March 20th, 2020 Dear Algebra 1 Students, We have learned so much together this year and you’ve worked extremely hard in your mastery of the algebra content. I am so proud of you and all you have mastered this year. Several of you have reached out to me to ask what you can do at home to stay on top of what you’ve previously learned, so I’ve put together this review packet for you to stay on top of your previous understanding. I understand that not everyone has access to internet or a printer at home, so I want you to know that this is simply a resource for you. At this time, I am not going to grade this out of fairness to everyone who is unable to access or work on the topics. But, if you are able to do so, then it will only help you. I need to await SJUSD’s decision for what to do going forward regarding assignments and grades, please stay tuned. If you are able to review some of the topics that we’ve learned together this year, then please start here. This packet covers Units 1, 2, 3, and part of Unit 4 (where we left off on March 13th). Please revisit all of your notes from August 2019 all the way to March 2020 (hopefully you kept all of your notes organized in your math binder!). If you lost some of your notes, then you have an abundance of resources online that you can access to review some of the topics. If you cannot get online, then please don’t stress and just do your best. J This is not meant to be an assignment, but a support packet. Here is a quick summary of resourceful websites that you can also access directly from my website www.wghsconti.weebly.com:

• Springboard Digital (you can log in using Clever) • Khan Academy (use the log-ins we created this year. I asked

each of you to record the log-in information in your phone/planner).

• Kuta Software Worksheets (pick and choose topics) • Desmos Online Grapher (useful for graphing)

I miss you all and hope that you and your families are doing well. Stay safe, stay healthy, stay educated. Mrs. Alexandra Conti WGHS Math Department AP Statistics | Algebra 1 avoinea@sjusd.org www.wghsconti.weebly.com

Algebra 1 Summary of Topics UNIT 1: EQUATIONS & INEQUALITIES August 2019 – September 2019

• Algebra vocabulary • Creating algebraic expressions from patterns • Simplifying algebraic expressions • Solving one-variable equations & checking solutions • Word problems: tables, patterns, expressions, equations • Creating, solving, & graphing one-variable inequalities • Creating, solving, & graphing Compound Inequalities

UNIT 2: FUNCTIONS September 2019 – November 2019

• Finding slope from graphs, equations, ordered pairs, and tables • Writing Slope-Intercept linear equations given graphs, tables, points • Finding the Slope-Intercept Form of an equation from Standard Form and vice Versa • Graphing lines from Slope-Intercept Form, Standard Form, Point-Slope Form • Graphing vertical and horizontal lines • Writing linear equations given a point and slope, or two points • Writing parallel and perpendicular lines • Writing Slope-Intercept Form, Standard Form, Point-Slope Form from Real Life • Relations & Functions • Domain & Range • Function Notation • Key Features of Graphs

UNIT 3: SYSTEMS OF EQUATIONS & INEQUALITIES November 2019 – January 2020

• Solve systems of equations by graphing • Solve systems of equations using substitution • Solve systems of equations using elimination • Using systems of equations to solve real-world problems • Systems of inequalities

UNIT 4: EXPONENTS, POLYNOMIALS, EXPONENTIAL FUNCTIONS, & RADICALS February 2020 – March 2020

• Exponent Properties • Exponent Word Problems & Applications • Exponential Functions • Polynomial Terminology • Adding & Subtracting polynomials • Multiplying polynomials • Factoring trinomials when a = 1 • Factoring trinomials when a ≠ 1 (not covered & not in packet) • Simplifying radical expressions & operations with radicals (not covered & not in

packet)

UNIT 5: QUADRATIC FUNCTIONS March 2020 – May 2020

• NOT COVERED YET & NOT IN THIS REVIEW PACKET

UNIT 1: EQUATIONS & INEQUALITIES Topic 1: Vocabulary Vocabulary Term Definition in your own words Constant

Variables

Coefficient

Exponent

Term

Like Terms

Expression

Equation

Solution

Sequence

Common Difference

Identify the parts of each algebraic expression or equation (constant, variable, etc).

