Review #2 (Yes, it’s extremely long.)

How many solutions would each of these equations have?

A. No solution B. Exactly 1 solution C. Infinitely many solutions (identity – all real numbers)

____________1. ( ) 23305724 −++=+ xxx ____________2. 84235 +=−++ xxx ____________3. ( ) ( )724532 +=+ xx ____________4. ( )1131447 +=+−+ xxx

____________5. 20397 +=− xx ____________6. 237295 +++=+ xxx ____________7. ( ) xxxx 62521539 −+=+−+

Solve for “x”. If the answers don’t come out even, you may write them as a fraction or a decimal. 8.

57

3=

x

12. 27

435=

+x

13. 5

324

9 −=

+ xx

14. 11928

1732=

−x

9. 45637

=x

10. x

1238=

11. 9113

19 x=

Use this information for the problems below: On a string of Christmas lights there are 9 red lights, 10 white lights, 11 green lights, 9 orange lights, 2 purple lights, 6 yellow lights, and 3 pink lights. Find these ratios. Write all in lowest terms. _______________________________________15. the ratio of orange lights to pink lights _______________________________________16. the ratio of white lights to red lights _______________________________________17. the ratio of purple lights to pink lights _______________________________________18. the ratio of green lights to yellow lights _______________________________________19. the ratio of colored lights (red, green, orange,

purple, yellow, or pink) to white lights ____________________ and ____________________20. Which two colors of lights are in a 1:1 ratio? ____________________ and ____________________21. Which two colors of lights are in a 5:1 ratio? For each problem, write a proportion and solve. 22. Nathan is 6 feet tall. His shadow is 20.5 feet long. The shadow of a tree is 98.4 feet long. How tall is

the tree?

Proportion: Solution: ____________ feet

23. A car can travel 285 miles on 11 gallons of gas. How much of gas will it take for the car to travel 800

miles?

Proportion: Solution: ____________ gallons

24. Rhonda is writing a paper for English class. So far she has written 3 pages, and she has a total of 645

words. If she must have 1500 words all together, how many pages should she write?

Proportion: Solution: ____________ pages

25. At the beginning of the season 240 fish are tagged in a lake by the Department of Natural Resources. During the season a total of 3600 fish are caught, and of those 180 were tagged. Use this information to estimate the total number of fish in the lake at the beginning of the season.

Proportion: Solution: ____________ fish

26. In a certain city, the tax on an $89 motel room is $11.79. At the same rate, what would be the tax on a

$117 motel room?

Proportion:

Solution: $____________

____________27. Tell which is the better buy (has the lower cost per ounce):

A. 33 ounces of ground coffee for $6.29 B. 21 ounces of ground coffee for $3.89

____________28. Tell which is the better buy (has the lower cost per minute):

A. a calling plan with 1000 free minutes for $49 a month B. a calling plan with 1200 free minutes $57 a month

The figures below are similar. Solve for “x”. ____________27. 5 8 17 x ____________28. 110 138 87 x

Solve these percent problems. _______________29. What is 70% of 80? _______________30. 19 is what percent of

114? _______________31. What is 53% of 75? _______________32. What is 130% of 80?

_______________33. 84 is 75% of what number?

_______________34. 18 is 36% of what

number? _______________35. 72 is what percent of

1152? _______________36. 26 is what percent of

325?

Find the problems involving percent of increase or decrease. 37. Before he got a raise, Eric made $5.95 an hour. After the raise, he made $6.50 an hour. _______________a. How much more does Eric make per hour now than he did before? _______________b. What is the percent of increase? 38. A phone that used to cost $98 is on sale for $58.80. _______________a. How much cheaper is the phone now than its original price? _______________b. What is the percent of discount? 39. You buy a meal that costs $17.40. You want to leave a 15% tip. _______________a. If you tip exactly 15%, how much should you tip? _______________b. How much is the total you spend, including the tip? 40. A graphing calculator normally costs $119. It is on sale for 25% off. You have to pay 7% tax on the

discounted price. _______________a. How much money do you save? _______________b. What is the discounted price? _______________c. How much is the tax? _______________d. What is the total price, including tax?

