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Resource Sheets NEW_Layout 1 4/10/14 10:21 AM Page 1

Table of Content English Resources Math Resources Algebra Resources Geometry Resources Trigonometry Resources Chemistry Resources US/World Resources

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Parts of Speech Noun Proper Nouns are capitalized and refer to specific persons, objects, ideas, or places. Common Nouns refer to any person, object, place or idea. Pronoun A pronoun takes the place of a noun. Verb A verb shows action or state of being. It also indicates the time of that state or action. Adjective Adjectives describe nouns by modifying them. They can specify color, size, number, etc. Adverb Adverbs are words which descrive verbs, other adverbs, or adjectives. They specify in what manner, when, how much, and where.

John house

Common Noun Examples: building boy city anger

desk

Tom washed his car on his day off. He worked on Friday. (past) I need to place the order. (present) He will present his report tomorrow. (future) The green van struck the metal pole near the third intersection. The crowd reacted violently when it was confronted.

Preposition Prepositions indicate how nouns and pronouns are related to another word in a sentence. Conjunction Conjunctions join words, clauses, and phrases.

Proper Noun Examples: White House Monday Slovakia

Paul stood behind the fence. The cat jumped onto the bed. Your drink options are either coffee or tea. John could not react fast enough because of a poorly healed foot.

Interjection Interjections are words that convey emotion. They are often indicated by the use of an exclamation point.

Wow! What a beautiful car!

Punctuation Period Use at the end of a declarative sentence. In addition, use a period at the end of an imperative sentence that does not express strong emotions. Comma Use to separate words and phrases in a series. Question Mark Use after all interrogative sentences. Exclamation Mark Use after sentences that express surprise or feeling. Semicolon Use to combine two closely related sentences.

We arrive at school each day at 8 am. (declarative sentence) Sit down. (imperative sentence) Bill has two dogs, one cat, and a hamster. Where did you go on vacation? His car looks fast! The road was bumpy and curvy; the scenery was grand.

Colon Use a colon to start a list or to formally introduce a statement.

He has three cars: a Mustang, Camaro, and a Duster.

Quotation Marks Use quotation marks around a direct quotation.

He said, “I want to go home.”

Apostrophe Use an apostrophe to show contracted words or to show possession.

it’s (for it is) Bill’s bike (possession)


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Figurative Language Simile A smile is a comparison between unlike things using the words “like” or “as.”

He was motionless like a statue. She was quiet as a mouse.

Hyperbole A Hyperbole is an extended exaggeration.

I have a ton of questions to ask.

Metaphor A metaphor is a comparison between unlike things in which one thing becomes another. Personifications Personification is attributing human characteristics to an inanimate object or animal.

Her eyes were sparkling diamonds. The fox begged the hunters to chase him.

Paragraph Writing 1. Write a topic sentence—The topic sentence tells the main idea of your paragraph. 2. List supporting ideas. 3. Make a rough outline—Eliminate irrelevant items. 4. Write the paragraph. 5. Add the clincher—A clincher sums up the paragraph. 6. Revise and edit—Make sure the sentence flow in an organized fashion. 7. Proofread—Read and correct grammar, spelling, etc. 8. Write the final copy.

Spelling Rules

1. I before E (field, yield), except after C: (deceive, conceive), or when there’s an “ay” sound (weigh, eight). Examples: their, weird, seize, either

2. If a word ends with a “y” and is preceded by a consonant, then the “y” becomes an “i.” If the preceding letter is a vowel, the “y” remains unchanged. Examples: heavy + er = heavier; portray + ed = portrayed 3. On words ending with a consonant preceded by a single vowel (drip, can, begin), double the consonant before adding -ing or -ed. Examples: drip + ing = dripping; tan + ed = tanned 4. If a word ends with a silent final “e” (bite, move, desire), drop the “e” if the suffix starts with a vowel (ing, ence). Keep the “e” if the suffix starts with a consonant (less, ty). Examples: use + able = usable; use + ful = useful Exceptions: argument, judgment, simply, truly, noticeable