1) 5!! − ! + 12

Expression or Equation? (Circle one).

12isa:___________________________

5isa:____________________________

xisa:____________________________

2isa(n):_________________________

2) !!! + 8! − 15

Expression or Equation? (Circle one).

!!!isa:___________________________yisa:____________________________

8isa:____________________________

-15isa:_________________________

Write an expression for each sentence (no equal signs!)

3) 12 more than twice a number. 4) 75 less than half of a number

Topic 2: Creating Algebraic Expressions 5) A pattern of small squares is shown to the right. a) Use the pattern to create a table to show the number

of small squares up to the fifth figure.

Figure Number Figure 0 Figure 1 Figure 2 Figure 3 Figure 4 Figure 5

Number of Small Squares

b) Write the number of small squares in the first through fifth figures as a sequence. Identify the common

difference. Sequence: Starting Value: Common Difference: c) Use the variable n to write an expression that could be used to determine the number of small squares

in any figure in the pattern. d)Usetheexpressionyoucreatedinpart(c)todeterminehowmanysquaresthereareinFigure20.Showyourworkandanswerthequestioninacompletesentence.

Topic 3: Simplifying Algebraic Expressions Simplify each expression. 6.3! + 7! − 5 + 8 7.4! + 10 − 6! + 3 − 5

8.2 6! + 5 − 14! 9.−3 −! + 6 − 16! + 25

10.10 7 − 3! − 35 + 40! 11.!! 6! − 50 − 5! + 48

Topic 4: Solving One-Variable Equations The Distributive Property is used to simplify expressions. The Properties of Equality state that you can perform the same operation on both sides of an equation without an effect to the solution. You can find these Properties of Equality on pg. 16 in your Springboard book OR on the YELLOW handout given to you first semester. I also pasted this into page 11 of this document! Distributive Property Addition Property of Equality

Multiplication Property of Equality Subtraction Property of Equality

Division Property of Equality Symmetric Property of Equality

Commutative Property of Addition/Mult. Associative Property of Addition/Mult.

Solve each equation. Check your solution. 12.7! + 3 = 17 13.!!!! = 8

14.6! − 15 = 9! + 3 15.! − 5 = 10 + 2! + 4!

16.−4 + 8! = 2(! − 16) 17.−24! + 1 − 5 = 8(−3! − 4)

18.18! + 4 = 6(3! + 10) 19.– 7! + 1 − 6 −7 −! = 36

Topic 5: Word Problems 20. You’re determined to get in super great shape and decide to check out the local deals for gym

memberships. Willow Glen’s 24-Hour Fitness charges an initiation fee of $50.00 and a monthly membership fee of $34.99. Another gym in Willow Glen called Orangetheory charges members $60 per month with no initiation fee.

(a) Complete the tables below to represent the total cost to attend either gym.

(b) Describe any patterns you notice in the table in complete sentences. (c) Represent the total cost of each gym as sequences. Identify the common difference. Sequence for 24-Hour Fitness: Com. Dif.: Sequence for Orangetheory: Com. Dif.: (d) Use the variable m to write expressions for the total cost of each gym for attending

m amount of months. (e) Use your expressions from part (d) to determine the total cost of 1 year (12 months)

at each gym.

OrangetheoryFitness

NumberofMonths TotalCost

0

1

2

3

4

24-HourFitness

NumberofMonths TotalCost

0

1

2

3

4

(f) Write an equation to represent the point at which the total cost of attending 24-

Hour Fitness is equal to the total cost of attending Orangetheory. (g) Solve your equation from part (f) and interpret your solution in 2-3 complete

sentences. 21. This week Joey studied for the Algebra 1 test 3 hours longer than Allie. Together, Joey and Allie studied for 11 hours. How many hours did each of them study?

a) Write an equation to represent this situation. Define your variable. b) Solve the equation you wrote in part (a) and interpret your solution in 1-2 sentences.

