIONS ANSWER KEY 111WEEK #26 - GRAPHING QUADRATICS ANSWER KEY 112WEEK #27 - INTRODUCTION TO FACTORING ANSWER KEY 113

UNIT 11 114

WEEK #28 - POLYNOMIAL OPERATIONS 115WEEK #29 - CLOSURE 116

UNIT 11 - KEYS 117

WEEK #28 - POLYNOMIAL OPERATIONS ANSWER KEY 118WEEK #29 - CLOSURE ANSWER KEY 119

UNIT 12 120



WEEK #30 - FACTORING 121WEEK #31 - COMPLETING THE SQUARE 122WEEK #32 - SYSTEMS AND QUADRATIC FORMULA 123

UNIT 12 - KEYS 124

WEEK #30 - FACTORING ANSWER KEY 125WEEK #31 - COMPLETING THE SQUARE ANSWER KEY 126WEEK #32 - SYSTEMS AND QUADRATIC FORMULA ANSWER KEY 127



Algebra 1 Common Core

Semester 1 SkillsNumbe

r 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.BF.3 Translate a graph in function notation

11 2 F.IF.6 Calculate Slope

12 2 S.ID.7 Interpret meaning of the slope and intercepts

13 2 F.BF.2 Construct an arithmetic sequence

14 2 F.BF.4 Find the inverse of a function

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

19 4 S.ID.1 Create box plots

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

21 4 S.ID.3 Understand the effects of outliers

22 4 S.ID.5 Use two way frequency tables to make predictions

23 4 N.QA.1 Convert Units

24 4 N.QA.3 Understand Accuracy

25 5 A.REI.3 Solve advanced linear equations

26 5 A.REI.1 A.CED.4 Solve literal equations and justify the steps

27 5 A.REI.3 Solve inequalities

28 5 A.REI.12 Graph inequalities

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

30 6 A.REI.6 Solve a system of equations by substitution

31 6 A.REI.5 Solve a system of equations by elimination



Semester 2 Skills

Number Unit CCSS Skill

32 7 F.LE.1b & F.LE.1c Distinguish between linear and exponential function

33 7 F.LE.1a Prove that a function is either linear or exponential

34 7 F.BF.1aWrite a function that describes a relationship between two

quantities

35 7 F.IF.3Recognize that sequences are functions, sometimes defined

recursively

36 7 F.BF.2Write arithmetic and geometric sequences both recursively

and with an explicit formula

37 7 F.LE.2Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a

description of a relationship, or two input-output pairs

38 8 A.SSE.1 Identify parts of an expression

39 8 F.IF.1 Identify a function and it’s domain and range

40 8 F.IF.5 Find an appropriate domain given a context41 8 F.IF.2 Evaluate exponential functions

42 8 N.RN.2 Change expressions using the rules of exponents

43 8 N.RN.1Explain how the definition of the meaning of rational

exponents follows from extending the properties of integer exponents to those values

44 8 F.IF.8.bUse the properties of exponents to interpret expressions for

exponential functions.

45 8 F.BF.1.aWrite a function that describes a relationship between two

quantities.

46 8 F.IF.7.eGraph exponential functions and identify intercepts and end

behavior47 8 F.BF.3 Translate exponential functions

48 8 F.IF.4Compare the key components of a linear function graph to an

exponential function graph.



49 8 S.ID.6.aFit a function to the data; use functions fitted to data to solve

problems in the context of the data.

50 9 F.LE.1.aProve that linear functions grow by equal differences over

equal intervals; and that exponential functions grow by equal factors over equal intervals.

51 9F.LE.1.b &

F.LE.1.cIdentify linear and quadratic functions

52 9 F.LE.3

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing

linearly, quadratically, or (more generally) as a polynomial function.

53 9 F.BF.1.b Combine functions using arithmetic

54 9 F.BF.1.b Understand situations using these combinations

55 9 F.LE.5Interpret the parameters in a linear or exponential function in

terms of a context.

56 10 A.SSE.1.a Understand what the parts of a quadratic mean

57 10 F.IF.1Understand function, domain and range in terms of a

quadratic function

58 10 F.IF.2Evaluate quadratic functions given a value of x in function

notation

59 10 F.BF.1.aWrite an equation for a quadratic function given a

relationship

60 10A.REI.10, F.IF.7.a

& F.IF.4Graph and create tables of quadratic functions and label key

features

61 10 F.LE.3

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing

linearly, quadratically, or (more generally) as a polynomial function.

62 10 F.BF.3Understand how to translate a quadratic function in a table,

an equation or on a graph

63 10 F.IF.8.a Factor simple quadratics

64 10 F.IF.8.a Understand the concept and implications of a zero



65 10 F.IF.9 Compare two quadratic functions to make decisions

66 11 A.APR.1 Add, subtract, and multiply polynomials

67 11A.APR.1 &

N.RN.3Identify sets that are closed under operations and those that

are not.68 12 A.SSE.3a Factor quadratic equations69 12 A.SSE.3a Solve quadratic equations by factoring70 12 A.SSE.3b Complete the square

71 12 F.IF.8 Use completing the square to find maximum and minimum values

72 12 A.REI.4 Use the quadratic formula to solve quadratic equations

73 12 A.REI.4 Be able to identify which process is best to solve a quadratic equation

74 12 A.REI.7 Solve a system of equations containing one quadratic and one linear function



Unit 1Weekly Assessments



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. Which of the following expressions are 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+12

x=4

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



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 __________________________________



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?



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



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?



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



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?



Unit 1 - KEYSWeekly Assessments



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. Which of the following expressions are 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+12

x=4

X = 2 x = 4

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



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


1000

2000

3000

4000

5000


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



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

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



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



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



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:



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.



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 equationF=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

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? _____________________



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.


Postcards15 cents each

Six for $1


Week #7 Continued

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

2 . Show

that the two functions are inverses.

