Download Algebra 1 EOC Review Key ()

1. Many times, sales employees are paid a base salary plus a commission --- a percentage of the
amount of merchandise value sold. Assume that a particular sales employee is paid $200 eer
week, with a 20% comml sjo on the amQU t they sell.
­
Which equation best represents t he to tal salary (T) per week that an employee ,is paid for selling any value of merchandise (m )? = 200 + 20m
~.
T
~
T=220m CQJ;)
T =
,..::9=::D.
T
a,+O.2m = 200 + 1.2m 2. A 1,SOO-gallon tank contai ns 200 gallons ofwa er Water begins to run into the tank at the rate of
Q gall ons per ho ur. After 2 hours, t he ra te increases to 80 gallons per hour. Wha t is the total
number of hours that the water can fl ow before the tank is fu ll, but not overfl owing?
:tP"iL 1 4h~urt 37. Sminutes
~
~
~
.~
@ ~o
alP ~ ~Iole.. +a
c;. -
17 hours, 20 minutes
\.......:..4
18 hours, 45 minutes
~
'--"'"
10
g(x)
and
- "...
+go
.y,S
-+,,<)
ibes the difference(s) between the graphs of:
3x
s-vvlc
0
2If.- e- vJ l\ ~. -h, ~ J. 2
--~~~~~---+----~~~--------------+VA~Sw~r
2..00
2. J 5 350 ~/<.-t 3So
16 hours, 22.5 minutes
3.
('to
6x - 5
­
,I
•
The graph of [(x) is twice as steep as the graph of g(x) \~
The graph of [( x ) is half as stee p ~hl graph of g(x)
The graph o f.1.f:tJ has ay-intercept of -5 while g(x ) has ay-intercept of -10.
~",l5.1?
-
The graph of f (x) has a lower v- intercept than the graph of g(x)
·-~lSe...
~SO
X:;
Ie..{ .31S,
~
•'31S
= 5x -
is 22-.. S
2
f -~K + I?- -:=- 5 x - "2­
-i~+
- 5)(. - L
-I~
~1'1
-G'J.
-Sy.
-II i- --
,A-
(, '" h our
4. Solve the equation for x :
7 - 3(2x - 4)
So
S)(. -;2. \
-5)(..
-.). 1
::- -II
Page 1 of 15
rA
5. Solve for x:
~
(f;)
x
=­313 47
I:!-/~
~ 4= 7()(-3)
2'2 -t t..t ( )( - S') ~ 7 (~ -3)
~
X
~
x=­
~
=-
7
'2..'L -t-l..\.x -12
.,---
=-7)(-.2\
55
3
29 x=-
7
: :. IX
~X
- 7)<
~7x
-3)(
-.:L \
-I
-3\ -;:'-3
6. Mr. Shaw begins traveling east on the freeway with a full tank of gasoline. His car has an 18-gallon
gas tank and ge ts 25 miles per gallon during highway trave .
Let m = the number ofmiles Mr. Shindler has driven
Let g =the number ofgallons ofgas remaining in his tank
Select which equation describes the relationship between the number of miles Mr. Shaw has
traveled and the number of gallons remaining in his gas t nk:
g = 18 - 25m
m
g
= 25g -18
m
= 18-25 25 m = - - 18
9
Justify your choice in the answer box below Support your answer using words, numbers, &/or
diagrams.
y'V'-: \ e ~
9"" [t~", s I, 0
')s
50
1(.,
lOD
\S IY ,s
-\
Jk
~,r ).-~~
~G'--\.o\<
~\o~
~C(
~ ).S
"{j
, s­
sh O ("v '5::.
~
is V\e.~"e..
- I
2S
oV\.L~ l e-ttp.-r C s L-U:l ;..oV ~
~ sl(jr­
'\.eS
~
7. Choose the correct solution to the equation
~Q';J
~
x=2 0
x =--
~
7
5
X
=-4
5
~ x =­ 7 3x.-{
-t'l
-~)<
4X + 3) 2­
~
9f< +
-~x
(o
-t,
-
. -­ 5
Page 2 of 15
8. Given the inequality:
•
-S<2X+S
-1
Solve for x:
12.