Topic 6: Creating, Solving, and Graphing Inequalities

Situation Write an inequality for the situation. 22.Thelegalspeedlimitonthefreewayisup

to70milesperhour.

23.Theminimummonthlypaymentonyourcreditcardbalanceis$30ormore.

24.Thetimeneededtofromhometoschoolmustbelessthan18minutes.

Solve each inequality and graph the solution on a number l ine. 25.2! − 7 ≥ 7 26.7 > 6 − 6!

27.4! + 4 − 2! < 8

28.3(−! + 3) ≥ 18

29.−2 ! − 4 + 3(! + 4) ≥ 8

30.– ! + 3 ≤ 18 + 2!

31.!!!! ≥ 2 32.Writeaninequalityforeachnumberline.(a) ______________(b) ______________

Topic 7: Writing & Graphing Compound Inequalities

33.Writeacompoundinequalitytodescribethefollowingsituation:ToearnaB+forthesemester,yourgradepercentagemustbe86.5%ormore,butlessthan89.5%.

34.Ahealthymaleneedstoeatmorethan1800caloriesbutlessthan3000caloriesperday.Writeaninequalityrepresentingthepossibleamountofcalorieshecouldeat.

35.Writeaninequalitythatdescribeseachgraph.(a)

(b)

36.Chrisneedstorentabikefromthebikeshop.Theychargehim$5perhourplusa$15depositfee.Hecanonlyaffordupto$28.00.

(a)Writeaninequalitytorepresentthesituation.Defineyourvariable.(b)Solveyourinequalityfrompart(b).Interpretyoursolution.

37.ACategory2Hurricanehaswindspeedsofatleast96milesperhourandatmost110milesperhour.WritethewindspeedofaCategory2hurricaneastwoinequalitiesjoinedbythewordandoror.

Topic 8: Solving Compound Inequalities

Solve and graph each compound inequality.

38.−3 + ! > −10 !" 10! + 7 < −93

39.10 − 7! ≥ 31 !" 8! − 9 ≥ 7

40.−2! + 7 > 1 !"# 4! + 3 ≥ −13

41.22 ≤ 8! − 2 ≤ 30

42.49 ≤ 10! − 1 < 89

43.2! − 9 > 9 !! − 10! + 1 ≥ −59

These are the Properties of Equality from page 16 of Springboard.

±±

Linear Equations

± ±

UNIT 2: FUNCTIONS

12. Identify the equation of the line graphed below. Prove by converting!

13. Identify the equation of the line graphed below. Prove by converting!

Topic 4: x- and y-Intercepts 14. 4x – y = 4 15. 12x – 8y = 24

Topic 5: Vertical & Horizontal Lines 16. y = -2 17. x = 5

Topic 6: Writing Linear Equations (Given a Point and Slope, or Two Points)

18. (-4, -7); slope = 3 19. (8, -9); slope = 54

−

A. 3x + 5y = 5

B. 3x – 5y = 5

C. 5x + 3y = 3

D. 5x – 3y = 3

A. 2x + y = 4

B. 2x – y = 4

C. x + 2y = 8

D. x – 2y = 8

!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!

!

!

! ! !

© Gina Wilson (All Things Algebra), 2012

Calculate the x- and y-intercepts. Calculate the x- and y-intercepts.

Select

Select

Check your answers at the end of each page! Help is available all week in tutorial and lunch.

20. (-3, -9) and (4, -2)

21. (-2, 7) and (6, -5)

Topic 7: Parallel & Perpendicular Lines

22. Describe the slopes of parallel lines.

23. Describe the slopes of perpendicular lines.

24. Which line is parallel to the line 5x – 2y = 18?

25. Which line is perpendicular to the line y = -3x + 2?

26. Write an equation that is parallel to y = -4x + 5 and passes through the point (-2, -1).

27. Write an equation that is perpendicular to 3x – 5y = 5 and passes through the point (9, -14).

Topic 8: Line of Best Fit

28. The number of students enrolled at Beach Manor Preschool during various years is given in the table below. Use the line of best fit to predict the number of students enrolled in 2010.