Words Often Misspelled accidentally accommodate achievement acquitted a lot anoint beneficial benefited broccoli cemetery changeable choose

chose compelled congratulations consensus coolly definitely despair desperate development embarrassment eminent exceed

existence exhilarate experience fiery foreign grandeur harass height immediately inadvertent incidentally independent

indispensable insistent irresistible irritable liquefy judgment liaison loneliness memento millennium noticeable occasion

occurrence performance permissible perseverance privilege professor pursue receive recommend repetition seize separate

sergeant severely specifically subpoena succeed succession supersede their tomorrow tyranny weird yield


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Grammar Errors Sentence Fragment A group of words, either short or long, which does not give a complete thought. Possessive Nouns Nouns which show ownership, connection, or possession. Remember these rules when forming the possessive of common nouns:

Incorrect—A blue convertible. Correct—The new car is a blue convertible. Tom’s book, the band’s music, Tanya’s mother Number 1 Example—cars becomes cars’ Number 2 Example—dog becomes dog’s

1. If the noun is plural and ends in an “s,” add an apostrophe. 2. If the noun does not end in an “s,” add an ’s. Misplaced Modifier The incorrect placement of a word or group of words in a sentence which indicates that it modifies one word, when it is supposed to modify another.

Incorrect—I saw the piano walking into the room. Correct—Walking into the room, I saw the piano.

Run-on Sentence Two or more complete sentences written as one, often separated only by a comma.

Incorrect—The time ran out quickly, we did not finish the test. Correct—The time ran out quickly. We did not finish the test

Tense Shift Changing or mixing verb tenses in sentences or paragraphs.

Incorrect—Tom bought the book and reads it quickly. Correct—Tom bought the book and read it quickly.

Active, Passive Voice Active Voice—The subject of a sentence performs the verb’s action. Passive Voice—The subject of the sentence receives the action of the verb.

Active Voice Example— He reads all the new novels. Passive Voice Example— All the new novels are read by him.

The active voice is easier to understand and most often preferred. Parallel Structure Writing which uses words, phrases, clauses, and sentences in the same grammatical form.

Incorrect—I enjoy swimming, walking by the pier and also to eat ice cream at the beach. Correct—I enjoy swimming, walking by the pier, and eating ice cream at the beach.

Capitalization Capitalize the Following 1. The first word in a sentence. 2. Days of the week, months, holidays, periods and eras in history, trade names, streets, formal documents, geographical names, political parties, holy days, and official titles. 3. Words such as history or math when the words are a part of a specific course, Do not capitalize these words when they indicate a field of study. 4. Words such as brother, mother, or doctor when they are a part of the title or when they are a substitute for the noun. 5. Points of the compass. Do not capitalize words that indicate simple direction. 6. Words that refer to the Supreme Being. Capitalize the word Bible, the books of the Bible, and the names of all holy books or sacred works. 7. The first word in a direct quote. 8. Words denoting religions, languages, nationalities, and races. 9. Names of organizations. 10. Degrees, titles, and abbreviations of organized groups. 11. The first word of a title, the last word, and all words in between except short conjunctions or prepositions. 12. The first word in a greeting or the closing of a letter.


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Words Often Confused accept accept a gift except everyday except today advice listen to good advice advise Counselors advise students. affect His speech affected the listeners. effect the effect of the sun already He already ate. all ready I was all ready to leave.

precede The National Anthem precedes the game. proceed Proceed with your report. principal the principal reason; a school’s principal principle the principle of good manners quiet the quiet night quite quite handsome

altar church’s altar alter alter the clothes; alter the report

right the right direction rite the religious rites write write a letter

angel angel in heaven angle a right angle

shone The sun shone on the valley. shown He was shown the evidence.