-
-7
5
- I 'J. < 2)( <
. . ..'. 2
.
>L
-­·~
L
• Represent the set of solutions on a number line:
eLk . . ",) ~ S
kc\ de 5
< ' ~\ ~
-, -<:, 0.2
~-\vJ()e'Y'-'
3
9. One worker at a gadget assembly factory can assemble 10 gadgets each hour. After working for 3
hours, the worker's supervisor starts to assemble gadgets also. The supervisor can assemble 12
gadgets each hour._Together, they assemble 140 gadgets. --\-v.Jo
S
So ~ J.....o ~
lo f<
-to..h( e.
How many hours did the worker assemble gadgets in order to have 140, total? Support your answer using words, numbers, and/or pictures. ~(S
"l­
~
-1
5
Co
w
3c)
S1­
--,~
~(o
0
~tl)~
()
I'U
~
TID
W(}./lt?( y
l£. € ( "
or-. L')
II~
l iD
'-.-7J
~
(,A.)(>
8
I
;-"2.-"1­
S~\t';~CN"
-;-2'1-­
How many hours will the worker assemble gadgets?
....... l+10. Solve the system of linear equations. '*" CQvl,,{
v..JL;t .
6t~~
I/"'1JI,..U
'b j
-3
1:"" 5
S
+ y = 13 -----.:')o~ -I S)'. - 5 j =- -(0
x + 5y = -5
+ x+ S~J :=..- - 'J
3x
{
()..." 5.v
v""-
b~ ~-.
(-5, 28)
~.
(-2,19)
~
(7,2)
e
-70
(5,-2)
Page 3 of 15
11. An ice cream store is keeping track of the number of chocolate and vanilla ice cream cones sold.
One day, the number of chocolate cones sold was 10 less than twice the number of vanilla cones
sold . A total of 140 cones w r sol that day.
•
•
•
•
Write equations to determine the number of chocolate cones sold that day.
Be sure to define your variables.
Use the equations to determine the number of chocolate cones sold that day.
Show your work using words, numbers, and/or diagrams.
)
~
J-)( -10
'--v---'"
-t I D
+10
-
3)<
'f. ~ ::
-
IS O
SO
~
-
2(50) -10
/00 - 10
~-;. C)D
12 _ After so Ivi ng the foil owing system 0 f equati 0 n,,_ (4
~ ~; ~
Sarah claimed that the system has no solution. Carl disagreed and said that the system has an
infinite number of solutions. Who is correct and why?
Who is correct?
Show work to justify your conclusion.
'1 ~ -2 ( '2)(- ­ ;')
L{)(
-zt'f
~
0 '1-­
~ 10
ID
10
-
-1 0
10
-
0
Explain how your work supports your conclusion:
Page 4 of 15
13. A moving box can hold at most 40 pounds- I hav at least 50 boo to load into the box. On
average, the hardcover books weigh twice as muc a
ack books.
• Write system of inequalities to represent the situati
o
•
-t~ ~
50
Define your variables.
=
~ 1f-l--.
,t.-v-t.{
(C>
~u....Jit.) S u
eta e.OS ~ 1-
'I(/.R...r
V\..e.R.
b0
(>
jL S
J-...\-L..e ;;).
~hvt- CLW\u u o"\:t
14. Tara's cell phone plan cost~ month, which includes 150 text messages. After she uses all
of those text messages, it will cost her 0.12 er text message.
• Write an equation or inequality that could be used to determine the total cost of her
cell phone bill if she sends more than 150 text messages .
• Be sure to define your variables.
Equation/inequal ity:
0., I I
definition of variable:
~ ~ # -l--e 'f-+s
')( + ~ S ::::. <j
po.. 5rl­
v\ -=--\-o{­.••...l
IS 0
<!..0
st-
J
Tara wants to spend no more than $48 -o n her cell phone bill. How many text messages can she
send, total? Support your answer with words, numbers, and/or diagrams.
0,,\ '2 )( -t- ~ S
- ~S
- ~c; ~
De I ~ "")(
13 .
'-..
