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HighSchoolMathTeachers Algebra 1 Weekly Assessment Package

Units 1-12

Created by: Jeanette Stein

©2017 HighSchoolMathTeachers

Show all work below. Name _________________________

2 Semester 1 Skills | Algebra 1 Weekly Assessments | ©2017 HighSchoolMathTeachers

Contents

SEMESTER 1 SKILLS 6

SEMESTER 2 SKILLS 8

UNIT 1 11

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

UNIT 1 - KEYS 19

WEEK #1 - KEY .............................................................................................................................................. 20 WEEK #2 - KEY .............................................................................................................................................. 21 WEEK #3 - KEY .............................................................................................................................................. 23 WEEK #4 -KEY .............................................................................................................................................. 25

UNIT 2 27

WEEK #5 ...................................................................................................................................................... 28 WEEK #6 ...................................................................................................................................................... 30 WEEK #7 ...................................................................................................................................................... 32

UNIT 2 - KEYS 34

WEEK #5 - KEY .............................................................................................................................................. 35 WEEK #6 - KEY .............................................................................................................................................. 37 WEEK #7 - KEY .............................................................................................................................................. 39

UNIT 3 41

WEEK #8 ...................................................................................................................................................... 42 WEEK #9 ...................................................................................................................................................... 43 WEEK #10 .................................................................................................................................................... 45

UNIT 3 - KEYS 46

WEEK #8 KEY ............................................................................................................................................... 47 WEEK #9 KEY ............................................................................................................................................... 48



WEEK #10 KEY.............................................................................................................................................. 50

UNIT 4 51

WEEK #11 .................................................................................................................................................... 52 WEEK #12 .................................................................................................................................................... 54 WEEK #13 .................................................................................................................................................... 57

UNIT 4 - KEYS 59

WEEK #11 KEY .............................................................................................................................................. 60 WEEK #12 KEY .............................................................................................................................................. 62 WEEK #13 KEY .............................................................................................................................................. 65

UNIT 5 67

WEEK #14 .................................................................................................................................................... 68 WEEK #15 .................................................................................................................................................... 69

UNIT 5 - KEYS 71

WEEK #14 KEY.............................................................................................................................................. 72 WEEK #15 KEY.............................................................................................................................................. 73

UNIT 6 75

WEEK #16 .................................................................................................................................................... 76 WEEK #17 .................................................................................................................................................... 78

UNIT 6 - KEYS 80

WEEK #16 KEY.............................................................................................................................................. 81 WEEK #17 KEY.............................................................................................................................................. 82

UNIT 7 - SEQUENCES & FUNCTIONS 84

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

UNIT 7 - KEYS 87

WEEK #18 - ANSWER KEY ................................................................................................................................ 88



WEEK #19 - ANSWER KEY ................................................................................................................................ 89

UNIT 8 - EXPONENTIAL FUNCTIONS 90

WEEK #20 - INTRODUCTION TO EXPONENTIAL FUNCTIONS ....................................................................................... 91 WEEK #21 - RADICAL FUNCTIONS ....................................................................................................................... 92 WEEK #22 - MODELING EXPONENTIAL FUNCTIONS ................................................................................................. 93

UNIT 8 - KEYS 95

WEEK #20 - ANSWER KEY ................................................................................................................................ 96 WEEK #21 - ANSWER KEY ................................................................................................................................ 97 WEEK #22 - ANSWER KEY ................................................................................................................................ 99

UNIT 9 - LINEAR AND EXPONENTIAL MODELS 101

WEEK #23 - COMPARING LINEAR AND EXPONENTIAL FUNCTIONS ............................................................................. 102 WEEK #24 - COMBINING LINEAR AND EXPONENTIAL FUNCTIONS ............................................................................. 104

UNIT 9 - KEYS 105

WEEK #23 - KEY .......................................................................................................................................... 106 WEEK #24 - KEY .......................................................................................................................................... 107

UNIT 10 - UNDERSTAND QUADRATIC FUNCTIONS 108

WEEK #25 - QUADRATICS AS FUNCTIONS ........................................................................................................... 109 WEEK #26 - GRAPHING QUADRATICS ................................................................................................................ 110 WEEK #27 - INTRODUCTION TO FACTORING ........................................................................................................ 111

UNIT 10 - KEYS 112

WEEK #25 - QUADRATICS AS FUNCTIONS ANSWER KEY ......................................................................................... 113 WEEK #26 - GRAPHING QUADRATICS ANSWER KEY .............................................................................................. 114 WEEK #27 - INTRODUCTION TO FACTORING ANSWER KEY ...................................................................................... 115

UNIT 11 - OPERATIONS ON POLYNOMIALS 116

WEEK #28 - POLYNOMIAL OPERATIONS ............................................................................................................. 117 WEEK #29 - CLOSURE .................................................................................................................................... 118

UNIT 11 - KEYS 119



WEEK #28 - POLYNOMIAL OPERATIONS ANSWER KEY ........................................................................................... 120 WEEK #29 - CLOSURE ANSWER KEY .................................................................................................................. 121

UNIT 12 - SOLVE QUADRATIC FUNCTIONS 122

WEEK #30 - FACTORING ................................................................................................................................ 123 WEEK #31 - COMPLETING THE SQUARE ............................................................................................................. 124 WEEK #32 - SYSTEMS AND QUADRATIC FORMULA ............................................................................................... 125

UNIT 12 - KEYS 126

WEEK #30 - FACTORING ANSWER KEY ............................................................................................................... 127 WEEK #31 - COMPLETING THE SQUARE ANSWER KEY............................................................................................ 128 WEEK #32 - SYSTEMS AND QUADRATIC FORMULA ANSWER KEY ............................................................................. 129



Algebra 1 Common Core

Semester 1 Skills Number 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



Number Unit CCSS Skill

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.1a Write a function that describes a relationship between two quantities

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

recursively

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

an explicit formula

37 7 F.LE.2 Construct 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 context

41 8 F.IF.2 Evaluate exponential functions

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

43 8 N.RN.1 Explain 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.b Use the properties of exponents to interpret expressions for

exponential functions.

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

46 8 F.IF.7.e Graph exponential functions and identify intercepts and end behavior

47 8 F.BF.3 Translate exponential functions

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

exponential function graph.

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

in the context of the data.



Week Unit CCSS Skill

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

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

51 9 F.LE.1.b F.LE.1.c

Identify 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.5 Interpret 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.1 Understand function, domain and range in terms of a quadratic

function

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

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

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

F.IF.4 Graph 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.3 Understand 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 11 A.APR.1 &

N.RN.3 Identify sets that are closed under operations and those that are not.



