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12th grade > ALL MATH > Flashcards

ALL MATH Flashcards

1
Q

natural numbers

A

positive not zero

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2
Q

whole numbers

A

zero and positive number

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3
Q

integer

A

positive and negative

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4
Q

rational

A

fraction, repeating/terminating deci

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5
Q

irrational

A

nonterminating deci, square root, pi

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6
Q

distance

A

rate x time

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7
Q

exponential function

A

y=nb^x

b=constant ratio: y2/y1

n= solve for by plugging in ordered pair. y intercept
-n: flect over x axis

y=ab^x + n
up n

y=a^(x+n)
shift left

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8
Q

even function

A

symmetric across y-axis
(-x,y)

make x negative, y should be the same as before

f(-x)=f(x)

all degree/powers is even

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9
Q

odd function

A

(-x,-y)
symmetric about the origin

make x negative, y will b opposite of before.

f(-x)= - f(x)

all degrees are odd

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10
Q

growth/decay

A

y= a(1+r)^t

y=a(1-r)^t

a= initial amt

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11
Q

finding final amount

compounded interest

A

A=p(1+r/n)^nt

P: initial amt
n: # compounded per year

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12
Q

arithmetic sequence

A

An= An-1 + d, where A1 =______

d= second # - first #
A1 = first term in sequence
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13
Q

arithmetic sequence

calculate

A

An= A1 + d(n-1)

n: term #

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14
Q

geometric sequence

A

An=An-1( r ) where A1= ____

An= a1 ( r )^n-1

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15
Q

measure of center

A

mean x~
not resistant to outliers

median-resistant

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16
Q

measures of variation

A
  • range
  • mean absolute variation (= actual # - mean)
  • IQR (Q3-Q1)
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17
Q

Boxplot

A

min,Q1, med,Q3,max

bigger side=skewd

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18
Q

correlation

A

r [-1,1]
strength of linear relationship

strong correlation= straightline, -1,1

weak: 0

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19
Q

scatterplot residuals

A

actual y-predicted y (from best line fit)

then graph, if it appears random then line best fit is appropriate

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20
Q

reflecting over a line

A

y=a
(x, 2a-y)

x=a
(2a-x,y)

y=x
(y,x)

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21
Q

rotate counterclockwise

A

90 (-y,x)
180 (-x,-y)
270 (y,-x)

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22
Q

proofs of triangle

A
  • reflexive property
  • sum of 2 sides of a triangle is bigger than the 3rd
  • vertical angles
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23
Q

exterior angle theorem

A

exterior angle=sum of 2 nonadjacent angle

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24
Q

transitive propert

A

a=b, b=c, a=c

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25
Q

supplementary

A

180

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26
Q

perpendicular bisector theorem

A

a point on a perpendicular bisector is equidistant from the endpoints of the segment

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27
Q

based angle theorem

A

if two sides of an angle are congruent, then the angles opposite are congruent

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28
Q

congruent triangle

A 
sss
sas
asa
aas
hl
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29
Q

cpctc

A

used to prove a side/angle of 2 triangles are congruent. first prove that the angles are congruent

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30
Q

similar triangles

A 
angles are congruent
sides are proportional
aa~
sss~
sas~
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31
Q

incenter

A

angle bisector
incircle
equidistant from sides at a right angle

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32
Q

circumcenter

A

perpendicular bisector

equidistant from vertices

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33
Q

centroid

A

medians, vertex to midpoint

2x point x

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34
Q

orthocenter

A

altitude: perpendicular segment from vertex to opp side

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35
Q

tangent to a circle

A

perpendicular to radius

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36
Q

circumference of a circle

A

2pir

pi* d

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37
Q

area of a circle

A

pi*r^2

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38
Q

calculate arc length

A

arc length = arc degree

circumference = 360

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39
Q

area of a sector

A

area of sector= arcdegree

area of circle 360

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40
Q

distance formula

A

/(x2-x1)^2 + (y2-y1)^2

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41
Q

midpoint

A

x1+x2 /2

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42
Q

partitioning a line segment

finding a point that is 2/5 distance from A-B

A

x= fraction(x2-x1)+ x1

for y, replace x with y

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43
Q

circle

center: (h,k)

