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SUMMER STUDY PACKET
HONORSPRE-CALCULUS
DearHonors Pre-Calculusstudent,
This summerpacketis designedto help you practiceusingthe conceptsyou learnedin
HonorsAlgebra 2 (or Algebra 2) so that you arepreparedto study HonorsPre-Calculusthis fall.
The contentand philosophyof this summerpacketis oonsistentwith our departmentgoalsand
will enablethe studentto:
(l) valuemathematics,
(2) becomeconfident in their ability to do mathematics,
(3) become mathematicalproblem solvers,
(4) communicatemathematically,and
(5) to reasonmathematically.
.
.
'
The exerciseswere takenfrom the ChapterTestssectionofthe Algebra II textbook.You
how to do 4!! the exercisesnoted@Qgg the first day of classes.If
areresponsiblefor @i4g
you donot know how to do a problemyou are expectedto usethe sourcesavailableto you
(notes,handouts,books,Interne! etc.) to figure it out indeoendentlv.The beststudy routine
during the summermonthsis to constantlyreview topicsand do a few problemseachday, not
attemptyour
answers,Pleaserememberto showall ofyour work on the worksheets
provided.Work neatly and in an organizedway.
The problemsshouldbe done in chronologicalorder.Eachproblemshouldincludea
summaryofthe problem statement,a completestep-by-stepsolution,and a boxedfinal answer.
You shouldnot usea calculatorto do the problems,but you may useyour calculatorto check
your answer.
This summerpacketcontainsa review of the following:
a. exponents
b. roots
c. algebraicexPressions
d. multiplyingpolynomials
e. factoring
f. fractions
g. solving linear equationsand word problems
h. solving quadraticequations
i. complex numbers
j. linear functions
k. quadraticfunction
l. inversefunctions
m. polynomial functions:graphsand zeros
n. polynomialdivision
o. rationalfunctions
The summerassignment
will not be collectedbut you areexpectedto know how to solve
all the problems.Therewill be a brief reviewof thesetopicsduringthe first weekof classand
thenyou will be formallyevaluated
on your knowledgeof thesetopics.This testwill countas
l0% of your first quartergrade.The preparedAP Calculusstudentshouldeasilyscoreover 90%
on suchan exam.
Chapter I Review
Graph the numbers on a number line. Then write the numbersin increasingorder.
Identify the property shown.
3.5o1=5
4.4+5+3=5+3+4
Select and perform an operation.
5. What is the difference of 9 and - 6 ?
6. What is the quotientof l5 and - 3 ?
Evaluatethe expression.
7 . 5 + 3o 4 + 2
8 .C 3 y- 6 - + )
9 . 2 x - 3 y w h e nx = - l & n dy = Q .
! 0 . 4 x 2+ 2 y w h e nx = 4 a n d y = 3 2 ,
Simplify the expression.
ll,3x2 +4y-2x2 -5y
12.-3Q,-z)2Q., -r)
Solve the expression.
1 3 .x - 4 - 4
14,2a+3=a-+
ls. I SQ*+ 2)- 6
16.2(x+2)- 4(x -l)+ a
17.lx+21-7
1 8 .l 2 y + l =
l 7
Solvethe equation for y.
1 9 .x * y = - 2
2 0 .x - l : 2
21.3(x+ y)- q
2 2+. * - t y - l
Solvethe inequality then graph your solution.
2 3 .3 x+ 3 > 1 2
24.4-x<2x-l
25.2(x+l<5
2 6 ,x + l < - 2 o r 2 x 2 6
27. The formula for the areaof a triangle is A = +bh .
a. Solvethe formulafor b.
b. What is the baseof a trianglewith an areaof 20 squareinchesanda heightof
5 inches?
Usethe pLAN method (Pick a variable, Look for key words, Do the Algebra, Check to seeif your
number makessense)to solvethe following problems.
-1, +2, -2,
28. you played6 roundsof golf lastweek.In relationshipto par,your scoreswere
+4, +6, and - 2. What was your average score for the week?