Week Unit CCSS Skill

68 12 A.SSE.3a Factor quadratic equations

69 12 A.SSE.3a Solve quadratic equations by factoring

70 12 A.SSE.3b Complete the square

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


11 Unit 1 | Algebra 1 Weekly Assessments | ©2017 HighSchoolMathTeachers

Unit 1 Weekly 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

2. Which of the following expressions are equivalent

to 10? Circle yes or no.

(−8) + 6(8 − 5) yes / no 3 + 6(5 + 4) ÷ 3 − 7 yes / no (−𝟒)(−𝟑) ÷ 𝟔 − 𝟐[𝟓 − (−𝟖) + (𝟔 ÷ 𝟐)] yes / no

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

a. a. 8𝑥 = 20 yes / no

b. b. 12 = 4𝑥 + 2 yes / no

c. c. 12 = 6𝑥 yes / no

4. Solve for x

3𝑥 + 4 = 10 2 +1

2𝑥 = 4

5. Graph: 𝑦 = 2𝑥 + 1

6. Graph: 2𝑥 + 3𝑦 = 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 − 2𝑥 + 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 = 4𝑥 − 2 yes / no

yes / no

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

2. Find the domain and range of the function.

𝑓(𝑥) = 𝑥2 + 2

Domain: __________________________ Range: ___________________________

3. 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 Red Bus $ 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?

_______________________________________

2. 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: _____________________________

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

label)

a. f(x-2)

b. f(x)+3

4. 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

5. 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?


19 Unit 1 - KEYS | Algebra 1 Weekly Assessments | ©2017 HighSchoolMathTeachers

Unit 1 - KEYS Weekly 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 + 2x Fill in the table.

𝒙 𝒚

0 15

1 17

2 19

3 21

2. Which of the following expressions are equivalent to

10? Circle yes or no.

(−8) + 6(8 − 5) yes / no

3 + 6(5 + 4) ÷ 3 − 7 yes / no

(−𝟒)(−𝟑) ÷ 𝟔 − 𝟐[𝟓 − (−𝟖) + (𝟔 ÷ 𝟐)] yes / no

3. Which equations are equivalent to 10 = 4𝑥? Circle

yes or no.

1. 8𝑥 = 20 yes / no

2. 12 = 4𝑥 + 2 yes / no

3. 12 = 6𝑥 yes / no

4. Solve for x

3𝑥 + 4 = 10 2 +1

2𝑥 = 4

x = 2 x = 4

5. Graph: 𝑦 = 2𝑥 + 1

6. Graph: 2𝑥 + 3𝑦 = 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 x

b. 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? NO

Why 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 − 2𝑥 + 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 = 4𝑥 − 2 yes / no

yes / no

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

2. 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

3. 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 Red Bus $ 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.

ANSWERS WILL 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)

2. 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

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

a. f(x-2)

b. f(x)+3

4. 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

5. 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 $0.75 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 2128 1984 235,825 2033 1985 237,924 2099 1986 240,133 2209 1987 242,289 2156 1987 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. If 12 = 𝑓(−9), give the coordinates of a point on the graph of f.

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



Week #6

1. Emma understands that the function, 𝑓(𝑥) =3.5𝑥 + 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. 1

3(4𝑥 + 1) = 9 b. 10 =

5𝑥−3

4



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

5. Let F assign to each student in your math class his/her locker number. Explain why F is a function.

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.

2. Suppose P1= (0,5) and P2= (3, −3). Sketch P1 and P2.

a. 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. 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 + 𝑏 contains the points P1 and P2.

Postcards 15 cents each

Six for $1



Week #7 Continued

3. Given 𝑓(𝑥) = 2𝑥 + 1 and 𝑔(𝑥) =𝑥

2−

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) =1

3𝑥 + 1

𝑔(𝑥) = −1

2𝑥 + 7

𝑓(𝑥) =____________________________________ 𝑔(𝑥) =____________________________________

6. The three graphs show the functions

𝑓(𝑥) = 2𝑥 𝑔(𝑥) = 2(𝑥 + 1) ℎ(𝑥) = 2𝑥 + 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:

x 0 5 10 15 y 22.50 18.75 15.00 11.25



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 2128 1984 235,825 2033 1985 237,924 2099 1986 240,133 2209 1987 242,289 2156 1987 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.

a. If 12 = 𝑓(−9), give the coordinates of a point on the graph of f. (-9, 12)

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

http://illustrativemathematics.org/illustrations/353



Week #6 - KEY

1. mma understands that the function, 𝑓(𝑥) =3.5𝑥 + 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 equation 𝐹 = 2.25𝑑 + 1.5. 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

c. What do the 2.25 and the 1.5 in the equation represent in terms of taxi rides? 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. 1

3(4𝑥 + 1) = 9 b. 10 =

5𝑥−3

4

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

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




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

5. 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. 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

br

o w ni

es

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.

2. 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 = -8/3 b = 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 +

𝑏 contains the points P1 and P2.

See website for full explanation http://illustrativemathematics.org/illustrations/377

Postcards 15 cents each

Six for $1

Number of Postcards

Pri

ce

(Do

llar

s)




Week #7 Continued

3. Given 𝑓(𝑥) = 2𝑥 + 1 and 𝑔(𝑥) =𝑥

2−

1

2. Show

that the two functions are inverses.

F(g(x)) = 2(𝒙

𝟐−

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) =1

3𝑥 + 1

𝑔(𝑥) = −1

2𝑥 + 7

𝒇(𝒙) =𝟏

𝟑(𝒙 + 𝟒) + 𝟏

𝒈(𝒙) = −𝟏

𝟐(𝒙 + 𝟒) + 𝟕

6. The three graphs show the functions

𝑓(𝑥) = 2𝑥 (Blue)

𝑔(𝑥) = 2(𝑥 + 1) (Red)

ℎ(𝑥) = 2𝑥 + 1 (Green)

Label the three graphs below.

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





Week #8

1. 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

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

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

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

2. Solve two step equations

5 − 3𝑥 = 11

3. Write a story problem for the following

equation.

2𝑥 + 4 = 10

4. Evaluate the function

𝑓(3) = 2𝑥2 − 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.

Year (x) Enrollment (y) 1980 15 1985 20 1990 22 1995 28 2000 37

2. Find the inverse of the function.

𝑦 = 3𝑥 − 7

3. Create a scatterplot and a table for the Average Cost of a Loaf of Bread. Use the graph to predict the cost

in 2050. Be sure to label your scatterplot appropriately.

