87 terms

act prep (c)

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Terms in this set (...)

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)
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
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
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