breath out of breath breathe breathe fresh air

sole the sole survivor soul body, soul, and spirit

capital nation’s capital; a capital idea capitol a capitol building

stationary a stationary object stationery correspondene written on stationery

cite to cite a source site a building site sight a terrible sight to see

steal to steal money steel a bridge made of steel

clothes to wear clothes cloths cloths for cleaning

than bigger than a bread box then We ate lunch, and then it was time for a nap.

coarse a coarse fabric; coarse language course a race course; a history course

there over there their their house they’re They’re not here.

complement An attractive tie complements the suite. compliment He complimented her attitude.

to to the car; to cheer too I want some too; too often two two soft drinks

counsel The teacher gave the student good counsel. council The council voted against the action.

troop Boy Scout troop troupe a theatrical troupe

desert a dry, hot desert dessert pie for dessert forth go forth into the crowd fourth fourth in line hoping hoping for a good grade hopping a hopping rabbit its the color of its eyes it’s It’s cloudy outside. loose a loose connection; loose clothing lose lose a toy mantel the fireplace mantel mantle (cape or cloak) He put on the mantle. passed passed a test; passed an automobile past lived in the past; past errors peace live in peace piece piece of cake

wander He wandered aimlessly. wonder I wonder what happened. weak weak from starvation week a week from today weather hot, humid weather whether It doesn’t matter whether we go or stay. who’s Who’s at the door? whose Whose house is this? your Your feet are dirty. your’re You’re angry.


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Equivalent Measurements English System Weight 1 pound (lb) 1 ton

= =

Length/Distance 1 foot (ft) = 1 yard (yd) = 1 yard = 1 mile (mi) = 1 mile = 1 nautical mile = 1 league =

16 oz 2000 lbs

12 inches 3 feet 36 inches 1760 yards 5,280 feet 1.15 miles 3 miles

Area 1 acre 1 sq. mile 1 sq. ft 1 sq. yard

= = = =

4840 sq. yds 640 acres 144 sq. inches 9 sq. ft.

Volume 1 tablespoon (T) 1 cup (c) 1 cup 1 pint (pt) 1 quart (qt) 1 quart 1 quart 1 gallon (gal)

= = = = = = = =

3 teaspoons (t) 16 T 8 fluid oz (fl.oz.) 2c 2 pt 4c 32 fl oz 4 qt

1 km2 1 metric ton (t)

= =

100 ha 1,000 kg

Metric System 1 m2 = 1 hectare (ha) =

10,000 cm2 10,000 m2

English/Metric Conversion If you know…

You can find…

By multiplying by…

inches feet yards miles

millimeter centimeters meters kilometers

25 30 0.9 1.6

Area

square inches square feet square yards square miles

square centimeters square meters square meters square kilometers

6.5 0.09 0.8 2.6

Mass

ounces pounds

grams kilograms

28 0.45

Liquid Volume

ounces pints quarts gallons

milliliters liters liters liters

30 0.47 0.95 3.8

degrees Fahrenheit

degrees Celsius

subtract 32 and multiply by 5/9

Length

Temperature


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Perimeter & Circumference Perimeter The distance around an object.

Circumference The distance around a circle.

Polygon 2(L + W)

Circle pd or 2pr

L

u di ra

W

r) s(

diameter (d)

Area L = length

w = width

h = height

s = side

b = base

Rectangle L•w

Parallelogram b•h

Square s2

Trapezoid 1/2 (b1 + b2) h

Circle pr2

Triangle 1/2 b • h

r = radius

Surface Area & Volume Surface Area Find the area of each face and total.

Volume of Prisms Find the area of the base (b) and multiply by the geight (h).

Rectangular Prism v=L•w•h

Cube v = s3

Cylinder Volume v = pr2h Surface Area sa = 2pr2 + 2prh

Cone v = 1/3 pr2h

Triangular Prism v=b•h

Sphere Volume v = 4/3 pr3 Surface Area sa = 4pr2

Pyramid Volume Find the area of the base (b); multiply by the geight (h); and divide by 3.

