geometry pcti summer packet 2021
TRANSCRIPT
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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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47. __________
48. __________
49. 50. __________
51. ____Atrianglewiththreeanglesthateachmeasurelessthan90°.____Atrianglewiththreecongruentsidesandthreecongruentangles.____Atrianglewithoneangle90°____Atrianglewithnocongruentsides.____Atrianglewithatleasttwocongruentsides.____Atrianglewithoneanglegreaterthan90°
____ Apolygonwiththreesides.