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(FinalExamReview–EndofUnit9) 1

FinalExamReview–EndofUnit9Unit9:Volume1. Thevolumeofaconeis152cubicmetersandtheheightoftheconeis6centimeters.Whatistheradiusofthe

conetothenearestwholenumber?

Unit8:Circles2. WhichofthefollowingstatementsareNOTtrue?

a. Atangentwillalwaysintersectacircleinexactlyonepoint.

b. Adiameterisatypeofchord.c. Achordwillalwaysintersectacircleinexactly

twopoints.d. Aradiusisatypeoftangent.

3. Arighttrianglewithsidesthelengthoftheradiusiswithinacircle.Iftheradiusofthecircleis4centimeters,whatistheareaoftheshadedregion?

Unit7:Quadrilaterals4. Whichofthefollowingstatementsaretrue?

a. Theoppositesidesofarectanglewillalwaysbebothparallelandcongruent.b. Aparallelogramhasexactlyonepairofparallelsides.c. Atrapezoidwillalwayshavetwopairsofoppositesidesthatareparallel.d. Allrhombiaresquares.

Unit6:RightTriangleTrigonometry5. Thefigureshownisasquare.

Whatistheareaofthesquare?

6. Inthediagramshown,a9-footslideisattachedtoaswingset.Theslidemakesa70˚anglewiththeswingset.Whichanswermostcloselyrepresentstheheightoftheslide?

7. Reginaisflyinganairplaneatanaltitudeof1700ft.Sheseesherhouseonthegroundata45˚angleofdepression.WhatisJoanna’shorizontaldistancefromherhouseatthispoint?

Unit5:SimilarTriangles8. Inthefigureshown,△ABCand△NMLareisosceles

triangleswithavertexangleatB&M,respectively.𝐴𝐵 ≅ 𝑁𝑀.Whichtheoremcouldbeusedtoprove△ABC ≅△NML?

9. WhichisNOTavalidconclusionthatyoucandrawfromthispicture?

a. ∠BAC ≅ ∠𝐷𝐶𝐸b. △ABC ~ △ 𝐶𝐷𝐸c. Slopeof𝐵𝐶 =slopeof𝐷𝐶d. ∠𝐵𝐶𝐴 ≅ ∠𝐷𝐸𝐶

9 2

9 70

1700 ft

45˚

A

B C N

ML

B

C

D

A E

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(FinalExamReview–EndofUnit9) 2

10. Twokidsdecidedtostringaropefromtheroofofa51yardtallbuildingtoawindowonthesideofa43yardtallbuildingsothattheycouldsendabucketfulloftoysintothewindow.Ontheirfirsttry,thebucketgotstuckonaclotheslineatpointA.Howfardidthebuckettraveldowntherope?

11. A75-meter-longsupportwirefora14-meter-talllightpolerunsfromthetopcornerofabuildingtoapointontheground,formingastraightline.Thelengthofthewirefromthetopofthebuildingtothetopofthelightpoleis40meters.Howtallisthebuilding?

Geometry:12. Whatisthenameofthereason

thatstates“Iftwoanglesarecongruenttoeachother,thentheyhaveequalmeasures.”a. TriangleSumTheoremb. CongruentSupplement

Theoremc. DefinitionofCongruenced. SegmentAdditionPostulate

13. WhichofthefollowingstatementsisNOTtrue?a. Thealtitudebisectsthe

vertexangleofanisoscelestriangle.

b. Anequilateraltriangleisalsoisosceles.

c. Thebaseanglesofanisoscelestrianglewillnotalwaysbecongruent.

d. Thealtitudeofanisoscelestriangleistheperpendicularbisectorofthebase.

14. WhichofthefollowingisNOTtrue?a. Alineandaplanecanhave

aninfinitenumberofpointsofintersection.

b. Alineandaplanecanhaveexactlytwopointsofintersection.

c. Alineandaplanecanhaveexactlyonepointofintersection.

d. Alineandaplanecanhavenopointsofintersection.