In 1930 a loaf was 9 cents, 1940 a loaf was 10 cents, 1950 a loaf cost 12 cents, 1960 a loaf cost 22 cents,

1970 a loaf was 25 cents, 1980 a loaf cost 50 cents, 1990 a loaf cost 70 cents, and in 2008 it was $2.79

Cost in 2050 = ____________________



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

𝑟 = −.86 𝑟 = .90 𝑟 = .80 𝑟 = −.10

_____________

_____________

_____________

_____________



Week #10

1. Explain the difference between causation and

correlation.

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

2. A relationship has an r value of 0.97. What does

this suggest about the two variables?

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

3. After studying student behavior for the past

decade, a group of teachers have noticed that

there is a strong correlation between the high

student grades and the number of sunny days. Is

it correct to conclude that the number of sunny

days causes the higher student grades? Justify

your answer.

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

4. In a study of 1000 adults ages 18 - 56,

researchers found that left handed individuals

were five times as likely to suffer a severe

injury to their dominant hand than those

individuals that were right handed. Does this

mean that being left handed causes injuries?

Explain your reasoning.

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________



Week #8 KEY

1. 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

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

b. What is the equation for the line of best fit? Answers may vary: y = 5x + 60

c. Predict the grade for a student who studied for 6 hours. Answers may vary: 90

2. Solve two step equations

5 − 3𝑥 = 11

x = -2

3. Write a story problem for the following

equation.

2𝑥 + 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 function

𝑓(3) = 2𝑥2 − 4

f(3) = 14



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 = 3𝑥 − 7

𝑦 =𝑥

3+

7

3

3. Create a scatterplot and a table for the Average Cost of a Loaf of Bread. Use the graph to predict the cost

in 2050. Be sure to label your scatterplot appropriately.

In 1930 a loaf was 9 cents, 1940 a loaf was 10 cents, 1950 a loaf cost 12 cents, 1960 a loaf cost 22 cents,

1970 a loaf was 25 cents, 1980 a loaf cost 50 cents, 1990 a loaf cost 70 cents, and in 2008 it was $2.79

Year 1930 1940 1950 1960 1970 1980 1990 2008 Cost .09 .10 .12 .22 .25 .50 .70 2.79

Cost in 2050 = Answers will vary



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

𝒓 = −. 𝟏𝟎

𝒓 =. 𝟗𝟎

𝒓 = −. 𝟖𝟔

𝒓 =. 𝟖𝟎



Week #10 KEY

1. Explain the difference between causation and

correlation.

Correlation measures the strength of the association

of two variables. Correlations range from strong to

weak. Causation means that change in one variable

causes change in the other variable. Correlation does

not imply causation.

2. A relationship has an r value of 0.97. What does

this suggest about the two variables?

As the independent variable increases, the

dependent variable increases as well. We do not

know that the change in one variable causes the

other so there is no causation.

3. After studying student behavior for the past

decade, a group of teachers have noticed that

there is a strong correlation between the high

student grades and the number of sunny days. Is

it correct to conclude that the number of sunny

days causes the higher student grades? Justify

your answer.

Based on the information given, we cannot conclude

that the sunny days result in higher student grades.

There could be a variety of other factors that

influence the student grades in addition to the

weather.

4. In a study of 1000 adults ages 18 - 56,

researchers found that left handed individuals

were five times as likely to suffer a severe

injury to their dominant hand than those

individuals that were right handed. Does this

mean that being left handed causes injuries?


This study does not mean that being left-handed

causes people to have more injuries. There could be

additional factors such as the activities that resulted

in injury, were both groups (L & R handed) doing the

same tasks, etc.



Week #11 1. Determine the standard deviation of the

following data.

34, 23, 45, 33, 38, 35, 34, 30, 37, 36

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 #12 1. 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?

__________________________________________________________________________________________________________________________

__________________________________________________________________________________________________________________________

_________________________________________________________________________________________________________________________



Week #12 Continued

3.

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.

For Against No

opinion Total

21 - 40 25 20 5 50 41 - 60 20 35 20 75 Over 60 55 15 5 75

Total 100 70 30 200 In the 21 to 40 age group, what percentage supports increasing the minimum wage? http://stattrek.com/statistics/two-way-table.aspx

0

2

4

6

100 95 90 85 80

2

1

6

5

4

Algebra Grades

Grade

Num

ber

ofS

tudent

s

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



Use the graph below to answer the questions.

5. Calculate the line of best fit.

0

5

10

15

0 2 4 6 8 10



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?

Hours spent studying

Test Score TOTAL

0 - 25 26 - 50 51 - 75 76 - 100 0 - 2 2 8 12 2 24 2 - 4 0 10 8 24 42 4 - 6 1 0 2 9 12 6 + 0 0 1 4 5 TOTAL 3 18 23 39 83

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 8.1 Los Angeles, CA 3.8

Chicago, IL 2.7 Houston, TX 2.1

Philadelphia, PA 1.5 Phoenix, AZ 1.4

San Antonio, TX 1.3

Outlier: _______________________________________________________________ Mean population with outlier: _____________________________________ Mean population without outlier: _________________________________ How does the outlier change the mean? ___________________________ _________________________________________________________________________



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 Key 1. Determine the standard deviation of the

following data.

34, 23, 45, 33, 38, 35, 34, 30, 37, 36

𝟔. 𝟗𝟓𝟕

2. For the group data 4, 4, 6, 10, 13, what is the

relationship between the mean and median?

Mean = 7.4 Median = 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 − 𝟕𝟎𝟗

𝟐𝟎𝟎𝟗 − 𝟏𝟗𝟖𝟎=

−𝟐𝟓𝟕

𝟐𝟗≈ −𝟐𝟎

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

≈ $𝟐𝟎𝟎𝟎 http://www.census.gov/compendia/statab/cats/income_expenditures_poverty_wealth.html





Week #12 Key

1. 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 __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.

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?

𝟐𝟓

𝟓𝟎= 𝟓𝟎%


0

2

4

6

100 95 90 85 80

2

1

6

5

4

Algebra Grades

Grade

Num

ber

ofS

tudent

s




Use the graph below to answer the questions.