A

(x-h)+(y-k) = r*

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44
Q

ellipse

center: (h,k)

A

(x-h)* + (y-h)* = 1
a* b*

a*= how long it is leftnright
b*= up and down (total)
focus is on the longest axis
c= /a*-b*
c= distant from center to foci
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45
Q

hyperbola

center (h,k)

A

(x-h)* - (y-k)* =1
a* b*
left and right

(y-k)- (x-h) =1
b* a*
up, down

c=/a+b
slope of asymptote: b/a

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46
Q

parabolas

A

up/down
y-k=1/4p(x-h)*

directrix-p-vertex-p-focus

left/right
x-h=1/4p(y-k)*

directrix-focus=focus-point

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47
Q

arc length=S

A

angle degree= s/r

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48
Q

degrees to radians

A

pi/180

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49
Q

coterminal

A

add/minus 360

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50
Q

reference angle

A

acute/always positive

51
Q

trig

A

sin: odd, y
cos: even, x
tan: odd, y/x

to find asymptote, state the first x value then see when the next one is=n.

52
Q

function trig

A

asin(bx-c) +d

a: amplitude max+min / 2
b: period 2pi/b (how long one cycle is

c: phase shift
boundaries
left: bx-c=o
right: bx-c=2pi

53
Q

cosectant

A

graph sine

asymptote where sign touches the midline

54
Q

secant

A

graph sign

55
Q

tangent/cotangent

A

period: pi/b

divide period/domain into 4 sections. 1 and 3 is amplitude

56
Q

inverse of trigs

A

switch x and y

is it a function: pass horizontal line test

57
Q

sin2A

A

2sinAcosA

58
Q

cos2A

A

cosA-sinA
1-2sinA
2cosA-1

59
Q

tan2A

A

2tanA

1-tan*A

60
Q

sin(x+y)

A

sinXcosY + cosXsinY

same sign

61
Q

cos(x+y)

A

cosXcosY - sinXsinY

opposite sign

62
Q

tan (x+y)

A

tanX+tanY
1-tanXtanY

same
opp

63
Q

pythagorean identity

A

sin0 + cos0 =1

tan0 + 1= sec0

1 + cot0 = csc0

64
Q

finding missing side/angle of triangle

A

a = b

sinA sinB

65
Q

ssa

A is acute
a<b></b>

A

a=bsinA one solution
a>bsinA two
a

66
Q

A is cute

a>_ b

A

one solution

67
Q

A is right/obtuse

A

ab one

68
Q

law of cosine

A

a=b + c* - 2bc x cosA

69
Q

to find area of triangle

A

.5absinC

70
Q

heron’s formula to find area of a triangle when given only sides

A

/s(s-a)(s-b)(s-c)

s=.5(a+b+c)

71
Q

complex numbers
imaginary
standard form

A

a+bi

+/-: add like terms, distribute -1

x: foil
divide: multiply by conjugate

72
Q

complex number polar form

R: modulus: magniture

argument: direction/angle

A

rcis0

+/-: convert to standard form

x: multiply modulus
add argument

divide: divide modulus
subtract argument

exponent: raise exponent to modulus
multiply exponent to argument

73
Q

vectors

A

directio and magnitude/length [v]

component form

adding two vertex=resultant

74
Q

linear combination form of vectors

A

-2i+8j

75
Q

direction magnitude form of vectors

A

[v]

unit vector, magnitude=1

component to direct/mag form: use tangent

76
Q

magnitude of vector

A

/x+y

77
Q

finding unit vector

A

1/[v] x V

or

78
Q

vector with weight

A

weight is vector going straight down

force/tension=magnitude

79
Q

velocity vector

A

speed(cos0i + sin0j)

80
Q

find vector given initial and terminal point

A

.

