Algebra1SummerHomework

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DearFutureAlgebra1Student,

IhopeyouareexcitedforyourupcomingyearinAlgebra1!Algebraallowsustodescribetheworldaroundusinaverypreciseandaccuratemanner.Itallowsustomakepredictions,andmodelsituationsthatvaryovertime.Thisbranchofmathematicsisfoundationalforallotherareasofmath.YourlevelofsuccessinAlgebra1willdirectlycorrelatetohowsuccessfulyouwillbeinyourfuturemathexperiences.

Asyouprobablyknow,yourhighschoolmathematicsclassesarecumulative.Thismeansthatyouwillneedtoutilizeconceptspreviouslylearnedtobesuccessful.Thepurposebehindthissummerhomeworkpacketistoreacquaintyouwiththenecessaryskillstobesuccessfulinthisyear’smathcourse.

PleasebepreparedtosubmitthisassignmentduringyoursecondAlgebra1class.Itwillbegradedforaccuracyaswellascompletion.Workneedstobeshowninaneatandorganizedmanner,anditisperfectlyacceptabletocompletethepacketonseparatesheetsofpaper.Justbesuretostapleanyextrapaperstothepacket.Also,donotrelyonacalculator.

ShowALLworkforeachproblemandtakeyourtime.Remember,thiswillbeyourfirstimpressiontoyournewmathteacher,andyouwanttomakesurethatitisapositiveone!Seebelowfordirectionsandhelpfulwebsites.Wehopeyouhaveawonderfulsummer!

Best,

WarehamHighSchoolMathDepartment

Assistancewillbeavailablefrom10:30AMto12PMonAugust9th,11th,and17thatWarehamHighSchoolfrom.Feelfreetostopbywithanyquestionsyoumighthave.Additionally,youmayemailyourquestionstoMrs.Cavicchiatkcavicchi@wareham.k12.ma.us.Toensurethefastestresponse,pleaseincludeyourname,summerassignmentname,and(ifpossible)apictureoftheproblemandyouraccompanyingwork.

HelpfulHints

• Beforeansweringanyquestions,readthroughthegivennotesandexamplesforeachtopic.• Thispacketistobesubmittedduringyoursecondalgebraclassperiod.• Allworkmustbeshowninthepacketoronaseparatesheetofpaperstapledtothepacket.Suggestionsfortimemanagement:Sincethereare9partstothispacket.Complete1partperday(approx.20mineachday),youcancompletethispacketin9days.

Part1–Integershttps://www.khanacademy.org/math/in-sixth-grade-math/integers-india/addition-integers/v/adding-integers-with-different-signs

Example:AddingIntegers

Usethenumberlinebelowtohelpyouwiththeproblemsthatfollowforadditionandsubtraction.

-3+-5=______

8+-2=______

7+-7=______

-3+5=______

-4+9=______

6+-13=______

-5+5=______

-6+6=______

5+-3=______

13+-4=______

8+-9=______

-5+-6=______

-14+6=______

-1+10=______

1+-10=______

-12+0=______

13+-13=______

10+-20=______

8+-16=______

-12+25=______

-3+7=______

-6+-2=______

-47+47=______

100+-25=______

-77+78=______

https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/core-algebra-foundations-negative-numbers/e/adding_and_subtracting_negative_numbers

Example:SubtractingIntegers

Rewriteeachasanadditionproblemandevaluate.Thefirsttwohavebeendoneforyou.

6–8=6+(-8)=-2

-4–(-8)=-4+(+8)=4

5–9= 8–5= -3–6=

-8–8=

4–9= -5–3= -9–4= 4–7=

7–2=

-1–6= -5–4= 6–(-8)= -6–(-8)=

-3–(-7)=

-1–(-8)= -14–(-4)= 17–(-8)= 14–(-5)=

Part2–OrderofOperationshttps://www.khanacademy.org/math/pre-algebra/order-of-operations/order-of-operations-ddp/v/introduction-to-order-of-operations

GroupingSymbolsExponentsMultiply&Divide(lefttoright)Add&Subtract(lefttoright)

Example1:

8 − 3 ∙ 2 − 33 ÷ 11 =8 − 6 − 3 =2 − 3 =−𝟏

Example2:

5 ∙ 2! − 2! −6 + 3 =5 ∙ 2! − 2! −3 =5 ∙ 4 − 8 −3 =20 − −24 =20 + +24 =

44

Evaluatetheproblemsbelow.Besuretouseorderofoperationsandcircleyourfinalanswer

1. 8 −2 − −4 ! =

2. −4 1 + 5 ! ÷ 6 − 42 + 5 =

3. −12! ÷ 4 − 3 ∙ 2! =

4. 8 − 4 2 + 5! ÷ 12 =

5. (−3)! ∙ 5 − 7 ! − −9 ÷ 3 =

6. −1 ∙ 2 − 6 ! ÷ 8 + 8 − 3 ∙ 4 =

G

Part3–SimplifyingExpressionshttps://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-manipulating-expressions/v/combining-like-terms-and-the-distributive-property

Example1:𝑛 − 7𝑛

= 1𝑛 − 7𝑛fillina‘1’infrontofvariableswithnocoefficient= 1𝑛 + (−7𝑛)rewriteanysubtractionby‘addingtheopposite’= −𝟔𝒏addlikeyouwouldintegers

Example2:𝑥 − 10 + 1 + 6𝑥= 1𝑥 − 10 + 1 + 6𝑥fillina‘1’infrontofvariableswithnocoefficient = 1𝑥 + −10 + 1 + 6𝑥rewriteanysubtractionby‘addingtheopposite’ = 1𝑥 + 6𝑥 + −10 + 1reorganizebyplacingvariablesandconstantsthatarealiketogether = 7𝑥 + −9 addlikeyouwouldintegers = 𝟕𝒙 − 𝟗changebacktosubtractionwherevernecessary

7. 10𝑛 + 9𝑛 = 8. 13𝑟 + 5𝑟 = 9. 𝑣 − 1 + 2 =

10. 8𝑏 + 𝑏 = 11. 8𝑘 − 7𝑘 = 12. 𝑎 + 12 + 8𝑎 − 9 =

13. 7𝑟 + 3 + 7 + 12𝑟 = 14. −12𝑚 − 7𝑚 = 15. −𝑥 − 8 − 3𝑥 =

Part4–SimplifyingExpressionswithDistributivePropertyhttps://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-manipulating-expressions/v/distributive-property-with-rational-terms

Example1: 3𝑥 + 2(5𝑥 − 7) = 3𝑥 + 2 5𝑥 + −7 rewriteanysubtractionby‘addingtheopposite’ = 3𝑥 + 10𝑥 + −14distributethe‘2’toeachtermintheparentheses = 13𝑥 + −14Addlikeyouwouldintegers = 𝟏𝟑𝒙 − 𝟏𝟒changebacktosubtractionwherevernecessaryExample2: 8𝑥 − 6(3 − 2𝑥) = 8𝑥 + −6 3 + −2𝑥 rewriteanysubtractionby‘addingtheopposite’ = 8𝑥 + −18 + 12𝑥distribute(multiply)the‘-6’toeachtermintheparentheses = 8𝑥 + 12𝑥 + −18reorganizebyplacingvariablesandconstantsthatarealiketogether = 20𝑥 + −18addlikeyouwouldintegers = 𝟐𝟎𝒙 − 𝟏𝟖changebacktosubtractionwherevernecessarySimplifythefollowingexpressionsusingthemethodsshownabove.

16. 9 − 3 2𝑥 − 4 =

17. −5 + 5 𝑥 + 4 = 18. 4 6𝑛 + 9 − 10𝑛 =

19. 14 − 3 4𝑛 − 1 =

20. −8𝑛 − 8 −4 − 2𝑛 = 21. 7𝑘 − 2 3𝑘 + 1 − 9 =

22. −6 + 5 8 − 𝑘 − 8𝑘 =

23. 𝑘 + 1 − 4 2𝑘 − 9 = 24. 9 − 3 −4 + 3𝑥 + 12𝑥 =

Part5–SolvingTwoStepEquationshttps://www.khanacademy.org/math/in-seventh-grade-math/simple-equations/equation-definition/v/why-we-do-the-same-thing-to-both-sides-two-step-equations

Example1:

Example2:

Example3:

Example4:

Solvethefollowingtwo-stepequationsusingthemethodsshownabove.

25. !!𝑎 − 6 = 1

26. !!+ 7 = −2 27. 5𝑦 − 4 = 7

28. 9 − 4𝑚 = 19

29. !!− 8 = −10 30. 6𝑡 + 3 = −7

31. 15 = −15 − 8𝑢

32. 0 = !!𝑦 + 8 33. 11 − !

!"𝑥 = 10

34. 50 = 8 + !!

35. −10𝑏 − 7 = 9 36. 18 = − !!"+ 20

Part6–SolvingEquationsthatRequireDistributivePropertyhttps://www.khanacademy.org/math/in-eighth-grade-math/linear-equations-one-variable/reducing-equations-simpler-form/v/solving-equations-with-the-distributive-property

Example1:

Example2:

Example3:

Solvethefollowingequationsusingthedistributiveproperty.