5. Calculate the line of best fit.

𝒚 = 𝒙 + 𝟐

0

5

10

15

0 2 4 6 8 10



Week #13 Key

1. Which number is more precise?

A. 40.67 feet B. 8.632 feet 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?

𝟐𝟒

𝟒𝟐≈ 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 8.1 Los Angeles, CA 3.8

Chicago, IL 2.7 Houston, TX 2.1

Philadelphia, PA 1.5 Phoenix, 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: __≈ 2.1 𝑚𝑖𝑙𝑙𝑖𝑜𝑛____



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 𝒌𝒎

𝟏 𝒉𝒓×

𝟏 𝒉𝒓

𝟏. 𝟔𝟎𝟗𝟑𝟒 𝒌𝒎× 𝟐 𝒉𝒓 ≈ 𝟔𝟐. 𝟏 𝒎𝒊

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

𝟏𝟐 𝒎𝒊

𝟏 𝒉𝒓×

𝟏 𝒉𝒓

𝟔𝟎 𝒎𝒊𝒏×

𝟏 𝒎𝒊𝒏

𝟔𝟎 𝒔𝒆𝒄×

𝟓𝟐𝟖𝟎 𝒇𝒕

𝟏 𝒎𝒊= 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.

3x + (3x – 12) = 𝑥

4

2. Solve for x.

3𝑥 = 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 #15

1. Solve and graph the inequality.

6𝑥 + 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 + 1

3= 4𝑥 − 7

4. In the formula 𝑃 =𝐹

𝐴 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, 8 12th-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 50 Wildebeest 50

Elk 45 Ostrich 40 Rabbit 35

How does the outlier change the mean?

Outlier: ____________________________________ Mean Population with Outlier: _________________ Mean Population without Outlier: ______________



Week #14 KEY 1. Solve for x.

3x + (3x – 12) = 𝑥

4

𝟔𝒙 − 𝟏𝟐 =𝒙

𝟒

𝐱 = 𝟐

2. Solve for x.

3𝑥 = 𝑎𝑥 + 5 + 𝑎

𝟑𝒙 − 𝒂𝒙 = 𝟓 + 𝒂

𝒙(𝟑 − 𝒂)

(𝟑 − 𝒂)=

𝟓 + 𝒂

𝟑 − 𝒂

𝒙 =𝟓 + 𝒂

𝟑 − 𝒂

3. What is the greatest possible error for a

measurement of 5 inches?

0.5 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 + 𝒙

𝟔= 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 𝒎𝒊

𝟔𝟒𝟎 𝒂𝒄𝒓𝒆𝒔×

𝟓𝟐𝟖𝟎 𝒇𝒕

𝟏 𝒎𝒊×

𝟓𝟐𝟖𝟎 𝒇𝒕

𝟏 𝒎𝒊= 𝟏𝟑𝟎, 𝟔𝟖𝟎 𝒇𝒕𝟐



Week #15 KEY


6𝑥 + 5 < 10 − 2𝑥

𝑥 <5

8

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 + 1

3= 4𝑥 − 7

𝒙 + 𝟏 = 𝟏𝟐𝒙 − 𝟐𝟏

𝒙 = 𝟐

4. In the formula 𝑃 =𝐹

𝐴 gives the pressure for P for

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

𝑷𝑨 = 𝑭

𝑨 =𝑭

𝑷

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, 8 12th-grade students: 4, 2, 0, 2, 3, 1

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

Ninth graders: 𝟐𝟒

𝟔= 𝟒

12th grade students: 𝟏𝟐

𝟔= 𝟐

The ninth grade students, on average, saw two more movies last month than the 12th 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 50 Wildebeest 50

Elk 45 Ostrich 40 Rabbit 35

How does the outlier change the mean? 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 = 2𝑥 − 6

𝑦 = −1

2𝑥 + 4

2. Solve the system using substitution.

{𝑥 + 2𝑦 = 12

𝑦 = 12⁄ 𝑥 − 3


{−2𝑥 − 3𝑦 = −7

𝑦 = 6𝑥 − 11


−5𝑥 + 4 < 3𝑥 − 6



5. Which number is the most precise? How do

you know?

a. 165.789 inches b. 56.89 inches

6. Solve for x.

5 − (𝑥 + 4) = 11𝑥 − 3



Week #17

1. Solve the system of equations by elimination.

{2𝑥 + 5𝑦 = 73𝑥 − 5𝑦 = 8


{𝑥 + 2𝑦 = 10

𝑦 = −3

4𝑥 + 6


{

12𝑥 + 6𝑦 = 10

𝑦 =2

3𝑥 − 1




5𝑥 + 6 <3𝑥 + 8

5


{12𝑥 + 6𝑦 = 63𝑥 − 5𝑦 = 8



Week #16 KEY


{𝑦 = 2𝑥 − 6

𝑦 = −1

2𝑥 + 4


{𝑥 + 2𝑦 = 12

𝑦 = 12⁄ 𝑥 − 3

𝒙 + 𝟐 (𝟏

𝟐𝒙 − 𝟑) = 𝟏𝟐

𝒙 = 𝟑

𝟑 + 𝟐𝒚 = 𝟏𝟐

𝒚 = 𝟒. 𝟓

(𝟑, 𝟒. 𝟓)


{−2𝑥 − 3𝑦 = −7

𝑦 = 6𝑥 − 11

−𝟐𝒙 − 𝟑(𝟔𝒙 − 𝟏𝟏) = −𝟕

𝒙 = 𝟐

𝒚 = 𝟔(𝟐) − 𝟏𝟏

𝒚 = 𝟏

(𝟐, 𝟏)


−5𝑥 + 4 < 3𝑥 − 6

−8𝑥 < −10

𝑥 >5

4

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

know?

a. 165.789 inches b. 56.89 inches

A

6. Solve for x.

5 − (𝑥 + 4) = 11𝑥 − 3

5 − 𝑥 − 4 = 11𝑥 − 3

1 − 𝑥 = 11𝑥 − 3

𝑥 =1

3



Week #17 KEY


{2𝑥 + 5𝑦 = 73𝑥 − 5𝑦 = 8

𝟓𝒙 = 𝟏𝟓

𝒙 = 𝟑

𝟐(𝟑) + 𝟓𝒚 = 𝟕

𝒚 =𝟏

𝟓

(𝟑, 𝟏𝟓⁄ )


{𝑥 + 2𝑦 = 10

𝑦 = −3

4𝑥 + 6


{

12𝑥 + 6𝑦 = 10

𝑦 =2

3𝑥 − 1

𝟏𝟐𝒙 + 𝟔 (𝟐

𝟑𝒙 − 𝟏) = 𝟏𝟎

𝟏𝟐𝒙 + 𝟒𝒙 − 𝟔 = 𝟏𝟎

𝒙 = 𝟏

𝟏𝟐 + 𝟔𝒚 = 𝟏𝟎

𝒚 = −𝟏

𝟑

(𝟏, −𝟏

𝟑)




