Dynamics of Geometry - HS

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MonroeTownshipHighSchool
MonroeTownship,NewJersey
Dynamics of Geometry
*SUMMERPREPARATIONPACKET*
Geometryisafast-paced,rigorouscoursethatwillprovideyouwiththefundamentaltoolsofgeometric
understandingthatwillsupportyouinallfutureadvancedmathematicscourses.Sinceyouwillbetaking
geometryaftersuccessfulcompletionofAlgebraI,theDynamicsofGeometryPreparationPacketcontains
reviewmaterialofthealgebraicconcepts,skills,andproceduresthatshouldbemasteredBEFOREentering
Geometryinthefall.
Essentially,thispacketprovidesareviewofthemajoralgebratopicsaswellasapreviewofgeometrictopics.
ThesectionsarebasedontheAchieveADPAlgebraIEnd-of-CourseExamContentStandardsandtheCommon
CoreStateStandards(CCSS).
Onlineresourcesareavailableat:
• http://www.khanacademy.org/
• http://tinyurl.com/youtube-mthsGeometry
• http://www.wolframalpha.com/examples/
Math.html
Thispracticeproblempacketistheonlyformalreviewoftheconcepts,procedures,andskillsthatyouwill
havebeforebeginningyourgeometrycourse.Yourteacherwillexpectyoutohavemasteredalltopics
includedhere.
Thiscollectionofproblemswillidentifythoseconceptsthatyouhavemasteredaswellasthoseyouwillneed
topracticeandreview.Youareexpectedtoseekextrahelpimmediatelyonthoseconceptswithwhichyou
havenotdemonstratedproficiency.Beresourceful–usetheonlineresourcesprovidedonthewebpage!
Youareexpectedtoseekextrahelpimmediatelyonthoseconceptswithwhichyouhavenotdemonstrated
proficiency.Beresourceful–usetheonlineresources!
ProblemshereareveryrepresentativeofthetypesofitemsyouwillneedtohavemasteredBEFORE
geometry…sowestronglyencouragethatyouincludeitinyoursummerfestivities!Goodluckandenjoy!J
Page1
**SHOWALLWORK**
Solveeachequationgivenin#1-5.Writeyouranswerintheblankprovided.Leaveanswerasanimproper
fraction.
1. 3x − 4 = 17 2. −5(2x − 8) = 80 ANSWER:_________
ANSWER:_________
ANSWER:_________
3.
1
( 4x − 16) = 84 2
4. 7x − 2 = 3x + 14
ANSWER:_________
5. 6x − 2 + 4x + 14 = 180
ANSWER:_________
Page2
Determinetheareaandperimeterofeachfiguredescribedin#6-7.Donotforgetyourunits.
Area=(length)x(width)
Perimeter=SumoftheSides
6.RECTANGLEwithlength 3.6 cmandwidth 4.2 cm
AREA:_________
PERIMETER:_________
7.SQUAREwithsidesoflength9mm
AREA:_________
PERIMETER:_________
Usingthegiveninformation,determineareaandcircumferencefor#8-9.Leaveyouranswerintermsof.
A = π r 2 C = 2π r 8.Areaandcircumferenceofacirclewithradius9inches. AREA:__________________
CIRCUMFERENCE:_________
9.Areaandcircumferenceofacirclewithdiameter12centimeters.
AREA:___________________
CIRCUMFERENCE:_________
Page3
UsethePythagoreanTheoremtodeterminethemissingsideinquestions10-12.Leaveinradicalform.
a 2 + b 2 = c 2 10.
x
15
x=_____________
20
11.
21
x
13
x=______________
x=______________
12.
5 10
9
x
13.Findtheslopeofthelinecontaining(-2,-8)and(-1,0).
SLOPE:___________________
14.Findtheslopeofthelineperpendiculartothelinecontaining(-3,2)and(4,-1).
SLOPE:___________________
Page4
15.Thecomplementofa 60° angleis________________.
16.Thesupplementofa 100° angleis________________.
17.Findxandthemeasureofthemissingangle.
40°
20°
3x°
x=______________
Angle=__________
18.Statethedifferencebetweenalineandalinesegment.Youmaywritesentencesordrawdiagrams.
Predictthenextnumberinthesequencegivenin#19-20.
19.-5,-2,4,13,___________
20. 48, 16,
16 16
, , ___________ 3 9
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21.Everyday,Michaelgoesforarunthroughthepark.Theparkisshapedlikeasquare.Hefollowsthepath
shownbythepoints.AbouthowfardoesMichaelrun?
-------------200m------------
22.Juliawantstopainttworectangularwallsofherbedroom.Onebedroomwallis15feetlongand8feet
high.Theotherwallis12feetlongand8feethigh.Shewantstoputtwocoatsofpaintonthewalls.She
knows1gallonofpaintwillcoverabout350squarefeetofawall.Willonegallonofpaintbeenough?Showall
ofyourworkandexplainyouranswerbelow.
Page6
23.TriangleABCisshowninthecoordinate-plane.Thetrianglewillberotated180degreesclockwisearound
thepoint(0,0)tocreatetriangleA’B’C’.DrawthenewtriangleA’B’C’onthecoordinateplane.
24.TriangleABCisshowinthexy-plane.Thetrianglewillbereflectedoverthey-axis.Drawthenewtriangle
A’B’C’onthecoordinateplane.
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25.Usingthediagrambelow,describethetransformationthatoccursfromtriangleABCtotriangleA’B’C’by
answeringthequestionsbelow.
a) Whatkindoftransformationoccurred?
b) Howdoyouknow?
c) Writearuleusingarrownotationdepicting
thetransformation.
26.Simplifythefollowingradicals.Leaveyouranswerinsimplestradicalform.
a)
72 b) 40 c) 288 d) 800 Page8
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