Use

WriIf th __{_ __{_ __{_ __{_ __{_ Use

46. 47. 48. 49.

e these seU

P

Q

R

S

Tte the col

he answer

___________

___________

___________

___________

___________

e this Ven

Which pe

Which pe

Which pe

Which pe

ets for theU = { red, o

P = { red, y

Q = { gree

R = { yellow

S = { red, o

T = { greenors that ar is the em

__________

__________

__________

__________

__________

nn diagram

eople are in

eople are in

eople are in

eople are no

problemsorange, y

yellow, blu

n, blue, in

w, blue, g

orange, in

n, yellow, re in each

mpty set, l

__________

__________

__________

__________

__________

m for the p

S ∩ T ?

V ∪ T ?

(S ∪ V) ∩ T

ot in (T ∪ S)

s below. ellow, gre

ue }

ndigo, viol

green }

ndigo, viol

blue } h of theseeave the

___________

___________

___________

___________

___________

problems

T ?

) ∪ V ?

een, blue,

let }

let }

e sets on tspace bla

__________

__________

__________

__________

__________

below.

indigo, vi

the lines.ank.

__________

__________

__________

__________

__________

iolet }

___}__41.

___}__42.

___}__43.

___}__44.

___}__45.

Find Q ∩

Find S ∩

Find P ∩

Find T ∪

Find Q ∪

T

P

Q

P

∪ S

Mat ____ ____ ____ ____

Gra

Wo ____ ____ SolvWri 60. 61.

tch these

_________5

_________5

_________5

_________5

aph these

uld each

_________5

_________5

ve for “x”.te your an

225 +x

173 +− x

graphs to

50.

51.

52.

53.

inequaliti

of these p

56. older

57. no mo

nswer as

90<

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es on the

phrases m

than

ore than

an inequa

ualities at

e number l

mean >, <,

ality.

t right.

lines prov

, >, or <.

______ ______

62.

63.

vided.

_______58.

_______59.

172 >+− x

5193 ≥+x

54.

55.

at least

shorter t

6>

115 −x

Choic

A.

B.

C.

D.

x < -3

x > 2

than

ces:

x > 4

x < 4

x < 4

x > 4

GraYou 64. 65. 66. 67.

68. Gra 69.

70.

71.

72.

73.

74.

aph these ur final an

12≤x

3−<x

10≥x

0<x a

Explain w

aph these

7=x

3<x

6≥x

3>x

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1=x

compounnswer sho

and 5≥x

or 0>x

or 2≤x

nd 5−>x

why the com

absolute

nd inequaould be ne

mpound inequ

expressio

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uality 2−≤x

ons on the

hed on th

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e number

e number

3 has no so

lines.

r line.

olution.

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81.

82.

83.

ve these a

62 <−x

ve these a57 >−x

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d the domoblem Re

({9

({5

absolute v

14<

absolute v58>

why 63 −x

main and elation

) ( ) (7,4,4,5, −

) ( ) (5,2,5,1, −

6 -1 3

value sen

value sen

12−≤ has

range of

) ( )}8,1,3,7 −

)}2,−

2

4

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tences fo

tences fo

no solution.

each relaDom

r “x”.

76.

r “x”. 78.

tion belowain

192 ≥+x

234 ≤+x

w.

51≤

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e

YES ____ ____ ____

____

____

____

S or NO:

_________8

_________8

_________8

_________8

_________9

_________9

Is each o

84. ( ){ 5,9

85. ( ){ ,1,5

86. x y4 12 -73 82 51 74 5

87. ( ) ({ ,1,1

91.

94.

of these re

( ) ( 3,7,4,4, −

( ) ( 2,5,2,5 −−

y 7

8 5 7 5

( ) ( )}1,3,1,2

__

elations a

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)}2

__________

function

______

______ ______

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______

?

