Math 2 Final Exam – Skills Review – Answer Keylps.lexingtonma.org/cms/lib2/MA01001631/Centricity/Domain/955/Math... · Math%2%Final%Exam%–%Skills%Review%–%Answer%Key% % 1)!!

Math 2: Algebra 2, Geometry and Statistics

Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434

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Math%2%Final%Exam%–%Skills%Review%–%Answer%Key%%1)!!a.!Recursive!Rule!! ! = 9, ! = 0

! ! − 1 + 2, ! > 0! Explicit!Rule!! ! = 2! + 9!

b.!Recursive!Rule!! ! = 3, ! = 0! ! − 1 + 3, ! > 0! Explicit!Rule!! ! = 3! + 3!

2)!a.!Explicit!Rule!! ! = !! − 2!b.!Recursive!Rule!! ! = 1, ! < 0

3!(! − 1), ! ≥ 0! Explicit!Rule!! ! = 1 ∗ 3!!3)!a.!This!is!a!relation;!the!same!input!(x=value)!can!give!you!more!than!one!output!(y=value).!b.!This!is!a!function;!each!input!has!a!unique!output.!4)!a.!Function;!each!x=value!has!exactly!one!y=value!b.!Relation;!for!example,!the!x=value!of!1!has!two!y=values.!c.!Function;!each!x=value!has!exactly!one!y=value!5)!a.!Relation,!the!input!of!2!has!two!outputs!(6!and!8).!b.!Function,!each!input!has!only!one!output.!6)!a.!Domain:!all!real!#’s,!Range!all!real!#’s!y≥ 6!b.!Domain:!all!real!#’s!! ≥ −4,!Range!all!real!#’s!! ≥ 0!c.!Domain;!all!real!#’s!x≠ −5,!Range!all!real!#’s!!! ≠ 0!7)!a.!Domain:![−2,!3)!Range:!(−3,!6]!b.!Domain:!(−2,!3]!Range:![−6,!3)!8)!a.!Domain:!{5,!6,!7,!8}!Range!{1,!3,!10,!12}!9)!a.!9! b.!−11! ! c.!−99! ! d.!243! ! e.!33! ! f.!129!10)!a.!4!! + 23! ! b.!!! − 12! + 41! c.!−4! + 36! ! d.!−4! + 3!11)!a.!!!! ! = !!!

! ! b.!!!! ! = !!!!! !

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a. ! ! b.! ! !13)!AB!=!8.1,!m!" = !

!,!mp!" = (−8.5, 2)!BC!=!8.2,!m!" = − !

!,!mp!" = (−1, 3)!CD!=!8.1,!!!" = !

!,!mp!" = −8,−1 !DA!=!8.2,!!!" = − !

!,!mp!" = (− !! , 0)!

14)!ABCD!is!a!parallelogram,!but!not!a!rhombus!or!a!rectangle.!15)!Vertical!tangents:!x!=!0!and!x!=!−4;! ! Horizontal!tangents:!y!=!2,!y!=!6!16)!! − 5 = − !

! (! + 4)!17)!You!can!easily!graph!all!of!these!on!your!calculator,!except!for!!! + !! = 1!which!is!a!circle!with!radius!1!centered!at!the!origin.!!18)!a.!Parent!function!is!! = !!,!moved!right!3!and!up!1.!

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b.!Parent!function!is!! = !,!reflected!over!the!y=axis!and!½!as!tall.!

!! !

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q x( ) = x – 3( )2 + 1

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r x( ) = –x

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c.!Parent!function!is!!! + !! = 16!(a!circle!with!radius!4).!It!is!shifted!right!1!and!is!1/3!as!tall.!

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d.!Parent!function!is!! = !!!it!is!½!as!wide.!

!!e.!Parent!function!is!! = ! ,!moved!right!2!and!½!as!tall.!!

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f.!Parent!function!is!! = !! − !,!reflected!over!the!x=axis!and!moved!right!2.!

!19)!a.! i.!! = !! ! ii.!moved!up!3!! ! ! iii.!! − 3 = !!b.! i.!! = !!! ! ii.!Right!3,!reflected!over!x=axis! iii.!–! = (! − 3)!!c.!! i.!! = ! ! ! ii.!Left!1,!reflected!over!x=axis! iii.!–! = ! + 1 !d.! i.!! = !!! ! ii.!Reflect!over!y=axis!(or!x=axis)! iii.!! = (−!)!!(or!–! = !!)!20)!a.!! = ! + 3 !! b.!! = !