4. Graph f ( x )=2 x+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 )=13

x+1

g ( x )=−12

x+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.



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


Days

Dollars Remaining x

0 5

5

10

10

15

20

15 20


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)




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=2.25 d+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.


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


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)



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


cookies

brownies

cookies

$


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.


Postcards15 cents each

Six for $1

Number of Postcards

Price (Dollars)



Week #7 Continued

3. Given f ( x )=2 x+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 )=13

x+1

g ( x )=−12

x+7

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

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


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



g ( x )=−12

(x+4)+7




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 equations5−3 x=11

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

4. Evaluate the functionf (3 )=2 x2−4



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 = ____________________



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

r=−.86r=.90r=.80

r=−.10

_____________0

5

10

15

00

5

10

15

0 _____________

_____________0

5

10

15

00

5

10

15

0 _____________



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 equations5−3 x=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


0 1 2 3 4 5 6

60

100

80


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



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

r=−.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



Week #111. Find the inverse of f ( x )=2 x−7 2. For the group data 4, 4, 6, 10, 13, what is the

relationship between the mean and median?

3. Create a box plot for the given data. 21, 20, 5, 18, 7, 16, 8, 5, 22, 19, 12, 9, 8, 20, 20



4. Find the rate of change between 1980 and 2009 of the given data. Write your answers as a full sentence.

The National Data Book

Number of dropouts (1,000)1980 1990 1995 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

16 to 17 years 709 418 406 460 399 346 323 452 303 464 448 416 452

http://www.census.gov/compendia/statab/cats/education/elementary_and_secondary_education_completions_and_dropouts.html

5. Predict how much money the average household will spend on clothes in 2020.

http://www.census.gov/compendia/statab/cats/income_expenditures_poverty_wealth.html





Week #121. Emma’s first test scores were 80%, 84%, 95%, and 82%.

Which of the following test scores would result in the greatest difference in Emma’s mean score?

a. 50%

b. 70%

c. 85%

d. 100%

2. Your grades are graphed below.Semester 1 Grades:

Semester 2 Grades:

The median has changed from _______to_______.

The upper quartile has changed from _______to _______.

The lower quartile has changed from _______ to _______.

What can you conclude about your grades? Can you conclude that every grade dropped?

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

__________________________________________________________________________________________



3.

0

2

4

6

100 95 90 85 80

2

1

6

5

4

What is the median grade? ___________

What is the mean grade? __________

4. A public opinion survey explored the relationship between age and support for increasing the minimum wage.

In the 21 to 40 age group, what percentage supports increasing the minimum wage?

http://stattrek.com/statistics/two-way-table.aspx




Use the graph below to answer the questions.

0

5

10

15

0

5. Calculate the line of best fit.



Week #13

1. Which number is more precise?

A. 40.67 feet B. 8.632 feet

Explain:

2. What percent of students that studied between 2 and 4 hours earned higher than a 75% on the test?

3. Identify the outlier in the data below. Find the mean of the population of the 7 largest cities in the United States with and without the outlier. How does the outlier change the mean?

City, State Population(Millions)

New York, NY 8.1Los Angeles, CA 3.8

Chicago, IL 2.7Houston, TX 2.1

Philadelphia, PA 1.5Phoenix, AZ 1.4

San Antonio, TX 1.3

How does the outlier change the mean?


Outlier: ____________________________________

Mean Population with Outlier: _________________

Mean Population without Outlier: ______________


4. The speed of a giraffe is 50 km/h. If the giraffe continues at the same speed, after 2 hours, how many miles has the giraffe traveled? (Hint: 1 mile = 1.60934 kilometers)

5. Convert 12 mph to feet per second. (Hint: 5,280 feet = 1 mile)

6. For the following situations, decide whether or not there is a correlation and whether it is a positive or negative correlation. Examine the factors and decide if there is enough evidence to state that there is causation as well.

The number of pizzas delivered to a school and the number of students in that school

Correlation? (yes or no)_________________________

Positive, negative, not applicable (NA)_________________________

Causation? (yes or no)_________________________



Week #11 Key1. Find the inverse of f ( x )=2 x−7

y= x2+3.5

2. For the group data 4, 4, 6, 10, 13, what is the relationship between the mean and median?

Mean = 7.4Median = 6

The mean is 1.4 greater than the median.

3. Create a box plot for the given data. 21, 20, 5, 18, 7, 16, 8, 5, 22, 19, 12, 9, 8, 20, 20



4. Find the rate of change between 1980 and 2009 of the given data. Write your answers as a full sentence.

The National Data Book

Number of dropouts (1,000)1980 1990 1995 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

16 to 17 years 709 418 406 460 399 346 323 452 303 464 448 416 452

542−7092009−1980

=−25729

≈−20

There are approximately 20 fewer dropouts per year from 1980 to 2009.


5. Predict how much money the average household will spend on clothes in 2020.

≈ $ 2000






Week #12 Key1. Emma’s first test scores were 80%, 84%, 95%, and 82%.

Which of the following test scores would result in the greatest difference in Emma’s mean score?

a. 50%

b. 70%

c. 85%

d. 100%

A

2. Your grades are graphed below.Semester 1 Grades:

Semester 2 Grades:

The median has changed from __86__to__78___.

The upper quartile has changed from _95____to __88___.

The lower quartile has changed from _76____ to __71___.

What can you conclude about your grades? Can you conclude that every grade dropped?

Overall the grades have dropped. I cannot conclude that every grade dropped. Maybe one went up a lot and

one when down a lot and they “switched places”.



3.

0

2

4

6

100 95 90 85 80

2

1

6

5

4

What is the median grade? __4______

What is the mean grade? __3.6______

4. A public opinion survey explored the relationship between age and support for increasing the minimum wage.

In the 21 to 40 age group, what percentage supports increasing the minimum wage?

