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PCTIGeometry

SummerPacket

2021

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Thispackethasbeendesignedtohelpyoureviewvariousmathematicaltopicsthatwillbenecessaryfor

yoursuccessinGeometry.INSTRUCTIONS:• Doallproblemswithoutacalculator.• Showallworkthatleadsyoutoeachsolutionontheattachedanswersheet.

• Youmayuseyournotesfrompreviousmathematicscoursestohelpyou.

• Youmustdoallworkwithoutanyhelpfromanotherperson.ALLworkshouldbecompletedandreadytoturninontheFIRSTDAYofschool.GRADING:• TwoweightedscorescombinedwillcountasoneProjectgrade.

o Onthefirstdayofschool,theteacherwillcheckforcompletion/effortofthepacket.§ Thiswillbeweightedas50%.

o Teacherwillthenreviewthepacketwiththestudents.§ Uponcompletionofthereview,thestudentswillbegivenanassessmentbasedonthesummerpacket.

§ Theassessmentwillbeweightedat50%.

DueDate:WednesdaySeptember8,2021ENJOYYOURSUMMER!!WEARELOOKINGFORWARDTOSEEINGYOU

INTHEFALL.

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AREYOUSTUCK????Belowisaquick“how-to”guideNumberSense&OperationsFindingPercentof1.Changethepercenttoadecimal2.MultiplythetotalamountbythedecimalChangingFractionstoDecimals1.Dividethenumeratorbythedenominator2.RoundtothenearesthundredthifneededChangingFractionstoPercent1.Dividethenumeratorbythedenominator2.Roundtothenearesthundredth3.Dropthedecimalpoint4.AddapercentsignSolvingMulti-StepOperations--PEMDAS1.Completeallcomputationinsidetheparenthesis,brackets,orabsolutevalue2.Carryoutallexponents3.Multiplyordivide,fromlefttoright4.Addorsubtract,fromlefttorightDistribution1.Multiplythe#orvariableoutsidetheparenthesisbyeachterminsidetheparenthesis2.Checkthesigns(+/-)MultiplyingExponentsvs.DividingExponents1.Add&Subtractexponents2.Multiply& DivideintegersSolvingwithAbsoluteValue1.Setuptwoequations2.Onewithapositiveanswer3.Onewithanegativeanswer4.SolveeachequationMultiplyingbyaFraction1.Multiplythenumeratorbyallvalues2.DividethisproductbythedenominatorEstimatingthevalueofaRadical(√)1.Forasquareroot,findtheclosestsquarenumber.2.Estimatethevalue(higher/lower)3.Ifit’sacuberoot,findtheclosestcubenumber4.Estimatethisvalue.MulitplyingBinomials

1.UseFOIL--first,outside,inside,lastPatterns,Relations,andAlgebraSolvingEquationsforOneVariable1.Distribute2.CombineLikeTerms3.Getallthevariablesontheleftside(+/-)4.Getallnumbervaluesontherightside(+/-)5.Dividebothsidesbythecoefficient6.Remember,whateveryoudotooneside,youmustdototheotherUsingProportionalRelationships1.DeterminetheParttoWholerelationship2.WritearatiofortheKNOWNparttowhole3.Determinethesecondratio--given/missinginformation4.SetupaproportionwithXrepresentingmissingvalueintheUNKNOWNratioPropertiesofProportions1.If!

"= #

$,then𝑎𝑑 = 𝑏𝑐

2.productofthemeans=productoftheextremesCrossmultiplytosolveformissingvariableRatiosusedinProportionalRelationships1.Part/Whole2.Percent(%)/1003.#ofdegrees/3604.sample/totalpopulation5.Part:PartSolvingSystemsofEquationsw/Substitution1)+/-thexterm,movetotherightside2)÷bythecoefficientofy(÷by#withy)3)Settheexpressionsequaltoeachother&solveforx.4)Substitutex&solvefory.5)Writesolutionasacoordinatepair(x,y).UsingtheEquationofaLine/Slope(m)𝑦 = 𝑚𝑥 + 𝑏 𝑚 = %!&%"

'!&'"

𝑦 − 𝑦( = 𝑚(𝑥 − 𝑥()Graphing:Beginwithb,andmovewithmParallelSlopes:𝑚( = 𝑚)Perpendicularslopes:𝑚( ∙ 𝑚) = −1

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WebsiteResourcesforextrahelp. • http://patrickjmt.com

• https://www.khanacademy.org

• http://cs.pcti.tec.nj.us/math/lessons/index.htm

• http://www.youtube.com/

• http://www.regentsprep.org/Regents/math/geometry• http://www.mathsisfun.com

• http://www.mathwarehouse.com

• http://mathbits.com

• http://www.themathpage.com

• http://mathplanet.com

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1. Whatisthegreatestcommonfactorof6d)and18d?a. 6d) b.6d

