Document 2541034

Name:____________________________________________________________________________________________________
RichardMontgomeryHighSchoolDepartmentofMathematics
SummerMathPacket
forstudentsentering
Algebra2/Trig*
Forthefollowingcourses:AAF,HonorsAlgebra2,Algebra2
(PleasegotheRMwebsitefortheTwo‐yearAlgebra2packet)
Thispacketmustbecompletedandreadytoturnintoyournewmathteacheronthefirstdayofschool.It
willbegradedandyouwillbetestedonthematerialinthispacketwithinthefirsttwoweeksofschool.
Below you will find a timeline for completing the packet. Your Algebra 2 teachers have recorded the
worked‐outsolutionsandpostedtheminaYouTubePlaylisthere:http://bit.ly/1GKbu2U.Youcan
typeinthelink,orusetheQRCodeatthebottomcornerofthispage.Youarenotrequiredtowatch
thesevideos.Onlywatchthemifyoufeelyouneedto.Therearelotsofproblems,butwewantyoutobeas
preparedandasreadyaspossiblefortheupcomingchallengesofyournewmathclass.
Youmayworkwithaclassmateorapeer.Youmayusetextbooksorothersourcestohelpyoucompletethe
packet, however, each student must submit their own packet, and each student is responsible for
understandingthematerialcontainedinthepacket.Calculatorsarenotnecessaryforanyoftheproblemsin
thispacket.Writeyourworkonthispacket,andmakesuretoshowanappropriateamountofworkforeach
question.Ifyouneedanothersheet,youmayattachit.Thisassignmentisareviewofskillsyoushouldhave
alreadylearned.KnowingtheseskillswillhelpyoubesuccessfulinyourAlgebra2class.
*ThissummerreviewpackethasbeendesignedtoreflectsomebrandnewchangesintheMCPSAlgebra2
curriculum based on Common Core standards, which include different and more rigorous topics such as
trigonometry.
SuggestedTimelineforCompletingAlgebra2/TrigSummerPacket
EstimatedTimetoComplete–2HoursPerWeek
Weekof:
Monday,July20,2015–Friday,July24,2015 Problems1‐8
Weekof:
Monday,July27,2015–Friday,July31,2015 Problems9‐16
Weekof:
Monday,August3,2015–Friday,August7,2015
Problems17‐24
Weekof:
Monday,August10,2015–Friday,August14,2015 Problems25‐32
Weekof:
Monday,August17,2015–Friday,August21,2015 Problems33‐40
Formulas
Formulasyoushouldbefamiliarwith.
EquationsofLines
Slope‐InterceptForm:
Point‐SlopeForm:
StandardForm:
ExponentialFunction
⋅ ExplicitFormulaforanArithmeticSequence: ExplicitFormulaforaGeometricSequence:
Formsofquadraticfunctions
VertexForm:
StandardForm:
FactoredForm:
0
0 ⋅
1
1 ⋅
1
Axisofsymmetry
QuadraticFormula:
If
√
0,then
.
Zero‐productproperty:
If ⋅
0,then
0or
0.
PythagoreanTheorem:
Inatrianglewithsides , ,andlongestside ,theequation
triangleisarighttriangle.
Distancebetweentwopoints ,
and
Slopeofalinecontainingtwopoints ,
Righttriangles
and
:
,
:
sin
opposite
hypotenuse
cos
adjacent
hypotenuse
tan
,
holdsifandonlyifthe
opposite
adjacent
2 1. GinoknowsthattheformulaforconvertingdegreesCelsius( )todegreesFahrenheit( )is
32.Healsoknowshowtotransformanequationintoanequivalentequation.Whichofthefollowingis
correctlysolvedforC?
A.
B.
5
C.
D.
160
2. Let and representtwonumberssuchthat
.Statewhethereachstatementbelowistrueorfalse.
Justifyyouranswer.
Statement
Trueor
Justification
False?
8
8
7
7
7
7 10
10
3.Belowisthesolutiontoaninequality,representedgraphically.
4.
4
3
2
1
0
1
2
3
4
Whichofthefollowinginequalitieshasthesolutiongraphedabove?
A.
3
6
B.
4
9
17
C.
2
10
14
Solvethefollowingexponentialequations.
(a) 3
3 (b) 25
5
(c) 9
27 3 DegreesFahrenheit
16 . There are many correct ways to solve this equation.
5. Vlad wished to solve the equation 64
Whichofthefollowingisnotacorrectfirststepinsolvingthisequation?
