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SECONDARY MATH II // MODULE 3
SOLVING QUADRATICS & OTHER EQUATIONS – 3.2
Mathematics Vision Project
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mathematicsvisionproject.org
3.2
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REA DY Topic:SimplifyingRadicalsAverycommonradicalexpressionisasquareroot.Onewaytothinkofasquarerootisthenumberthatwillmultiplyby itself tocreateadesiredvalue.Forexample: 2is thenumber thatwillmultiplyby itself toequal2.And in likemanner 16isthenumberthatwillmultiplybyitselftoequal16,inthiscasethevalueis4because4x4=16.(Whenthesquarerootofasquarenumber istakenyougetanicewholenumbervalue.Otherwiseanirrationalnumber isproduced.)Thissamepatternholdstrueforotherradicalssuchascuberootsandfourthrootsandsoforth.Forexample: 8! isthenumberthatwillmultiplybyitselfthreetimestoequal8.Inthiscaseitisequaltothevalueof2because2!=2x2x2=8.Withthisinmindradicalscanbesimplified.Seetheexamplesbelow.
Example1:Simplify 2020= 4 ∙ 5 = 2 ∙ 2 ∙ 5=2 5
Example2:Simplify 96!
96! = 2! ∙ 3!=2 3!
Simplifyeachoftheradicals.1. 40 2. 50 3. 16!
4. 72 5. 81! 6. 32
7. 160! 8. 45 9. 54!
READY, SET, GO! Name PeriodDate
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SECONDARY MATH II // MODULE 3
SOLVING QUADRATICS & OTHER EQUATIONS – 3.4
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
3.4
Needhelp?Visitwww.rsgsupport.org
SET Topic:RadicalnotationandradicalexponentsEachoftheexpressionsbelowcanbewrittenusingeitherradicalnotation, !!! orrational
exponents!!! .Rewriteeachofthegivenexpressionsintheformthatismissing.Expressinmost
simplifiedform.
RadicalForm ExponentialForm
13. 5!!
14.
16
!!
15. 5! ∙ 3!!
16. 9!! ∙ 9
!!
17. !!"!!"!
18. 27!!!!!
19.32!!"243!!"
!
20. 9!!!!!!
!!
Solvetheequationsbelow,useradicalsorrationalexponentsasneeded.
21. ! + 5 ! = 81 22. 2 ! − 7 ! + 3 = 67
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SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.2
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
1.2
READY Topic:DistributivePropertySimplify.Firstusethedistributivepropertyandthencombinetheliketerms.
Example:
!" !" + ! + ! !" + ! → !"!! + !" + !" + ! → !"!! + !" + !" + ! → !"!! + !!" + !
1.2x 5x + 3 + 7 5x + 3
2.8x x + 1 + 2 x + 1
3.6x x − 10 − 1 x − 10
4.1x 3x + 4 + 5 3x + 4
5. 3x 8x + 3 − 4 8x + 3
6.5x 2x + 6 + 2 2! + 6
7.7x −5x + 2 − 13 −5x + 2
8.−4x 12x + 3 + 3 12x + 3
SET Topic:ComparingAreaandperimeterCalculatetheareaandperimeterofeachfigurebelow.Theareamaybewrittenasaproduct.Includethecorrectunitonyouranswer.(Youranswerswillcontainavariable.)9. 10.
a.Perimeter:______________________ a.Perimeter:______________________
b.Area:____________________________ b.Area:____________________________
READY, SET, GO! Name PeriodDate
liketermsSimplifiedform
(x+1)in
(x+1)inxcm
xcm
8
SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.2
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
1.2
11. 12.
a.Perimeter:______________________ a.Perimeter:______________________
b.Area:____________________________ b.Area:____________________________
13. 14.
a.Perimeter:______________________ a.Perimeter:______________________
b.Area:____________________________ b.Area:____________________________
15.Comparetheperimetertotheareaineachofproblems(9-14).
Inwhatwayarethenumbersandunitsintheperimetersandareasdifferent?
GO Topic:GreatestCommonFactorFindtheGCFforthegiventerms.
16.15abc2and25a3bc 17.12x5yand32x6y 18.17pqrand51pqr3
19.7x2and21x 20.6x2,18x,and-12 21.4x2and9x
22.11x2y2,33x2y,and3xy2 23.16a2b,24ab,and16b 24.49s2t2and36s2t2
(a+5)ft
(b+3)ft ami
bmi
(x+3)m
(x–2)m
(x+4)in
(x+1)in
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IM2 Week: 4/20/20 – 4/24/20
Concept: Functions
1 Sue hits a ball from a height of 4 feet. The height of the ball above the ground is a function of the horizontal distance the ball travels until it comes to rest on the ground. Consider this complete graph of the function.
2 Consider the function 𝑓𝑓(𝑥𝑥) = 10𝑥𝑥 + 25. Identify an appropriate domain for the function if it is used to model each of the following contexts.
3 The graph shows the population of mice in a study, modeled as a function of time. The study begins on day 0 and ends on day 200.
Determine whether each statement is true according to the graph. Select True or False for each statement.
4
SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.5
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
1.5
READY Topic:RecognizingFunctionsIdentifywhichofthefollowingrepresentationsarefunctions.IftherepresentationisNOTafunctionstatehowyouwouldfixitsoitwas.
1.D={(4,-1)(3,-6)(2,-1)(1,2)(0,4)(2,5)} 2.Thenumberofcaloriesyouhaveburnedsincemidnightatanytimeduringtheday.
