semester 2 final review gordon

GeometrySemester2FinalExamReview2015-16BurkeP12Chapter12Probability:Page668:Example1-5.Page677:Example3,4.Page672:3,9,13;Page680:3,4,12,13.

1. Fivecoinsareflippedatthesametime.a) Whatisthetotalnumberofoutcomes?b) Whatistheprobabilityofgettingany

singlecombination?c) Ifthosesamecoinsareflipped,whatis

theprobabilitythattheywillshowupaseitherallheadsoralltails?

2. Abagcontains5red,3white,and2blue

marbles.IfthemarblesAREreplacedaftereachpick,findthefollowingprobabilities:

a. P(red,red,blue)b. P(red,red,red)c. P(red,white,blue)d. P(white,white,blue)e. P(blue,blue,blue)

3. Abagcontains5red,3white,and2blue

marbles.IfthemarblesARENOTreplacedaftereachpick,findthefollowingprobabilities:

a. P(red,red,blue)b. P(red,red,red)c. P(blue,blue,blue)d. P(red,white,blue)e. P(white,white,blue)

4. Youthrowadartattheboardbelow.Your

dartisequallylikelytohitanypointinsidethesquareboard.a) Whatistheareaofthesquare?b) Whatistheareaofthe2incircle?c) Whatistheareaofthe5incircle?d) Whatistheprobabilitythatyourdart

doesnotlandinoneofthetwocircles?

Chapter8Similarity:Page418:Example1,2,3.Page430:Example3.Page446:Example1,2;Page423:3-8,Page431:22,Page450:3-8,17-18.

5. Ifthetwotrianglesbelowaresimilar,findthemissingsideandtheirscalefactor,given:∆𝐾𝐿𝐽~∆𝑄𝑅𝑃

6. Ifthetwotrianglesbelowaresimilar,solveforxandtheirscalefactor,given:∆𝐴𝐵𝐶~∆𝐹𝐸𝐷

7. Atreeisstandingnexttoa100ft.highbuilding.Thetreecastsa30ft.shadowandthebuildingcastsa50ft.shadow.Howtallisthetree?

8. Aschoolflagpolecastsashadowthatis45feetlong.Atthesametime,aboywhoisfivefeeteightinches’tallcastsashadowthatis51incheslong.Howtallistheflagpoletothenearestfoot?

9.

Lesson6.5Inequalitiesinonetriangle&Lesson9.1Pythagoreantheorem:Page337:Example3-5.Page465:Example2-5.Page340:11-24;Page468:1-14,21-26.

10.

11.

12. Giventhepolygons,identifyasnotatriangle,acutetriangle,obtusetriangleorrighttriangle.a) Sidelengthsof:15,10,and8.

b) Sidelengthsof:14,10and24.

c) d)

13. Afencewithdimensionsasshownisbeingconstructedintheshapeofarighttriangle,howlongmusttheothersidebe?

14.

Chapter9Righttriangles&Trigonometry:Page488:Examples1-2,4.Page494:Examples1,6.Page502:Examples1,2,3.Page491:3-12,25;Page498:3-8,17-22;Page505:3-6,13-18,27.

15. Inthetrianglebelow,findSinC,CosCandtanCasaratio.

a.b.

16. Usethetriangletoanswerthequestions,

a.Whichtrigonometricratiosareequivalentto3/5?b.Whichtrigonometricratiosareequivalentto4/5?c.Whichtrigonometricratiosareequivalentto4/3?

17. Thetrianglesbelowaresimilar.TriangleRTUhassidelengthsRT=39,RU=36andTU=15respectively.Selecttheangleswhosecosineequals12/13.

18. Inthetrianglebelow,solveforx.

19. IfanacuteangleofarighttrianglehasaSineratioof40/41andaCosineratioof9/41,whatwouldbeitsTangentRatio?

GeometrySemester2FinalExamReview2015-16BurkeP1220. Ifanacuteangleofarighttrianglehasa

Sineratioof9/41andaCosineratioof40/41,whatwouldbeitsTangentRatio?

21. Atreestands100ft.tall.Itcastsashadowof50ft.upontheground.Whatistheangleofelevationfromthetipoftheshadowtothetopofthetree?

22. Youaremeasuringtheheightofatree.Youranglemeasuringdeviceis3.5feettall.Youstand40feetfromthebaseofthetree.Theangleofelevationtothetopofthetreeis65o.Findtheheightofthetreetothenearestfoot.

23. Inthefollowingproblems,findthemissingsidelength.

a.

b.

c.

d.

Chapter7Quadrilaterals:Page367:Example1,2.Page389:Example1,2.Page372:3-6;Page394:29-34,65-70;Page404:31-34

24. Theimagebelowisaparallelogram,solveforx,TSandRU.

25. Theimagebelowisaparallelogram,solveforxandfindthemeasureofallangles.

26. Theimagebelowisaparallelogram,solve

forxandfindthemeasureofallangles.