2550

=50 %





Use the graph below to answer the questions.

0

5

10

15

0

5. Calculate the line of best fit.

y=x+2



Week #13 Key

1. Which number is more precise?

A. 40.67 feet B. 8.632 feetB

Explain: Because the units are the same, the number of decimal places will determine which number is more precise.

2. What percent of students that studied between 2 and 4 hours earned higher than a 75% on the test?

2442

≈57 %

3. Identify the outlier in the data below. Find the mean of the population of the 7 largest cities in the United States with and without the outlier. How does the outlier change the mean?

City, State Population(Millions)

New York, NY 8.1Los Angeles, CA 3.8

Chicago, IL 2.7Houston, TX 2.1

Philadelphia, PA 1.5Phoenix, AZ 1.4

San Antonio, TX 1.3

How does the outlier change the mean? When removing the outlier the mean decreased by 0.9 million.


Outlier: __New York, NY_____

Mean Population with Outlier: __≈ 3.0 million_______

Mean Population without Outlier: __≈ 2.1million____


4. The speed of a giraffe is 50 km/h. If the giraffe continues at the same speed, after 2 hours, how many miles has the giraffe traveled? (Hint: 1 mile = 1.60934 kilometers)

50 km1hr

× 1hr1.60934 km

×2hr ≈ 62.1 mi

5. Convert 12 mph to feet per second. (Hint: 5,280 feet = 1 mile)

12mi1 hr

× 1 hr60 min

× 1min60 sec

× 5280 ft1mi

=17.6 ft /sec

6. For the following situations, decide whether or not there is a correlation and whether it is a positive or negative correlation. Examine the factors and decide if there is enough evidence to state that there is causation as well.

The number of pizzas delivered to a school and the number of students in that school

Correlation? (yes or no)_____yes______________

Positive, negative, not applicable (NA)___positive____________

Causation? (yes or no)______no_________________



Week #14

1. Solve for x.

3 x+(3 x – 12)= x4

2. Solve for x.3 x=ax+5+a

3. What is the greatest possible error for a measurement of 5 inches?

4. The mean of the following data is 17. Find the value of x.

14, 22, 8, 17, 15, x

5. Given the box and whisker graph, find the following.

Minimum: __________________

Maximum: __________________

Upper Quartile: ______________

Lower Quartile: ______________

Median: ____________________

6. There are 640 acres in a square mile and 5280 feet in one mile. How many square feet are there in 3 acres?



Week #151. Solve and graph the inequality.

6 x+5<10−2x

2. Your test scores for your history class so far in the class were 74%, 82%, 76%, 75%, and 80%. On the last test of the year, you studied hard and earned a 100%. How did this change your test average?

3. Solve for x.

x+13

=4 x−7

4. In the formula P= FA gives the pressure for P for a

force F and an area A. Solve this formula for A.

5. Six ninth-grade students and six 12th-grade students were asked: How many movies have you seen this month? Here are their responses.

Ninth-grade students: 5, 1, 2, 5, 3, 812th-grade students: 4, 2, 0, 2, 3, 1

a. How does the mean compare for each of these data sets.



6. Identify the outlier in the data below. Find the mean of the speed of the animals with and without the outlier. How does the outlier change the mean?

Animal Speed(MPH)

Peregrine Falcon 200 +Cheetah 70

Lion 50Wildebeest 50

Elk 45Ostrich 40Rabbit 35



Outlier: ____________________________________

Mean Population with Outlier: _________________

Mean Population without Outlier: ______________


Week #14 KEY

1. Solve for x.

3 x+(3 x – 12)= x4

6 x−12= x4

x=2

2. Solve for x.3 x=ax+5+a

3 x−ax=5+a

x (3−a )(3−a )

= 5+a3−a

x= 5+a3−a

3. What is the greatest possible error for a measurement of 5 inches?

.5 feet

(The greatest possible error is half of the unit of measure to which a measure is rounded.)

4. The mean of the following data is 17. Find the value of x.

14, 22, 8, 17, 15, x

76+x6

=17

x=26

5. Given the box and whisker graph, find the following.

Minimum: ____2________

Maximum: ____16___________

Upper Quartile: ___11_________

Lower Quartile: ___4________

Median: ____6______________

6. There are 640 acres in a square mile and 5280 feet in one mile. How many square feet are there in 3 acres?



3 acres × 1 mi640 acres

× 5280 ft1 mi

× 5280 ft1 mi

=130,680 ft2

Week #15 KEY1. Solve and graph the inequality.

6 x+5<10−2 x

x<58

2. Your test scores for your history class so far in the class were 74%, 82%, 76%, 75%, and 80%. On the last test of the year, you studied hard and earned a 100%. How did this change your test average?

Average 1: 387

5≈ 77.4

Average 2: 487

6≈ 81.2

The test average increased by ≈ 3.8 points.

3. Solve for x.

x+13

=4 x−7

x+1=12 x−21

x=2

4. In the formula P= FA gives the pressure for P for a

force F and an area A. Solve this formula for A.

PA=F

A=FP

5. Six ninth-grade students and six 12th-grade students were asked: How many movies have you seen this month? Here are their responses.

Ninth-grade students: 5, 1, 2, 5, 3, 812th-grade students: 4, 2, 0, 2, 3, 1

a. How does the mean compare for each of these data sets.



Ninth graders: 246

=4

12th grade students: 126

=2

The ninth grade students, on average, saw two more movies last month than the 12 th graders.

6. Identify the outlier in the data below. Find the mean of the speed of the animals with and without the outlier. How does the outlier change the mean?

Animal Speed(MPH)

Peregrine Falcon 200 +Cheetah 70

Lion 50Wildebeest 50

Elk 45Ostrich 40Rabbit 35


The outlier increased the mean by 21.7 MPH.


