ALL MATH Flashcards
(124 cards)
1
Q
natural numbers
A
positive not zero
2
Q
whole numbers
A
zero and positive number
3
Q
integer
A
positive and negative
4
Q
rational
A
fraction, repeating/terminating deci
5
Q
irrational
A
nonterminating deci, square root, pi
6
Q
distance
A
rate x time
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
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
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
10
Q
growth/decay
A
y= a(1+r)^t
y=a(1-r)^t
a= initial amt
11
Q
finding final amount
compounded interest
A
A=p(1+r/n)^nt
P: initial amt
n: # compounded per year
12
Q
arithmetic sequence
A
An= An-1 + d, where A1 =______
d= second # - first # A1 = first term in sequence
13
Q
arithmetic sequence
calculate
A
An= A1 + d(n-1)
n: term #
14
Q
geometric sequence
A
An=An-1( r ) where A1= ____
An= a1 ( r )^n-1
15
Q
measure of center
A
mean x~
not resistant to outliers
median-resistant
16
Q
measures of variation
A
- range
- mean absolute variation (= actual # - mean)
- IQR (Q3-Q1)
17
Q
Boxplot
A
min,Q1, med,Q3,max
bigger side=skewd
18
Q
correlation
A
r [-1,1]
strength of linear relationship
strong correlation= straightline, -1,1
weak: 0
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
20
Q
reflecting over a line
A
y=a
(x, 2a-y)
x=a
(2a-x,y)
y=x
(y,x)
21
Q
rotate counterclockwise
A
90 (-y,x)
180 (-x,-y)
270 (y,-x)
22
Q
proofs of triangle
A
- reflexive property
- sum of 2 sides of a triangle is bigger than the 3rd
- vertical angles
23
Q
exterior angle theorem
A
exterior angle=sum of 2 nonadjacent angle
24
Q
transitive propert
A
a=b, b=c, a=c
25
supplementary
180
26
perpendicular bisector theorem
a point on a perpendicular bisector is equidistant from the endpoints of the segment
27
based angle theorem
if two sides of an angle are congruent, then the angles opposite are congruent
28
congruent triangle
```
sss
sas
asa
aas
hl
```
29
cpctc
used to prove a side/angle of 2 triangles are congruent. first prove that the angles are congruent
30
similar triangles
```
angles are congruent
sides are proportional
aa~
sss~
sas~
```
31
incenter
angle bisector
incircle
equidistant from sides at a right angle
32
circumcenter
perpendicular bisector
| equidistant from vertices
33
centroid
medians, vertex to midpoint
2x point x
34
orthocenter
altitude: perpendicular segment from vertex to opp side
35
tangent to a circle
perpendicular to radius
36
circumference of a circle
2*pi*r
| pi* d
37
area of a circle
pi*r^2
38
calculate arc length
arc length = arc degree
| circumference = 360
39
area of a sector
area of sector= arcdegree
| area of circle 360
40
distance formula
/(x2-x1)^2 + (y2-y1)^2
41
midpoint
x1+x2 /2
42
partitioning a line segment
| finding a point that is 2/5 distance from A-B
x= fraction(x2-x1)+ x1
for y, replace x with y
43
circle
| center: (h,k)
(x-h)*+(y-k)* = r*
44
ellipse
| center: (h,k)
(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
```
45
hyperbola
| center (h,k)
(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
46
parabolas
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
47
arc length=S
angle degree= s/r
48
degrees to radians
pi/180
49
coterminal
add/minus 360
50
reference angle
acute/always positive
51
trig
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
function trig
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
cosectant
graph sine
| asymptote where sign touches the midline
54
secant
graph sign
55
tangent/cotangent
period: pi/b
| divide period/domain into 4 sections. 1 and 3 is amplitude
56
inverse of trigs
switch x and y
is it a function: pass horizontal line test
57
sin2A
2sinAcosA
58
cos2A
cos*A-sin*A
1-2sin*A
2cos*A-1
59
tan2A
2tanA
| 1-tan*A
60
sin(x+y)
sinXcosY + cosXsinY
same sign
61
cos(x+y)
cosXcosY - sinXsinY