Year 1984 1987 1990 1993 1996 1999 2002

Entrants 39 45 52 61 72 78 85

A. y = 52 x + 1 B. y =

52

− x – 7

C. y = 25 x – 4

A. 3x + y = 4 B. x + 3y = 24 C. 3x – y = 5 D. x – 3y = 3

© Gina Wilson (All Things Algebra), 2012

D. y = 25

− x + 2

Writing Equations from Real-Life

51 57 63 69 75

Let the year 1984 represent “t = 0”.

a) Write a linear equation to model the data table. b) How many students are enrolled in the year 2017?

Check your answers at the end of each page! Help is available all week in tutorial and lunch.

29. The table below shows Luke’s golf score each week he participated in a golf tournament. Use the

line of best fit to estimate Luke’s score for week 12.

Topic 9: Word Problems 30. MaryAnn is printing pictures from her recent trip to Europe. An online print shop charges $0.15 per

4x6 inch print, along with a flat rate shipping charge of $3.00. If MaryAnn has $35 to spend, how

many prints can she order?

31. At Smith Mountain Lake Boat Rentals, it cost $25 per hour to rent a pontoon boat, plus a one-time

charge for cleaning. The Bengel family rented a boat from 11 am – 6:30 pm and paid $226.50. If

the Jones Family rented a boat from 8 am – 1 pm, how much did they pay?

32. Clint is in study hall reading The Hunger Games. After 20 minutes, he is on page 151. After 45

minutes, he is on page 181. How many pages had Clint read prior to study hall?

33. Alaina is selling wreaths and poinsettias for her chorus fundraiser. Wreaths cost $27 each

poinsettias cost $20 each. If she sold 15 poinsettias and made $543, how many wreaths did she

sell?

Week 1 2 3 4 5 6

Score 95 92 89 88 86 84

© Gina Wilson (All Things Algebra), 2012

86 83 80

a) What was Luke’s golf score on “Week 0”? b) Write a linear equation to represent Luke’s predicted golf score. Define your variables.

Check your answers at the end of each page! Help is available all week in tutorial and lunch.

Topic 10: FUNCTIONS & RELATIONS

VOCABULARY (Use notes or Google)

INPUT: OUTPUT:

MAPPING (show picture): ORDERED PAIRS:

RELATION: FUNCTION:

EXAMPLES

Determine whether the ordered pairs and equations represent functions, & explain why or why not.

34) (4, 5) , (6, 3), (7, 2)

35) (4, 5) , (4, 3), (5, 2)

36) (1, 2,) , (3, 4) , (5, 6)

37) (4, 5), (6, 4), (7, 4)

VERTICAL LINE TEST EXAMPLES

38)Doesthisgraphrepresentafunction?ExplainwhyorwhynotusingtheVerticalLineTest.

39)Doesthisgraphrepresentafunction?ExplainwhyorwhynotusingtheVerticalLineTest.

PRACTICE: Determine if each example is a “Function” or “Not a Function”. Letters of Functions: ____________________________________________________ Not Functions: __________________________________________________________ Topic 11: DOMAIN AND RANGE

VOCABULARY

DOMAIN: RANGE:

DOMAIN & RANGE EXAMPLES

For each function, identify the domain and range in interval or set notation.

40)

41)

42)

43) 44)

46. Find the domain and range of the following graph: A. !: 2,12 ,!: (5,8) B. !: 2,∞ ,!: [5,∞) C. !: [2,12],!: [5,8] D. !: (2,∞),!: (5,∞)

Topic 12: FUNCTION NOTATION

EXAMPLESUsethefunctionmachinestofindthe(input,output)orderedpairsforthefollowingvalues.

