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Math (Probability (sample space (listing outcomes, 2d grids, tree diagram)…
Math
Probability
sample space
listing outcomes
2d grids
tree diagram
combined events: P(AUB)=P(A)+P(B)-P(ANB)
conditional events (for dependent): P(ANB)=P(A)P(B/A)
mutually exclusive/disjoint events: P(AUB)=P(A)+P(B) OR P(ANB)=0
independent events: P(ANB)=P(A)P(B)
complementary events: P(A)+P(A')=1
conditional event: P(A/B)=P(AUB)/P(B)
venn diagram
Functions
Domain and range
Composite function: (fog)(x)
Inverse function: f-1(x)
Rational function
y=(ax+b)/(cx+d)
vertical asymp: y=a/c
horizontal asymp: denominator\=0
y=1/(x+b)+k
vertical asmp: y=k
horizontal asymp: x=-b
Exponential function: a*b^(x-c)+d
law of exponents
Quadratics
standard form: y=ax2+bx+c
line of symmetry: -b/2a
factorized form: y=a(x-p)(x-q)
vertex form: y-a(x-h)2+k
methods to solve for x
quadratic formula: delta
"complete the square": (x+1)2=0
"factorization": (x-1)(x+2)=0
Transforming functions
dilation: y=pf(x) OR y=f(qx)
reflection: y=--f(x) OR y=f(-x)
translation: y=f(x-a)+b
transformation of cubed functions:
Descriptive stats
measuring center
mean, median, mode
describing distribution
positively skewed, negatively skewed, symmetric
measuring spread
range, Q1, Q2, Q3, IQR, variance, SD
outlier
upper boundary: upper quartile+1.5*IQR
lower boundary: lower quartile-1.5*IQR
diagrams
boxplot
cummulative frequency graph
Linear modeling
describing correlation
direction (pos, neg), linearity (straight, curved), strength (strong, weak), outlier, causation (proportional, x proportional)
correlation coefficient (GDC)
sign (direction), size (strength)
line of best fit (GDC)
intrapolation/extrapolation
Discrete random variables
discrete probability distribution table
expectation: E(X)=mean=np
fair game: E(X)=0
variance: np(1-p)
binomial distribution: P(X=r)=(nr)p^r(1-p)^(n-r)
Log
natural log: ln(y)=loge(y)=n
natural log laws
inverse log: fx=ax; fx-1=loga(x)
domain, range, asymptote
plain log: logx(y)=n
plain log laws
Sequence and series
sequence
arithmetic: Un=(n-1)d
geometric: Un=u1*r^(n-1)
series
arithmetic: Sn=n/2(U1+Un) OR Sn=n/2(2u1+(n-1)d)
geometric
finite: Sn=(u1(r^n-1))/r-1 OR Sn-(u1(1-r^n))/1-r
infinite
convergent: Sn=u1/(1-r) /r/<1
divergent: Sn=infinite /r/>1
Sigma notation
Trig
Trig functions
sin, cos, tan
amplitude (max+min/2), period (2*3.14/b, 2/b),mean line (max-min/2), frequency (1/period)
domain and range
transformation (shift a and b, dilate)
Trig triangle
area: 1/2absinC
sin: a/sinA=b/sinB
cos: a2=b2+c2-2bc*cosA
Trig identities
Unit circle
radian and degree
radian
Arch length=r0
Area of sector: 1/20r^2
degree
Arch length=(n3.14r)/180
Area of sector: (n3.14r^2)/360
conversion between radian and degree
THE unit circle
cos=x, sin=y, tan=y/x
Calculus
Differential calculus
Differential cal app
kinematics
rates of change
optimization
Differential cal rules
power rule, chain rule, product rule, quotient rule
derivative of exponents, of log/ln, of trig
first and second derivative
properties of curves
horizontal tangent: f'(x)=0 find x
normal
external point
tangent
stationary point: f'(x)
local min
local max
stationary inflection
inflection: f''(x)
stationary inflection
non-stationary inflection
Integral calculus
Integral cal rules
Integral cal app
area under a curve
area between two functions
kinematics
volume of revolution
Vector
Vector theory
Vector app
Binomial
general term: Tr+1=(nr)
a^(n-r)
b^r
question types
find constant term
find term involving x5
find coefficient
find coefficient of x5 in expansion of ()()6
find the fifth term: T5=Tr+1; r=4
Normal distribution
Miscellaneous question