Square Pyramid v = 1/3 bh

Trianglular Pyramid v = 1/3 bh

Rectangular Pyramid v = 1/3 bh


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Multiplication Table 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16

1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

2

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

3

3

6

9

12

15

18

21

24

27

30

33

36

39

42

45

48

4

4

8

12

16

20

24

28

32

36

40

44

48

52

56

60

64

5

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

6

6

12

18

24

30

36

42

48

54

60

66

72

78

84

90

96

7

7

14

21

28

35

42

49

56

63

70

77

84

91

98

8

8

16

24

32

40

48

56

64

72

80

88

96

9

9

18

27

36

45

54

63

72

81

90

99

10

10

20

30

40

50

60

70

80

90

100 110 120 130 140 150 160

11

11

22

33

44

55

66

77

88

99

110 121 132 143 154 165 176

12

12

24

36

48

60

72

84

96

13

13

26

39

52

65

78

91

104 117 130 143 156 169 182 195 208

14

14

28

42

56

70

84

98

112 126 140 154 168 182 196 210 224

105 112

104 112 120 128

108 117 126 135 144

108 120 132 144 156 168 180 192

“Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.” —Albert Einstein—


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Mathematical Symbols Listed below are commonly encountered symbols. Angle: –

Less than/equal to: £

Pi: p

Arc: «

Line segment: —

Ray: Æ

Greater than: >

Not equal: ≠

Right angle:

Greater than/equal to: ≥

Parallel: ||

Set: {}

Less than: <

Perpendicular: ^

æ­æææ Quadratic Equation if ax2 + bx + c = 0, then x = ______________ -b ±­ √ b2 - 4ac 2a Special Products (a - b)2 = a2 - 2ab + b2 (a - b)(a + b) = a2 - b2 (a + b)(c + d) = ac + ad + bc + bd (a + b)(a + c) = a2 + ac + ab + bc

(a + b)2 = a2 + 2ab + b2 a(b + c) = ab + ac (a + b)3 = a3 + 3a2b + 3ab2 - b3 (a - b)3 = a3 - 3a2b + 3ab2 - b3

Equations of a Line (m = slope; b = y intercept) Slope of a Line m =______ y2 - y1 x2 - x1

Slope–Intercept Form y = mx + b

Point–Slope Form (y - y1) = m (x - x1)

Logarithms Log xr = r Log x Log (xy) = Log x + Log y Log (x/y) = Log x - Log y Log x = n ´ x = 10n (common log)

Logax = ´ x = an (log to the base a) Ln x = n ´ x = en (natural log) _ 3.14159265 p­ ~ _ 2.71828183 e~

Law of Exponents If a, b Œ R, a, b ≥ 0, and \p, fq, r, s are Œ Q then: 1. 2. 3. 4. 5.

aras = ar+s ar/as = ar-s (ar)s = ars (ab)r = arbr (a/b)r = ar/br (b ≠ 0)

6. a0 = I (a ≠ 0) 7. a-r = I/ar (a ≠ 0) 8. ar/s = s√æ­ ar = (s√æ­ a)r a1/2 = √æ­ a a1/3 = 3 √æ­ a

Variation Models For variables x, y, and z where k is a positive constant called the constant of variation. Direct Variation y = kx or y/x = k Inverse Variation y = k/x or xy = k Joint Variation z = kxy


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Angles and Triangles All angles of a triangle add up to 180º Right angle: equals 90º

Straight angle: equals 180º

Obtuse angle: greater than 90º but less than 180º

180°

115°

90° Acute angle: less than 90º but greater than 0º

Equilateral triangle: all sides equal; all angles equal 60°

6

Isosceles triangle: two sides equal; two angles equal

40°

45° B 60° Scalene triangle: no sides equal; no angles equal

Right triangle: one angle is 90º

85° 65°

60°

c

b

7

70°

Pythagorean theorem: sides a and b are legs; side c is hypotenuse; a2 + b2 = c2 angles. This applies only c to right angles.

