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Geometry Summer Packet For Incoming HHS9
Students:
TheGeometryTeamfromHHS9hasdeterminedthereare6areasof
AlgebraIand8thGradeMathSkillsthatarevitalforastudenttobe
successfulinHighSchoolGeometry.Toensurethateverystudentis
fullypreparedtoentertherigorofahighschoolmathclass,weare
assigningeveryMiddleSchoolAlgebraIstudentthetaskof
completingthispacketoverthesummer.
*Students:agradewillbetakenonthecompletionofthispacket
duringyourfirstweekofGeometryatHHS9.Youmustshowall
workwrittenneatlyforeveryproblem.Youmaydotheworkon
anotherpaper,butitmuchbeattachedwhenturninginthe
assignment.AllGeometrystudentswillbegivenaMajorGrade
TestoverthecontentsofthisPacketonFridayyourfirstweekin
Geometry.Pleasemakeitapersonalgoaltogetofftoagreatstartin
thisclassbyworkingthroughthepacketandusingthevideosfor
review.
Welookforwardtohavingyouinourclassesnextyear!!
Sincerely,
TheHHS9GeometryTeamMrs.Barger-CoachEssary-Ms.Keys
VideostoHelpPrepareforHSGeometryTopic1:SolvingEquations1. Solveequationswithvariablesonbothsides
https://www.khanacademy.org/math/in-eighth-grade-math/linear-equations-one-variable/solving-equations-variable-both-sides/v/multi-step-equations-1
2. Solveequationswithfractions https://www.youtube.com/watch?v=10TJfOy3H-w3. Solvemulti-stepequations
http://mathvids.com/lesson/mathhelp/84-solving-multi-step-equations
Topic2:FactoringPolynomialsTherearemanydifferentmethodsoffactoring.StudentswillcometoHHS9from3different
MiddleSchools.Ihavelistedseveralmethodsbelowtohelpyoureviewfactoring.Ihopethat
atleastonemethodlooksfamiliartoyou.
1. FactorusingtheACMethodhttps://youtu.be/AYkaCZUT4O4
2. FactorusingtheBoxMethodhttps://youtu.be/YFf7oDJp1pQ
3. FactorusingtheXMethodhttps://youtu.be/aSMSIZZ0uR4
4. FactoringSpecialProductshttps://youtu.be/_J7vn-_ekPM
Topic3:SolvingQuadratics1. SolvebyFactoring
https://www.sophia.org/tutorials/solving-quadratics-by-factoring-4https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials-topic/solving-quadratics-factoring/v/example-1-solving-a-quadratic-equation-by-factoring
2. SolveusingtheQuadraticFormula
https://www.sophia.org/tutorials/the-quadratic-formula--11https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-using-the-quadratic-formula/v/using-the-quadratic-formula
Topic4:SolvingSystemsofEquations1. SolveSOEbySubstitution
http://www.teachertube.com/video/solving-systems-by-substitution-242476
2. SolveSOEbyElimination
http://www.teachertube.com/video/solving-systems-of-equations-by-elimination-277735
https://www.sophia.org/tutorials/solving-systems-of-equations-by-elimination--2
Topic5:Simplifying&MultiplyingRadicals
1. SimplifyingRadicals
https://www.educreations.com/lesson/view/simplifying-radicals-using-factor-
trees/2603284/
2. MultiplyingRadicals
http://www.virtualnerd.com/algebra-1/radical-expressions-