Outlier: ____Peregrine Falcon____________

Mean Population with Outlier: __70_________

Mean Population without Outlier: ___48.3_________


Week #16

1. Solve the system of equations by graphing.

{ y=2 x−6

y=−12

x+4

2. Solve the system using substitution.

{x+2 y=12

y=12

x−3


{−2x−3 y=−7y=6 x−11

4. Solve and graph the inequality.

−5 x+4<3 x−6



5. Which number is the most precise? How do you know?

a. 165.789 inchesb. 56.89 inches

6. Solve for x.5−( x+4 )=11 x−3



Week #17

1. Solve the system of equations by elimination.

{2 x+5 y=73 x−5 y=8


{ x+2 y=10

y=−34

x+6


{12 x+6 y=10

y=23

x−1




5 x+6< 3x+85


{12x+6 y=63 x−5 y=8



Week #16 KEY


{ y=2 x−6

y=−12

x+4

(4, 2)


{x+2 y=12

y=12

x−3

x+2( 12

x−3)=12

x=3

3+2 y=12

y=4.5

(3 , 4.5)


{−2x−3 y=−7y=6 x−11

−2 x−3 (6 x−11)=−7

x=2

y=6 (2 )−11

y=1

(2 , 1)


−5 x+4<3 x−6

−8 x←10

x> 54



5. Which number is the most precise? How do you know?

a. 165.789 inchesb. 56.89 inches

A

6. Solve for x.5−( x+4 )=11 x−3

5−x−4=11 x−3

1−x=11x−3

x=13



Week #17 KEY


{2 x+5 y=73 x−5 y=8

5 x=15

x=3

2 (3 )+5 y=7

y=15

(3 , 15)


{ x+2 y=10

y=−34

x+6

(4 , 3)


{12 x+6 y=10

y=23

x−1

12 x+6 ( 23

x−1)=10

12 x+4 x−6=10

x=1

12+6 y=10

y=−13

(1 ,−13)




5 x+6< 3x+85

25 x+30<3 x+8

22 x<22

x<1


{12x+6 y=63 x−5 y=8

12 x+6 y=6−12 x+20 y=−32

26 y=−26

y=−1

12 x+6 (−1 )=6x=1

(1 ,−1)



Week #18 - Understanding Interest

1. Classify the following functions. (Circle the correct answer.)a. y=2x Linear Exponentialb. You have $100 and add $20 per week

Linear Exponentialc. y=2x Linear Exponentiald. You begin with a penny and double it every week.

Linear Exponentiale. y=1

2x Linear Exponential

2. Graph the function.f ( x )=3x

x -1 0 1 2 3f (x)

3. Evaluate the following function. Show your work. f ( x )=(−2)x+1

a. f (0 )=¿ ______b. f (1 )=¿______c. f (3 )=¿¿

4. Which situation will give you a better return on your money? (show your work)a. $100 per day for one year. b. $0.01 doubled every day for one month



(30 days).

Week #19 - Sequences

1. Classify the following functions. Circle the correct answer.a. y=2x Linear Exponentialb. y=3 x Linear Exponentialc. You have $100 and add $10 per week

Linear Exponentiald. You begin with a penny and triple it every week.

Linear Exponential

e. y=3x Linear Exponential

2. Graph the function. f ( x )=2.5x

x -1 0 1 2 3f (x)

3. Evaluate the following function. Show your work.f ( x )=(−3)x+4

a. f (0 )=¿ ______b. f (1 )=¿______c. f (3 )=¿¿



4. Simplify the expression.a. x2 ∙ x5 = _________________b. ( x2 )5= _________________




Week #18 - Answer Key

1. Classify the following functions. (Circle the correct answer.)a. y=2x Linear Exponentialb. You have $100 and add $20 per week

Linear Exponentialc. y=2x Linear Exponentiald. You begin with a penny and double it every week.

Linear Exponentiale. y=1

2x Linear Exponential

2. Graph the function.f ( x )=3x

x -1 0 1 2 3f (x) 1/3 1 3 9 27

3. Evaluate the following function. Show your work. f ( x )=(−2)x+1

a. f (0 )=¿ (-2)0 + 1 = 1 + 1 = 2b. f (1 )=¿(-2)1 + 1 = -2 + 1 = -1c. f (3 )=¿ (-2)3 + 1 = -8 + 1 = -74. Which situation will give you a better return on your money? (show your work)a. $100 per day for one year. Money = 100(days) = 100(365) = $36,500.00b. $0.01 doubled every day for one month (30 days).



Money = 0.01(2)number of daysMoney = 0.01(2)30 = $10,737,418.24Situation b will give you a better return on investment.




1. Classify the following functions. Circle the correct answer.a. y=2x Linear Exponentialb. y=3 x Linear Exponentialc. You have $100 and add $10 per week

Linear Exponentiald. You begin with a penny and triple it every week.

Linear Exponential

e. y=3x Linear Exponential


x -1 0 1 2 3f (x) 0.4 1 2.5 6.25 15.625

3. Evaluate the following function. Show your work.f ( x )=(−3)x+4

a. f (0 )=¿ (-3)0 + 4 = 1 + 4 = 5b. f (1 )=¿(-3)1 + 4 = -3 + 4 = 1c. f (3 )=¿ (-3)3 + 4 = -27 + 4 = -23



4. Simplify the expression.a. x2 ∙ x5 = x7

b. ( x2 )5= x10



Unit 8 Weekly Assessments



Week #20 - Introduction to Exponential Functions

1. Which is better?a. Getting $100 per day for one month?b. Doubling $0.01 every day for one month?

Explain:


x -1 0 1 2 3f (x)

