87 terms

Herondale01PLUS

Area of a square

A= side²

Area of a Rectangle

A=length(width)

Area of a Parallelogram

A= base(height)

Area of a Rhombus

½(diagonal₁) (diagonal₂)

Area of a triangle

A=½(base)(height)

Area of a Trapezoid

A=½(base₁+base₂)x(height)

Area of a Circle

A=πr²

Perimeter of a square

P=4(side)

Perimeter of a rectangle

P=(2xlength)+( 2xwidth)

Perimeter of a triangle

P= side₁+side₂+side₃

Circumference of a circle

C=πd

Volume of a cube

V=side³

Volume of rectangular solid

V= (length)(width)(height)

Volume of a pyramid or cone

V=1/3(area of base)(height)

Volume of a cylinder

V=(area of base(πd))(height)

Distance between points (x₁,y₁) and (x₂,y₂)

d=√(x₂-x₁)²+(y₂-y₁)²

Slope of a line between points (x₁,y₁) and (x₂,y₂)

m= (y₂-y₁)/(x₂-x₁)

pythagorean theorem

a²+b²=c²

mean

average; add all terms together and dive by number of terms

median

middle term; order terms least to greatest

interest

(principal)(rate)(time)

distance

(rate)(time)

total cost

(#of units)(price per unit)

quadratic formula

x=-b+(√b²-4ac/2a)

Inequalities "and"

intersection

Inequalities "or"

union

Proportion: comparison of two rations

cross- multiply to solve

Absolute value

distance from zero; always positive

Probability

# of favorable outcomes/#of total possible outcomes

Permutation

an arrangement where order is important

Combination

order does not matter

Complex numbers

i=√-1; i²=-1, i³=-i; i⁴=1

Slope of a line

rise/ run→change in y/change in x →

(y₂-y₁)/(x₂-x₁)

(y₂-y₁)/(x₂-x₁)

slope intercept form of a line

y=mx+b; m=slope b=y-intercept

Midpoint formula

[(x₁+x₂/2), (y₁+y₂/2)]

Complementary angles

add to 90°

Supplementary angles

add to 180°

angles in a triangle add to

180°

scalene triangles

all 3 sides are different lengths

isosceles triangles

2 sides have the same length, the angles opposite the congruent sides are also congruent

equilateral triangles

all 3 sides and angles are equal (60°)

Special right triangles 30-60-90

short side=x; long side=x√3; hypotenuse= 2x

Special right triangles 45-45-90

short sides both = x; hypotenuse= x√2

equation of a circle

(x-h)²+(y-k)²+r²; center-(h,k) radius-r

sin

opp/hyp

cos

adj/hyp

tan

opp/adj

csc

hyp/opp

sec

hyp/adj

cot

adj/opp

graph of sinx

odd function

graph of cosx

even function

graph of tanx

odd function

Period

distance along the x-axis to complete one full cycle before the graph starts to repeat its self

Amplitude

the graphs height from the "home" line to the highest or lowest point

convert radians to degrees

multiply by 180°/π

convert degrees to radians

multiply by π/180°

Declarative sentence

ends with a period and makes a statement

Imperative sentence

ends with a period or exaltation point; gives command or makes a request

Interrogative sentence

ends with a question mark; asks a question

exclamatory sentence

ends with an exclamation point; shows sudden or strong feelings

abbreviation

ends with a period

use a comma and coordinating conjunction

(and, but, or, nor, for, yet) to join two independent clauses .

use a single comma to

indicate that a word or words have been omitted, avoid possible misreadings, separate three or more items in a series, separate two or more adjectives preceding a noun, set off words used in direct address, introduce modifying phrases or clauses, separate parts of dates and addresses; set off well, yes, no, or why at the beginning of sentence

appositives

word following a noun that explains and identifies it

use a colon

before listed items introduces by suck words as "as follows or the following", to introduce a formal statement or quotation, between the chapter and verse of bible references, between the hour and minute of a time reference, after the salutation of a business letter

uses italics when

underlining the titles of books, magazines, newspapers, plays, works of art, and the names of ships, trains, aircraft, and spacecraft; foreign words and phrases;

uses a semicolon

between independent clauses if you do use a comma and coordinating conjunction; between independent clauses joined by transitional words

apostrophe

to form the possessive case of nouns, write the plural spelling of a word, contractions, plurals of letters numbers signs and words

Subject verb agreement

the verb of a sentence must agree with its subject in number

singular subjects take singular verbs and plural subjects take plural verbs

singular subjects take singular verbs and plural subjects take plural verbs

Nominative case pronouns

may be used as subjects or predicate nominatives

nominative case pronouns (predicate nominatives)

I, he, she, we , they, who, whoever, you, it

Possessive Case Pronouns

show ownership or relationship

1st person singular

my, mine

1st person plural

our, ours

second person singular and plural

your, yours

third person singular

his, her, hers, its

third person plural

their, theirs

Special case pronouns

who or whoever if pronoun is used as a subject or as a predicate nominative;

whom or whomever if the pronoun is used as a direct object of preposition

whom or whomever if the pronoun is used as a direct object of preposition

Objective case pronoun

pronouns may be used as direct objects and as indirect objects or objects of prepostions

objective case pronouns (objects of prepositions)

me, her, us, them, whom, whomever, you, it

predicate nominative

come after linking verbs

linking verbs

am, were, taste, look, grow, is, be, feel, appear, remain, are, being, smell, become, stay, was, been, sound, seem

direct objects and indirect objects

come after action verbs

a pronoun used as an appositive must be

in the same case as the word to which it refers

adjective

a word that modifies a noun or pronoun

verb tenses

indicate the time expressed by the verb; past, present, or future