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(FinalExamReview–EndofUnit7) 1

FinalExamReview–EndofUnit7Unit7:QuadrilateralsForQuestions1-9,Circleallcapitalizedtermsthatapply:

1. ConsecutiveanglesofarectanglearealwaysCONGRUENT,COMPLEMENTARYand/orSUPPLEMENTARY.2. ThediagonalsofarectanglealwaysareCONGRUENT,PERPENDICULAR,PARALLEL,BISECTEACHOTHERand/or

BISECTTHEVERTEXANGLES.3. TheoppositesidesofarectanglearealwaysCONGRUENT,PERPENDICULAR,and/orPARALLEL.4. TheconsecutivesidesofarectanglearealwaysCONGRUENT,PERPENDICULAR,and/orPARALLEL.5. ArectanglewillalwayshaveexactlyZEROpairs,ONEpairorTWOpairsofparallelsides.6. ArectanglewillalwayshaveexactlyZEROpairs,ONEpairorTWOpairsofcongruentsides.7. Ifaquadrilateralhasnopairsofparallelsides,thenitcouldbeaKITE,TRAPEZOID,PARALLELOGRAM,

RECTANGLE,and/oraRHOMBUS.8. Ifaquadrilateralhasexactlyonepairofparallelsides,thenitcouldbeaKITE,TRAPEZOID,PARALLELOGRAM,

RECTANGLE,and/oraRHOMBUS.9. Ifaquadrilateralhasexactlytwopairsofparallelsides,thenitcouldbeaKITE,TRAPEZOID,PARALLELOGRAM,

RECTANGLE,and/oraRHOMBUS.Unit6:RightTriangleTrigonometry10. Thefigureshownisasquare.

Whatistheareaofthesquare?

a. 32squareunitsb. 32 2squareunitsc. 64squareunitsd. 256 squareunits

11. Inthediagramshown,a18-footrampisattachedtoaplatform.Therampmakesa75˚withtheplatform.Whatistheheightoftheplatform?

12. Claytonisflyinganairplaneatanaltitudeof1200ft.Sheseesherhouseonthegroundata60˚angleofdepression.WhatisJoanna’shorizontaldistancefromherhouseatthispoint?

Unit5:SimilarTriangles13. Inthefigureshown,△ABDand

△CBDareisoscelestriangleswithacongruentvertexangleatD.Whichtheoremcouldbeusedtoprove△ABD ≅△CBD?

a. HLc.SASb. AASd.SSS

14. Abirdisflyinginastraightlineoutofawindowonthesideofa42yardtallbuildingtowardtheroofofa46yardtallbuilding.AphotographertakesapictureofthebirdatpointA.Atthatmoment,howfaristhebirdfromtheroof?

15. A96-foot-longsupportwirefora15-foottallpostrunsfromthetopcornerofabuildingtoapointontheground,formingastraightline.Thelengthofthewirefromthetopofthebuildingtothetopofthelightpostis78feet.Howtallisthebuilding?

16. WhichareNOTvalidconclusionsthatyoucandrawfromthispicture?

a. △ABC ≅△ 𝐷𝐵𝐸b. △ABC ~ △ 𝐷𝐵𝐸c. Slopeof𝐴𝐷 =slopeof𝐷𝐵d. !"

!"= !"

!"

e. !"!"= !"

!"

f. 𝐴𝐶 ≅ 𝐷𝐸g. 𝐷𝐵 ≅ 𝐸𝐵

8

75˚18 ?1200 ft

A

B

CD

4642

3

28

A DBC E

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(FinalExamReview–EndofUnit7) 2

Geometry:17. Whatisthenameofthereason

thatstates“On △ABC,𝑚∠𝐴𝐵𝐶 +𝑚∠𝐵𝐶𝐴 +𝑚∠𝐶𝐴𝐵 = 180˚.”a. CongruentSupplement

Theoremb. TriangleSumTheoremc. AngleAdditionPostulated. DefinitionofaMidpointe. DefinitionofCongruencef. SegmentAdditionPostulateg. AdditionPropertyof