3. Evaluate the following function. Show your work.f ( x )=(−2.5)x+1.25

a. f (0 )=¿ ______b. f (1 )=¿______c. f (3 )=¿¿

4. Properties of Exponents – Products and Powersa. (5 a2) (3 b4 )=¿¿

b. (−x2 y3 ) (2 x4 y )=¿¿

c. ( 4 x2)2=¿____________________

d. (3 a b2 ) (2 a3b2)3=¿

5. Properties of Exponents – Quotientsa. ( a

b )4= _________________



_______________________ b. ( 3 x2

y )2= __________________



Week #21 - Radical Functions

1. Rewrite the following problems with fractional exponents then simplify.a. ∜ 16

b. ∛ 27

c. √121

2. Rewrite the following expressions in radical form.a. 1614

b. 172813

c. 823

3. Simplify the following expressions in simplest radical form. Rationalize the denominator if necessary.a. 63√4

b. √ 265

c. 5√7√5

4. Identify each equation as growth or decay then identify the rate of growth or decay.Equation GrowthOr Decay Rate as a %

a. f(x) = 2(0.5)x

b. d(x) = 1.25(1.05)x

c. g(x) = -3(0.63)x

5. Write an exponential function for the table. Determine the rate and if the relationship is growth or decay. Identify the rate as a percent.x y0 42 1

x y1 203 50098 Unit 12 - KEYS | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers


Week #22 - Modeling Exponential Functions

1. Graph the following exponential functions on the same coordinate plane: f ( x )=2x and g ( x )=0.5 (2 )xCompare the two graphs2. Graph the following exponential functions on the same coordinate plane: f ( x )=2x and g ( x )=2x+2Describe the differences between the two graphs.

3. Graph the following exponential functions on the same coordinate plane:f ( x )=0.5x g ( x )=0.5x+2Describe the differences between the two graphs.

4. Compare the following functions:Function f ( x )=2x+3 g ( x )=3 (2 )x

Typey-interceptChangeDomainRange



Week #22 - Modeling Exponential Functions continued

5. Given the following table of values, determine if the graph represents a linear or exponential function. Sketch a graph and estimate the equation of best fit. Then use technology to assess your prediction. Explain any possible reasons for differences. x 1 2 3 4 5 6y 2 5 9 10 12 20

Predicted equation: ______________________________________________(using sketched graph on the right)Actual equation: __________________________________________________(using technology)




1. Which is better?a. Getting $100 per day for one month?T = 100(30) = $3,000.00b. Doubling $0.01 every day for one month?T = 0.01(2)30 = $10,737,418.24

Explain: Answers will vary


x -1 0 1 2 3f (x) 4/7 1 1.75 3.0625 5.359375

3. Evaluate the following function. Show your work.f ( x )=(−2.5)x+1.25

a. f (0 )=¿ (-2.5)0 + 1.25 = 1 + 1.25 = 2.25b. f (1 )=¿(-2.5)1 + 1.25 = -2.5 + 1.25 = -1.25c. f (3 )=¿ (-2.5)0 + 1.25 = 1 + 1.25 = 2.25

4. Properties of Exponents – Products and Powersa. (5 a2) (3 b4 )=¿ 15a2b3

b. (−x2 y3 ) (2 x4 y )=¿ -2x6y4

5. Properties of Exponents – Quotientsa. ( a

b )4

=¿ a4

b4 103 Unit 12 - KEYS | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers


c. ( 4 x2)2=¿ 16x4

d. (3 a b2 ) (2 a3b2)3=¿ 24a10b8

b. ( 3 x2

y )2= 9 x4

y2


1. Rewrite the following problems with fractional exponents then simplify.a. ∜ 16 = 1614=2

b. ∛ 27 = 2713 =3

c. √121 = 12112=11

2. Rewrite the following expressions in radical form.a. 514 = 4√5

b. 172813 = 3√1728

c. 823 = 3√82 or ( 3√8 )2

3. Simplify the following expressions in simplest radical form. Rationalize the denominator if necessary.a. 63√4

= 3 3√2

b. √ 265

= √1305

c. 5√7√5

= √35

4. Identify each equation as growth or decay then identify the rate of growth or decay.Equation GrowthOr Decay Rate as a %

a. f(x) = 2(0.5)x Decay 50%b. d(x) = 1.25(1.05)x Growth 5%c. g(x) = -3(0.63)x Decay 37%

5. Write an exponential function for the table. Determine the rate and if the relationship is growth or decay. Identify the rate as a percent.104 Unit 12 - KEYS | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers


x y0 42 1x y1 203 500

f(x) = 4(0.25)xDecay - 75% f(x) = 4(5)xGrowth - 400%




1. Graph the following exponential functions on the same coordinate plane: f ( x )=2x and g ( x )=0.5 (2 )xCompare the two graphs

Answers will vary.

2. Graph the following exponential functions on the same coordinate plane:f ( x )=2x and g ( x )=2x+2Describe the differences between the two graphs.

Answers will vary.3. Graph the following exponential functions on the same coordinate plane:f ( x )=0.5x g ( x )=0.5x+2Describe the differences between the two graphs.

4. Compare the following functions:Function f ( x )=2 x+3 g ( x )=3 (2 )x

Type Linear Exponentialy-intercept 3 3Change Add 2 Multiply by 2Domain All real values All real valuesRange All real values y ≥ 0



Answers will vary.



Week #22 - Modeling Exponential Functions continued

5. Given the following table of values, determine if the graph represents a linear or exponential function. Sketch a graph and estimate the equation of best fit. Then use technology to assess your prediction. Explain any possible reasons for. x 1 2 3 4 5 6y 2 5 9 10 12 20

Predicted equation: Answers will vary(using sketched graph on the right)Actual equation: y = 1.86(1.50)x(using technology)Answers will vary.