29. Ticketsto the local amusement
park are129.50pesoseach.You and four of your friendsgo
To the park.You find someone'swallet at the park.Your friendswant you to pocketthe
wallet,but you decideto returnit to the authorities.They ownerrewardsyou with 1000pesos
and free food coupons.You'refeelingprettygenerousanddecideto pay for all the tickets.
How much rewardmoneywill you haveleft over?
30. Two more than twice a numberis equalto itself.Find the number.
Chapter2 Review
Graph the relation.Then tell whether the relation is a function.
l.
x
_J
-
-l
0
v
-2
0
I
2
2
3
3
2.
-3
-2
3
3
x
v
t
.
r
a
4
I
0
I
3
4
2
2
I
.
. r J
\
Evaluatethe function for the given value of x.
3 . " fG ) - 2 5 - 2 x w h e nx - 4
Graph the equatio
_
-lx *
5 . 'v = 2
: : : :
: : : : : : : :
a. "f(*)= xz + 5x + I when x =l
7.4x-l=8
8.x=-2
Competethe following formulas:
9. Slope-intercept
10. Slope
ll. Point-slope
Write an equationof the line that has the given properties.Leaveyour answerin slopeintercept form.
'
12.slope:
l2
y-intercept:2
13.slope:I
point: (2, -3)
14.points:
(3, 4), (-1, 0)
15. Write an equationof the line that passesthrough(4,3) and is parallelto the
l i n eY = . r + 1 .
16.Write an equationof the line thatpasses
through(-2,3) and is perpendicular
t o t h e l i n ey - 2 x + 1 .
Graph the inequality in the coordinateplane.
1 7 .y > - l
-)
1 8 .y t ; x + l
J
Graph the function.
ft.ifx>o
19.f (x)=
' 1n'",.
lz,,f.r< 0
2r. f (x)- lxl+I
23.
22.f(*):ll.- ol
Studentticketsfor a football gamecost$2 each.Adult ticketscost$4 each.
Ticket salesat lastweek'sgametotaled$2800.Write a linearmodelthat shows
the differentnumberof studentsand adultswho couldhaveattendedthe game.
Thengraphthe model.Make sureto labelthe x- andy-axes.
24.
Determinewhetherthe datashowdirectvariation.If so,write an equationrelating
x andv.
x
v
25,
4
-3
8
t2
t6
20
24
4
-9
-t2
-15
-18
Draw a scatterplot of the data.Thentell whetherthe datahavea positivecorrelation,
a negativecoffelation,or relativelyno correlation.Draw a line of bestfit.
x
v
2
-3
I
4
. ' 5
e
3
-3
3
-2
5
0
6
5
Chapter3 Review
writethe onsweros
Solvethe systemby grophing.lf thereisexoctlyone solution,
on orderedpoir.
2x-v=5
l'-"
*y=-3
''
3 x+ v = l
,, --2- 6x
V-x=l
3.A
x+y- 5
Solvethe systemusingony olgebroic method.
4.3x-2y-10
5x+3y--15
- x+!=2
5.
!=2x+5
Grophthe systemof lineorinequolities.
7.
x + 2 v> 4
x-y<3
v32
8.x<3
2x+3y>6
3x '5,y = l0
6. -9x+l5y=-39
Findthe minimumond moximumvoluesof the objectivefunctionsubjectto the
givenconstroints.
Usethe grophbelowto showthe feosibleregion.
9. Objective Function:C = 4x + 5y
C o n s t r o i n t;s; ::
x+y<6
1 0 .O b j e c t i v e F u n c t i o n : C - 3 x + 2 y
x>0
Y>
Constroints: ?
x + 3 v< l 5
4x+y< l6
pesoseoch, but ore now on sole
I 1. At o musicstore,compoct discscost 149.50
for I 29.50pesoseoch. lf you bought20 compoct discsin the postmonthond
spento totol of 2750 pesos,how monydid you buy on sole?
