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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.
Common Noun Examples: building boy city anger
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.
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
square inches square feet square yards square miles
square centimeters square meters square meters square kilometers
6.5 0.09 0.8 2.6
ounces pints quarts gallons
milliliters liters liters liters
30 0.47 0.95 3.8
subtract 32 and multiply by 5/9
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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
Area L = length
w = width
h = height
s = side
b = base
Trapezoid 1/2 (b1 + b2) h
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
10 11 12 13 14 15 16
100 110 120 130 140 150 160
110 121 132 143 154 165 176
104 117 130 143 156 169 182 195 208
112 126 140 154 168 182 196 210 224
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: £
Line segment: —
Greater than: >
Not equal: ≠
Greater than/equal to: ≥
Less than: <
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
90° Acute angle: less than 90º but greater than 0º
Equilateral triangle: all sides equal; all angles equal 60°
Isosceles triangle: two sides equal; two angles equal
45° B 60° Scalene triangle: no sides equal; no angles equal
Right triangle: one angle is 90º
Pythagorean theorem: sides a and b are legs; side c is hypotenuse; a2 + b2 = c2 angles. This applies only c to right angles.
Complementary angle: two angles add up to 90º
Supplementary angle: two angles add up to 180º
Complete angle rotation: equals 360º
“The shortest distance between two points is under construction.” —Bill Sanderson—
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Circle Theorems C is the center of the circle
–x = 90º PQ is a diameter
–a = –b angles subtended on the same arc AB
Congruency Cases C
S.S.S. (Side, Side, Side) DABC @ DDEF
S.A.S. (Side, Angle, Side) DABC @ DKLM
A.S.A. (Angle, Side, Angle) DABC @ DQRS
Z H.S. (Hypotenuse, Side) DABC @ DXYZ
“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
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)
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
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
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
Quad II sin +
Quad I all ratios+
Quad III tan +
Quad IV cos +
Trigonometric & Circular Function Graph s y
y = cos x
-π/2 0 -1
3π/2 2π 5π/2
y = sin x
y 1 y
-π 2 -1
y = tan x
π 2 π
W Re Os
Pb Bi Po At Rn
Sn Sb Te
Ac Th Pa
Np Pu Am Cm Bk Cf
Es Fm Md No Lr
La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
Pt Au Hg Tl
Rf Db Sg Bh Hs Mt Ds Rg
Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br
Zr Nb Mo Tc Ru Rh Pd Ag Cd In
Key of Elements
H Other Metals
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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
Louisiana (LA) Baton Rouge Maine (ME) Augusta Maryland (MD) Annapolis Massachusetts (MA) Boston Michigan (MI) Lansing Minnesota (MN) Saint Paul Mississippi (MS) Jackson Missouri (MO) Jefferson City Montana (MT) Helena Nebraska (NE) Lincoln Nevada (NV) Carson City New Hampshire (NH) Concord New Jersey (NJ) Trenton New Mexico (NM) Santa Fe New York (NY) Albany North Carolina (NC) Raleigh North Dakota (DN) Bismarck
Ohio (OH) Columbus Oklahoma (OK) Oklahoma City Oregon (OR) Salem Pennsylvania (PA) Harrisburg Rhode Island (RI) Providence South Carolina (SC) Columbia South Dakota (SD) Pierre Tennessee (TN) Nashville Texas (TX) Austin Utah (UT) Salt Lake City Vermont (VT) Montpelier Virginia (VA) Richmond Washington (WA) Olympia West Virginia (WV) Charleston Wisconsin (WI) Madison Wyoming (WY) Cheyenne
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