Week #23 - Comparing Linear and Exponential Functions

1. Graph the functions f ( x )=2 x and g ( x )=2x on the same coordinate plane. Label each graph and determine the growth over each interval.0 > x > 1 1 > x > 4 4 > x > 8

f (x)g(x )

2. Verify that the difference between each integer value of the function f ( x )=10 (1.05 ) x is not steady.

x f ( x )=10 (1.05 ) x Change

3. Given the two functions: f ( x )=x and g ( x )=1.25x, over what interval is the linear function changing faster than the exponential?

4. Use the functions below to answer the following questions:f ( x )=7x g ( x )=7 x

a. When will f(x) surpass g(x)?b. When will g(x) ever surpass f(x)?c. Which function will have a larger range value with a domain of 7.2?



Week #24 - Combining Linear and Exponential Functions

1. Use the following functions to answer the questions: f ( x )=2 x g ( x )=−3 x+4 h ( x )=0.5 x−2

a. f ( x )+g ( x )

b. g ( x )−f ( x )

c. g (f ( x ) )−h(x)

d. h ( x )−f ( g (x))

2. Identify the initial amount and the change represented in each situation:a. The amount of money in a savings account can be modeled by the function f ( x )=10 (1.05 ) x

b. The number of people in attendance at a high school performance can be modeled by the function a ( x )=375−2x

c. The amount of a radioactive substance can be modeled by the function r ( x )=25 (0.86 ) x



Week #23 - Key

1. Graph the functions f ( x )=2 x and g ( x )=2x on the same coordinate plane. Label each graph and determine the growth over each interval.0 > x > 1 1 > x > 4 4 > x > 8

f (x) 2 2 2g(x ) 1 2 4

2. Verify that the difference between each integer value of the function f ( x )=10 (1.05 ) x is not steady.x f ( x )=10 (1.05 ) x Change-2 10 (1.05 )−2=9.0703 --1 10 (1.05 )−1=9.5238 0.45350 10 (1.05 )0=10 0.47621 10 (1.05 )1=10.5 0.52 10 (1.05 )2=11.025 0.525

3. Given the two functions: f ( x )=x and g ( x )=1.25x, over what interval is the linear function changing faster than the exponential?

Based on the graph, from x values of 1.35 to 10.57, the linear function is increasing faster than the exponential.

4. Use the functions below to answer the following questions:f ( x )=7x g ( x )=7 x

a. When will f(x) surpass g(x)?When x > 7b. When will g(x) ever surpass f(x)?When 0.219 < x < 7c. Which function will have a larger range value with a domain of 7.2?

f (7.2 )=77.2=1,215,362.65682



g (7.2 )=7 (7.2 )=50.4f (x) will have a larger range value

Week #24 - Key

1. Use the following functions to answer the questions: f ( x )=2 x g ( x )=−3 x+4 h ( x )=0.5 x−2

a. f ( x )+g ( x ) = 2 x−3 x+4=−x+4

b. g ( x )−f ( x ) = −3 x+4−2 x=−5 x+4

c. g (f ( x ) )−h(x) = −3 (2 x )+4−(0.5 x−2)g (f ( x ) )−h(x) = −6 x+4−0.5 x+2g (f ( x ) )−h(x)=−6.5 x+6

d. h ( x )−f ( g (x)) = 0.5 x−2−2(−3 x+4)h ( x )− f ( g (x))=0.5 x−2+6 x−8 h ( x )− f ( g (x))=6.5 x−10

2. Identify the initial amount and the change represented in each situation:a. The amount of money in a savings account can be modeled by the function f ( x )=10 (1.05 ) x

10 is the initial amount of money in the account and the interest rate is 5%b. The number of people in attendance at a high school performance can be modeled by the function

a ( x )=375−2x

The performance started with 375 people and two people left for every unit of time (x)c. The amount of a radioactive substance can be modeled by the function r ( x )=25 (0.86 ) x

The 25 represents the amount of 114 Unit 12 - KEYS | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers


the substance at the beginning. The decay rate is 14%.




Week #25 - Quadratics as Functions

5. Identify the domain and range of the 6. The following expressions are 116 Unit 12 - KEYS | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers


following graph. equivalent. Which form most clearly identifies the vertex of the quadratic? Explain your reasoning.−12

x2+3 x−2.5

−12

( x−1 ) ( x−5 )

−12

( x−3 )2+2

12

(1−x ) ( x−5 )7. Write the output, using function notation, of the following functions given the input of -2.d. f ( x )=x2−3 x+1

e. f ( x )=−x2+ 12

x−3

f. f ( x )=34

x2+x−4

Week #26 - Graphing Quadratics



1. Create a table of the functionf ( x )=−1

2x

2

+3 x−4Be sure to choose two x-values that are right of the axis of symmetry and two x-values that are left of the axis of symmetry. You must identify the axis of symmetry, vertex, and y-intercept. Identify the x-intercepts if they are in your table. Explain how you know they are the x-intercepts.xy

2. Use the following graph to identify which graph appears to represent an exponential function. Explain your reasoning.

3. a. Describe how g ( x )=−2 x2+4 and h ( x )=2 x2 are different. b. Describe how both g ( x ) and h(x ) compare to the function f ( x )=x2



Week #27 - Introduction to Factoring

1. Factor each of the following and determine the zeros.a. f ( x )=x2+4 x−5

b. f ( x )=x2+x−6

c. f ( x )=x2+2 x−20

2. Parabola A has x-intercepts at 2 and -4 with a y-intercept of -5. Whereas parabola B is modeled by the function g ( x )=−x2−4 x+6. Which parabola has the lowest vertex?

4. The height vs time graph of object 1 is given in the graph below. The height of object 2 is given by the function h2 (t )=−2.5 t2+10. Which object reaches its maximum height first?