opposite sign
62
tan (x+y)
tanX+tanY
1-tanXtanY
same
opp
63
pythagorean identity
sin*0 + cos*0 =1
tan*0 + 1= sec*0
1 + cot*0 = csc*0
64
finding missing side/angle of triangle
a = b
| sinA sinB
65
ssa
A is acute
a
a=bsinA one solution
a>bsinA two
a
66
A is cute
| a>_ b
one solution
67
A is right/obtuse
ab one
68
law of cosine
a*=b* + c* - 2bc x cosA
69
to find area of triangle
.5absinC
70
heron's formula to find area of a triangle when given only sides
/s(s-a)(s-b)(s-c)
s=.5(a+b+c)
71
complex numbers
imaginary
standard form
a+bi
+/-: add like terms, distribute -1
x: foil
divide: multiply by conjugate
72
complex number polar form
R: modulus: magniture
argument: direction/angle
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
vectors
directio and magnitude/length [v]
component form
adding two vertex=resultant
74
linear combination form of vectors
-2i+8j
75
direction magnitude form of vectors
[v]
unit vector, magnitude=1
component to direct/mag form: use tangent
76
magnitude of vector
/x*+y*
77
finding unit vector
1/[v] x V
| or
78
vector with weight
weight is vector going straight down
| force/tension=magnitude
79
velocity vector
speed(cos0i + sin0j)
80
find vector given initial and terminal point
.
81
permuatation
order matters
nPr= n!/(n-r)!
n: # of things you choose from
r: actual # of things you chose
82
combination
order does not matter
| nCr= n! / r!(n-r)!
83
how many different ways/outcomes
multiply the number of possibilities
flip a coin 4 times, possible outcomes?
2x2x2x2
84
how many diff ways can the letters b arranged
```
total# !
#! x #!
```
#=number of each letter
85
P(AuB)
P(A) + P(B) - P(AnB)
86
independent if
P(AnB)= P(A) x P(B)
87
P(A given B)
P(AnB)
| P(B)
88
more C/P
```
#uhave C uwant x _C_
total C needed
```
89
prediction based on rate
nCx . p^x (1-p)^n-x
binompdf
90
at most _/_
binomcdf
at least
1-binomcdf
91
finding expected value from frequency table to probability distribution
x(Px) + x(Px)
92
graphing log
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
absolute value
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
i
/-1
95
i*
-1
96
i^3
-i
97
i^4
1
98
i^high number
```
divide exponent by 4
.25= i
.5 = i*
.75=i^3
no decimal= i^4
```
99
complex conjugate
(a+bi)(a-bi)
100
factoring
ac= x/a
| b =+
101
quadratic formula
b*-4ac=0 one real
| 0 two real
102
parabola up/down
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
inequalities with polynomials and shading a number line
find zeros
| x shade away
104
midpoint formula
(x1+x2/2, y1+y2/2)
105
multiplying dividing poynomial fraction
cancel things out diagonal
106
adding/subtracting polynomial fraction (rational)
find common denominator than multiply each fraction by it, cancel things out
107
rational expression
horizontal asymptote
end behavior
based on degree
N>D none
N
108
rational expression
vertical asymptote
domain
set denominator to zero
109
rational expression
zeros
set numerator to zero
110
deviation
n=sample size
| variation: (each data entry-mean)*
111
calcualting standard deviations
mean+/- mean deviation
two standard deviation
mean+/- 2(msd)
112
a*-b*
(a+b)(a-b)
113
a*+b*
(a+bi)(a-bi)
114
(a+b)*
a*+2ab+b*
115
(a-b)*
a*-2ab+b*
116
(a+b)^3
a^3+ 3a*b+3ab*+ b^3
117
(a-b)^3
a^3- 3a*b+3ab* - b^3
118
a^3 + b^3
(a+b)(a*-ab+b*)
| s o ap
119
pascal triangle
| apand (a+b)^
```
^
0 (1)
1 (11)
2 (121)
3 (1331)
4 (14641)
5 (1,5,10,10,5,1)
```
120
sum of finite geometric series
a1(1-r^)
1-r
^= nth term
121
sum of infinite geometric series
a1
| 1-r
122
dividing polynomials
divide Xs= put on top
multiply answer by left of box
use upside down box for x+a
123
critical values
vertical asy,ptotes
(y interecpts)
roots
124
radical graph
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
