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IM2

IM2 Week: 4/6/20 – 4/10/20

Concept: Rational Exponents and Radicals

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SECONDARY MATH II // MODULE 3

SOLVING QUADRATICS & OTHER EQUATIONS – 3.2

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

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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SET Topic:RadicalnotationandradicalexponentsEachoftheexpressionsbelowcanbewrittenusingeitherradicalnotation, !!! orrational

exponents!!! .Rewriteeachofthegivenexpressionsintheformthatismissing.Expressinmost

simplifiedform.

RadicalForm ExponentialForm

13. 5!!

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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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IM2 Week: 4/13/20 – 4/17/20

Concept: Polynomials

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QUADRATIC FUNCTIONS – 1.2




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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:____________________________


liketermsSimplifiedform

(x+1)in

(x+1)inxcm

xcm

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b.Area:____________________________ b.Area:____________________________

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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.

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READY Topic:RecognizingFunctionsIdentifywhichofthefollowingrepresentationsarefunctions.IftherepresentationisNOTafunctionstatehowyouwouldfixitsoitwas.

1.D={(4,-1)(3,-6)(2,-1)(1,2)(0,4)(2,5)} 2.Thenumberofcaloriesyouhaveburnedsincemidnightatanytimeduringtheday.

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4.x -12 -8 -6 -4f(x) 25 25 25 25

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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.


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Figure 1

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CB

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Figure 2

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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.

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IM2 Week: 4/27/20 – 5/1/20 

Concept: Quadratics

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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.

4 The graph represents 𝑓𝑓(𝑥𝑥) and the table shows some values of another quadratic function 𝑔𝑔(𝑥𝑥).






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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?


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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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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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