-o
X <­
--
be ... r--J
1'2­
IO~ .. 3 Explain what your answer means: ~
To \Le e f -I~ b, l \ LJ
-1-<)'-t-c;
~
(SID
-tf. Y Z) ~l~s~)es.
IO~
2SY;
""
Page 5 0/15
15. Fred, Thomas, and Zachary worked at the ice cream store in the mall. Last week, Fred earned
more money than Thomas, but less than Zachary. The graph shows the money earned by Zachary
~
a nd Thomas.
~
:> ',
r<
1;
W EEKL Y PAY VS. N UM BER OF HOU RS W OR K ED
...ro
",
400
0
0
c
:.?OO
;>.
r.
a..
Ho u rs Worked
Which area of the graph represents Fred's possible weekly pay, and why?
P because that represents more than Thomas.
T because that represents more than Zachary and less than Thomas.
P because that represents more than both Zachary and Thomas.
T because that represents more than Thomas and less than Zachary.
16. Which is the graph of the solution set of the system of inequalities?
Se;Q- c.t
cLJ+.e J
G
~
~-2y~ ~O
=>
r
L.V\J ~ -_
X -t_
ID
- -
-'2­
-1--2­
2x + y > 0
G -:=d:----.......\ yo
-­
- _..x
5h
lJ
~'\.0 t-
be.
b"sl·J
- - - \;t
-­
.:-- -. _--- 'Tf boVf..i­
Sko·lJ b~
'o~
C{.~D".It-
Page 6 of 15
17. Look at the system of linear inequalities.
'~
5\oe~DvJ
~
{~ y <JJ
-\~ ""e(~" ~+ y ~
s\.o~
_\.1\
~
-I
-I
8
I.~'--,x+g
<.. -!
~
>X
-
3
~J ~ol~ ~
-I
-
.~
s
3 ~}OCN~ Jt,:e fOS~ slo~
Which gra ph represents'1:he solutions to the system of linear inequalities?
~,
~ Ch~~~~'~"+'~~~~~
r~J~
:, J,
~~v.l~
18. Graph A is the graph of y
= 2cfi
and graph B is the graph of
Which statement about the two graphs is true? ~
Both graphs A and B rise at the same rate.
.­
-t'-r-'\..-l ~
~ Graph B rises at a faster rate than graph A. ~l s..e... §
Graph A rises at a faster rate than graph 8. --h-- v e..... ~ The y-intercept of graph A is above the y-intercept of graph B. ~:." L~
19. In 2000, there wer 4800 p,eople who attended the state basketball tournament. The enrollment
has been increasing 3% annually since then.
• Create an equation that would determine the total number of people who will attend
after x years. (Let x = 0 represent the year 2000 .)
(
)
x
Page 7 of 15
20. Solve the equation 2 x = 68.
o
A.
8
~
x 5
ifJr
x=6
o c.
x
o D.
x
,
= 34
0
7
c;
7, rJ 0
:; ~ G~
J ~ ~ CO~ 7
.
M.ec\L-.
~\
2
= 64
~ (o~ ~
21. In the laboratory, a bacteria population grows in size every hour, as shown in the table. A new
bacteria culture is started with 20 bacteria.
•
Create a function that describes the size of the bacteria population, pet), in terms of the
number of hours, t.
•
Predict the number of bacteria in 7 days.
)
• After how many hours will the population first exceed 10,000?
I OJ DOu ::-
a) 7 hours
COT
-
8hou~
X
L/-O( 2 ')
\
O\v-€
50 S; ~ GLA eL L.:...:­
c) 9 hours
'1 J
if0 ('L-') '7 '= S \ U) d) 10 hours
LiO(7.,J
B
~ IOIl..J.10
,0
t{O(z..) ~YO,~~O
22. The student population at a high school has been decreasing each year, as shown in the table.
Years # students -~5
Write a function, for t 2: 1 to represent the number of students, Set), based on the number of
students from the previous year, Set - 1).
S (t;) =SCI")
S[ t::- -
I") - ~ 5
= 1'2 30
Page 8 of 15
. ~
s\tv'-\--
J
~~v
23. Consider a sequence given by the formula: fen) = 5 - 8(n - 1)
Which of the following is an equivalent sequence?