12.You hove o choice between two lunch combinotions.A molletewith o
refrescocost 20 pesos,while o toco dorodo with o refrescocost 33 pesos.
hos budgeted
You need to purchoselunch for 50 people ond your business
1260for food. How mony of eoch type of combinotion con you purchose?
Chapter5 Review
Completethe informotion
below.Thengrophthe quodroticfunction.
l. y--2(x+4)2 -3
Verf ex:
Axisof symmetry:
Y
X
2. / = * Q - e ) ( x + z )
Vertex:
Axisof symmetry:
X
Y
3. ! = 3 x 2 - 6 x + 8
Vertex:
Axisof symmetry:
X
Y
Solvethe quodroticequotionby foctoring.
4 . 1 2 =x 2- x
5. 9x2-49-o
6 . - 3 x 2 + 2 4 x - 3 6= 0
Solvethe equotionby completingthe squore.
7. x'+8x-22-0
Forproblems8 ond 9, solvethe quodrotic equotion usingony oppropriote
method. Provideo brief explonotionon why you chose thot method.
8. 3(r - 5)' = 27
9. x'-10x+4=0
the expression.
Forproblemsl0 to 11,simplify
r 0 .( s - 8 r ) - Q - t r i )
1r. (5+zDQ- 3t)
- i
12.7
3+i
Findthe discriminontof the equotion ond give the number ond type of solutions
of the equotion.
- 6 x+ l 4 - 0
13.2x2
14.x2-5x-lt=o
Completethe inforrnotion
below.Thengrophthe quodroticinequolity.
l5.y < x' +2x-8
Verfex:
Zeros:
v
X
Writeo quodroticfunctionin vertexform for the porobolo shown.
I 6.Vertexform y - aG- h)2+ k
Vertex:
( - 3 ,- 1 1 - -
I
I
"t
V\
I
I
t
{- 5 , - 5 }
\
Writeo quodroticfunctionin interceptform for the poroboloshown.
8. G*tXzx'-x+l)
Foctorthe polynomiol.
9 . 1 0 0 x '- 9 y '
ll. y3-8
1 2 . l l r t y + l 0 x 2 y 2- 5 r y t
Solvethe equotion.
1 3 .x 2 = 8 l
1 4 . 5 x 3= 3 0 x- 2 5 x 2
1 5 . x 3+ 4 x 2 - x - 4 - 0
Divide.Usesyntheticdivisionif possible.
1 6 . ( r '- 7 x z + t 2 x + 6 ) + 8 ' - 2 x - z )
17. Qx' + llxz + l8x + 9)+ (x + 3)
I 7.lnterceptform y - a(x- pk - q)
r cx +y
2. 8'v'\'
3.
x 4y 4
tr
4.+. ("yf'
Describethe end behovior of the groph of the polynomiolfunction.Then
evoluote for x : -2,-1,0,1,2
5 . v = 2 x r+ x ' - 8 x - 4
X
f(-)+_
oS xi*oo
f(*)+
oS x-)-o
v
Performthe indicotedoperotion
6. (:r' - x' + +)- Q*' + x' +2)
7. (x-ty)ft-4y)
Describehowto obtointhe grophof g(r)fromthe grophof f@-^l;.
ll.s(r)-1fya4-2
Motch the functionwithitsgroph.
12."f(x)={r2
1 3 ./ ( x ) = - J x + 1
1 a .f ( x ) - { x - z
A.
B.
C.
!'
I
I
\
f
--J,
16.f(.)-4ffi-2
v.
f
I
r
.r
Grophthe function.Includethe porentgroph.
I s. /(x) - fJ 16
ai 12
,fl
I
. Jq
Listoll the possiblerotionolzerosof f usingthe rotionolzerotheorem.Thenfind oll
the zerosof the function.
18.f(x)=xt+x'-10x+8
Chapter7 Review
Evoluotethe expression.
1.lF'
2. 27%
3.!m
^(H^
Simplifythe expression.
5. 3/' .3%
6. ^ls4+{ns
T.t{6.s{40
,(ffi^
,OtF
Evoluotethe expression.