InversesandOtherFunctions:15. Ajoggerpassesbyhischildhoodhome2hoursafter

thehalfwaymarkonhisroadtrip.Thegraphmodelshimtravelingataconstantspeed.Whichequationbestrepresentsthegraph?

a. 𝑓 𝑥 = 3𝑥 − 6b. 𝑓 𝑥 = 3𝑥 − 6 c. 𝑓 𝑥 = 3𝑥 + 6 d. 𝑓 𝑥 = 3𝑥 + 6

16. Giventhefunction𝑓 𝑥 = 9𝑥 + 18,writetheinversefunction.

Quadratics:17. Writeafunctioninvertexform

thatrepresentsaparabolathatistranslated8unitstotherightand2upfromthefunction𝑓 𝑥 = 𝑥!?

18. Whatistherangeofthefunctionrepresentedbythegraph?Writeyouranswerinthefollowingformat:“Allrealnumbers____thanorequalto_____.”

19. Howisthisgraphdifferentfromagraphofthefunction𝑓 𝑥 = 𝑥!(listalltransformations)?

36

51 43

4

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(FinalExamReview–EndofUnit9) 3

20. Whataretherootsofthequadraticequation?

𝑦 = 2𝑥! + 7𝑥 − 30a. 𝑥 = −6and𝑥 = 2.5b. 𝑥 = 6and𝑥 = −2.5c. 𝑥 = −6and𝑥 = 5d. 𝑥 = 6and𝑥 = −5

21. Whichpolynomialdoesthegraphrepresent?

a. 𝑦 = (𝑥 − 4)(𝑥 − 1)b. 𝑦 = (𝑥 + 4)(𝑥 + 1)c. 𝑦 = 𝑥 − 4 𝑥 + 1 d. 𝑦 = (𝑥 + 4)(𝑥 − 1)

22. Whatarethesolution(s)tothesystemofequationsshown?

23. AsmallrocketonalunaroutpostaroundJupiterwaslaunchedfroma96-meterplatform.Theheightoftherocketismodeledbythefunctionℎ 𝑡 = −4𝑡! + 8𝑡 + 96,where𝑡istimeinsecondsandℎ 𝑡 istheheightoftherocketinmeters.a. Whatwillbethevalueofℎ 𝑡 whentherockethitstheground?b. Findthetimewhentherockethitstheground,clearlyshowinghowyouusedtheequation.

Polynomials:24. Simplifytheexpression.

9𝑥! − 1 + (−12𝑥! − 7𝑥! + 8𝑥)

25. Simplifytheexpression.6𝑥 − 9 !

26. Whatistheproductofthepolynomials?𝑥 − 3 and 6𝑥! − 5𝑥 − 11

27. UnderwhichoperationsarethesetofwholenumbersNOTopen?a. Additionb. Subtractionc. Multiplicationd. Division

28. Inwhichsetsdoesthenumber12NOTbelong?a. Rationalnumbersb. Integersc. WholeNumbersd. NaturalNumberse. IrrationalNumbersf. RealNumbersg. ImaginaryNumbers

FinalExamReview–EndofUnit9Answers:

1. 5m 2. D 3. 16𝜋 − 8 4. A5. 81 6. 3.1ft 7. 1700ft 8. SAS9. C 10. 24yd 11. 30m 12. C13. C 14. B 15. B 16. 𝑓!! 𝑥 = !

!𝑥 − 2

17. 𝑓 𝑥 = 𝑥 − 8 ! + 2 18. Allrealnumberslesthanorequalto–3.

19. Translatedright1unitanddown2units

20. A

21. B 22. −2,−3 23. a.ℎ 𝑡 = 0b.6sec. 24. −3𝑥! − 7𝑥! + 8𝑥 − 125. 36𝑥! − 108𝑥 + 81 26. 6𝑥! − 23𝑥! + 4𝑥 + 33 27. A&C 28. G