48)

a) x=-5b) b)x=3

49)a)x=4b)x=-2

47. Find the domain and range of the following mapping: A. !: −2,3 ,!: [2,10] B. !: ! ≥ −2,!:! ≥ 2 C. !: − 2 ≤ ! ≤ 3,!: 2 ≤ ! ≤ 10 D. !: −2,−1,0,1,2,3 ,!: {2,4,6,8,10}

50)Letf(t)=thenumberofpeople(inmillions)whohaveownaflyingcartyearsaftertheyear3000.

Explainthemeaningofthefollowingstatements:a. EXAMPLE:f(0)=8

t= 0 represents the year 3000, whereas 8 represents the number of people (inmillions)thathaveflyingcarsintheyear3000.

So,f(0)=8meansthatthereare8millionpeoplethatownflyingcarsintheyear3000.

b. f(5)=15c. f(10)=12d. f(11)=Ke. f(b)=25

51)Evaluatef(6)forf(x)=3x-1052)Isthisrelationafunction?{(1,2),(4,5),(4,1)}Explainwhyorwhynot.53)Identifythedomainandrange:{(6,12),(5,20),(14,3)}

Topic 13: KEY FEATURES OF GRAPHS

This graph us Continuous because points are connected.

Vocabulary(seenotesorgoogle) Independent Variable

Dependent Variable

Continuous

Discrete

Y-intercept

Relative Maximum

Relative Minimum

Extrema

Domain

Range

IndependentVariable

AbsoluteMaximum:y=110feet

RelativeMaximum:y=90feet

RelativeMinimum:y=30feetAbsoluteMinimum:y=10feet

Dependent

Variable

Domain:[0,1250]

Range:[10,110]

54) The Ferris Wheel Example (from your notes)

YoucanyourfriendsdecidetoridethemagicalFerrisWheelandyourfavoritethemepark.UsetheSTEPSbelowtomapyourheightontheferriswheelbasedonthetimeyouhavespentridingtheferriswheel.

STEPS TO GRAPH HEIGHT ON THE FERRIS WHEEL

After you graph, label the vocabulary words on the graph similar to the Rollercoaster example.

1)Youclimbthestepsandgetontheferriswheel,5feetabovetheground.

2)Theferriswheelstartsmoving,andafter10secondsyouare35feetintheair

3)Theferriswheelcontinuesmoving.10moresecondspass,andyouareatthetopoftheferriswheel,55feetintheair.

4)Theferriswheelcontinuesmoving,and20secondslater,youarebackdownatthebottom,5feetabovetheground.

5)Theferriswheelcontinuesgoingaround,and20secondslater,youarebackattheverytop,55feetintheair.

6)Theferriswheelstops(youarestillatthetop),andyouwaitfor20secondsassomemorepeoplegetontheferriswheel.7)Theferriswheelisnotspinninganymore,butbecomesmagical,andoverthenext10secondsyoubounce50morefeetupintheair!(Youarenow105feetabovetheground)

8)10secondslater,youfallbackdown50feettotheoriginalposition.

9)Theferriswheelcontinuesmoving,and20secondslater,youarebackdownatthebottom,5feetabovetheground.

Time(Seconds)

Height(feet)

UNIT 3: SYSTEMS OF EQUATIONS & INEQUALITIES

Topic 1: Solve the Systems of Equations by Graphing Directions: Solve the system of equations by graphing to find the point of intersection.

55.! = − !! ! + 3

! = !! ! − 3 Solution:_____________

56.. ! = −1 ! = − !

! ! + 4 Solution:_____________

57.! + y = 1 − !