5𝑥 + 6 <3𝑥 + 8

5

𝟐𝟓𝒙 + 𝟑𝟎 < 3𝒙 + 𝟖

𝟐𝟐𝒙 < 22

𝒙 < 1


{12𝑥 + 6𝑦 = 63𝑥 − 5𝑦 = 8

𝟏𝟐𝒙 + 𝟔𝒚 = 𝟔 −𝟏𝟐𝒙 + 𝟐𝟎𝒚 = −𝟑𝟐

𝟐𝟔𝒚 = −𝟐𝟔

𝒚 = −𝟏

𝟏𝟐𝒙 + 𝟔(−𝟏) = 𝟔 𝒙 = 𝟏

(𝟏, −𝟏)


84 Unit 7 - Sequences & Functions | Algebra 1 Weekly Assessments | ©2017 HighSchoolMathTeachers

Unit 7 - Sequences & Functions

Weekly Assessments



Week #18 - Understanding Interest

1. Classify the following functions.

(Circle the correct answer.) a. 𝑦 = 2𝑥 Linear Exponential

b. You have $100 and

add $20 per week

Linear Exponential

c. 𝑦 = 2𝑥 Linear Exponential

d. You begin with a

penny and double it

every week.

Linear Exponential

e. 𝑦 =1

2𝑥 Linear Exponential

2. Graph the function.

𝑓(𝑥) = 3𝑥

𝒙 -1 0 1 2 3

𝒇(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


Circle the correct answer.

a. 𝑦 = 2𝑥 Linear Exponential

b. 𝑦 = 3𝑥 Linear Exponential

c. You have

$100 and add

$10 per week

Linear Exponential

d. You begin

with a penny

and triple it

every week.

Linear Exponential

e. 𝑦 = 3𝑥 Linear Exponential


𝑓(𝑥) = 2.5𝑥

𝒙 -1 0 1 2 3

𝒇(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


(Circle the correct answer.)


b. You have $100 and

add $20 per week

Linear Exponential

c. 𝑦 = 2𝑥 Linear Exponential

d. You begin with a

penny and double it

every week.

Linear Exponential

e. 𝑦 =1

2𝑥 Linear Exponential


𝑓(𝑥) = 3𝑥

𝒙 -1 0 1 2 3

𝒇(𝒙) 1/3 1 3 9 27


work.

𝑓(𝑥) = (−2)𝑥 + 1

a. 𝑓(0) = (-2)0 + 1 = 1 + 1 = 2

b. 𝑓(1) = (-2)1 + 1 = -2 + 1 = -1

c. 𝑓(3) = (-2)3 + 1 = -8 + 1 = -7

4. 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) = $36,500.00

b. $0.01 doubled every day for one month (30

days).

Money = 0.01(2)number of days

Money = 0.01(2)30 = $10,737,418.24

Situation b will give you a better return on investment.





Circle the correct answer.


b. 𝑦 = 3𝑥 Linear Exponential

c. You have $100

and add $10

per week

Linear Exponential

d. You begin

with a penny

and triple it

every week.

Linear Exponential

e. 𝑦 = 3𝑥 Linear Exponential


𝑓(𝑥) = 2.5𝑥

𝒙 -1 0 1 2 3

𝒇(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 = 5

b. 𝑓(1) = (-3)1 + 4 = -3 + 4 = 1

c. 𝑓(3) = (-3)3 + 4 = -27 + 4 = -23

4. Simplify the expression.

a. 𝑥2 ∙ 𝑥5 = x7

b. (𝑥2)5= x10


90 Unit 8 - Exponential Functions | Algebra 1 Weekly Assessments | ©2017 HighSchoolMathTeachers

Unit 8 - Exponential Functions 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:


𝑓(𝑥) = 1.75𝑥

𝒙 -1 0 1 2 3

𝒇(𝒙)


work.

𝑓(𝑥) = (−2.5)𝑥 + 1.25

a. 𝑓(0) = ______

b. 𝑓(1) = ______

c. 𝑓(3) = _______

4. Properties of Exponents – Products and

Powers

a. (5𝑎2)(3𝑏4) = ________________________

b. (−𝑥2𝑦3)(2𝑥4𝑦) = __________________________

c. (4𝑥2)2 = ____________________

d. (3𝑎𝑏2)(2𝑎3𝑏2)3 =_______________________

5. Properties of Exponents – Quotients

a. (𝑎

𝑏)

4

= _________________

b. (3𝑥2

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. 161

4⁄

b. 17281

3⁄

c. 82

3⁄

3. Simplify the following expressions in simplest

radical form. Rationalize the denominator if

necessary.

a. 6

√43

b. √26

5

c. 5√7

√5

4. Identify each equation as growth or decay then

identify the rate of growth or decay.

Equation Growth

Or 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 y

0 4

2 1

x y

1 20

3 500



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)𝑥

Compare the two graphs


the same coordinate plane: 𝑓(𝑥) = 2𝑥 and

𝑔(𝑥) = 2𝑥 + 2

Describe the differences between the two

graphs.


the same coordinate plane:

𝑓(𝑥) = 0.5𝑥 𝑔(𝑥) = 0.5𝑥+2


graphs.

4. Compare the following functions:

Function 𝑓(𝑥) = 2𝑥 + 3 𝑔(𝑥) = 3(2)𝑥

Type

y-intercept

Change

Domain

Range



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 6

y 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) = $3,000.00

b. Doubling $0.01 every day for one

month?

T = 0.01(2)30 = $10,737,418.24

Explain: Answers will vary


𝑓(𝑥) = 1.75𝑥

𝒙 -1 0 1 2 3

𝒇(𝒙) 4/7 1 1.75 3.0625 5.359375


work.

