Introduction to Statistics and Calculus

IntroductiontoStatistics

andCalculus

SummerAssignment

EnclosedyouwillfindtwopartstothisAssignment.Part1consistsofPre‐RequisiteSkillsPracticethatreviewconcepts

learnedinPre‐CalculusandAlgebra2.TheseconceptsareessentialtoyourunderstandingofCalculus.Youare

expectedtocompleteallexercisescontainedinthispacket,showingallworkwhennecessary.Part2consistsofa

projectinvolvinganapplicationtoreal‐life.Youwilldiscoverthatexamplesforallofthequestionscanbefoundthrough

abasicsearchhowevertherearefreeinternetsitesthatyoucanusethatwillofferfullinstructiononthevarious

mathematicalconcepts.Anexcellentsourceiskhanacademy.comwhichcoversmanyacademicareas.Includedonthe

nextpageisatablecontainingKhanAcademylinksonhowtocompleteeachtypeofquestion.

Thisassignmentwillbecollectedonthefirstdayofclass.

Anystudentwhodoesnothavetheassignmentwillbegive n

onebytheteacher.Theteacherwillinformtheparent/guardianofthemissingassignmentandthatthereisan

opportunityforthechildtocompleteit.Lateprojectswilllose10pointseachday. Summer assignments will

begradedas aquiz.

This quiz gradewill consist of20%completionand

80%accuracy.Completionisdefinedashavingallworkshowninthespaceprovidedtoreceive fullcredit,anda

parent/guardiansignature.

AnystudentwhoregistersasanewattendeeofTeaneckHighSchoolafterAugust15thwillhaveanextraweekto

completethesummerassignment.

StudentNam

e:__________________________________________________________________________________

Parent/GuardianSignature:________________________________________________________________________

Parent/GuardianName(Pleaseprint):_______________________________________________________________

Pre‐RequisiteSkillsPracticeReferences

Question Topic Link(AtKhanAcademy.org,undermath,unlessspecified)

1 GraphingLinear

Equations

http://www.khanacademy.org/math/algebra/linear‐equations‐and‐

inequalitie/v/linear‐equati ons‐in‐standard‐form

AlgebraÆGraphinglinearequationsandinequalitiesÆLinearEquationsin

StandardForm

2 Graphing

Quadratic

Equations

http://www.khanacademy.org/math/algebra/quadtratics/v/graphing‐a‐

quadratic‐function

AlgebraÆQuadraticsÆGraphingaQuadraticFunction

5–8 Evaluating

Functions

http://www.khanacademy.org/math/algebra/algebra‐functions/v/evaluating‐

functions

AlgebraÆFunctionsÆEvaluatingFunctions

9‐10 Compound

InterestFunctions

http://www.khanacademy.org/math/precalculus/v/interest‐‐part‐2

PrecalculusÆInterest(Part2)–(Youmaywanttowatchthiswholeseriesto

betterunderstandcompoundinterest.)

11‐13 DomainandRange http://www.khanacademy.org/math/algebra/ck12‐algebra‐1/v/domain‐and‐

range‐of‐a‐function

MathÆAlgebraÆck12.orgAlgebra1ExamplesÆDomainandRangeofa

Function

14‐15 WritingLinear

Equations

http://www.khanacademy.org/math/algebra/linear‐equations‐and‐

inequalitie/v/linear‐equati ons‐in‐slope‐intercept‐form

AlgebraÆGraphinglinearequationsandinequalitiesÆLinearEquationsinSlope

InterceptForm

16‐17 SolveaQuadratic

Equationusingthe

QuadraticFormula

http://www.khanacademy.org/math/algebra/quadtratics/v/quadratic‐equation‐

part‐2

AlgebraÆQuadraticsÆQuadraticEquationPart2

18–20 Rewriteradical

expressionswith

rationalexponents

http://www.khanacademy.org/math/algebra/exponents‐radicals/v/zero‐‐

negative‐‐and‐fractional‐exponents

AlgebraÆExponentsandRadicalsÆZero,NegativeandFractionalExponents

21‐23 Evaluate

expressionswith

rationalexponents

http://www.khanacademy.org/math/algebra/exponents‐radicals/v/level‐3‐

exponents

AlgebraÆExponentsandRadicalsÆLevel3Exponents

24‐25 Supplyand

Demand/Break

Evenpoints

http://www.khanacademy.org/math/algebra/systems‐of‐eq‐and‐ineq

AlgebraÆSystemsofEquationsandInequalities,selectanymethodtohelpyou

solvetheseproblems.

ProjectPortionRefere

nce

CompoundInterest



https://www.khanacademy.org/math/trigonometry/exponential_and_logarithmic_func/continuous_compoundi

ng/v/introduction‐to‐interest

TrigonmoetryÆExponentialandLogarithmicfunctionsÆContinuouscompoundingande

GraphingPiecewiseFunctions



http://www.purplemath.com/modules/graphing3.htm

Purplemath.com,SelectLessonsIndexonright‐handside,UnderBeginningAl gebratopics,selectgraphing

overview,thenselect

Polynomials, radicals, rationals,& piecewise

GradingRubric:

Part1:

Pre‐RequisiteSkillsReview(75pointstotal)

CorrectAnswerswithworkshown:2pointsx25=50pointsmaximum

Completedwithworkshown:1pointx25=25pointsmaximum

Part2:

Project(115points)

Showedcalculationsforallsavingsplansandgraphedallfunctions:15points

Correctlycalculatedforeachsavingsplan:3x15=45pointsmaximum

Correctlygraphedeachfunction:3x15 =45pointsmaximum

AnsweredFinalquestionwithexplanation:10points 

Parent/Guar

dianSignature:

(10points)

TotalPoints:

Part1(75)+Part2(115)+Parent/GuardianSignature(10)= 200

Name__________________________________________________________ Date:_______________

IntroductiontoStatisticsandCalculus SummerAssignment

GraphingFunctions:Linear,andQuadratic.