! ! + ! = −3 Solution:_____________

58.Each family in a neighborhood is contributing $20 worth of food to the neighborhood picnic. The Schmidt family is bringing 12 packages of buns. The hamburger buns cost $2.00 per package and the hot dog buns cost $1.50 per package. How many packages of each type of bun did they buy? Solution:_____________

TOPIC 2: Solve the Systems of Equations by Substitution 59. y = x + 5 4x + y = 20 Solution:_____________

60. y – 4x = 3 2x – 3y = 21 Solution:_____________

61. x + 2y = −1 4x – 4y = 20 Solution:_____________

62. Cathy wants to buy a gym membership. One gym has a $150 joining fee and costs $35 per month. Another gym has no joining fee and costs $60 per month. a) In how many months will both gym memberships cost the same? What will that cost be? b) If Cathy plans to cancel in 5 months, which is the better option for her? Explain.

TOPIC 3: Solve the Systems of Equations by Elimination 63. x – 2y = − 19 5x + 2y = 1 Solution:_____________

64. 3x + 4y = 18 −2x + 4y = 8 Solution:_____________

65. 2x + y = 3 − x + 3y = − 12 Solution:_____________

TOPIC 4: Solve the Systems of Equations Using a Method of Your Choice! 66. x + 4y = 2 3y + x = 10 Solution:_____________

67. – x + 2y = 3 4x – 5y = − 3 Solution:_____________

68. y = − 4x y = 2x + 3 Solution:_____________

TOPIC 5: Explain What Method To Use To Solve:

! = ! − 3 ! = −! − 1

69.Method:

70.Nowsolvethesystemusingyourchosenmethod:

Solution:_____________

TOPIC 6: Determine the Error Made When Solving the System

! = 12 !

! = −! + 3 (− 6, − 3)

71. Explain what the error is: 72. Solve it correctly:

TOPIC 7: Determine The Error Made When Solving The Following System of Equations: 2x + y = 14 y = 14 – 2x − 3x + 4y = − 10 − 3x + 4(14 – 2x) = − 10 − 3x + 56 – 2x = − 10 − 5x + 56 = − 10 − 5x = − 66 x = 66/5 = 13.2 73. What is the error? 74. Solve the system from above correctly.

TOPIC 8: Systems of Equations WORD PROBLEMS

75. A local boys club sold 176 bags of mulch and made a total of $520. They sold hardwood mulch for $3.50 per bag and pine bark mulch for $2.75 per bag. How bags of each type of mulch did they sell?

76. Roses cost $2.50 each and daisies cost $1.75 each. Sam spent $24.75 to buy a dozen flowers for his mother. The bouquet contained both roses and daisies. How many of each type of flower where in the bouquet?

77. Angelo runs 7 miles per week and increases his distance by 1 mile each week. Marc runs 4 miles per week and increases his distance by 2 miles each week. In how many weeks will Angelo and Marc be running the same distance? What will that distance be?

y = 14 – 2(13.2) = 14 – 26.4 = − 12. 4

(13.2, − 12. 4)

TOPIC 9: Systems of Inequalities 78. y < 3x + 1 y ≥ − 2x – 3 Graph!

79. 4x + y > 2 x – y + 6 < 0 Graph!

80. !! ! − ! ≤ 3

!! ! + y > − 1

Graph!

81. Jeobany makes $2 profit on every cup of coffee he sells and $1 on every cookie he sells. He wants to sell at least 5 cups of coffee and at least 5 cookies per day. He wants to earn at least $10 per day. Show and describe all the possible combinations of coffee and cookies that Jeobany needs to sell to meet his goals. List two possible combinations.

TOPIC 10: Write a System of Inequalities for the Graphs Provided 82.

System of Inequalities: Choose a solution: ________ Choose a non-solution: _____

83.

System of Inequalities: Choose a solution: ________ Choose a non-solution: _____

TOPIC 11: System of Inequalities Word Problems

84.Raeganisbuyingavocados&limestomakeguacamole.Avocadoescost$1.50eachandlimescost$0.50each.Shehas$15tospend.Raeganwantstobuyatleast7avocadoes.Additionally,sheneedstobuymorethan2limes.a)Definethevariablesxandy.b)WritethesystemofinequalitiestorepresentRaegan’ssituation.c)Graphyoursystem.Labelyouraxes.d)Identifyareasonabledomainandrange:Domain:_________________Range:__________________e)CanRaeganbuy10avocadoesand1lime?Justifyyouransweralgebraicallyorgraphically.