,-r (
t'
Qst)'
| \-%
\rrlr)
solutions.
Solvethe equotion.Checkfor extroneous
3/
4 . 2 x / a+ 7 = 2 3
.
,t/
3x+l+ 5 = 3
6 . 2 ( x + 2 f t- 6
3x+7-
8.x-4-
2 x+ l
l0-3x
r 8 Review
Usethe givenvoluesto writeon equotion
Thevorioblesx ond y voryinversely.
=
y
4.
y.
x
relotingx ond Thenfind when
1 .x - - 2 , 1 = 2
2 . x - g' .' v - !
2
)
3 .x = - - . v = 1 2
J
Thevorioblez voriesjointlywithx ond y. Usethe givenvoluesto writeond
equotionrelotingx,y,ond z.Thenfindzwhenx = -l ond y = 4.
4.x-2,y=4,2--z
5 .x= 4 , ! = r , z = - l
6. Describehow you would obtointhe grophof y = ++
x-l
7 fromthe grophof
I
y - - . U s ec o m p l e t e s e n t e n c e sS
. p e l l i n go n d g r o m m o rc o u n t .
x
Gropheoch functlon.Includethe porentgrophond osymplotes.
7 . 'y -
- )'
x-l
+3
8 . -v -
'? - Z
x+4
a
D
Performlhe indicoted operotlon. Simplifythe resull.
r' vc' . v - 3
g. * *5t
2 v v
, . ,.
(t+t)'
x-l
, A -x t - 3 x '
| \r.
3x+6
y-1
y-3
.2x-2
' ) r,, x'-5x+4.x'|
t
z.
'---------------
xt -8x2 + l5x
--- -
-
x
x+l
I A
6x2-l8x-60
3x
2x-3
t
_2 + _ 3
't 4 x xY
'v'
3
l
_+x ' )
l0
1' vA'
x+l
l
-+- 3
2 x+l
x
3x+6
2 x 2+ x - 6
-L-.-
Simplitythe complex froction.
-
Solvelhe equoflon. Check eoch sofullon.
3
r.'
a r . -
x+l
x-2
l3
3
3x+3
- - =
18.
3 - 4
x-2 *-1- x'-5x+6
Equationswith RationalExpressionword problems
t . The numeratorof a fractionexceedsthe dominatorby 8.Thefractionwhich resultsfrom
subtracting3 from both the numeratorand the denominatorequals3. Find the original
fraction.
2 . The denominatorof a fractionis one lessthantwice the numerator.Adding 7 to both the
numeratorand denominatorresultsin a fraction which equals 7110.Find the original
fraction.
3 . The sum of the numeratorand denominatorof a fraction is 95. Reducedto lowestterms.
the fractionequals5/14.Find the fraction.
4. The denominatorof the fraction is one more than twice the numerator.When the
numeratoris increasedby 8 and the denominatoris increasedby 10,the resultingfraction
equals2/5.Findthe originalfraction.
5 . The dimensionsof a photographare I 2.5 centimeters
by l7 centimeter.The photograph
is to be framed so that the outsidedimensionsof the framedphotographwill be in the
ratio 39148.Find the width of the frame.(Assumeuniform width.)
6. Clara invested$200,000more in a businessthan her partner,Faye.If eachhad invested
$100,000more,the ratio of their investmentwould be2:3. Find the amountinvested.
7. Clyde Burt has213as much money investedat I I Yoas the amountinvestedat l2%. The
total yearly return from theseinvestmentswas $l1,600. How much was investedat each
rate?
8 . The numeratorof a fraction is 6 less than the denominator.When the numeratoris
increasedby 3 and the denominatoris increasedby 2, the resultingfraction equals%.
Find the numeratorof the original fraction.
Distance/Rate/TimeWord Problems
a
a
to
l. A businessconsultanttravelsbetweentwo citiesby planein l0 hourslessthan it takes
speed
average
the
and
make the trip by train. The averagespeedof the planeis 480 km/h
of the train is 80 km/h. Find the distancebetweenthe cities.