Equalityh. CongruentComplement

18. Whichofthefollowingstatementsaretrue?a. Anisoscelestrianglecannot

havethreesidesthatarealldifferentlengths

b. Thebaseisbisectedbythealtitudeofanisoscelestriangle

c. Thealtitudeofanisoscelestriangledoesnotcreatetwocongruenttriangles

d. Anisoscelestrianglecanhavethreecongruentsides

e. Thevertexangleonanisoscelestriangleisbisectedbythealtitude

f. Thebaseanglesonanisoscelestrianglearenotcongruent

g. Onanisoscelestriangle,theperpendicularbisectorofthebaseisthealtitude

19. Whichofthefollowingaretrue?a. Twolinescanintersectat

exactlytwodistinctpointsb. Theintersectionofaplane

andalinecanhappenatexactlythreedistinctpoints

c. Twoplanescanhaveaninfinitenumberofintersectionpoints

d. Alineandaplanemayhavenopointsofintersection

e. Twoplanescanintersecteachotheratasinglepoint

f. Alinecanintersectaplaneatasinglepoint

g. Alinecanintersectaplaneataninfinitenumberofpoints

InversesandOtherFunctions:20. Giventhefunction𝑓 𝑥 = −4𝑥 + 36,writetheinversefunction.

21. Aregionaltrainpassesbyacertaintrainstationhalfwayalongitstripeachday.Thegraphmodelsthetraintravelingataconstantspeed.Whichequationbestrepresentsthegraph?

a. 𝑓 𝑥 = 𝑥 + 20 b. 𝑓 𝑥 = 20 − 𝑥 c. 𝑓 𝑥 = 𝑥 + 20d. 𝑓 𝑥 = 20𝑥

Quadratics:22. Writeafunctioninvertexform

thatrepresentsaparabolathatistranslated3unitstotheleftand5unitsupfromthefunction𝑓 𝑥 = 𝑥!.

23. Whataretherootsofthequadraticequation?

𝑦 = 3𝑥! + 𝑥 − 24

24. Whatistherangeofthefunctionrepresentedbythegraph?

25. AsmallrocketonalunaroutpostaroundJupiterwaslaunchedfroma45-meterplatform.Theheightofthe

rocketismodeledbythefunctionℎ 𝑡 = −5𝑡! + 40𝑡 + 45,where𝑡istimeinsecondsandℎ 𝑡 istheheightoftherocketinmeters.a. Whatwillbethevalueofℎ 𝑡 whentherockethitstheground?b. Findthetimewhentherockethitstheground,clearlyshowinghowyouusedtheequation.

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(FinalExamReview–EndofUnit7) 3

26. Howhasthisgraphbeentranslatedfromagraphofthefunction𝑓 𝑥 = 𝑥!?

27. Completethefactoredformofpolynomialshowninthegraphbelow.

𝑦 = (𝑥___________)(𝑥___________)

28. Whatarethesolution(s)tothesystemofequationsshown?

Polynomials:29. Simplifytheexpression.

7𝑥! − 9𝑥 + (−5𝑥! − 5𝑥! + 2)

30. Simplifytheexpression.3𝑥 − 15 !

31. Whatistheproductofthepolynomials?𝑥 + 4 and 2𝑥! − 3𝑥 − 7

32. UnderwhichoperationsarethesetofintegersNOTopen?a. Additionb. Subtractionc. Multiplicationd. Division

33. Inwhichsetsdoesthenumber−9NOTbelong?a. Rationalnumbersb. Integersc. WholeNumbersd. NaturalNumberse. IrrationalNumbersf. RealNumbersg. ImaginaryNumbers

FinalExamReview–EndofUnit7

ANSWERS1.CONGRUENT&SUPPLEMENTARY 2.CONGRUENT&BISECTEACHOTHER 3.CONGRUENT&PARALLEL4.PERPENDICULAR 5.TWOPAIRS 6.TWOPAIRS 7.KITE8.TRAPEZOID 9.PARALLELOGRAM,RECTANGLE&RHOMBUS10.c.64squareunits 11.4.7ft 12.692.8ft 13.c.SAS14.16yd 15.80ft 16.a,d,f,&g 17.b.TriangleSumThm18.a,b,d,e&g 19.c,d,f&g 20.𝑓 𝑥 = !

!!+ 9 21.d.𝑓 𝑥 = 20𝑥

22.𝑓 𝑥 = 𝑥 + 3 ! + 5 23.𝑥 = −3 𝑜𝑟 𝑥 = !! 24.𝑦 ≤ 9 25a.0m 25b.9sec

26.left3&down2units 27.𝑦 = (𝑥−3)(𝑥+2) 28. −3,−6 & (3, 0) 29.−5𝑥! + 2𝑥! − 9𝑥 + 230.9𝑥! − 90𝑥 + 225 31.2𝑥! + 5𝑥! − 19𝑥 − 28 32.a,b&c 33.c,d,e&g