𝑓(𝑥) = (−2.5)𝑥 + 1.25

a. 𝑓(0) = (-2.5)0 + 1.25 = 1 + 1.25 = 2.25

b. 𝑓(1) = (-2.5)1 + 1.25 = -2.5 + 1.25 = -

1.25

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

4. Properties of Exponents – Products and

Powers

a. (5𝑎2)(3𝑏4) = 15a2b3

b. (−𝑥2𝑦3)(2𝑥4𝑦) = -2x6y4

c. (4𝑥2)2 = 16x4

5. Properties of Exponents – Quotients

a. (𝑎

𝑏)

4

= 𝒂𝟒

𝒃𝟒

b. (3𝑥2

𝑦)

2

= 𝟗𝒙𝟒

𝒚𝟐



d. (3𝑎𝑏2)(2𝑎3𝑏2)3 = 24a10b8


1. Rewrite the following problems with

fractional exponents then simplify.

a. ∜16 = 𝟏𝟔𝟏

𝟒⁄ = 𝟐

b. ∛27 = 𝟐𝟕𝟏

𝟑⁄ = 𝟑

c. √121 = 𝟏𝟐𝟏𝟏

𝟐⁄ = 𝟏𝟏

2. Rewrite the following expressions in

radical form.

a. 51

4⁄ = √𝟓𝟒

b. 17281

3⁄ = √𝟏𝟕𝟐𝟖𝟑

c. 82

3⁄ = √𝟖𝟐𝟑 or (√𝟖

𝟑)

𝟐

3. Simplify the following expressions in

simplest radical form. Rationalize the

denominator if necessary.

a. 6

√43 = 𝟑√𝟐

𝟑

b. √26

5 =

√𝟏𝟑𝟎

𝟓

c. 5√7

√5 = √𝟑𝟓

4. Identify each equation as growth or decay

then identify the rate of growth or decay.

Equation Growth

Or 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.

x y

0 4

2 1

x y

1 20

3 500

f(x) = 4(0.25)x Decay - 75%

f(x) = 4(5)x Growth - 400%




1. Graph the following exponential functions on the

same coordinate plane:

𝑓(𝑥) = 2𝑥 and 𝑔(𝑥) = 0.5(2)𝑥

Compare the two graphs

Answers will vary.


the same coordinate plane:

𝑓(𝑥) = 2𝑥 and 𝑔(𝑥) = 2𝑥 + 2


graphs.

Answers will vary.

3. Graph the following exponential functions on the

same coordinate plane:

𝑓(𝑥) = 0.5𝑥 𝑔(𝑥) = 0.5𝑥+2

Describe the differences between the two graphs.

Answers will vary.

4. Compare the following functions:

Function 𝑓(𝑥) = 2𝑥 + 3 𝑔(𝑥) = 3(2)𝑥

Type Linear Exponential

y-intercept 3 3

Change Add 2 Multiply by 2

Domain All real values All real values

Range All real values y ≥ 0



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 6

y 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.



Unit 9 - Linear and Exponential Models Weekly Assessments


102 Unit 9 - Linear and Exponential Models | Algebra 1 Weekly Assessments | ©2017 HighSchoolMathTeachers

Week #23 - Comparing Linear and Exponential Functions

1. Graph the functions 𝑓(𝑥) = 2𝑥 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) = 7𝑥

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) = 2𝑥 𝑔(𝑥) = −3𝑥 + 4 ℎ(𝑥) =

0.5𝑥 − 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) = 2𝑥 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 2

𝒈(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 0.4535

0 𝟏𝟎(𝟏. 𝟎𝟓)𝟎 = 𝟏𝟎 0.4762

1 𝟏𝟎(𝟏. 𝟎𝟓)𝟏 = 𝟏𝟎. 𝟓 0.5

2 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) = 7𝑥

a. When will f(x) surpass g(x)?

When x > 7

b. When will g(x) ever surpass f(x)?

When 0.219 < x < 7

c. 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. 𝟒

𝒇(𝒙) will have a larger range value



Week #24 - Key

1. Use the following functions to answer the

questions:

𝑓(𝑥) = 2𝑥 𝑔(𝑥) = −3𝑥 + 4 ℎ(𝑥) =

0.5𝑥 − 2

a. 𝑓(𝑥) + 𝑔(𝑥) = 𝟐𝒙 − 𝟑𝒙 + 𝟒 = −𝒙 + 𝟒

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

c. 𝑔(𝑓(𝑥)) − ℎ(𝑥) = −𝟑(𝟐𝒙) + 𝟒 − (𝟎. 𝟓𝒙 − 𝟐)

𝒈(𝒇(𝒙)) − 𝒉(𝒙) = −𝟔𝒙 + 𝟒 − 𝟎. 𝟓𝒙 + 𝟐

𝒈(𝒇(𝒙)) − 𝒉(𝒙) = −𝟔. 𝟓𝒙 + 𝟔

d. ℎ(𝑥) − 𝑓(𝑔(𝑥)) = 𝟎. 𝟓𝒙 − 𝟐 − 𝟐(−𝟑𝒙 + 𝟒)

𝒉(𝒙) − 𝒇(𝒈(𝒙)) = 𝟎. 𝟓𝒙 − 𝟐 + 𝟔𝒙 − 𝟖

𝒉(𝒙) − 𝒇(𝒈(𝒙)) = 𝟔. 𝟓𝒙 − 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 the substance at the beginning. The decay rate is 14%.



Unit 10 - Understand Quadratic Functions Weekly Assessments


109 Unit 10 - Understand Quadratic Functions | Algebra 1 Weekly Assessments | ©2017 HighSchoolMathTeachers

Week #25 - Quadratics as Functions

5. Identify the domain and range of the following

graph.

6. The following expressions are equivalent.

Which form most clearly identifies the vertex

of the quadratic? Explain your reasoning.

−1

2𝑥2 + 3𝑥 − 2.5

−1

2(𝑥 − 1)(𝑥 − 5)

−1

2(𝑥 − 3)2 + 2

1

2(1 − 𝑥)(𝑥 − 5)

7. Write the output, using function notation, of

the following functions given the input of -2.

d. 𝑓(𝑥) = 𝑥2 − 3𝑥 + 1

e. 𝑓(𝑥) = −𝑥2 +1

2𝑥 − 3

f. 𝑓(𝑥) = 3

4𝑥2 + 𝑥 − 4



Week #26 - Graphing Quadratics

1. Create a table of the function

𝑓(𝑥) = −1

2𝑥2 + 3𝑥 − 4

Be 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 y

2. Use the following graph to identify which graph

appears to represent an exponential function.


3. a. Describe how 𝑔(𝑥) = −2𝑥2 + 4 and

ℎ(𝑥) = 2𝑥2 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 + 4𝑥 − 5

b. 𝑓(𝑥) = 𝑥2 + 𝑥 − 6

c. 𝑓(𝑥) = 𝑥2 + 2𝑥 − 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 − 4𝑥 + 6.

Which parabola has the lowest vertex?