_________1

_________8

_________9

_______95.

188.

89. ( ) ({ 3,5,2

90 . ( ) ( ){ ,1,5,2,6

_________

) ( ) (,8,4,7,3 −

( ) ( )7,5,3,4−

____93.

) ( )}0,8,4,2−

) ( ) ( )}3,3,9,6, }

You are given these functions: • ( ) 15 += xxf

• ( ) 962 ++= xxxg • ( ) 4xxh =

• ( ) 23 +−= xxk

• ( ) 5=xp Find these values. ____________96. ( )5f ____________97. ( )2−f ____________98. ( )0f ____________99. ( )3f ____________100. ( )4g ____________101. ( )2−g ____________102. ( )3−g

____________102. ( )0g ____________103. ( )2h ____________104. ( )1−h ____________105. ( )0h ____________106. ( )9k ____________107. ( )5−k ____________108. ( )13p

Using the same functions given above, answer these questions. ____________109. If ( ) 46=xf , what is x? ____________110. If ( ) 11=xk , what is x? Find these values. ____________111. What is ( )( )2gf ? ____________112. What is ( )( )1−kh ? ____________113. What is ( )( )4fk ? ____________114. What is ( )( )( )1fff ? ____________115. What is ( )( )( )( )( )( )( )( )( )( )7−pkhgfkhgfp ?

____

____ ____

____ Giv ____ ____ ____ ____

_________1

_________1

_________1

_________1

en the do

__________

__________

__________

__________

16. Given

17. In the

18. In the

19. Given

omain, find

___________

___________

___________

___________

n the function

function abo

function be

n the function

d the rang

__________

__________

__________

__________

n below, wha

ove, if ( ) =xf

low, if ( ) =xf

n above, wh

ge of these

______120.

______121.

______122.

______123.

at is ( )3f ?

3= , what is

6−= , what i

at is ( )0f ?

e function

( ) 5 −= xxf

( ) 2xxg =

( ) xxf 2−=

( ) 3 += xxf

s x ?

is x ?

ns.

2− Domain

Domain = {

Domain =

9+ Domain

= { 7, 9, 12

{ -2, -1, 0, 1,

{ -10, -5, 0,

= { -8, 0, 14

2, 20 }

2 }

5, 10, 15 }

4 }

Gra 124.

125.

126.

aph these

X -3 -1 2 0 3 4

X -2 -1 0 1 2 3

Circle the

relations.

y 4 3 2 1 0 -1

y -4 -2 0 2 4 6

e function th

. Then te

at is non-lin

ll whether

near?

r the relattions are linear or n

Linear or

Linear or

non-linear

r Non-Linear

r Non-Linear

.

r?

r?

_

_

____

Use

____

____

____

__________

__________

_________1

e the grap

_________1

_________1

_________1

___127.

___128.

27. Which

A.

B.

C.

D.

ph at right

28. What

29. Use thtempe

30. Use thtempe

Which grahigher acc

Which graincreases,

h statement

The comornin

The prin the m

. The prmornin

. The prmornin

for the qu

was the tem

he graph to eerature was

he graph to eerature will b

aph matchescident rates t

aph matches, the price de

best describ

ompany’s stong and incre

rice of the comorning and

rice of the cong and was u

rice of the cong and was u

uestions b

mperature at

estimate what 6:30am.

estimate whbe at 11:00a

the statemethan middle-

the statemeecreases.”

bes the grap

ock was uncased in the a

ompany’s stod decreased

ompany’s stounchanged i

ompany’s stounchanged i

below:

8:00am?

hat the

hat the m.

ent: “Both y-aged driver

ent: “For ma

h at right?

changed in thafternoon.

ock was unc in the aftern

ock increasein the aftern

ock decreasin the aftern

young driversrs.”

any items, a

he

changed noon.

ed in the oon.

sed in the oon.

s and old dri

s the numbe

ivers have

er sold