Z. It takes 24 minutesless to travel to an airport by taxi than it doesto make the trip by
taking a bus. The averagespeedwhentravelingby taxi is 80 km/h and the averagespeed
when travelingby bus is 60 km/h. Find the distanceto the airport.
3. A bus trip of 300 kilometerswould havetaken 415as long if the averagespeedhasbeen
increasedby 15 km/h. What was the speedof the bus?
36
4. The seedof a boat in still water is 9 kmih. It takesthe boat twice as long to travel
distance
kilometers upstream on the Hurm River as it does to travel the same
downstream.Find rate of the current.
50
5. An airplanepilot found that it took 213as muchtime to travel 1800kilometerswith a
the
km/h tailwind as it took to travel the samedistancewith 100 km/h headwind.Find
speedof the planein still air.
the
6. A planetakesoff and flies eastat a rate of 300 km/h. On the returntrip flying west,
plane'sspeedis 250 km/h. The planehasenoughfuel for a safeflying time of 3 % hours.
How far eastcan the planefly? Roundyour answerto the nearestwhole kilometer.
7. A man has3 % hoursin which to give somefriendsa tour of the surroundingcountryside.
How far from the housecan the tour extendif the speedon the trip out is 25 km/h andthe
speedon the returntriP is 40 km/h.
g. Gloriajogged from her home to Rock creek,a distanceof 16 miles. Then she walked
homeat a ratethat was 215ofher jogging rate.The roundtrip took 7 hours.Find Gloria's
jogging and walking ratesfor the tripg. A Light plane has a speedof 120 mph in still air. On a certainday, the pilot flies 700
miles with tailwind. On the returntrip, the planecovers 517of this distancein the same
time. What is the sPeedof the wind?
faster
10. The averagespeedsof two carsare in the ratio 4:5. Eachcar travels100 miles.The
of
speed
average
the
car coversthis distancein 30 minuteslessthan the slow car. Find
eachcar.
Work/ Rate Problems
l. Fredcan sweepthe snowfrom a sidewalkin 4 minuteswhile Sarahcan do in 3 minutes.
is
Working together,how long will ittake themto sweepthe sidewalk?(HINT: Fred's rate
Sarah'srateis l/3 sidewalk/minute.)
1/4 sidewalk/minutes.
2' If Ann can sweepthe leavesfrom ayardin 6 minutesand Gracecando it in g minutes,
how
much canthey get doneworkingtogetherfor 3 minutes?
3. Joancanpainta housein 6 days.Tom canpaintit in 9 days.If Joanworksalone for
2days
andthenI joined by Tom, how longwould it taketo painithe house?(HINT: the
equationis
ll6tl+(ll6t2+ll9t21=l wheretl is the time Joan*orkr alone, andt2 is the time
they work
together.)
4. Tom canprocessa batchof bills in 8 hours.It takesBill l0 Hoursto do the
sameJob.How
long would it take themtogetherto completethe work?
5. Suecanassemble
a bicyclein 10 minutes.Her sistertakesl5 minutesto do the samejob.
How long would it takeif they work together?
6' SamChu canplow oneof his fieldswith a tractorin 4 days.It takeshis neighbor
l2 daysto
plow the samefield. How longwill it takeSamChu if his neighborhelpshim?
7. Ruth can mow a certainstrip of lawn with her mower in 20 minutes,and Jane
can mow it
with hersin 30 minutes.How long would it take if they did this together?
8. If one pipe can fill a tank in 3 hours,a secondpipe in 4 hours,and a third in 5 hours,
how
Iong will it taketo fill the tank if all threepipei arebeingused?
9' SueEllers,workingalone,canpainta housein l2days. If ClydeGalluphelps,
it takesonly 4
days.How long would it takeClyde Gallupalone?
10' Art can do a job alonein 8 days.After he hasbeenworking alone for 2days,
he is joined by
Pete.They finish thejob togetherin 2 moredays.How long would it takepeteto
do the work
alone?
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