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) = −2.5𝑡2 + 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 ≤ 5

Range: -1 ≤ y ≤ 15

2. The following expressions are equivalent.

Which form most clearly identifies the vertex

of the quadratic? Explain your reasoning.

−1

2𝑥2 + 3𝑥 − 2.5 Standard form

−1

2(𝑥 − 1)(𝑥 − 5) Intercept form

−1

2(𝑥 − 3)2 + 2 Vertex form

1

2(1 − 𝑥)(𝑥 − 5) Intercept form

The 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 − 3𝑥 + 1

𝒇(−𝟐) = (−𝟐)𝟐 − (−𝟐) + 𝟏 𝒇(−𝟐) = 𝟒 + 𝟒 + 𝟏 𝒇(−𝟐) = 𝟗 (−𝟐, 𝟗)

b. 𝑓(𝑥) = −𝑥2 +1

2𝑥 − 3

𝒇(−𝟐) = −(−𝟐)𝟐 +𝟏

𝟐(−𝟐) − 𝟑

𝒇(−𝟐) = −𝟒 − 𝟏 − 𝟑 𝒇(−𝟐) = −𝟖 (−𝟐, −𝟖)

c. 𝑓(𝑥) = 3

4𝑥2 + 𝑥 − 4

𝒇(−𝟐) =𝟑

𝟒(−𝟐)𝟐 + (−𝟐) − 𝟒

𝒇(−𝟐) = 𝟑 − 𝟐 − 𝟒 𝒇(−𝟐) = −𝟑 (−𝟐, −𝟑)



Week #26 - Graphing Quadratics Answer Key 1. Create a table of the function

𝑓(𝑥) = −1

2𝑥2 + 3𝑥 − 4

Be 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 5 y -1.5 0 0.5 0 -1.5

The axis of symmetry is found by using = −𝒃

𝟐𝒂 . 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.


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) = −2𝑥2 + 4 and

ℎ(𝑥) = 2𝑥2 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 + 4𝑥 − 5

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

b. 𝑓(𝑥) = 𝑥2 + 𝑥 − 6

(x - 3)(x + 2) = 0 x = -2 and x = 3 c. 𝑓(𝑥) = 𝑥2 + 8𝑥 − 20

(x - 2)(x + 10) = 0 x = 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 − 4𝑥 + 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.

2. 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) = −2.5𝑡2 + 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.


116 Unit 11 - Operations on Polynomials | Algebra 1 Weekly Assessments | ©2017 HighSchoolMathTeachers

Unit 11 - Operations on Polynomials

Weekly Assessments



Week #28 - Polynomial Operations

6. Use the following expressions in the problems below:

𝑏(𝑥) = 𝑥 − 4 𝑓(𝑥) = 2𝑥 − 4 𝑔(𝑥) = 𝑥2 − 3𝑥 + 6

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

a. 𝑓(𝑥) + 𝑔(𝑥)

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 = 3𝑥

𝐷 = 𝑥2 − 4𝑥 + 3 𝐸 = −2𝑥2 − 3 𝐹 = 10𝑥 + 1

𝐺 = 7𝑥2 − 4𝑥 𝐻 = 4𝑥3 − 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) = 2𝑥 − 4 𝑔(𝑥) = 𝑥2 − 3𝑥 + 6

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

a. 𝑓(𝑥) + 𝑔(𝑥)

(𝟐𝒙 − 𝟒) + (𝒙𝟐 − 𝟑𝒙 + 𝟔) 𝒙𝟐 − 𝒙 + 𝟐

b. ℎ(𝑥) + 𝑗(𝑥)

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

c. 𝑗(𝑥) − 𝑓(𝑥)

(𝒙𝟒 − 𝟑𝒙𝟐 + 𝒙 − 𝟗) − (𝟐𝒙 − 𝟒) 𝒙𝟒 − 𝟑𝒙𝟐 − 𝒙 − 𝟓

d. 𝑔(𝑥) − ℎ(𝑥)

(𝒙𝟐 − 𝟑𝒙 + 𝟔) − (𝟐𝒙𝟐 − 𝟑𝒙 + 𝟔) −𝒙𝟐

e. 𝑏(𝑥) ⋅ 𝑘(𝑥)

(𝒙 − 𝟒)(𝒙 + 𝟕) 𝒙𝟐 + 𝟑𝒙 − 𝟐𝟖

f. 𝑏(𝑥) ⋅ 𝑗(𝑥)

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

𝐷 = 𝑥2 − 4𝑥 + 3 𝐸 = −2𝑥2 − 3 𝐹 = 10𝑥 + 1

𝐺 = 7𝑥2 − 4𝑥 𝐻 = 4𝑥3 − 𝑥2 + 4 𝐽 = 3𝑥

a. 𝐴𝐵

(𝒙 − 𝟒)(𝒙 + 𝟒) 𝒙𝟐 − 𝟏𝟔 b. 𝐹 − 𝐺

(𝟏𝟎𝒙 + 𝟏) − (𝟕𝒙𝟐 − 𝟒𝒙) −𝟕𝒙𝟐 + 𝟏𝟒𝒙 + 𝟏 c. 𝐽𝐷

(𝟑𝒙)(𝒙𝟐 − 𝟒𝒙 + 𝟑) 𝟑𝒙𝟑 − 𝟏𝟐𝒙𝟐 + 𝟗𝒙 d. 𝐸 + 𝐻

(−𝟐𝒙𝟐 − 𝟑) + (𝟒𝒙𝟑 − 𝒙𝟐 + 𝟒) 𝟒𝒙𝟑 − 𝟑𝒙𝟐 + 𝟏 e. 𝐴𝐷 − 𝐵𝐶

(𝒙 − 𝟒)(𝒙𝟐 − 𝟒𝒙 + 𝟑) − (𝒙 + 𝟒)(𝟑𝒙) (𝒙𝟑 − 𝟖𝒙𝟐 + 𝟏𝟗𝒙 − 𝟏𝟐) − (𝟑𝒙𝟐 + 𝟏𝟐𝒙) 𝒙𝟑 − 𝟏𝟏𝒙𝟐 + 𝟕𝒙 − 𝟏𝟐 f. 𝐺(𝐹 + 𝐶)