equations/simplify/multiply-divide/multiplication-example
Topic6:FindingArea,SurfaceAreaandVolumeshttp://www.virtualnerd.com/geometry/surface-area-volume-solid/pyramids-codes-area/regular-pyramid-lateral-surface-areas
Topic1:SolvingEquationsSolvethefollowingequationsthathavevariablesonbothsides:
1. 6r+7=13+7r
3. −7x−3x+2=−8x−8
5. −14+6b+7−2b=1+5b
7. n−3n=14−4n
2. 5+2x=2x+6
4. −8n+4(1+5n)=−6n−14
6. 4n–40=7(−2n+2)
8. −31−4x=−5−5(1+5x)
Solvethefollowingequationswithfractions:
1. 32
43 =t
3. t53
32 −=
5. 21
43 =x
7. 43
65 =− x
9. 21
532 =−y
2. 31
52 −=−y
4. 421
41 =+ t
6. xxx213
41 +−=+
8. 232
31 −=+ mm
10. 141
32 −=+ mm
Solvethefollowingmulti-stepequations:
1. 6(3m+5)=66
3. 3(4y–8)=12
5. –5(x–3)=–25
7. 42=3(2–3h)
9. –10=5(2w–4)
2. 3p–4=31
4. x–2(x+10)=12
6. –15=5(3q–10)–5q
8. –3=–3(2t–1)
10. 11.3–7.2f=–3.82
Topic2:FactoringPolynomialsFactorthepolynomialsbelowcompletely:
1. x2+5x+6 2.x2–2x–3
3. x2–5x 4.x2–4
5. 2x²–18x–72 6.x²–12x–28
7. 4x²–20x+25 8.24x2–6
9. 2x²–x–3 10.8x²–10x–3
8. 2x²–11x+21 12.6x2+26x+24
Topic3:SolvingQuadraticsSolvethefollowingquadraticsbyfactoring:1. x2–11x+19=-5
2. n2+7n+15=5
3. n2+3n–12=6
4. 9x2–24x+16=0
5. 7r2–14r=-7
6. 2x2–3x–2=0
SolvethefollowingquadraticequationsusingtheQuadraticFormula:
1. 6x2+11x–35=0
2. f2+9f+4=0
3. m2–3m–1=0
4. 3x2+8x+2=0
5. 4t2–9t+1=0
6. 3w2+8w+3=0
Topic4:SolvingSystemsofEquations
SolvethefollowingSystemsofEquationsUsingSubstitution:
1. 2x–9y=14x–7=-6y
2. -5x+2y=9y–7x=0
3. 3x+4y=-23x–3y=1
4. x+3y=254x+5y=9
5. -5x+y=-2-3x+6y=-12
6. -7x–2y=-13x–2y=11
SolvethefollowingSystemsofEquationsbyElimination:
1. -5x+8y=0-7x–8y=-96
2. -7y–4x=17y–2x=53
3. x–2y=14x+3y=9
4. 8y–9x=-35y–8x=10
5. -5y+6x=403y–8x=-46
6. -9y+4x–11=0-3y+10x+31=0
Topic5:Simplifying&MultiplyingRadicalsSimplifythefollowingradicals:
1. 60 2.− 128
3. 5 320 4.2 45
5. 20 504 2 6.
217 2
Multiplyandthensimplifythefollowingradicals:
1. 5 ⋅ 45
3. 6 ⋅ 30
5. 6 ⋅ 2
2. ( 5 )2
4. 4( 10)2
6. 25 ⋅ 25
Topic6:FindingArea,SurfaceAreaandVolumesAREA
Triangle A = 12bh
RectangleorParallelogram A = bh
Trapezoid A = 12b1 + b2( )h
SURFACEAREA Lateral TotalPrism S = Ph S = Ph + 2B
Pyramid S = 12Pl S = 1
2Pl + B
Cylinder S = 2πrh S = 2πrh + 2πr2 VOLUMEPrismorCylinder V = Bh
PyramidorCone V = 13Bh
Inthissection,besuretowriteeachformula,showthevaluesyousubstitutein,and
thenwriteyouranswerwithunitsofmeasure.]
1. Findtheareaofthetriangle.
2. Findtheareaofthetriangle.
3. Theperimeterofarectangleis20centimeters.Thelengthis6centimeters.Whatistheareaoftherectangle?Besuretodrawandlabeladiagram.
4. Findtheareaoftheparallelogram.
5. Findtheheightoftheparallelogram.
6. Findtheareaofthetrapezoid.
7. Findtheareaofthetrapezoid.
8. Findthevolumeofthepyramid.Thebaseisrectangular.
9. Acylinderhasaradiusof13cmandaheightof22cm.Findthesurfaceareaandvolume.
10. Find the surface area and volume of the triangular prism below.
22cm
13cm