A. 2
2
B. 4
4
C. 16
16 6. Whichofthefollowingexpressionsisequalto5 ?
B. 10 C. 2 A. 25 7. Thegraphbelowrepresentsthetemperature( )indegreesFahrenheitinsideofafreezerasafunction
oftime.Thevariable representsthetime,inhours,sincemidnight.
F
TemperatureinaFreezer
4
3
2
1
t(timeinhours)
0
2
4
6
1
3
7
5
–1
–2
–3
–4
(a) Whatisthedomainofthefunction?
(b) Whatistherangeofthefunction?
(c) Whatisthemeaningofthe ‐intercept?
(d)Atwhattime istheminimumtemperaturereached?
(e) Onwhatintervaloftimeisthetemperaturedecreasing?
(f) Whatdoesthestatement
5
2representinthecontextofthesituation?
4 8. For each relation below, determine whether or not the relation represents a function. Justify your
answer.
(a)
(b)
(c) 2, 7 , 4, 7 , 2, 12 , 6, 11 (d)
4, 9 , 6, 11 , 11, 15 , 10,9 (e)
(f)
4 2 5 4 5 7 4 8 8 1 9 2 7 9 9.Whatisthenumberofsolutionsforthissystemofequationsbelow?
7
7
A.
B.
C.
D.
0solutions
exactly1solution
exactly2solutions
aninfinitenumberofsolutions
5 10.Thegraphoftwofunctions,
and
,areshownbelow.
Foreachproblem,writethecorrectsymbol, , ,or intheboxbetweenthetwostatements.
(a)
2 2 (b)
The ‐interceptof
The ‐interceptof
(c)
1 ⋅ 3 2
2 11.Arectanglehasalengththatis6incheslongerthanitswidth.If represents,thewidth,writean
expression,intermsof ,fortheareaoftherectangle.
12. Fillinthenumberthatcompletesthesquare.
(a)
6
(b)
12
(c)
7
________
________
________
6 13.Twofunctions,
and
arerepresentedbelow.
ComparethestatementsbelowincolumnsAandB.Intheemptyspaceattheendofeachrowinthetable,
writethecolumnletter(AorB)oftheexpressionthathasthegreatervalue.Ifbothexpressionareequal,
write .
(a)
(b)
(c)
(d)
(e)
ColumnA
ColumnB
1 3
Themaximumvalue
of
0
4
4
Thevalueof that
0
makes
5
,
10
and
The ‐interceptof
2 ∙ 4
5
3
4
14. Findtheslopeofthelinethatpassesthrough
Whichisgreater(orarethey
equal)?
5,1 and 7, 3 .
7 Sketchthegraphofthefunction,thengivetheinformationrequested.
15.
4
Vertex:
LineofSymmetry:
‐intercepts:
‐intercept:
5
Domain:
Range:
Intervalonwhich
isincreasing:
Intervalonwhich
isdecreasing:
16.Usetheanswerbankbelowtocompletethefollowingstatements.
ANSWERBANK
difference
linear
ratio
exponential
arithmetic
geometric
(a) Anexplicitruleforanarithmeticsequencewouldbea(n)_________________function.
(b) Therecursiveformula
0
20,
30 ∙
1 representsa(n)__________________sequence;
itsexplicitrulewouldbea(n)_________________________function.
(c) Thesequence10,12,14,16,18,20hasaconstant__________________________________of2.
(d)Thesequence10,20,40,80,160hasaconstant____________________________________of2
8 17.Matchthefollowinggraphstoitscorrespondingequation.
1)
A.
3
5 2)
3
5
3)
3
5
4)
3
5
B.
C.
D.
18.Graphthelines.Accuratelyplotandlabelatleast3pointsoneachgraph.
(a)
3
1
(b) 3
2
6
9 Foritems19and20,afunctionoftimeisgiven.Ineachitem,determinetheaveragerateofchangeonthe
giveninterval.Givetheunitsforyouranswer.
19.
Time
(seconds)
0
1
2
3
4
5
Distance(feet)
Averagespeedontheinterval
0
5
20
45
80
125
2
5:
Units:
20.
50
Averagerateofbacteriagrowthon
theinterval1
6.
45
40
NumberofBacteria
35
30
25
20
Units:
15
10
5
012345678910
Time(hours)
21.Solvetheliteralequations.
a Solvefor :
b Solvefor :2
3
12
0
10 22.Thefollowingquestionsexploretherelationshipbetween
and
,andthe
effectof , ,and intransformingthefunction
|
(a) Whichofthefollowinggraphsrepresentsthefunction
3|?Whichonerepresents
| | 3?