! ! ! ! c.!–! = ! ! ! d.!! + 5 = ! !e.!! + 4 = ! !! f.!! − 3 = ! !or!! = ! − 3 !21)!a.!! − 3 = !!! ! b.!! = (−!)!! ! c.!–! = (! + 3)!! d.!! = (2!)!!e.!Impossible,!domain!is!all!ℝ! f.!! − 3 = (! + 2)!!! !

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22)!a.!124°!! b.!56°! ! c.!56°! ! d.!38°! ! e.!38°! ! f.!76°! ! g.!66°!h.!104°! k.!76°! ! n.!86°! ! p.!38°! ! q.!38°! ! r.!76°! ! s.!38°!t.!104°!! v.!76°! ! w.!104°!23)!! 1.!Sometimes! ! 2.!Always! 3.!Always! 4.!Always!! 5.!Always! !

6.!Sometimes! ! 7.!Always!24)!! i.!∆!!"# ≅ !∆!"#!by!SAS!and!∆!"#! ≅ !∆!"#!by!SAS! ii.!∆!"#! ≅ !∆!"#!by!ASA!

iii.!CBD!(congruent!parts!are!not!corresponding)! ! iv.!CBD!(not!enough!parts)!v.!∆!"#! ≅ !∆!"#!by!SSS! ! vi.!∆!"#! ≅ !∆!"#!by!AAS!vii.!∆!"#! ≅ !∆!"#!by!AAS!! viii.!∆!"#! ≅ !∆!"#!by!SAS! !ix.!∆!"#! ≅ !∆!"#!by!SSS!

25!&!26!are!proofs.!Check!these!with!your!teacher!or!compare!with!a!classmate.!27)!! a.!k!=!7!! b.!k!=!5! c.!k!=!6!! d.!k!=!7!28)!! a.! !!!!! ! b.! !!!!! ! c.!!!"! ! d.!27!!"!!! e.15!! ! f.3!!!!!29)!! a.!4 2! ! b.!11! ! c.!3 5! ! d.! !! ! ! e.!! !

! ! ! f.! !! !30)!

a.!4! ! b.!5! ! c.!3! ! d.! !!"! ! e.!!!!31)!! a.!rational,!can!be!written!as!!"##!"" ! ! b.!rational,!can!be!written!as!!!!! c.!rational,!can!be!written!as! !!"! ! d.!irrational,!non=perfect!square!under!radical.!32)!! a.!(3! − 5)(2! + 3)! ! b.!(! − 7)(! + 6)! ! c.!(2! + 3 2)(2! − 3 2)!! d.!(2! + 3)(! + 3)! ! e.!(! + 3)(2!! + 6! − 1)! f.!(3! + 4)(3! − 4)!! g.!5!(! + 4)(! − 1)! ! h.!(4! + 1)(4! − 1)! ! i.!(! + 8)!!33)!! a.!3! 5! − 3 5! + 3 = 0; ! = 0, !! ,−

!!! b.! 5! − 3 ! + 3 = 0; ! = ! !! ,−3!

! c.!(! − 7)! = 0, ! = 7! ! ! ! d.! 2! + 3 ! + 6 = 0; ! = !− !! ,−6!

34)!Answers!will!vary,!but!possible!answers!are!given!below.!! a.!! ! = !! + 2!!! ! ! b.!! ! = 13!! − 12!35)!!! a.!ℎ ! = !! + 2!! − 3! + 5! b.!! ! = 2!! + 4!! − 3! − 4!! c.!! ! = 3!! − 2!! + !!+…!!36)!!! a.!! = − !

! , 1! ! b.!no!real!solutions!∆!= −48!! c.!! = 2,−4!! d.!! = 0,−25! ! e.!! = − !

! , 3! ! ! ! f.!! = 0,−4!! !



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37)!! a.!! = 6 ! + !

! (! − 3)! ! b.!! = 2(! + 3)(! − 4)!! c.!! = 3(! − 3)! + 5! ! ! d.!! = −4(! − 2)! + 7!38)!!a.!!

!Vertex:!(4,!3);!Zeros!(5,!0)!and!(3,!0);!Axis!of!symmetry!x!=!4;!y=intercept!(0,!−45);!mirror!point!(8,!=45)!!

b.!!