81
Q

permuatation

A

order matters
nPr= n!/(n-r)!

n: # of things you choose from
r: actual # of things you chose

82
Q

combination

A

order does not matter

nCr= n! / r!(n-r)!

83
Q

how many different ways/outcomes

A

multiply the number of possibilities

flip a coin 4 times, possible outcomes?
2x2x2x2

84
Q

how many diff ways can the letters b arranged

A

=number of each letter

total# ! 
#! x #!
85
Q

P(AuB)

A

P(A) + P(B) - P(AnB)

86
Q

independent if

A

P(AnB)= P(A) x P(B)

87
Q

P(A given B)

A

P(AnB)

P(B)

88
Q

more C/P

A 
#uhave C uwant x _C_
total C needed
89
Q

prediction based on rate

A

nCx . p^x (1-p)^n-x

binompdf

90
Q

at most /

A

binomcdf

at least
1-binomcdf

91
Q

finding expected value from frequency table to probability distribution

A

x(Px) + x(Px)

92
Q

graphing log

A

passes through (1,1)

log(x-n)
shift right

logx+n
up n

-logx
reflect over x

domain: (x-n)>0
asymptote (x-n)=0
x intercept: set it to zero

93
Q

absolute value

A

piecewise
turn left into negative
replace lines with paranthesis
to find the turning point, set paranthesis to zero
number before parantesis is slope for right

94
Q

i

A

/-1

95
Q

i*

A

-1

96
Q

i^3

A

-i

97
Q

i^4

A

1

98
Q

i^high number

A 
divide exponent by 4
.25= i
.5  = i*
.75=i^3
no decimal= i^4
99
Q

complex conjugate

A

(a+bi)(a-bi)

100
Q

factoring

A

ac= x/a

b =+

101
Q

quadratic formula

A

b*-4ac=0 one real

0 two real

102
Q

parabola up/down

A

vertex form
y=a(x-h)*+k

to find vertex from standard form:-b/2a

a: positive up
a: strech/shrink
- a: reflect overx

103
Q

inequalities with polynomials and shading a number line

A

find zeros

x shade away

104
Q

midpoint formula

A

(x1+x2/2, y1+y2/2)

105
Q

multiplying dividing poynomial fraction

A

cancel things out diagonal

106
Q

adding/subtracting polynomial fraction (rational)

A

find common denominator than multiply each fraction by it, cancel things out

107
Q

rational expression

horizontal asymptote

A

end behavior
based on degree
N>D none
N

108
Q

rational expression

vertical asymptote
domain

A

set denominator to zero

109
Q

rational expression

zeros

A

set numerator to zero

110
Q

deviation

A

n=sample size

variation: (each data entry-mean)*

111
Q

calcualting standard deviations

A

mean+/- mean deviation

two standard deviation
mean+/- 2(msd)

112
Q

a-b

A

(a+b)(a-b)

113
Q

a+b

A

(a+bi)(a-bi)

114
Q

(a+b)*

A

a+2ab+b

115
Q

(a-b)*

A

a-2ab+b

116
Q

(a+b)^3

A

a^3+ 3ab+3ab+ b^3

117
Q

(a-b)^3

A

a^3- 3ab+3ab - b^3

118
Q

a^3 + b^3

A

(a+b)(a-ab+b)

s o ap

119
Q

pascal triangle

apand (a+b)^

A 
^
0 (1)
1 (11)
2 (121)
3 (1331)
4 (14641)
5 (1,5,10,10,5,1)
120
Q

sum of finite geometric series

A

a1(1-r^)
1-r

^= nth term

121
Q

sum of infinite geometric series

A

a1

1-r

122
Q

dividing polynomials

A

divide Xs= put on top
multiply answer by left of box

use upside down box for x+a

123
Q

critical values

A

vertical asy,ptotes
(y interecpts)
roots

124
Q

radical graph

A

domain: [0, infinity)
/x+n
shift left

starting point: x+n=0

/-x = reflect over y

-/x = reflect over x

3/x goes both ways

12th grade (39 decks)

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