37. 3 2𝑥 + 5 = 39

38. 8 7 − 𝑦 = −24 39. −4 8 + 5𝑛 = 8

40. 6 3𝑥 − 5 − 7𝑥 = 25

41. −2 5 + 6𝑚 + 16 = −90 42. 15 𝑡 + 2 + 9𝑡 = 6

43. 7𝑤 − 3 4𝑤 + 8 = 11

44. −3 3𝑥 + 15 − 10 + 𝑥 = 35 45. 11 4 − 6𝑦 + 5 13𝑦 + 1 = 9

Part7–SolvingEquationswithVariablesonBothSideshttps://www.khanacademy.org/math/in-eighth-grade-math/linear-equations-one-variable/solving-equations-variable-both-sides/v/equations-3

Example1:

Example2:

Solvethefollowingequationsusingtheexamplesaboveasguidance.

46. 7𝑦 = 33 − 4𝑦

47. 2𝑥 + 48 = 10𝑥 48. 5𝑡 − 26 = 18𝑡

49. −30𝑛 = −27𝑛 − 63

50. 4𝑥 + 4 = 2𝑥 + 36 51. 9𝑦 − 1 = 𝑦 − 25

52. 14𝑝 − 8 = 22 + 20𝑝

53. 𝑧 + 81 = 9𝑧 − 7 54. −15𝑣 − 40 = 23 − 8𝑣

Part8–Slopehttps://www.khanacademy.org/math/algebra/two-var-linear-equations/slope/v/slope-of-a-line

Example1–Findtheslopeofagraph:

1. Choose2pointsontheline.We’lluse

AandB.2. TogetfrompointAtopointbewe

havetoriseup4andgototheright3.3. 𝑆𝑙𝑜𝑝𝑒 = ∆!

∆!= !"#$

!"#= !

!

*NOTE:Upandrightyieldpositivevalues,whiledownandleftyieldnegativevalues.

Example2–Findslopefrom2points:

(2,1)and(-1,3)

𝑆𝑙𝑜𝑝𝑒 =𝑅𝑖𝑠𝑒𝑅𝑢𝑛

=∆𝑦∆𝑥

=2−3

= −𝟐𝟑

Example3–Findslopefromatable:

x y10 1-2 -54 -2-8 -8

𝑆𝑙𝑜𝑝𝑒 =

𝑅𝑖𝑠𝑒𝑅𝑢𝑛

=∆𝑦∆𝑥

=−6−12

=𝟏𝟐

Findtheslopeofthefollowinggraphs.Useexample1tohelpyou.

55.

56. 57.

58. 59.

Findtheslopeofthefollowingpoints.Useexample2tohelpyou.https://www.khanacademy.org/math/algebra/two-var-linear-equations/slope/v/slope-of-a-line-2

60. (9,2)and(3,-1)

61. (-4,-8)and(-2,0)

62. (8,3)and(2,5)

63. (-5,8)and(-4,2)

64. (-3,-3)and(0,0)

65. (1,-4)and(6,-2)

66. (0,-1)and(4,-7)

67. (2,5)and(9,1)

68. (-3,1)and(-7,4)

∆𝑦 = +2

∆𝑥 = −3

∆𝑦 = −6∆𝑥 = −12

Part9–GraphingLinearEquationsusingSlopeandY-intercepthttps://www.khanacademy.org/math/algebra-basics/core-algebra-graphing-lines-slope/core-algebra-graphing-slope-intercept/v/graphing-a-line-in-slope-intercept-form

Example1:Graphingequationsiseasywhentheequationisintheformy=mx+bwhere‘m’istheslopeand‘b’isthey-intercept.Theslopeisameasureofhowsteepthelineis,andthey-interceptiswherethelineintersectsthey-axis.Tographtheline𝑦 = − !

!𝑥 + 2,identifytheslopeandy-intercept.Theslopeis− !

!,andthey-interceptis2.

1. Plotapointonthey-axisat2,since2isthey-intercept.(See1)2. Placeyourpencilonthatpointandcountdown3andtotheright4,sincetheslopeis

− !!.(Note:Iftheslopewere!

!,youwouldcountup3andtotheright4.)(See2)

3. Usearulertodrawalineacrossthewholegraphthroughthetwopoints.(See3)

Graphthefollowinglinearequationsonthecoordinateplanesprovided.Usetheexampleabovetoguideyourwork.

69. 𝑦 = !!𝑥 + 1

70. 𝑦 = !!𝑥 − 3

71. 𝑦 = − !!𝑥 + 3

1

2

3