27. Theimagebelowisanisoscelestrapezoid,findthemeasureoftheindicatedangleandallotherangles.

28. Writeifthestatementsbelowaresometimes,alwaysornevertrue.

a. Allrectanglesaresquares.b. Allquadrilateralsare

parallelograms.c. Allparallelogramsare

rectangles.d. Allparallelogramsare

quadrilaterals.e. Thediagonalsofanisosceles

trapezoidbisecteachother.f. Thediagonalsorarhombusare

perpendicular.g. Thediagonalsofakiteare

congruent.h. Thediagonalsofarectangleare

congruent.i. Thediagonalsofaparallelogram

areperpendicular.

Chapter10&11Circles:Page538:Example1,2,3.Page594:Example1,2,5.Page602:Example1,3.Page542:3-14;Page598:3-10;Page606:3-10,15-18.

29. Findthecircumferenceofacircleintermsof𝜋andtothenearesttenthwithadiameterof36cm.

30. Findtheareaofacircleintermsof𝜋andtothenearesttenthwithadiameterof36cm.

31. Findtheareaofacircleintermsof𝜋,withacircumferenceof36𝜋.

32. Inthefollowingimage,findthelengthofthearcandtheareaofthesector.

33. Inthefollowingimage,findthelengthofthearcandtheareaofthesector.

34. Inthefollowingimage,findthelengthofthearcandtheareaofthesector.

35.

Chapter11AreaandVolume:Page610:Example1.Page626:Example1,2.Page636:Example1.Page642:Example1,2.Page616:3-6;Page631:3-10;Page639:5,6;Page645:3-10

36. Findtheareasofthefollowingtrianglesa. b.

37. Calculatetheareaoftheshadedregionsbelow.

a. b.

38. Usethefigurebelow,

a. Calculatetheheightofthetriangle.b. Calculatetheareaofthetriangle.

39. Usethefigurebelow,

a. Calculatetheheightoftheparallelogram

b. Calculatetheareaoftheparallelogram.

GeometrySemester2FinalExamReview2015-16BurkeP1240. Usethefigurebelow,

a. Calculatetheheightoftheparallelogram.

b. Calculatetheareaoftheparallelogram.

41. Inthefollowingproblems,findtheareaof

theshadedregion.

a. Findtheareaofthesquare.b. Findtheareaofthecirclec. Findtheareaoftheshadedregion.d. Whatistheprobabilitythatadart

landsontheshadedregion?

42. Inthefollowingproblems,findthesurfaceareaandvolumeofthesolid.

a.

b.

c.

d.

e.

f.

g.

h.

Tipstostudyforfinal:a. Showallyourworkonaseparatepaper.b. NoNotesallowed.c. Equationsheetwillbeprovided.d. Makeastudygroupandpracticetheproblemssuggested.Checkyouranswerswiththebackofthebook.

e. Yourelectronicdeviceswillnotbeallowed.

f. Getagoodnightsleepthenightbeforeandeatahealthybreakfast.

g. Ifcaughtcheatingthedistrictpolicywillapply–receiveazeroscoreandparentcontactwillbemade.

GeometryFinalExamEquationSheet

Probability:• TheoreticalProbability:!(#) = &'()*+-../0-+/)1*-'23-(*4

5-2/16'()*+-.-'23-(*4

• ExperimentalProbability:!(#) = &'()*+-.4'33*44*4

&'()*+-.2+7/14

• IndependentEvents:! #89:; = !(#) ∙ !(;)

• DependentEvents:! #89:; = !(#) ∙ !(;8=>?@#)

SimilarPolygons:

• If∆#;B ∼ ∆DEF,o CorrespondingAnglesarecongruent∠# ≅ ∠D, ∠; ≅ ∠E, ∠B ≅ ∠Fo CorrespondingsidelengthsareproportionalJK

LM= KN

MO= NJ

OL= P,wherekisthescalefactor.

TriangleInequality:Foranytriangle∆#;B,#; + ;B > #B,#B + ;B > #;,and#; + #B > ;BPythagoreanTheorem:

• Foranyrighttriangle,8S + TS = US,wherecisthehypotenuseofthetriangle• If8S + TS = US,then∆#;Btriangleisarighttriangle.• If8S + TS > US,then∆#;Bisacute.• If8S + TS < US,then∆#;Bisobtuse.

TrigonometricRatios(SohCahToa):forrighttriangles

Circles:W = XYY = W

X

AreaFormulas:Circle Parallelogram/

RectangleTrapezoid

Rhombus/Kite

Triangle

RegularPolygon(i.e.Hexagon)

2A rπ= A bh= ( )1 212

A h b b= + 1 212

A d d= 12

A bh= 12

A aP=

SurfaceAreaandVolume:

Prism Cylinder Pyramid Cone Sphere2SA PH B= +

V BH= 2

2

2 2SA rH r

V r H

π π

π

= +

= 2

PlSA B= +

3BHV =

2SA rl rπ π= + 2

3r HV π

=

24SA rπ=

343

V rπ=

P=PerimeterofbaseB=areaofbaseH=heightofsolid

Z[\] =^__^`abc

de_^bcfg`c ] = Z[\hi(

^__^`abcde_^bcfg`c

)

jkZ] =lWmlncfb

de_^bcfg`c ] = coshr(

8:s8U?9>ℎuvw>?9xy?

)

z{\] =^__^`abclWmlncfb

] = tanhr(wvvwy�>?8:s8U?9>

)θ

adjacent

opposite

CB

AF

E

D