IM9AdvancedProblemSets
ProblemSet1:LinearExpressions,Equations,andSystems
1)Thefiguretotherightshowsthegraphsoftwolines.
a) Usethefiguretoestimatethecoordinatesofthepoint
thatbelongstobothlines.
Thesystemofequationsforthetwolinesis:
4𝑥 + 3𝑦 = 20
3𝑥 − 2𝑦 = −5
b) Whatisthebestwaytosolvethissystemandwhy?
c)Solvethesystemusingthemethodyouchoseinparta)
2)Simplifytheexpression𝑘 − 2 𝑘 − 2 − 𝑘 − 2bywritingitwithoutusingparentheses.
3)Confirmthatthefivepointsinthetableontherightalllieonasingleline.
Writeanequationfortheline.
4)Thefollowingiscalleda“DiamondProblem.”Thenumbersinsideeach
diamondallobeythesamepatternorrule.
a)Studythediamondsbelowandexplainwhatyouthinkthepatternis.
b) Usethepatternyoudiscoveredinparta)tofillinthediamondsbelow.
ProblemSet2:LinearExpressions,Equations,andSystems
1) Ineachofthefollowing,useappropriatealgebraicoperationstoremovetheparenthesesand
combineliketerms.Leaveyouranswersinasimpleform.
a) 𝑥 2𝑥 + 2(𝑥 + 5)
b) 2𝑥 5𝑥 − 2 + 3(6𝑥 + 7)
c) 5𝑚 3𝑚 − 2𝑛 + 4𝑛(3𝑚 − 2𝑛)
IM9AdvancedProblemSets
2) Sketchagraphof𝒚 + 𝟐 = 𝟐(𝒙 − 𝟒).
a) Whatformisthisequationwrittenin?
b)Writetheequationinslope-interceptform.
3)Ahorsethiefridingat8mphhasa32-mileheadstart.Theposseinpursuitisridingat10mph.
Inhowmanyhourswillthethiefbecaught?
4) Rememberingthepatternyoufoundlastclass,solvethefollowingdiamondproblems.
ProblemSet3:LinearEquations,Area
1) Answerthefollowinginvolvinglinearfunctionsandrighttriangles.
!
a) Graphtheline𝑦 = − ! 𝑥 + 6.Callthisline𝑙! .
b) Findthexandy-interceptsof𝑙! .
c) Atriangleisformedby𝑙! ,thex-axisandthey-axis.Findthelengthsofall3sidesofthis
triangle.
d) Findtheareaofthistriangle.
e) Findanequationofthelineparallelto𝑙! thatpassesthroughthepoint 4, 6 .Callthisline
𝑙! .Hint:Usepointslopeform𝑦 − 𝑦! = 𝑚 𝑥 − 𝑥! .
f) Findanequationofalineperpendicularto𝑙! thatpassesthroughtheorigin.Callthisline𝑙! .
g) Graphlines𝑙! and 𝑙! onthesamegraphas𝑙! .
2) Solvethefollowingdiamondproblems.
IM9AdvancedProblemSets
ProblemSet4:LinearEquations,PythagoreanTheorem,andSA&V
1) Find the equation of the three lines that form the triangle shown
on the right.
2) Solve the following diamond problems:
3)Usethefiguretotherighttoanswerthefollowingquestions
aboutthepyramid.
a)Findtheslantheight,s,ofthepyramid.
b)Findtheheightofthefigureh.
!
c)Findthevolumeofthefigure.Recallthat𝑉!"# = ! 𝐵ℎ,whereB
istheareaofthebase.
d)Thevolumeofthispyramidisone-thirdthevolumeofwhat
figure?Drawthefigure.
ProblemSet5:LinearFunctions,Equations,Inequalities
1) Whichofthefollowingrepresentlinearfunctionsandwhy?
A
x
0
3
4
6
y
3
5
7
9
B
x
-3
-1
1
3
y
10
20
30
40
C
x
4
5
7
9
y
0
4
12
20
!
2) Solve! 3𝑥 + 14 = 7𝑥 + 6byfirstmultiplyingbothsidesoftheequationby3,before
applyingthedistributiveproperty.Isthisabetterwaytosolvetheequation?Explain.
IM9AdvancedProblemSets
3) Recallthatthesymbol“>”means“greaterthan.Forexample,4 > 2.Ifwewrite𝑥 > 2this
means“allnumbersxthataregreaterthan2.Theseareallcalledinequalities.
Doesaninequalityoftheform𝑎𝑥 > 𝑏always,sometimesornevergiveasolutionofthe
form𝑥 > 𝑐?Giveexamplestosupportyouranswer.
4) Solvethefollowingdiamondproblems:
ProblemSet6:LinearFunctions,Domain&Range,andSurfaceArea
1) Ihave120cmofframingmaterialtomakeapictureframe.Theframewillbethemost
pleasingtotheeyeifitsheightis2/3ofitswidth.WhatdimensionsshouldIuse?
2) ThefiguretotherightshowsaCUBEthathasbeenhollowed
outinthemiddle(meaningyoucanputyourarmthrough
themiddleportion,andthereisnotoporbottom).Answer
thefollowing:
a) Supposethefigurewasnothollowedout,wouldthe
surfaceareaofthenon-hollowedoutfigurebelarger
thanthesurfaceareaofthefiguretotheright?Explain
b) Calculatethesurfaceareaofthefigureontheright.
c) Aflyisbuzzingaroundthefigureandwilllandrandomly
onthesurface.Whatistheprobabilitythatitwillland
insidethehollowedoutmiddle?
3) Findthedomainandrangeofthefollowingfunctions.
a.
b.
IM9AdvancedProblemSets
ProblemSet7:Systems,Radicals,andFunctionEvaluation
1) Wheredothelinesx+y=5.5and4x+3.5y=20.75intersect?
2) SimplifythefollowingradicalexpressionsWITHOUTUSINGYOURCALCULATOR.
a) 48b) 50 75
c) 72 + 128
3)Twofunctions,f(x)andg(x),aregivenbelow.Evaluateeachfunctionforthegivenvalues.If
thefunctioncannotbeevaluated,giveareasonwhy.Recallthatf(2)meanstoplug2intothe
equationwhereeveryouseeanx.
𝑥! + 𝑥
!
𝑓 𝑥 =
𝑔 𝑥 = 𝑥! 𝑥! − 1 −𝑥
a)g(-1)g(0)g(1)
b)f(-1)f(0)f(1)
4)SolvethefollowingDiamondProblems
IM9AdvancedProblemSets
Answers!