UNIT 4: EXPONENTS, POLYNOMIALS, EXPONENTIAL FUNCTIONS, RADICALS Topic 1: Exponent Properties & Simplifying Exponent Expressions

Property Name Symbolic Form Product Property of Powers Quotient Property of Powers Power of a Power Power of a Product Power of a Quotient Zero Power Property Negative Power Properties Rational Exponent Property 1 Rational Exponent Property 2

Simplify each expression. No negative exponents. 85. 4!! = 86. 5! ∙ 2! = 87. −2!!! ∙ 3!!! = 88. (−!!!!! ∙ −2!!!!!)!! =

89. − !!!!!!!!!!!!∙!!!!!! = 90.

!!!(!!!!!)!! =

91. !!!!

!!!!∙!!!!!!!= 92.

(!!!!!)!!!!!!!∙!!!!!! =

93. 216!! = 94. 81!!! = 95. 243!/! = 96. 196!/! =

97. !!"!!/!

98. !!"!!/! =

Topic 2: Exponent Word Problems & Applications

The density of a substance is the determined by dividing its mass by its volume.

Example 1 from notes: Suppose an iceberg in the ocean

has a mass of 59,049 kilograms (kg) and a volume of 81 cubic

meters. Compute the density of the iceberg (don’t forget units!). State givens:

Example 2 from notes: Suppose a substance has a density of 20!!" grams/cm!. It’s volume is

3!! cm!. Compute the mass of the substance (don’t forget units!). State givens:

Practice with Word Problems 99. The formula for the area of a square is ! = !!, where s is the side length of the square. Suppose a

square garden has a side length of 2!!!! feet. What is the area of the square garden? Don’t forget units!

100. The formula for the area of a rectangle is ! = ! ∙! where L is the length and W is the width.

Suppose a rectangular classroom has a length of 5!!!!! feet and a width of 8!!!!! feet. What is

the area of the rectangular classroom? Don’t forget units!

102. As you recall from the previous problem, the area of a rectangle is ! = ! ∙! where L is the length

and W is the width. Suppose your new flatscreen TV has a surface area of 10!!!!! inches! and a

width of 5!!!!!! inches. What is the length of the TV screen? Don’t forget your units!

103. An asteroid is 10!" !"!"# away from earth, and it is travelling at a speed of 10! !"#$% !"# !"#. How

many days will it take the asteroid to reach planet earth?

104. When a caterpillar larvae hatches, it weighs only 10!! !"#$%. However, each day it is able to eat

10! times it’s body weight. How many grams of food can the larvae eat each day?

105. A seed on a dandelion weighs 10!! !"#$%. The dandelion itself can weigh up to 10! !"#$%. How many times heavier is a dandelion than its seeds?

106. Naomi and Douglas each have a baseball card collection. Naomi has two thousand baseball cards in

her collection. Douglas has (4!)! baseball cards in his collection. Who has more baseball cards? Show your work and explain.

107. Handy Electrics has decided to give a total of 192! dollars ($) to their Sales Managers as an end-of-

year BONUS! If the company has 8! managers and the money is divided equally among them, how much will each Sales Manager get as their end-of-year bonus?

108. The volume of a cube is given by the formula ! = !! where s is the length of the side. Use this formula to find the volume of the cube shown below. Simplify

answer fully.

! = !!!!!!"

109. The volume of a rectangular prism is given by the formula ! = ! ∙! ∙ ! where L is the length,

W is the width, and H is the height. Use this formula to find the volume of the cube shown below. Simplify answer fully.

110. The volume of a rectangular prism is given by the formula ! = ! ∙! ∙ ! where L is the length,

W is the width, and H is the height. Use this formula to

find the Width of the cube shown below. Simplify answer

fully.

