Neil Garrigan: Electric Drive Technology Considerations for Aircraft Propulsion
Review #2 - Bishop Garrigan High School · Use this information for the problems below: On a string...
Transcript of Review #2 - Bishop Garrigan High School · Use this information for the problems below: On a string...
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<
657 ≤
o the ineq
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
6≤x
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
lities. eatly graph
uality 2−≤x
ons on the
hed on th
2 and ≥x
e number
e number
3 has no so
lines.
r line.
olution.
Solv 75. Solv77. 79. FindPro80.
81.
82.
83.
ve these a
62 <−x
ve these a57 >−x
Explain w
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
6
8
tences fo
tences fo
no solution.
each relaDom
r “x”.
76.
r “x”. 78.
tion belowain
192 ≥+x
234 ≤+x
w.
51≤
Range
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
) ( )}8,1, −
)}2
__________
function
______
______ ______
__92.
______
?
_________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