Week #25 - Quadratics as Functions Answer Key

1. Identify the domain and range of the following graph.

Domain: -2 ≤ x ≤ 5Range: -1 ≤ y ≤ 15

2. The following expressions are equivalent. Which form most clearly identifies the vertex of the quadratic? Explain your reasoning.−12

x2+3 x−2.5 Standard form−12

( x−1 ) ( x−5 ) Intercept form−12

( x−3 )2+2 Vertex form12

(1−x ) ( x−5 ) Intercept formThe third option is written in vertex form of

f ( x )=a ( x−h )2+k

and is easiest to identify the vertex of (3, 2)

3. Write the output, using function notation, of the following functions given the input of -2.a. f ( x )=x2−3 x+1

f (−2)=(−2)2−(−2)+1f (−2)=4+4+1f (−2)=9 (−2,9) b. f ( x )=−x2+ 1

2x−3

f (−2 )¿−(−2 )2+12

(−2 )−3

f (−2 )=−4−1−3f (−2 )=−8 (−2 ,−8)c. f ( x )=3

4x2+x−4



f (−2 )¿ 34

(−2 )2

+(−2 )−4

f (−2 )=3−2−4f (−2 )=−3 (−2 ,−3)

Week #26 - Graphing Quadratics Answer Key1. Create a table of the functionf ( x )=−1

2x

2

+3 x−4Be sure to choose two x-values that are right of the axis of symmetry and two x-values that are left of the axis of symmetry. You must identify the axis of symmetry, vertex, and y-intercept. Identify the x-intercepts if they are in your table. Explain how you know they are the x-intercepts.x 1 2 3 4 5y -1.5 0 0.5 0 -1.5

The axis of symmetry is found by using x=−b

2 a . The point (3, 0.5) is the vertex. This can be found by plugging the axis of symmetry back into the equation resulting in 0.5 as the y-value of the vertex.The y-intercept is the value of the function when x is 0. For this function, the y-intercept is -4. The x-intercepts can be found by looking the points that have an x-value of 0. For this function the points (2, 0) and (4, 0) are the x-intercepts

2. Use the following graph to identify which graph appears to represent an exponential function. Explain your reasoning.

Although graphs A and B are both curved upwards, graph B seems to be exponential due to its increase being greater than graph A.



3. a. Describe how g ( x )=−2 x2+4 and h ( x )=2 x2 are different. g(x) and h(x) open in opposite directions, the y-intercept of g(x) is 4 units higher than h(x).

b. Describe how both g ( x ) and h(x ) compare to the function f ( x )=x2

g(x) is vertically stretched (skinnier), opens the opposite direction and the y-intercept is shifted up 4 units when compared to f(x)h(x) is vertically stretched (skinnier), opens the same direction and has the same y-intercept when compared to f(x)



Week #27 - Introduction to Factoring Answer Key

1. Factor each of the following and determine the zeros.a. f ( x )=x2+4 x−5

(x - 5)(x + 1) = 0x = 5 and x = -1

b. f ( x )=x2+x−6

(x - 3)(x + 2) = 0x = -2 and x = 3

c. f ( x )=x2+8 x−20

(x - 2)(x + 10) = 0x = 2 and x = -10

1. Parabola A has x-intercepts at 2 and -4 with a y-intercept of -5. Whereas parabola B is modeled by the function g ( x )=−x2−4 x+6. Which parabola has the lowest vertex?

By plotting the three points for parabola A and determining the vertex for parabola B, you can see that the vertex for parabola A is going to be lower than for parabola B.

3. The height vs. time graph of object 1 is given in the graph below. The height of object 2 is given by the function h2 (t )=−2.5 t2+10. Which object reaches its maximum height first?

The time object 1 reaches its maximum is about 0.75. The time object 2 reaches its maximum is at 0. Therefore, object 2 reaches its maximum height first.



Week #28 - Polynomial Operations

6. Use the following expressions in the problems below:b ( x )=x−4 f ( x )=2 x−4 g ( x )=x2−3 x+6

h ( x )=2 x2−3 x+7 j ( x )=x4−3 x2+x−9 k ( x )=x+7

a. f (x)+g¿)

b. h(x )+ j(x )

c. j(x )− f (x)

d. g(x )−h(x )

e. b (x) ⋅k (x )

f. b (x) ⋅ j(x )



Week #29 - Closure

6. Complete the following operations using the expressions below. Explain if the operation is closed or not.A=x−4 B=x+4 C=3 x

D=x2−4 x+3 E=−2x2−3 F=10 x+1

G=7 x2−4 x H=4 x3−x2+4 J=3x

a. AB

b. F−G

c. JD

d. E+H

e. AD−BC

f. G(F+C)



Week #28 - Polynomial Operations Answer Key

7. Use the following expressions in the problems below:b ( x )=x−4 f ( x )=2 x−4 g ( x )=x2−3 x+6

h ( x )=2 x2−3 x+7 j ( x )=x4−3 x2+x−9 k ( x )=x+7

a. f (x)+g(x )

(2 x−4 )+¿)x2−x+2

b. h(x )+ j(x )

(2 x¿¿2−3 x+7)+(x4−3 x2+x−9)¿x4−x2−2 x−2

c. j ( x )−f (x )

(x¿¿4−3 x2+ x−9)−(2 x−4)¿x4−3x2−x−5

d. g(x )−h¿)( x2−3 x+6 )−(2 x¿¿2−3 x+6)¿−x2

e. b (x) ⋅k (x )

( x−4 ) ( x+7 )x2+3 x−28

f. b (x) ⋅ j(x )

(x−4)(x4−3x2+x−9)x5−4 x4−3 x3+13x2−13 x+36



Week #29 - Closure Answer Key

7. Complete the following operations using the expressions below. Explain if the operation is closed or not.A=x−4 B=x+4 C=3 x