~u
~
~
)
~
.
fen)
fen)
= 5n = fen -
1 with [(1)
1)
+5
(t- ~
i
o,J
e.(
=8
with [(1)
= 8 &--wrv~
5f-v.-t \:­
fen) = fen - 1) - 8 with [(1) = 5 fen)
= fen -
1) - 8n with [(1)
=5
~
..
7'>
[(x) =
24. Given the functions:
~x + 5
g(x) = 5
and
Gf
Select all he statements that apply to the functions: (4 pts)
@
-+VII i!..., ~
.
+Vue fo.. . . f~) ~~j u
[(x) and g(x) have the same y-intercept;
b)
[(x) and g(x) are linear functions;
c)
[(x) and g(x) are decreasing
Jd)\ [(x)
C/
functions; ~ ll:W<. £--c. y 1;-)
{yve
.h,v-
<)­
fur C'cr
is an increasing function, g(x) is a decreasing function.
--t-<" v e..
e.,
tv.)
25. The graph of a function is shown.
\
Which of the following equations is
represented by the graph? (1 ptJ
o
[(x) ~2Gr
«; - I"~
~ [(x) = ~(2)X
26. Given the function [(x) =
(§3J
~
always
when x > -3
Ixl + 3 , for what values of x is the function positive?
'-----\
\)
.5~,4e A \/ r ~
%11->'(;'
~ whenx>3 ~
never Page 9 of 15
letr 3
~ ~ JvwV"\ y
\j.-s~ 5h~ ~fet.t
V-s~ s\r-lf~J c1c .\)", f ~ o..-v--J .s.tv~hke(
6cr
27. Graph A is the graph ofy = Ix + 31 - 4 and graph B is the graph of y = 31xl - s.
~
Which statement about the two graphs is true?
~
~
~
Graph A and B have the same slope.
..G-.....lS-<­
Graph A is Jess steep than graph B. -\YvL­
r ll
~ Graph B has a y-intercept that is 4 units above the y-intercept of Graph A. ~l ~ .- l rs
~
-\V
Graph B has a vertex that is S units,abov] the vertex of Graph A.
-C-c,-l'>e-- ', h "
~elo...) ~.t-- ~o
-t~
v
p
~ +ko.:::;r­
1&
2S. Given the functions: g(x) = -(x - 3)2 + 2 and {(x) = x 2 ,
describe the graph shifts needed to create the graph of g(x) from the graph of {(x).
v~(~W' 3
~~rr< J (re 0kc+.e(.A)
\J p
\
tN(!:y-
'?<
-C-'.)l-I
S
2­
29. A group of functions are shown.
...",2
a(x)
d(x)
= Ix + SI \l{~
=. -Ixl - 3 w~f'
hex)
e(x)
~.I
= 31xl
= Ix ­ 31 + 4 ,..
{J;.,
\(V.\ \"
c(x)
= Ixl + S
{(x)
= Ixl - ,~ ~v-.
v
'"' \
Sort the functions based on the graph shifts compared to the parent function. Write the function's
letter in the correct category below. You may need to write a letter in more than one box.
30. Choose the equation that matches the graph:
'/-- y =
~
-Ix - 21 + s if-
y=-lx+21-S
'!
-2.
skc,\QL-­
~
/(\ y = - (x + 2 ) 2 + .S "'-k.(A­
y = -(x - 2)2 + S V
'/<..
f
,~
Page 10 0/15
31. You are a full time employee at a marketing firm. In order to maintain full-time status you must
work .minimum of 25.hours a week, and you cannot work more th a n 45 ho urs in a week. You
make $20 per hour.
•
Define the domain and range variables in the context of the problem.
•
Express the domain and range as inequalities .
Define range
variable:
Define domain
...- {:/ l
_
variable:
"f: /" ~':::>
~ :::. a ~ t-
.
SOD -
Domain inequality: --"'-_ _ _"--_ _
32 . Given that {(x)
= 3(5x -
2), find x when {(x)
'-l~~3~'L)
-1 <& -:: -\ S
33. Given the function:
)<
What are the doC
~
8
':J <- 9uv
~l
= -18.
-<a
f(Xre~ -Ie
~
-
34. Look at the function .
fa , c1
\...-ekt
: valuate
+ I '1.. + I
f(
-2).