C
D
A B
y
y
y
y
x
x
x
. Matchtheequationslistedbelow
(b) Thegraphtotherightrepresents
withthegraphsI,II,II,andIV.
_________
_________
4 x
_________
5
_________
II
I
III
IV
11 4
23. Theequations
6and
7aregraphedonthecoordinateplanebelow.
O
(a) Whatarethesolutionstotheequation
4
5
7?
4
(b) Whatarethesolutionstotheinequality
5
7?
24. Solvethefollowinglinearequations.
(a)
(c)
4 3
2
3 –2
1
(e) 7
4
(g) 2
7
6 (b) 2 4
0
(d) 6
2
(f)
4
2
5
7
(h) 4 1
6
8
6 2
1
2
4 19
55
2 3
2
1 12 25. Findtheslopeofthelinecontainingthepoints 6,5 and 3,9 .
26. Findthe ‐interceptandthe ‐interceptoftheline3
4
48.
27. Findanequationofthelinewithslope3/5and ‐interceptof 4.
28. Findanequationofthelinethatpassesthroughthepoints 1,2 and 3, 4 .
29. Findanequationofthelinethatpassesthroughthepoint
equation
3
1.
1,4 andisparalleltothelinewith
30. Findanequationofthelinethatpassesthroughthepoint
equation
2.
2, 5 andisperpendiculartothelinewith
31. Computethevalueofeachofthefollowing.
4.
(a) Evaluate
3 – 5if
1if
3.
(b) Evaluate
4
14 when
2.
(c) Evaluate
13 32. Completelysimplifyeachofthefollowing.Simplifyanyradicalexpression(donotwriteasadecimal).
4
7
2
7
8 (a)
3
4
2
7
13
3
2
8 (b) 39
(c)
7 3 (d)
12
12 (e)
2 3
2 (g) 3
5 3
5 (h) 2
3 3
1 (f)
6
5 ⁄ (k) 11 ∙ (j)
(i)
(l)
(m)
(n)
3
5
(o) √50
(p) √100
(q √32
(r)
(s)
(t)
3√20
√14√7
14 33. Completelyfactoreachofthefollowing.(HINT:Whenfactoring,firsttakeoutanycommonfactors,then
factorusingthedifferenceofsquaresmethodorsomeothermethodoffactoring.)
20 (b) 7
21 (a) 5
16
64
(d)
49
(c)
72
(f) 3
5
2
(e)
(g)
7
12
(h) 2
15
(i) 8
16
(j)
6
3
3
(k)
10
24
(l)
2
6 (m) 4
49
(n) 3
11
6
(o) 81
1
(p) 3
8
5
(q) 3
11
10
(r) 6
3
18 (s) 6
13
5
(t) 10
7
12
15 34. Solveeachofthefollowingbyfactoring.
(a) 2
1
(c) 3
3
10
0
0
(b)
16
0
(d)
6
0
(e) 2
13
15
(g) 4
24
0
0
(f)
7
8
0
6
0
35. Solveeachofthefollowingusingthequadraticformula.
3
2 0
(b)
5
(a) 2
4
1 0
(d) 2
8
(c)
5
0
16 36. Solvethequadraticequationbytakingasquareroot.
(a)
7
81
(b)
5
64
37. Fortheitemsbelow,determinethesideoftherighttrianglemarked .
(a)
(b)
5 10
7
12 38. Thelengthsofthethreesidesofatrianglearegiven.Determinewhetherthetriangleisarighttriangle.
(a) Lengthsare12,16,and30.
(b) Lengthsare2,3,and4.
39. Findthedistancebetweenthepairofpoints.
(a)
7, – 2 and – 6, 3 .
(b)
– 6, 3 and 2, 9 17 40.Givenright∆
,usetheitembanktoidentifythefollowing.Itemsmaybeusedmorethanonce.
ItemBank
∠ ∠ ∠ (a)Legopposite∠ (g)Cosineratioof∠ (b)Legopposite∠ (h)Tangentratioof∠ (c)SineRatioof∠ (i)TheanglewhoseSineratiois
(d)Cosineofratio∠ (j)TheanglewhoseTangentratiois
(e)Tangentratioof∠ (k)Hypotenuse
.
(f)Sineratioof∠ 18