𝑐. 3d) d.3d

2. Findthevalueof√49.a. 4 b.7

c.24 d.988

3. Round17.081tothenearesttenth.a. 17 b.17.1

c.17.08 d.17.8

4. WhatistheratioofABtoBC,insimplestform?

a. 1:1 b.2:3

c.3:2 d.4:3

5. Whichofthefollowinghasaunitrateof17milesperhour?a. 60milesin2hours

b. 85milesin5hours

c. 90milesin10hours

d. 120milesin15hours

6. Identifythepointgraphedonthenumberline.

a. -1.5

b. -2.2

c. -2.5

d. -3.5

7. Whichofthefollowingrepresentsaray?a.

b.

c.

d.

8. Classifytheangle.

a. Straight b.obtuse

c.Right d.acute

9. WhatistheanglemeasureofSTU?

a. 20° b.50°

c.70° d.130°

10. Selectthebestdescriptionforangles1and2.

a. verticalangles

b. linearpair

c. adjacentangles

d. supplementary

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11. Twoanglesofatriangleare32°and110°.Whatisthemeasureofthethirdangle?a. 218° b.142°

𝑐.180° d.38°

12. Giventherighttrianglebelow,whatisx?

a. 9.2 b.10.8

c.84 d.116

13. FindtheperimeterofrhombusABCD.

a. 32.4 b.262.44

c.64.8 d.268.96

14. Whatistheareaofatrianglewithaheightof20metersandabaseof16meters?a. 160m2 b.320m2

b. 640m2 d.656m2

15. SolveI=Prtforr.a.

b. Irt

c.

16. Findthecircumference.

a. 81𝜋 b.18𝜋

𝑐.36𝜋 d.9𝜋

17. Writetheequationorinequality: The difference of a number c and 17 is more than 33

a. c–17=33 b.17–c=33

c.c–17>33 d.c-17<33

18. Determinethevolumeofacubewithsidelength12ft.

a. 36ft3

b. 144ft3

c. 864ft3

d. 1728ft3

d.Ipt

19. Whatis224 ÷ 14? a. 16 b.14

I Pt

P It

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c.12 d.8

20. Findthedifference.18 − 6.8a. 12.2 b.11.2

c.2.2 d.1.2

21. Findtheproduct.0.6 ∙ 1.5a. 0.9 b.9.0

c.9.9 d.90

22. Divide12.24 ÷ 2a. 2.05 b.6.12

c.8.24 d.24.40

23. Findtheproductinsimplestformof*+∙ ),.

a. *- b. .

)(

𝑐. /+ d.(

)

24. Subtract+0− (

,.

a. /0 b.1

𝑐. ), d.1 (

0

25. Subtract(−15 − 3)a. −18

b. −12

c. 12

d. 18

26. Multiply15(−4)

a. −60 b.−11

c.11 d.60

27. Simplify> */(11

a. > /(1 b.)

-

𝑐.>/- d./

-

28. Evaluate|12 − 14 − 6|

a. −32 b.8

𝑐. − 8 d.32

29. Simplifytheexpression2(8 − 3) − 6a. 7 b.4

c.1 d.−2

30. Whichexpressionisequivalenttotheexpression6(𝑠 − 6)

a. 6𝑠 − 6 b.𝑠 − 6

c. s–36 d.6𝑠 − 36

31. Simplify18 − 𝑐 + 9𝑐 + 6a. 24 + 8𝑐) b.32𝑐

𝑐.24 + 8𝑐 d.−18𝑐 + 15𝑐

32. Whichequationcorrespondstothestatement“thelength_oftherectangleisfourtimesthewidthw”.a. 𝑤 = 4 + 𝑙 b.𝑤 = 4𝑙

c.𝑙 = 4𝑤 d.𝑙 = 4 + 𝑤

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33. Divide02#

)2!

a. 02#

)2 b.)2

#

02!