!Vertex!(0.75,!−20.25);!zeros!(3,!0)!and!(− !

! , 0);!Axis!of!symmetry!x!=!!!;!y=intercept!(0,!−18)!;!mirror!point!(1.5,!−18)!

c.!Vertex! !"!" , 42.04 ;!zeros! !! , 0 !and! − !! , 0 ;!Axis!of!symmetry!1 !

!";!y=intercept!(0,−5);!mirror!point! !"! ,−5 !

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39)!!Completing!the!square! ! ! ! ! ! Quadratic!Formula!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!40)!!! a.!

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!"!"! ! b.!!!! ! c.!!!! ! d.!"!"! ! e.! !!!"#! !

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41)!!! a.! !"#!!"" = 0.4;!40%!of!students!always!do!their!homework.!! b.! !"#!!"" = 0.31;!31%!of!students!never!do!their!homework!! c.!0;!mutually!exclusive,!you!can’t!both!always!and!never!do!your!homework.!! d.!0.4+0.31!=!0.71;!71%!is!the!combined!percentage!of!students!who!do!all!their!!

homework!and!none!of!their!homework!e.!0;!mutually!exclusive,!you!can!be!on!honor!roll!and!not!on!honor!roll!f.!!"!!"# = 0.98;!98%!of!the!students!who!do!no!homework!are!not!on!honor!roll.!g.!!"#!"# = 0.40;!40%!of!students!on!honor!roll!do!all!their!homework.!h.!!"#!"# = 0.33;!33%!of!the!students!who!do!all!their!homework!are!on!honor!roll.!

42)!These!are!independent.!P(H)!=!P(H|A)!and!P(A)!=!P(A|H)!(they!round!to!the!same!whole!percentage!point).!43)!These!are!not!independent.!P(H)!≠!P(H|S)!and!P(S)!≠!P(S|H)!44)!!

a)!SL!=!5.2! MI!=!10! m∠!=120°! m∠! =!85°! m∠!!=!80°!b)!AP!=!8! EI!=!7! ! SN!=!15! YR!=!12!

45)!!! a.!Yes,!all!sides!are!proportional!and!all!angles!are!congruent.!! b.!No,!sides!are!not!proportional!46)!! a.!∆!"#!~!∆!"#!by!AA!similarity!! b.!∆!"#!~!∆MKL!47)!! ∠!"#! ≅ ∠!"#!(Given)!! ∠!! ≅ ∠!!(Reflexive!Property)!! ∆!"#!~!∆!"#!by!AA!similarity!48)!x!=!33!49)!The!tree!is!34!ft!6!inches!tall!50)!The!statue!is!30!feet!tall!51)!! a.!a!=!4!cm! b.!Ratio!of!areas!=!36:1! c.!R!=!20!cm! ! d.!Ratio!is!8:125!52)!! a.!w!=!18!cm! b.!x!=!7.4!cm! c.!76.3!cm! d.!a!=!28.3°! e.!t!=!42.8°! f.!z!=!76.1°!53)!The!kite!is!337.80!ft!above!the!ground!54)!Tamara!is!standing!49.2!ft!from!the!flagpole.!55)!! a.!u!=!v!=!8! b.!x!=!8 3,!y!=!!" !

! ! c.!a!=!22,!b!=!22!56)!!! a.!A!=!94.18!!!! b.!A!=!64 3!!!!57)!!! a.!Area!=!!!!!cm2! b.!Area!=!!!!!cm2!! !



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58)! !a.!r!=!10!cm! ! b.!x!=!135°!

59)!! a.!! − 2!units2! b.!196!–!49!!2!! c.!!"! !!units2! ! d.!6!units!60)!! a.!m∠!"# = 40°! arc!XN!=!180°!! arc!MN!=!100°!! b.!a!=!50°! ! b!=!60°! c!=!70°!! c.!x!=!160°! ! d.!!x!=!9°! e.!x!=!42°! f.!x!=!70°!61)!! a.!m∠!"# = 65°!! b.!x!=!58°! w!=!244°! z!=!58°!! c.!!

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Math 2 Final Exam – Skills Review – Answer Keylps.lexingtonma.org/cms/lib2/MA01001631/Centricity/Domain/955/Math... · Math%2%Final%Exam%–%Skills%Review%–%Answer%Key% % 1)!!