-: : Ci)
- \-->.r
1-0 " , :)
\
~
L \A.~\.­
,1..)
v - -.J
n and ra a Domain: -5 ::; x ::; 8, Range: -3 ::; Y ::; 3 ~ Domain: -5 ::; x ::; 8, Range: -4 ::; Y ::; 4 ~
Domain: -3 ::; x ::; 2.5, Range: -4 ::;y::;3
~
Domain: -4 ::; x ::; 4, Range: -5 ::; Y ::; 8
Page 11 of 15
re
r
35. Which of the following is ll.Q!a function?
Domain
2
c(<.tv! +- ~ ed- a.,........ "1-' v?\.l J e.. bvt- ClLV'- .(e.r-e~ A.. L..J Vc~ lve....
Range 9
{(4, 1), (7, -2), (-2 ,4), (1 , 2)} ~
8
1-9 7 t:;
-y-vc\.lve.
>----+---+---+---,--~. ~J 2 l~ ~ .
~llJ~S
L) ­ '­
The graph shows the functions { (x)
= (x -
1)2 - 4 and g(x )
,
36. Identify the value(s) of x
for which {( x ) = g(x)
~ -~~ c,yc~.s
)(~--d-
SR,---K~
-4
-3
~
( ') 38. Over which interval(s)
U
~
5
:\
\
3
I
,~
1
\
-5
'f-J},
6
\ ~
~ ~ ~
is {( x ) < g(x )?
~
~(x)
,.
\
~
37. Over which interval(s)
ce",-te
=­ x +3 .
is fc: mcreaSin; ) i
--
~
1
- I
1\
\
-3
-~
,
f'. V
2. 0I
1
'\,
I
I , ,
J
1f'...4
!~ ~I
v
S
fi
f
.\
6
""­ I':
.; '
Nx
f'
5
~
I
• d iltS"
)
If'- c... -<.
6
~;;x-'f
39 . Identify the vertex, x-intercepts, and y intercept of {( x ).
'\j
U ~x-'f-
Lt) - 4 ')
'j(-ivd- (-1 / 0') (~/»)
II) - ', N\- ~ (' 0) -"3)
Page 12 of 15
'X 40. At a particular company, every employee ceceives a
4%cDI;v~;~cease ~:~c~al~~~5":~ "
to
What impact does this have on the mean and on the range of employee salar;es at the company? '/.. I ,
~ The mean increases but the range does not change.
Jjj ~ The mean does not change but the range increases.
§
The mean and range both increase.
o
D. The mean and range do not change.
'7 .2A.)
~.J 'Y'2--
~ts..e-
e....
--\v v
o~' ~
IOVi:>
f. 1.0""
10'10
41. A company decides to give everyone of its employees a $1000 raise. What happens to the mean
and median of the salaries as a result?
-\-v-v;
S () ~
SO~)
GOD
~ Mean stays the same, median increases by $1000
~
Mean increases by $1000, median stays the same
~ Mean and median stay the same
B
L""""" tA..- (A."",- ,
{'~
-t!.9L-
I I.? 0.....
(,1 0 1.)
\
$8000 per week
$350 per week
tslLRvJe,
Which statistical measure best describes the typical salary, and why? ~
­
t- I ()a
G:1-{l\ ~
V\I'-Q..~....... ~ ~ t l: 0.-..
42. A company decides to pay its employees the following salaries: $250 per week
':::. "
' 7(,1 D
(V\t\-la..", ')
Mean and median both increase by $1000.
$200 per week
~
The mean, because it is not affected by extreme values.
~J. c;.L ~ The mean, because it is the average of everyone's salary. -\-Yv ~~ ~
The median, because it is not affected by extreme values . ~- The median, because it is the average of everyone's salary. ~lS--e-
43. The box plot below shows the ages of football players on a school's football team.
M
0.. ,
----1 14
I
15
17
16
18
Select all of the statements that are supported by the box plot:
j)4..
The youngest player on the team is 15.
~ The median age of the players is 17.
@
~ l~
%-.1 s.<­
25% of the players are between 17 and 18 years old.
