Name: ____________________________________________ (Final Exam Review – End of Unit 8) 1 Final Exam Review – End of Unit 8 Unit 8: Circles 1. Identify each segment as a tangent, secant, or a chord. A. B. C. D. E. F. 2. A right triangle with sides the length of the radius is within a circle. If the radius of the circle is 8 centimeters, what is the area of the shaded region? Unit 7: Quadrilaterals 3. Which parts of a rectangle are always congruent? a. All sides b. Opposite sides c. Consecutive sides d. Diagonals 4. Which parts of a rectangle are always parallel? a. All sides b. Opposite sides c. Consecutive sides d. Diagonals 5. Which parts of a rectangle are always perpendicular? a. All sides b. Opposite sides c. Consecutive sides d. Diagonals Unit 6: Right Triangle Trigonometry 6. The figure shown is a square. What is the area of the square? 7. In the diagram shown, a 9-foot slide is attached to a swing set. The slide makes a 62˚ angle with the swing set. Which answer most closely represents the height of the slide? 8. Joanna is flying an airplane at an altitude of 4300 ft. She sees her house on the ground at a 45˚ angle of depression. What is Joanna’s horizontal distance from her house at this point? Unit 5: Similar Triangles 9. Two kids decided to string a rope from the roof of a 52 yard tall building to a window on the side of a 49 yard tall building so that they could send a bucket full of toys into the window. On their first try, the bucket got stuck on a clothesline at point A. How far did the bucket travel down the rope? 10. A 63-meter-long support wire for a light pole runs from the top corner of a 28-meter-tall building to a point on the ground, forming a straight line. The length of the wire from the top of the building to the top of the light pole is 36 meters. How tall is the light pole? 5 2 9 62 4300 ft 45˚ 20 52 49
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Name:____________________________________________
(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
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