30° C

Complementary angle: two angles add up to 90º

a

C

A

Supplementary angle: two angles add up to 180º

Complete angle rotation: equals 360º

“The shortest distance between two points is under construction.” —Bill Sanderson—

a

70° B

b A


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Circle Theorems C is the center of the circle

–x = 90º PQ is a diameter

X

–a = –b angles subtended on the same arc AB

D

X

C 2x

P

a

C

Q

A

b

C B

Congruency Cases C

F

A

B

D

E

C

S.S.S. (Side, Side, Side) DABC @ DDEF

M

A

B

K

L

C

S.A.S. (Side, Angle, Side) DABC @ DKLM

S

A

B

Q

R

C

A.S.A. (Angle, Side, Angle) DABC @ DQRS

Z H.S. (Hypotenuse, Side) DABC @ DXYZ

A

B

X

Y

“Where there is matter, there is geometry.” —Johannes Kepler—


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Trigonometry æ Sin 45º = I / √ 2 æ Cos 45º = 1 / √ 2

1 + tan2q = sec2q

Tan 45º = 1

1 + cot2q = csc2q

Tanq = sinq / cosq

cos2q – sin2q = cos2q

Sin2q + cos2q = 1

Sin (A+B) = sin A cos B + cos A sin B Sin (A-B) = sin A cos B – cos A sin B Sin 2A = 2 sin A cos A æ­æ­æ­æ­æ­æ­ sin 1/2A√= ±­­­­ (1 - cos A)/2 cos (A+B) = cos A cos B - sin A sin B

1

45º

2 45º

cos (A-B) = cos A cos B + sin A sin B cos 2A = cos2A - sin2A = 2 cos2 A - 1 = 1 - 2 sin2 A æ­æ­æ­æ­æ­æ­ cos 1/2A √= ±­­­­ (1 - cos A)/2 tan (A+B) = tan A + tan B/(1 - tan A tan B)

1

tan (A-B) = tan A - tan B/(1 + tan A tan B) tan 2A = 2 tan A/(1 - tan2 A) æ­æ­æ­æ­æ­æ­æ­æ­æ­æ­ tan 1/2A √= ±­­­­ (1 - cos A)/(1 + cosA) = 1 - cos A/sin A = sin A/1 + cos A

“If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.” —John Louis von Neumann—


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Trigonometry 60º 1

æ­ Sin 60º = √ 3/2

Sin 30º = 1/2 æ­ Cos 30º = √ 3/2 Tan 30º = I/ √3æ­

2 30º

Cos 60º = 1/2 æ­ Tan 60º = √3

3 Sinq = y/r (opposite/hypotenuse) = I/cscq Cosq = x/r (adjacent/hypotenuse) = 1/secq Tanq = y/x (opposite/adjacent) = 1/cotq

r θ

Law of Sines: a/sinA = b/sinB = c/sinC Law of Cosines: a2 = b2 + c2 – 2bc cos A b2 = a2 + c2 – 2ac cos B c2 = a2 + b2 – 2ab cos C

B

c A

x

CAST

a

S

Quad II sin +

Quad I all ratios+

A

T

Quad III tan +

Quad IV cos +

C

C

b

y

Trigonometric & Circular Function Graph s y

y = cos x

1

x

-π/2 0 -1

π/2

π

3π/2 2π 5π/2

y = sin x

y 1 y

-3π 2

-π 2 -1

y = tan x

0

3π 2

π 2 π

x

-π/2

-1

x 0

π/2

π

3π/2

2π 5π/2


12

44.956

56

55

88

87

[223]

[226]

Fr Ra

137.33

radium

132.91

francium

Cs Ba

87.62

barium

85.468

caesium

88.906

39

yttrium

Y

38

37

Rb Sr

40.078

strontium

39.098

rubidium

41

niobium

50.942

V

23

vanadium

10.811

B

25

manganese

26

iron

Transition Metals

Alkaline-Earth Metals

27

cobalt

Inert Gases

Nonmetals

28

nickel

29

copper

Unknown Elements

Actinide Series

30

zinc

31

gallium

26.982

Al

13

aluminium

10.811

B

5

boron

91.224

92.906

73

tantalum

51.996

42

molybdenum

54.938

43

technetium

55.845

44

ruthenium

58.933

45

rhodium

58.693

46

palladium

47

silver

63.546

180.95

105

dubnium

95.96

[98]