D=x2−4 x+3 E=−2x2−3 F=10 x+1

G=7 x2−4 x H=4 x3−x2+4 J=3x

a. AB

( x−4 ) ( x+4 )x2−16

b. F−G

(10 x+1 )−(7 x2−4 x )−7 x2+14 x+1

c. JD

(3 x ) ( x2−4 x+3 )3 x3−12x2+9 x

d. E+H (−2 x2−3 )+( 4 x3−x2+4 )4 x3−3 x2+1

e. AD−BC

( x−4 ) ( x2−4 x+3 )−( x+4 ) (3 x )(x¿¿3−8 x2+19 x−12)−(3 x¿¿2+12x )¿¿x3−11 x2+7x−12

f. G(F+C)

(7 x¿¿2−4 x)((10 x+1 )+(3 x ))¿(7 x¿¿2−4 x)(13 x+1)¿91 x3−45 x2−4 x



Week #30 - Factoring

1. Factor each of the following quadratics.a. f ( x )=x2+4 x−5 b. f ( x )=x2−8x+7

c. f ( x )=2 x2+ x−6 d. f ( x )=6 x2+10 x−24

2. Solve each of the quadratics by factoring:a. f ( x )=x2−11 x−60 b. 0=x2+17 x+72

c. −x2+ x+20=0 d. 2 x2+15 x+7=0



Week #31 - Completing the Square

3. Rewrite each quadratic in vertex format by completing the squarea. f ( x )=x2+16 x+71 b. f ( x )=x2−2x−5

c. f ( x )= (x+5 ) ( x+4 ) d. f ( x )=−9 x2−162 x−731

4. Complete the square to determine the minimum/maximum values for each quadratic.a. f (x)=x2+10 x+33 b. f ( x )=x2−6x+5



c. f ( x )=x2+4 x d. f ( x )=6 x2+12 x+13

Week #32 - Systems and Quadratic Formula

1. Use the quadratic formula to determine the solutions for the following quadratic functions if possible. Round your answers to the nearest hundredth if necessary.a. x2−9 x−8=0

b. 10 x2+6 x+2=0

c. −3 x+2=−2 x2+5 x−6

d. −0.25 x2+1.62 x−3.39=0

2. Solve each quadratic using any method. Explain your choice of method for solving.d. −x2−14=x2+10x

e. x2=−3 x+1

f. (x+9)2−64=0

g. (2 x+5 ) (−4 x+7 )=0



3. Solve the following systems using any method.a. { f ( x )=−2 x+4

g (x )=−2 x2+3 x−2 b. { f ( x )=13

x−2

g (x )=x2−3 x−2

c. { f ( x )=−6g (x )=4 x2+4 x−5 d. { f ( x )=−2

5x+3

g (x )=−2x2−4 x+9




Week #30 - Factoring Answer Key

1. Factor each of the following quadratics.a. f ( x )=x2+4 x−5

(x+5)(x−1)

b. f ( x )=x2−8x+7

(x−7)(x−1)

c. f ( x )=2 x2+ x−6

(2 x−3)(x+2)

d. f ( x )=6 x2+10 x−24

2(3 x−4)(x+3)

2. Solve each of the quadratics by factoring:a. f ( x )=x2−11 x−60

( x−15 ) ( x+4 )=0(−4 , 0)∧(15 ,0)

b. 0=x2+17 x+72

( x+9 ) ( x+8 )=0(−9 , 0 )∧(−8 , 0 )

c. −x2+ x+20=0

( x+4 ) (x−5 )=0(−4 , 0)∧(5 ,0)

d. 2 x2+15 x+7=0

( x+7 ) (2 x+1 )=0(−7 , 0)∧(−0.5 ,0)



Week #31 - Completing the Square Answer Key

1. Rewrite each quadratic in vertex format by completing the squarea. f ( x )=x2+16 x+71

f ( x )= (x+8 )2+7

b. f ( x )=x2−2x−5

f ( x )= (x−1 )2−6

c. f ( x )= (x+5 ) ( x+4 )

f ( x )= (x+4.5 )2−0.25

d. f ( x )=−9 x2−162 x−731

f ( x )=−9 ( x+9 )2−2

2. Complete the square to determine the minimum/maximum values for each quadratic.a. f (x)=x2+10 x+33

f ( x )= (x+5 )2+8(−5 ,8)

b. f ( x )=x2−6x+5

f ( x )= (x−3 )2−4(3 ,−4)



c. f ( x )=x2+4 x

f ( x )= (x+2 )2−4(−2 ,−4)

d. f ( x )=6 x2+12 x+13

f ( x )=6 (x+1 )2+7(−1 ,7)

Week #32 - Systems and Quadratic Formula Answer Key1. Use the quadratic formula to determine the solutions for the following quadratic functions. Round your answers to the nearest hundredth if necessary.a. x2−9 x−8=0

(-0.82, 0) and (9.82, 0)b. 10 x2+6 x+2=0

No real solutionsc. −3 x+2=−2 x2+5 x−6

(2, 0)d. −0.25 x2+1.62 x−3.39=0

No real solutions

2. Solve each quadratic using any method. Explain your choice of method for solving.Explanations of method chosen will vary

a. −x2−14=x2+10x

No real solutionb. x2=−3 x+1

(-3.30, 0) and (0.30, 0)c. (x+9)2−64=0

No real solutiond. (2 x+5 ) (−4 x+7 )=0

(-2.5, 0) and (1.75, 0)3. Solve the following systems using any method. Round answers to the nearest hundredth if necessary.a. { f ( x )=−2 x+4

g (x )=−2 x2+3 x−2

NO SOLUTION−Graphs don ' t intersect

b. { f ( x )=13

x−2

g (x )=x2−3 x−2

(−2,0)∧(3.33 ,−0.89)



c. { f ( x )=−6g (x )=4 x2+4 x−5

(−0.5 ,−6)

d. { f ( x )=−25

x+3

g (x )=−2 x2−4 x+9

(−2.85,4 .14 )∧(1.05 ,2.58)


Show all work below. Name - … · Web viewWeek #23 - Comparing Linear and Exponential...

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