02» 0% of the players are between 15 and 17 years old.
~ The Q.:!ean ag,e of the players is 16.5 ye?rs old.
+V-U e.....
'
ve.... l ~*'I..-..
cev-..: +-
L
h'
vo...-....~
Q (:.
tvv--
-
\au/,-")
\
~ .S
,
~
~ Only one player is 14.5 years old.
\f\O-\-
@!
\s-V'-o ~ V'
(L
~ '."J
S(f" ~ h ~
Page 13 of 15
44. The two-way frequency table below shows the results of a survey regarding transportation to
school at a high school: '7 0
Ride the bus
Drive a car
Walk or ride bike
Freshmen
130
20 0
150
Sophomores
70
25
25
120
Juniors
55
15
60
130
Seniors
10
10
80
100
Total
265
70
165
500
\ "J.>O
Select ALL of the statements that are supported by this data:
•
.
L' C, U
,
'1'
total
-;" :/
(~
,/
iY' ~ -s
W""
~R
2-
y. 0/ c
'\ V'"
vr
(;
":>
.
~i> '>(-.'0'
-\N) e~
v ' ~
c~,JL9 ~ e. . ,~II)
v,/ ~~
(,~9..
~ D ~ -z.-.c.o
~ The relative frequency of th~hmen riding th~gher than the relative frequency of
the combined other classes riding the blJ,s.
...:-
, 0+ 551" I {)
~.e",,-.
5D ()
_
-
2- 7
en
0 ..
$: The joint frequency of,sophomores driving i~wer than the joint frequency of
D=. .o~alking or ri di9 their bikes.
::'> 2s ~ SO CI
-::. .0
S
~The marginal frequency of seniors is higher than the marginal frequency of students drivin
school.
""' ..:, SbC) :::. O. 7.100
;, I ~ 5 -;-' 5DV :::. .. ?3
::> to .~ The relative frequency of juniors who DON'T drive is lower than the relative frequency of s~
10 -=.., 500 c. O ..-lL\
,
,0 -;'
0, I ~ The graph shows the stock value for a technology company.
45. Which equation represents a line to fit the
data?
~
." " ' /
1
~ Y=2x+20
Stock Value
~
~ lb ~
~
7
® Y=8X+20 ..'t~
80
\
'IS
70
Vi' 60
...
cLDses+­
.!!! 50
'0
~
~ y = 0.125x + 20 --\vO . M.l ~
S~
~ 30
til
> 20 s (,If
~ y = lOx +20
10
.-\-tN
~~~
0
<"­
t;\.!) rf
0
00
$60
B. $1 b
C.
$70
Uf-­
1
2
3
4
5
6
7
8
9
10 11 12
years since 1999
46 . What is the most likely value of the stock in
year 10?
0 A.
40
~cvv-.
~
l~~
0 D. $75
47. Lucy did a study on the number of hours students spend studying and their grades. She found
that there was a strong positive correlation between the two.
Page 14 of 15
rS'x:
~ -to
,ee/­
c\.v lA-~
( '
Which scatterplot shows the strong, positive correlation of her data?
~
\-G.~
~
CO.J(? <;
v
j)?~ ~~------------~
48. Samantha surveyed a group of adults to gather data on their height and weight. She put her
results into this graph:
300
}',O
+
50
()
o
5
10
15
20
25
30
Height beyond 50 inches tall
The line of best fit for this graph is: y = lOx + 50
where x = # inches taller than 50 incn
and y
= weight in pounds
Which of the foIlowing statements is a generalization of the slope of the line's equation?
~
~
~
~
I 0 po I.' ""L-:;. ( 1-))
CN ~y 1­ .. ""c.~ ()<:)
For every inch a person grows, he will gain 10 pounds ,
-. .\4;. ~ -r ~'-b() v t- ~ pe-.--s ~ C'I €A' -\-\ Irr--.e..
For every inch a person grows, he wil1lose 10 pounds
Ifperson A is one inch taller than person B, it is likely that person A is 10 pounds
heavier t han person B.
~If per§Qn A is one inch taller than person B, it is likely that person B is 10 pounds
heavier than person A.
JVVV\.A
Page 15 of 15