75

rhenium

101.07

76

osmium

106

seaborgium

183.84

107

bohrium

186.21

108

hassium

190.23

W Re Os

74

tungsten

102.91

109

meitnerium

192.22

Ir

77

iridium

106.42

65.38

48

cadmium

69.723

49

indium

79

gold

107.87

cerium

58

lanthanum

57

33

arsenic

30.974

P

15

phosphorus

14.007

N

7

nitrogen

34

selenium

32.065

S

16

sulfur

15.999

O

8

oxygen

35

bromine

35.453

Cl

17

chlorine

18.998

F

9

fluorine

[264]

59

60

praseodymium neodymium

[266]

61

promethium

[277]

62

samarium

[268]

80

114.82

81

thallium

195.08

110

196.97

111

darmstadtium roentgenium

63

europium

[271]

64

gadolinium

[272]

65

terbium

200.59

66

dysprosium

204.38

74.922

51

antimony

78.96

52

tellurium

121.76

83

bismuth

127.60

84

polonium

85

astatine

126.90

I

53

iodine

79.904

86

radon

131.29

Xe

54

xenon

83.798

67

holmium

207.2

68

erbium

208.98

69

thulium

[209]

70

ytterbium

[210]

71

lutetium

[222]

Pb Bi Po At Rn

82

lead

118.71

Sn Sb Te

50

tin

72.64

Kr

36

krypton

39.948

Ar

18

argon

20.180

Ne

10

neon

4.0026

90

89

140.91

91

protactinium

[227]

232.04

231.04

Ac Th Pa

140.12

thorium

138.91

actinium

238.03

U

92

uranium

144.24

150.36

94

plutonium

151.96

95

americium

157.25

96

curium

158.93

97

berkelium

162.50

98

californium

[237]

[244]

[243]

[247]

[247]

[251]

Np Pu Am Cm Bk Cf

93

neptunium

[145]

167.26

100

fermium

168.93

101

mendelevium

173.05

102

nobelium

174.97

103

lawrencium

[252]

[257]

[258]

[259]

[262]

Es Fm Md No Lr

99

einsteinium

164.93

La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

[262]

[261]

112.41 mercury

Pt Au Hg Tl

78

platinum

Rf Db Sg Bh Hs Mt Ds Rg

104

rutherfordium

178.49

Hf Ta

72

hafnium

32

germanium

28.086

Si

14

silicon

12.011

C

6

carbon

Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br

24

chromium

Atomic Mass

Element Name

Zr Nb Mo Tc Ru Rh Pd Ag Cd In

40

zirconium

47.867

22

titanium

Ti

21

scandium

Element Symbol

5

boron

Key of Elements

Atomic Number

Ca Sc

20

19

K

24.305

calcium

22.990

potassium

Na Mg

9.0122

magnesium

11

Be

Li

6.941

4

3

sodium

beryllium

lithium

1.0079

2

He

Lanthanide Series

H Other Metals

1

Alkali Metals

helium

hydrogen

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Periodic Table of Elements


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United States Map

United States Capitals Alabama (AL) Montgomery Alaska (AK) Juneau Arizona (AZ) Phoenix Arkansas (AR) Little Rock California (CA) Sacramento Colorado (CO) Denver Connecticut (CT) Hartford Delaware (DE) Dover Florida (FL) Talahassee Georgia (GA) Atlanta Hawaii (HI) Honolulu Idaho (ID) Boise Illinois (IL) Springfield Indiana (IN) Indianapolis Iowa (IA) Des Moines Kansas (KS) Topeka Kentucky (KY) Frankfort

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