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



Unit 12 - Solve Quadratic Functions

Weekly Assessments


123 Unit 12 - Solve Quadratic Functions | Algebra 1 Weekly Assessments | ©2017 HighSchoolMathTeachers

Week #30 - Factoring

1. Factor each of the following quadratics.

a. 𝑓(𝑥) = 𝑥2 + 4𝑥 − 5 b. 𝑓(𝑥) = 𝑥2 − 8𝑥 + 7

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

2. Solve each of the quadratics by factoring:

a. 𝑓(𝑥) = 𝑥2 − 11𝑥 − 60 b. 0 = 𝑥2 + 17𝑥 + 72

c. −𝑥2 + 𝑥 + 20 = 0 d. 2𝑥2 + 15𝑥 + 7 = 0



Week #31 - Completing the Square

3. Rewrite each quadratic in vertex format by completing the square

a. 𝑓(𝑥) = 𝑥2 + 16𝑥 + 71 b. 𝑓(𝑥) = 𝑥2 − 2𝑥 − 5

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

4. Complete the square to determine the minimum/maximum values for each quadratic.

a. 𝑓(𝑥) = 𝑥2 + 10𝑥 + 33 b. 𝑓(𝑥) = 𝑥2 − 6𝑥 + 5

c. 𝑓(𝑥) = 𝑥2 + 4𝑥 d. 𝑓(𝑥) = 6𝑥2 + 12𝑥 + 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 − 9𝑥 − 8 = 0

b. 10𝑥2 + 6𝑥 + 2 = 0

c. −3𝑥 + 2 = −2𝑥2 + 5𝑥 − 6

d. −0.25𝑥2 + 1.62𝑥 − 3.39 = 0

2. Solve each quadratic using any method.

Explain your choice of method for solving.

d. −𝑥2 − 14 = 𝑥2 + 10𝑥

e. 𝑥2 = −3𝑥 + 1

f. (𝑥 + 9)2 − 64 = 0

g. (2𝑥 + 5)(−4𝑥 + 7) = 0

3. Solve the following systems using any method.

a. {𝑓(𝑥) = −2𝑥 + 4

𝑔(𝑥) = −2𝑥2 + 3𝑥 − 2

b. {𝑓(𝑥) =

1

3𝑥 − 2

𝑔(𝑥) = 𝑥2 − 3𝑥 − 2

c. {𝑓(𝑥) = −6

𝑔(𝑥) = 4𝑥2 + 4𝑥 − 5

d. {𝑓(𝑥) = −

2

5𝑥 + 3

𝑔(𝑥) = −2𝑥2 − 4𝑥 + 9



Week #30 - Factoring Answer Key

1. Factor each of the following quadratics.

a. 𝑓(𝑥) = 𝑥2 + 4𝑥 − 5

(𝒙 + 𝟓)(𝒙 − 𝟏)

b. 𝑓(𝑥) = 𝑥2 − 8𝑥 + 7

(𝒙 − 𝟕)(𝒙 − 𝟏)

c. 𝑓(𝑥) = 2𝑥2 + 𝑥 − 6

(𝟐𝒙 − 𝟑)(𝒙 + 𝟐)

d. 𝑓(𝑥) = 6𝑥2 + 10𝑥 − 24

𝟐(𝟑𝒙 − 𝟒)(𝒙 + 𝟑)

2. Solve each of the quadratics by factoring:

a. 𝑓(𝑥) = 𝑥2 − 11𝑥 − 60

(𝒙 − 𝟏𝟓)(𝒙 + 𝟒) = 𝟎 (−𝟒, 𝟎) 𝒂𝒏𝒅 (𝟏𝟓, 𝟎)

b. 0 = 𝑥2 + 17𝑥 + 72

(𝒙 + 𝟗)(𝒙 + 𝟖) = 𝟎 (−𝟗, 𝟎)𝒂𝒏𝒅 (−𝟖, 𝟎 )

c. −𝑥2 + 𝑥 + 20 = 0

(𝒙 + 𝟒)(𝒙 − 𝟓) = 𝟎 (−𝟒, 𝟎) 𝒂𝒏𝒅 (𝟓, 𝟎)

d. 2𝑥2 + 15𝑥 + 7 = 0

(𝒙 + 𝟕)(𝟐𝒙 + 𝟏) = 𝟎 (−𝟕, 𝟎) 𝒂𝒏𝒅 (−𝟎. 𝟓, 𝟎)



Week #31 - Completing the Square Answer Key

1. Rewrite each quadratic in vertex format by completing the square

a. 𝑓(𝑥) = 𝑥2 + 16𝑥 + 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) = −9𝑥2 − 162𝑥 − 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 + 10𝑥 + 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 + 4𝑥

𝒇(𝒙) = (𝒙 + 𝟐)𝟐 − 𝟒 (−𝟐, −𝟒)

d. 𝑓(𝑥) = 6𝑥2 + 12𝑥 + 13

𝒇(𝒙) = 𝟔(𝒙 + 𝟏)𝟐 + 𝟕 (−𝟏, 𝟕)



Week #32 - Systems and Quadratic Formula Answer Key 1. Use the quadratic formula to determine the

solutions for the following quadratic

functions. Round your answers to the

nearest hundredth if necessary.

a. 𝑥2 − 9𝑥 − 8 = 0

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

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

(2, 0) d. −0.25𝑥2 + 1.62𝑥 − 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 solution

b. 𝑥2 = −3𝑥 + 1

(-3.30, 0) and (0.30, 0)

c. (𝑥 + 9)2 − 64 = 0

No real solution

d. (2𝑥 + 5)(−4𝑥 + 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) = −2𝑥 + 4

𝑔(𝑥) = −2𝑥2 + 3𝑥 − 2

𝑵𝑶 𝑺𝑶𝑳𝑼𝑻𝑰𝑶𝑵 − 𝑮𝒓𝒂𝒑𝒉𝒔 𝒅𝒐𝒏′𝒕 𝒊𝒏𝒕𝒆𝒓𝒔𝒆𝒄𝒕

b. {𝑓(𝑥) =

1

3𝑥 − 2

𝑔(𝑥) = 𝑥2 − 3𝑥 − 2

(−𝟐, 𝟎) 𝒂𝒏𝒅 (𝟑. 𝟑𝟑, −𝟎. 𝟖𝟗)

c. {𝑓(𝑥) = −6

𝑔(𝑥) = 4𝑥2 + 4𝑥 − 5

(−𝟎. 𝟓, −𝟔)

d. {𝑓(𝑥) = −

2

5𝑥 + 3

𝑔(𝑥) = −2𝑥2 − 4𝑥 + 9

(−𝟐. 𝟖𝟓, 𝟒. 𝟏𝟒) 𝒂𝒏𝒅 (𝟏. 𝟎𝟓, 𝟐. 𝟓𝟖)

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