1) 3y

18x



-10 -5 5 10

-5

-10

-10 -5 5 10

-5

-10

2) y

x



4

-10 -5 5 10

-5

-10

-10 -5 5 10

-5

-10

InterpretingGraphs

3) Thepopulationofaformerlyendangeredmouseisnowontherise.Thepopulation,N,overthelast8years

canberepresentedwiththefollowinggraph.

Whenwasthemicepopulationthelowest?

4) Thefollowinggraphshowsthestockpriceofanewinternetcompanyoverthefirst18monthsaftertheinitial

publicofferingofitsstock.

StockPrice

(indollars)



2 4 6 8 10 12 14 16 18

Month

Whatwasthestockpricetothenearestdollarinthefourteenthmonth?

Evaluatethefunction.

5) Findf(

5.2)whenf(x)



2x

0.90.

6) Findf(k

1)whenf(x)

2x



2x

2.

7) Thenumberofpeoplepresentatastadiumforabigrockconcertcanbeestimatedwiththefollowingfunction:

y

13252x

0.79



0.42x



102,

whereyisthenumberofpeoplepresentandxistheamountoftimeafter 3:00P.M.onthedayoftheconcert.

Predictthenumberofpeoplepresentat7:00PM.

8) Acellularphonecompanydeterminesamonthlybillfromthexnumberofminutesofusage.Theamountof

thebill,B(x),(indollars)isgivenbythefunction:

B(x)

29.87

0.12x.

Determinethe

billofacustomerwhouseshercellularphone32.00minutesduringthemonth.

CompundInterest.

9) Suppose$4000isinvestedat7%.Howmuchisintheaccountattheendof1year,ifinterestiscompounded

hourly

10)

oanwantstostartanannuitythatwillhave $260,000 initwhensheretiresin21 years.Howmuchshouldshe

initiallyinvestinherannuitytodothisiftheinterestis6%compoundedannually?

StatethedomainandtherangeforthefunctionsinNumbers11

13 andwritetheminsetnotation.

Example:{x|3<x<12}.

11)

-10-8-6-4-2 2 4 6 810

-2

-4

-6

-8

-10

-10-8-6-4-2 2 4 6 810

-2

-4

-6

-8

-10

12)

-10 10

-10

-10 10

-10

13) Thefollowinggraphapproximatesthenumbery,inthousands,ofgraduatesfromnursingschoolsintheU.S.

since1985(Source:StatisticalabstractoftheUS).Theequationofthisgraphisthefunctiongivenby

y



0.036t

+0.605t



1.87t



4.67t+82.5

2468101214

105

years since 1985

1000's of nursing graduates

(13.1, 0)

2468101214

105

years since 1985

1000's of nursing graduates

(13.1, 0)

Usethegraphtoapproximatethedomainandrangeofthefunctionandwriteinsetnotation.

Findanequationoftheline:

14) withm



containing(1,

9).

15) (

9)and(

4)

SolvingQuadratics.

16) x



3x

9

0

17) x



8x

3

Converttoanexpressionwitharationalexponent.

18)

19)

20)

Evaluatetheexpression.

21) 81

1/4

22) 64

4/3

23) 32

4/5

Findtheequilibriumpointforthesupplyanddemandcurves.Roundanswerstotwodecimalplaces.

24) D(p)

900

20p,S(p)

280

10p

Quantity(q)

10 20 30 40 50

1000

900

800

700

600

500

400

300

200

100

10 20 30 40 50

1000

900

800

700

600

500

400

300

200

100

Price(p)

25) D(p)

10

p,S(p)

 p

6

Quantity(q)

123456789

Price

(p)

Part2:Project

YouhavejustgraduatedfromeighthgradeandafteryourgraduationpartyyourGreatAuntMillietells

youshehasaspecialgiftforyou.Eachyear,forthenextfouryearsshewillgive$2000.00onJune30.

Thismeansyouwillreceive$2000onthefollowingdates:

•

June30,2015

• June30,2016

• June30,2017

• June30,2018

YourAuntmak

esonestipulationtohergift:Youmustinvestthemoneyinasavingsaccountsothatyou

willhavethemoneytohel ppayforcollege.

Afterdoingsomeresearchyoufindthatthefollowinginterestratesforthreebanksinyourarea:

• BankofAmerica–0.05%,compoundeddaily

• TDBank–0.125%,compounded monthly

• HudsonCitySavings–0.25%,compoundedquarterly

Step1:

Calculatetheamountofmoneythatwouldbeintheaccountsattheendofeachyear(July1to

June30).RememberthatyouaremakingadepositeveryJuly1of$2000.00.

Step2:

Grapheachofthefunctionsonthesamegraph. 

Whichaccountwouldbethebestonetoinvestinandwhy?