!=!"

! !!

!= !"!! !!

!"

! = !"!!!!

!=!"

! !!!

"

! = !"#$!"!!" !"#$! !""#

! = !"!!"!!"

!=?

! =?

Topic 3: Exponential Functions Exponential Function Definition (see your notes!) Wherea=_______________________________,b=____________________________,andx=_________________________.

Exponential Growth Exponential Decay

111.! ! = !(!.!")!

a)Isthisexponentialgrowthordecay?Why?

b)Initialvalue:__________________________

c)Growth/DecayFactor:_______________

d)Growth/DecayRate:_________________

e)Filloutthetable&graph.

112.! ! = !"!# !!!

a)Isthisexponentialgrowthordecay?Why?

b)Initialvalue:__________________________

c)Growth/DecayFactor:_______________

d)Growth/DecayRate:_________________

e)Filloutthetable.

113. ! ! = !(!.!)!

a) Initial value: __________________

b) Decay Factor: _______________

c) Decay Rate: _________________

d) Fill out the table.

114.! ! = ! ! !

a) Initial value: __________________

b) Decay Factor: _______________

c) Decay Rate: _________________

d) Fill out the table.

Working Backwards: Write the Exponential Equation for each Table

115.GrowthorDecay?Why?InitialValue:____________Factor:_______________Equation:_________________________________________

x y0 1801 64.82 23.3283 8.398

116.GrowthorDecay?Why?InitialValue:____________Factor:_______________Equation:_________________________________________

x y0 81 322 1283 5124 40485 24576

117. Dirty Bathroom Problem

One single bacteria lands on a kitchen counter. It divides into two parts every 5 minutes. Fill out the chart below to show how many bacterium are on the counter:

Show your work for filling in the table:

How many 5-minute periods are there in one hour? _____ How many bacteria are on the counter after one hour? _______

Plot as many points from your table that fit on the graph. Label and unit your axes!

Describe the pattern you see. Include if the data increases, decreases, is linear, not linear, constant, or non-constant.

# of 5 minute periods

0 1 2 3 4 5 6 7 8 9 10 11

# of bacteria 1 2 4

Come up with an equation for the table and graph:

Topic 4: Polynomials Terminology Vocabulary (see notes on Polynomial Terminology) Monomial

Binomial Trinomial Polynomial

Degree of any Polynomial

Standard Form of a Polynomial

EXAMPLE

118. Fill out the following table for each polynomial. Polynomial Degree

“FirstName”UsingDegree

#ofTerms “LastName”Using#ofTerms

7

4x+6

8x2+3x+2

10x3 15x4–2x3+

3x

119.Writeeachpolynomialinstandardform.

a. 1091187 22 +−+− xxxx b. 222 7611 xxx −+

Topic 5: Adding & Subtracting Polynomials Simplify each problem & write the final answer in Standard Form.

Simplify each problem & write the final answer in Standard Form. Write the perimeter of each figure in Standard Form. 128. 129.

Adding polynomials is essentially the same as “combining like terms”.

Subtracting polynomials is similar, but you will need to “distribute the -1” to each term of the second polynomial (switch all the signs).

Topic 6: Multiplying Polynomials (when a = 1)

Determine the product of the binomials using either Box Method OR the FOIL.

130.(! − 2)(! + 7)

131.(3! − 2)(! − 5)

132.(! − 5)(! + 5)

133. ! + 10 !

Additional Practice: multiply each pair of binomials. Show your work. 134.) (!+ !)(!− !)

135.) (!+ !)(−!"+ !)

136.) (!+ !)(!− !)

137.) (!+ !)!

138.) (!− !)(−!+ !)

Topic 7: Factoring Polynomials (when a = 1) Factor each trinomial. Show your work.

139)!! + !" + !

140) !! − ! − !"

141)!! − !" − !" 142) !! + !" + !"

Practice Problems Factor each completely.