Semester 2 Final Review Gordon - … Semester 2 Final Exam Review 2015-16 Burke P12 ... You are...
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Geometry Semester 2 Final Exam Review 2015-16 Burke P12 Chapter 12 Probability: Page 668: Example 1-5. Page 677: Example 3, 4. Page 672: 3, 9, 13; Page 680: 3, 4, 12, 13. 1. Five coins are flipped at the same time. a) What is the total number of outcomes? b) What is the probability of getting any single combination? c) If those same coins are flipped, what is the probability that they will show up as either all heads or all tails? 2. A bag contains 5 red, 3 white, and 2 blue marbles. If the marbles ARE replaced after each pick, find the following probabilities: 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. A bag contains 5 red, 3 white, and 2 blue marbles. If the marbles ARE NOT replaced after each pick, find the following probabilities: 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. You throw a dart at the board below. Your dart is equally likely to hit any point inside the square board. a) What is the area of the square? b) What is the area of the 2 in circle? c) What is the area of the 5 in circle? d) What is the probability that your dart does not land in one of the two circles? Chapter 8 Similarity: Page 418: Example 1, 2, 3. Page 430: Example 3. Page 446: Example 1, 2; Page 423: 3-8, Page 431: 22, Page 450: 3-8, 17-18. 5. If the two triangles below are similar, find the missing side and their scale factor, given :∆~∆ 6. If the two triangles below are similar, solve for x and their scale factor, given :∆~∆ 7. A tree is standing next to a 100 ft. high building. The tree casts a 30 ft. shadow and the building casts a 50 ft. shadow. How tall is the tree? 8. A school flagpole casts a shadow that is 45 feet long. At the same time, a boy who is five feet eight inches’ tall casts a shadow that is 51 inches long. How tall is the flagpole to the nearest foot? 9.
Transcript of Semester 2 Final Review Gordon - … Semester 2 Final Exam Review 2015-16 Burke P12 ... You are...
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
