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(FinalExamReview–EndofUnit8) 1
FinalExamReview–EndofUnit8Unit8:Circles1. Identifyeachsegmentasatangent,secant,orachord.
A.B.C.D.E.F.
2. Arighttrianglewithsidesthelengthoftheradiusiswithinacircle.Iftheradiusofthecircleis8centimeters,whatistheareaoftheshadedregion?
Unit7:Quadrilaterals3. Whichpartsofarectangleare
alwayscongruent?a. Allsidesb. Oppositesidesc. Consecutivesidesd. Diagonals
4. Whichpartsofarectanglearealwaysparallel?a. Allsidesb. Oppositesidesc. Consecutivesidesd. Diagonals
5. Whichpartsofarectanglearealwaysperpendicular?a. Allsidesb. Oppositesidesc. Consecutivesidesd. Diagonals
Unit6:RightTriangleTrigonometry6. Thefigureshownisasquare.
Whatistheareaofthesquare?
7. Inthediagramshown,a9-footslideisattachedtoaswingset.Theslidemakesa62˚anglewiththeswingset.Whichanswermostcloselyrepresentstheheightoftheslide?
8. Joannaisflyinganairplaneatanaltitudeof4300ft.Sheseesherhouseonthegroundata45˚angleofdepression.WhatisJoanna’shorizontaldistancefromherhouseatthispoint?
Unit5:SimilarTriangles9. Twokidsdecidedtostringaropefromtheroofofa
52yardtallbuildingtoawindowonthesideofa49yardtallbuildingsothattheycouldsendabucketfulloftoysintothewindow.Ontheirfirsttry,thebucketgotstuckonaclotheslineatpointA.Howfardidthebuckettraveldowntherope?
10. A63-meter-longsupportwireforalightpolerunsfromthetopcornerofa28-meter-tallbuildingtoapointontheground,formingastraightline.Thelengthofthewirefromthetopofthebuildingtothetopofthelightpoleis36meters.Howtallisthelightpole?
5 2
9 62
4300 ft
45˚
20
52 49
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(FinalExamReview–EndofUnit8) 2
11. Inthefigureshown,△ABCand△DEFareisoscelestriangleswithavertexangleatB&E,respectively.𝐴𝐶 ≅ 𝐷𝐹and∠𝐴 ≅ ∠𝐶.Whichtheoremcouldbeusedtoprove△ABC ≅△DEF?
12. WhichisNOTavalidconclusionthatyoucandrawfromthispicture?
a. ∠ABD ≅ ∠𝐶𝐷𝐵b. △ABD ≅△ 𝐶𝐷𝐵c. Slopeof𝐴𝐵 =slopeof𝐷𝐶d. 𝐵𝐷 ≅ 𝐷𝐵
Geometry:13. Whatisthenameofthereason
thatstates“IfpointMisonsegmentLNthen𝐿𝑀 +𝑀𝑁 =𝐿𝑁.”a. CongruentSupplement
Theoremb. TriangleSumTheoremc. SegmentAdditionPostulated. DefinitionofaMidpoint
14. WhichofthefollowingstatementsisNOTtrueaboutisoscelestriangles?a. Atleasttwoanglesmustbe
congruent.b. Thealtitudewillalways
bisectthebase.c. Thealtitudewillcreatetwo
congruenttriangles.d. Anisoscelestrianglecannot
have3congruentsides.
15. WhichofthefollowingisNOTtrue?a. Twoplanescanintersectin
exactlyonepoint.b. Twoplanescanintersectin
aninfinitenumberofpoints.c. Alineandaplanecanhave
aninfinitenumberofintersectionpoints.
d. Parallelplaneswillneverintersect.
InversesandOtherFunctions:16. Aregionaltrainapproachesacertaintrainstation
beforereversingdirectioneachday.Thegraphmodelsthetraintravelingataconstantspeed.Whichequationbestrepresentsthegraph?
a. 𝑓 𝑥 = 20𝑥 + 40b. 𝑓 𝑥 = 20𝑥 + 40 c. 𝑓 𝑥 = 20𝑥 d. 𝑓 𝑥 = 40𝑥 + 40
17. Giventhefunction𝑓 𝑥 = 4𝑥 − 28,writetheinversefunction.
Quadratics:18. Whichpolynomialdoesthe
graphrepresent?
a. 𝑦 = (𝑥 − 2)(𝑥 + 6)b. 𝑦 = (𝑥 + 2)(𝑥 − 6)c. 𝑦 = (𝑥 − 2)(𝑥 − 6)d. 𝑦 = (𝑥 + 2)(𝑥 + 6)
19. Whatistherangeofthefunctionrepresentedbythegraph?Writeyouranswerinthefollowingformat:“Allrealnumbers____thanorequalto_____.”
20. Howisthisgraphdifferentfromagraphofthefunction𝑓 𝑥 = 𝑥!(listalltransformations)?
B
CA
E
FD
A B
CD
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(FinalExamReview–EndofUnit8) 3
21. Whataretherootsofthequadraticequation?
𝑦 = 4𝑥! − 5𝑥 − 6a. 𝑥 = 2and𝑥 = −0.75b. 𝑥 = −2and𝑥 = 0.75c. 𝑥 = 2and𝑥 = −3d. 𝑥 = −2and𝑥 = 3
22. Writeafunctioninvertexformthatrepresentsaparabolathatistranslated3unitstotheleftand7unitsupfromthefunction𝑓 𝑥 = 𝑥!?
23. Whatarethesolution(s)tothesystemofequationsshown?
24. AsmallrocketonalunaroutpostaroundJupiterwaslaunchedfroma24-meterplatform.Theheightofthe
rocketismodeledbythefunctionℎ 𝑡 = −2𝑡! + 2𝑡 + 24,where𝑡istimeinsecondsandℎ 𝑡 istheheightoftherocketinmeters.a. Whatwillbethevalueofℎ 𝑡 whentherockethitstheground?b. Findthetimewhentherockethitstheground,clearlyshowinghowyouusedtheequation.
Polynomials:25. Simplifytheexpression.
8𝑥! − 11𝑥 + (5𝑥! − 3𝑥! + 12)
26. Simplifytheexpression.7𝑥 − 10 !
27. Whatistheproductofthepolynomials?𝑥 + 10 and 5𝑥! + 𝑥 − 8
28. UnderwhichoperationsarethesetofnaturalnumbersNOTclosed?a. Additionb. Subtractionc. Multiplicationd. Division
29. Inwhichsetsdoesthenumber−7NOTbelong?a. Rationalnumbersb. Integersc. WholeNumbersd. NaturalNumberse. IrrationalNumbersf. RealNumbersg. ImaginaryNumbers
FinalExamReview–EndofUnit8Answers:
1. a.Tangentb.Secantc.Tangentd.Chorde.Chordf.Secant 2. 64𝜋 − 323. B&D 4. B 5. C 6. 257. 4.2ft 8. 4300ft 9. 12yd 10. 12m11. ASA 12. B 13. C 14. D15. A 16. A 17. 𝑓!! 𝑥 = !
!𝑥 + 7 18. A
19. Allrealnumbersgreaterthanorequalto1. 20. Translatedleft1unitandup3units 21. A22. 𝑓 𝑥 = 𝑥 + 3 ! + 7 23. 1, 1 & (5, 1) 24. a.ℎ 𝑡 = 0b.4sec. 25. 5𝑥! + 5𝑥! − 11𝑥 + 1226. 49𝑥! − 140𝑥 + 100 27. 5𝑥! + 51𝑥! + 2𝑥 − 80 28. B&D 29. C,D,E&G
