Honors Geometry - HS

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MonroeTownshipHighSchool
MonroeTownship,NewJersey
Honors Geometry
*SUMMERPREPARATIONPACKET2018*
HonorsGeometryisafast-paced,rigorouscoursethatwillprovideyouwiththefundamentaltoolsof
geometricunderstandingthatwillsupportyouinallfutureadvancedmathematicscourses.
SinceyouwillbetakingHonorsGeometryaftersuccessfulcompletionofAlgebraI,theHonorsGeometry
PreparationPacketcontainsreviewmaterialofthealgebraicconcepts,skills,andproceduresthatshouldbe
masteredBEFOREenteringHonorsGeometryinthefall.Thispracticeproblempacketistheonlyformal
reviewoftheconcepts,procedures,andskillsthatyouwillhavebeforebeginningyourHonorsGeometry
course.Yourteacherwillexpectyoutohavemasteredalltopicsincludedhere.
Thiscollectionofproblemswillidentifythoseconceptsthatyouhavemasteredaswellasthoseyouwillneed
topracticeandreview.Youareexpectedtoseekextrahelpimmediatelyonthoseconceptswithwhichyou
havenotdemonstratedproficiency.
Page1
*** ALL WORK MUST BE SHOWN THROUGHOUT THE PACKET ***
OPERATIONSONNUMBERSANDEXPRESSIONS
Simplifyeachexpression.Leaveanswersinsimplifiedradicalform.
1.
325 ANSWER:______________
3 + 12 + 20 + 80 ANSWER:______________
2.
3. 2 3(4 + 3)
ANSWER:______________
4.
2
32 ANSWER:______________
5. (3 2) + (2 5)
2
2
ANSWER:______________
Simplifyeachexpression.Allanswersshouldcontainpositiveexponents.
6.
x3 x 6 ANSWER:______________
7.
(-5 x 2 y -3 )-2
ANSWER:______________
8.
6 x5 y 2 z 3
4 x8 yz 3 ANSWER:______________
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9. Findthecircumferenceofacirclewith A = 36 cm 2 .
Roundtothenearesttenthsifnecessary.
CIRCUMFERENCE:______________
10.
11.
UsethePythagoreanTheoremtodeterminethelengthofthe
missingsideoftherighttriangle.
9
5 10
x=______________
x
Findtheperimeterandareaofthegivenrectangle.
Roundtothenearesttenthsifnecessary.
10"m
PERIMETER:______________
AREA:__________________
8"m
12.
13.
14.
15.
GraphQuadrilateral FGHJ thathasvertices
F (−4,−1) , G (−2,−5) , H (4,−2) ,and J (2,2) .
Findtheslopeforeachofthefollowingsides: FJ, JH , GH .
Identifywhichsides,ifany,areparallel,perpendicular,
orneither.
Findthelengths(distance)ofthefollowingsides: FJ, JH .
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LINEARRELATIONSHIPS
1
16.Solvetheequation: (27 x + 18) = 12 + 6( x - 4)
3
x=______________
ANSWER:______________
1
17.Theareaofatriangleis A = bh .Solvetheareaformulaforb.
2
18.Graphusingthex-andy-interceptsfortheequation 3x - 4 y = 9 X-Intercept:______________
Y-Intercept:______________
19.Writeanequationfortheperimeteroftheregularhexagonattheright.
Doesyourequationmodel“directvariation”?
x PERIMETEREQUATION:___________________
x DIRECTVARIATION?(YesorNo)
x x
x
x
Page4
For#20-21,usethegiveninformationtowriteanequationinpoint-slopeform.Then,rewritetheequation
intoslope-interceptformandthenstandardform.
2
20.Writetheequationofthelinethatpassesthrough(3,-9)andisparallelto y = − x + 2 3
Point-Slopeform:___________________________
Slope-Interceptform:________________________
Standardform:_____________________________
21.Writetheequationofthelinethatpassesthrough(-4,7)andisperpendiculartothelineformedbythe
points (3,−6) and (11,−2) 22.Solvetheinequality: 2 x - 5 £ 10
23.Solve: 5 < 4 x - 11 < 13 Point-Slopeform:___________________________
Slope-Interceptform:________________________
Standardform:_____________________________
ANSWER:_____________________
ANSWER:_____________________
Page5
24.Solvethesystembysubstitution.Checkyoursolution!
ANSWER:______________
8 x + 4 y = -4
y = 2x + 3
25.Solvethesystembyelimination.Checkyoursolution! ANSWER:______________
2y = 7 − 5x
4x − 16 = y
26.Thetotalcostof10gallonsofregulargasolineand15gallonsofpremiumgasolineis$32.75.Premium
gasolinecosts$0.20morepergallonthanregular.Whatisthecostpergallonofeachtypeofgasoline?
Besuretodefineyourvariables!
ANSWER:______________________
27.WhatistheAREAoftheregiondescribedbythesystem
x≤3
oflinearinequalities: y ≤ 1
?
x+ y≥0
Page6
NON-LINEARRELATIONSHIPS
28.Solvetheproportion:
2 3
x
=
x
6 3
29.WriteatrinomialtorepresenttheAREAofthetrapezoidrepresented.
2x+1
1
Recallthattheareaofatrapezoidis A = h(b1 + b2 ) .
2
x+3
2x+4
Multiply.
30. (3x - 4)2 31. ( x 2 + 6 x - 8)( x - 6) Factoreachexpression.
32. x 2 + 10x − 24 33. −12x 2 − 36x − 27 34. 64x 2 − 121 Solveeachequation.
35. x 2 + 42 - 6 x = 7 x 36. 6 x 2 - 12 x = 0 37. 6x 3 − 4x 2 − 72x = 2x 2 Page7
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