𝑐. )02 d.02

)

34. Simplify5𝑔(𝑔 − 9ℎ)a. 6𝑔) − 14𝑔ℎ b.5𝑔) − 45𝑔ℎ

𝑐. 5𝑔) + 5𝑔 − 9ℎ d.6𝑔) − 9ℎ

35. Simplify9𝑥 − 4𝑦 + 5𝑥 − 2𝑦a. 8𝑥𝑦 b.14𝑥) − 2𝑦)

𝑐.14𝑥 − 21 d.14𝑥 − 6𝑦

36. Whatistheproductof(𝑦 + 2)(𝑦 − 8)a. 𝑦) + 6𝑦 − 16 b.𝑦) − 6𝑦 − 16

𝑐. 𝑦) − 6𝑦 + 16 d.𝑦) + 6𝑦 + 16

37. Whatistheproductof(2𝑥 − 4)(2𝑥 − 4)?a. 4𝑥) − 16

b. 4𝑥) + 16𝑥 − 16

c. 4𝑥) − 16𝑥 + 16

d. 4𝑥) + 16

38. Factor5𝑥, − 15𝑥)a. 5𝑥) b.𝑥)(5𝑥 − 15)

𝑐. 5𝑥)(𝑥 − 3) d.3𝑥)(𝑥 − 5)

39. Factorthepolynomial,𝑥) + 5𝑥 + 6completely.

a. (𝑥 + 6)(𝑥 + 1)

b. (𝑥 + 3)(𝑥 + 2)

c. (𝑥 − 3)(𝑥 − 2)

d. (𝑥 − 6)(𝑥 + 1)

40. Solvetheequation14𝑐 − 6 = 22

a. 𝑐 = +. b.𝑐 = 2

𝑐.𝑐 = 28 d.𝑐 = 308

41. Whatvalueofxmakesthisequation2𝑥 +18 = 5𝑥true?

a. 𝑥 = −6 b.𝑥 = 4

𝑐.𝑥 = 2.6 d.𝑥 = 6

42. Solve𝐴 = ()𝑏ℎforh.

a. ℎ = 3)" b.ℎ = 2𝐴𝑏

𝑐.ℎ = )"3 d.ℎ = )3

"

43. Evaluatetheexpression18÷6+4•3

a. 15 b.20

𝑐.21 d.16

44. Whichpairoflinearequationsrepresentparallellines?

a. F 𝑦 = 2𝑥 + 3𝑦 = −2𝑥 + 5

b. G𝑦 = −6𝑥 − 5𝑦 = (

*𝑥 − 5

c. G𝑦 = −4𝑥 − 3𝑦 = − (

/𝑥 + 7

d. F𝑦 = 8𝑥 + 2𝑦 = 8𝑥 − 5

45. Solvetheproportion-.= '

/1

a. 𝑥 = 5 b.𝑥 = 25

𝑐.𝑥 = 10 d.𝑥 = 37

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46. WhichorderedpaircorrespondstopointS?

a. (−3,3) b.(−2,1)

𝑐.(3,2) d.(−3,−2)

47. Solvefory.𝑦) − 16 = 9

a. 𝑦 = ±25 b.𝑦 = ±5

𝑐.𝑦 = ±4 d.𝑦 = ±3

48. Whatvaluecompletesthesquarefortheexpression𝑥) − 6𝑥 +____?

a. 36 b.12

c.9 d.3

49. Solve𝑥$ − 4𝑥 − 5 = 0byfactoring.

a. -1,-5 b.-1,5c.1,-5 d.1,5

50. Findthevalueofx.

a. 10 b.40c.14 d.42

51. Directions:Writetheletterofthetermnexttoitsdefinition.

Definition Term

____ Atrianglewiththreeanglesthateachmeasurelessthan90°.

a. Triangle

b. Acutetriangle

c. Obtusetriangle

d. Righttriangle

e. Scalenetriangle

f. Isoscelestriangle

g. Equilateraltriangle

____ Atrianglewiththreecongruentsidesandthreecongruentangles.

____ Atrianglewithoneangle90°

____ Atrianglewithnocongruentsides.

____ Atrianglewithatleasttwocongruentsides.

____ Atrianglewithoneanglegreaterthan90°

____ Apolygonwiththreesides.

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ANSWERSHEET

1. __________

2. __________

3. __________

4. __________

5. __________

6. __________

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7. __________

8. __________

9. __________

10. __________

11. __________

12. __________

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13. __________

14. __________

15. __________

16. __________

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17. __________

18. __________

19. __________

20. __________

21. __________

22. __________

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23. __________

24. __________

25. __________

26. __________

27. __________

28. __________

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29. __________

30. __________

31. __________

32. __________

33. __________

34. __________

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35. __________

36. __________

37. __________

38. __________

39. __________

40. __________

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41. __________

42. __________

43. __________

44. __________

45. __________

46. __________

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47. __________

48. __________

49. 50. __________

51. ____Atrianglewiththreeanglesthateachmeasurelessthan90°.____Atrianglewiththreecongruentsidesandthreecongruentangles.____Atrianglewithoneangle90°____Atrianglewithnocongruentsides.____Atrianglewithatleasttwocongruentsides.____Atrianglewithoneanglegreaterthan90°

____ Apolygonwiththreesides.

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