3.
4.x -12 -8 -6 -4f(x) 25 25 25 25
5.
6.
SET
Topic:Comparingratesofchangeinlinear,quadratic,andexponentialfunctionsThegraphattherightshowsatimevs.distancegraphoftwocarstravelinginthesamedirectionalongthefreeway.7.Whichcarhasthecruisecontrolon?Howdoyouknow?8.Whichcarisaccelerating?Howdoyouknow?9.Identifytheintervalinfigure1wherecarAseemstobegoingfasterthancarB.10.Forwhatintervalinfigure1doescarBseemtobegoingfasterthancarA?11.Whatinthegraphindicatesthespeedofthecars?12.AthirdcarCisnowshowninthegraph(seefigure2).All3carshavethesamedestination.Ifthedestinationisadistanceof12unitsfromtheorigin,whichcardoyoupredictwillarrivefirst?Justifyyouranswer.
READY, SET, GO! Name PeriodDate
12
10
8
6
4
2
5 10
B
A
Figure 1
12
10
8
6
4
2
5 10
CB
A
Figure 2
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SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.5
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
1.5
GO Topic:IdentifyingdomainandrangefromagraphStatethedomainandrangeofeachgraph.Useintervalnotationwhereappropriate.
13a.Domain__________b.Range___________
14a.Domain__________b.Range___________
15a.Domain__________b.Range___________
16a.Domain__________b.Range___________
17a.Domain__________b.Range___________
18a.Domain__________b.Range___________
19a.Domain__________b.Range___________
20a.Domain__________b.Range___________
21.Arethedomainsof#19and#20thesame?Explain.
8
6
4
2
–2
–4
8
6
4
2
–2
–4
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IM2 Week: 4/27/20 – 5/1/20
Concept: Quadratics
1
2 Given the function
Graph and identify the x-intercepts and maximum of the function.
3 Circle the number that will create an equation that is true for all values of 𝑥𝑥.
SECONDARY MATH II // MODULE 3
SOLVING QUADRATICS & OTHER EQUATIONS – 3.5
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
3.5
Needhelp?Visitwww.rsgsupport.org
REA DY Topic:Convertingmeasurementofarea,areaandperimeter.Whileworkingwithareasissometimesessentialtoconvertbetweenunitsofmeasure,forexamplechangingfromsquareyardstosquarefeetandsoforth.Converttheareasbelowtothedesiredmeasure.(Hint:areaistwodimensional,forexample1yd2=9ft2because3ftalongeachsideofasquareyardequals9squarefeet.)1.7yd2=?ft2 2.5ft2=?in2 3.1mile2=?ft2
4.100m2=?cm2 5.300ft2=?yd2 6.96in2=?ft2
SET Topic:Transformationsandparabolas,symmetryandparabolas7a.Grapheachofthequadraticfunctions.
! ! = !!! ! = !! − 9
ℎ ! = (! + 2)! − 9b.Howdothefunctionscomparetoeachother?c.Howdog(x)andh(x)comparetof(x)?
d.Lookbackatthefunctionsaboveandidentifythex-interceptsofg(x).Whatarethey?e.Whatarethecoordinatesofthepointscorrespondingtothex-interceptsing(x)ineachoftheotherfunctions?Howdothesecoordinatescomparetooneanother?
READY, SET, GO! Name PeriodDate
33
SECONDARY MATH II // MODULE 3
SOLVING QUADRATICS & OTHER EQUATIONS – 3.5
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
3.5
Needhelp?Visitwww.rsgsupport.org
8a.Grapheachofthequadraticfunctions.! ! = !!
! ! = !! − 4ℎ ! = (! − 1)! − 4
b.Howdothefunctionscomparetoeachother?c.Howdog(x)andh(x)comparetof(x)?
d.Lookbackatthefunctionsaboveandidentifythex-interceptsofg(x).Whatarethey?e.Whatarethecoordinatesofthepointscorrespondingtothex-interceptsing(x)ineachoftheotherfunctions?Howdothesecoordinatescomparetooneanother?9.Howcanthetransformationsthatoccurtothefunctionf(x)=x2beusedtodeterminewherethex-interceptsofthefunction’simagewillbe? GO Topic:FunctionNotationandEvaluatingFunctionsUsethegivenfunctionstofindthemissingvalues.(Checkyourworkusingagraph.)10. !(!) = !! + 4! – 12 11.!(!) = (! – 5)! + 2a.! 0 = _______
b.! 2 = ______
!. ! ! = 0, ! = ______
!. ! ! = 20, ! = ______
a.! 0 = ______b.! 5 = _______c.! ! = 0 , ! = _______d.! ! = 16, ! = _______
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SECONDARY MATH II // MODULE 3
SOLVING QUADRATICS & OTHER EQUATIONS – 3.5
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
3.5
Needhelp?Visitwww.rsgsupport.org
12.! ! = !! − 6! + 9 13.! ! = (! − 2)! − 3a.! 0 = _______b.! −3 = ______c.! ! = 0 , ! = _______d.! ! = 16, ! = _______
a.! 0 = ______b.! 5 = _______c.! ! = 0 , ! = _______d.! ! = −3, ! = _______
14.! ! = (! + 5)! 15.! ! = − ! + 1 ! + 8a.! 0 = _______b.! −2 = ______c.! ! = 0 , ! = _______d.! ! = 9, ! = _______
a.! 0 = ______b.! 2 = _______c.! ! = 0 , ! = _______d.! ! = 4, ! = _______
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