Cheatography
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Fraction RulesCommon Denominators
a/b + c/d = ad + bc/bd
Multiplication
a/b * c/d = ac/bd
Reciprocal
1/(a/b) = b/a 
LinesGiven point (c,d) and slope m, the unique line that satisfies this is the set of all points (x,y) such that
m = yd/xc
slope is change in y/change in x
Parallel, Perpendicular
y=2x+4 and y=2x+3 are parallel
y=2x+4 and 2y=4x+8 are same line
y=2x+4 and y = 1/2x+6 meet perpendicularly
Parallel lines never meet, same slope
Perpendicular lines meet once at right angles and slopes are negative reciprocals 
Quadratic Functions: Parabolasf(x) = ax^{2} + bx + c
Zeros given by the quadratic formula:
b +/ sqrt(b^{2}  4ac)/2a
Coordinate point (b/2a,( b^{2} +4ac)/4a) 
Geometric EquationsCircles: Circumference 2(pi)r Area (pi)r^{2}
Cylinders: Surface area 2(pi)r x h + 2(pi)r^{2} Volume: (pi)r^{2}h
Sphere: Surface area 4(pi)r^{2} Volume 4/3(pi)r^{3} 
Geometric FormulasSOHCAHTOA
SOH = sin(x) = a/c
CAH = cos(x) = b/c
TOA = tan(x) = a/b
180 degrees = (pi)rad
Divide arclength by radius to get radian measure
Special Angles
Degree Radian Cosine Sine Tangent
0 0 1 0 0
30 (pi)/6 sqrt3/2 1/2 1/sqrt3
45 (pi)/4 1/sqrt(2) 1/sqrt(2) 1
60 (pi)/3 1/2 sqrt(3)/2 sqrt(3)
90 (pi) 0 1 undefined 
Theory of Geometric SeriesS = p + pr + pr^{2} + pr^{3} + ... + pr^{n}
Sr = p + pr + pr^{2} + pr^{3} + ... + pr^{n} + pr^{n+1}
S  Sr = p  pr^n+1
S = ppr^{n+1}/1r 
  Negative Exponentsa^{m} = 1/a^{m}
1/a^{m} = a^{m} 
Multiplication and Scientific NotationMultiplication and Division:
 Convert into scientific notation
 Add/subtract exponents
 Multiply/divide coefficients
 Convert to scientific notation
 2.3E4 x 9.5E7/1.6E10 = 2.3x9.5/1.6E(4+710) 
Absolute ValuesAbsolute Values often generate "and" and "or" situations.
Examples:
x<1: 1<x and x<1 1<x<1
x>1: x>1 or x<1
2x+3> 1: 2x+3>1 or (2x+3)>1
x>1 or x<2 
Exponential Rulesexp(a)exp(b) = exp(a+b)
[exp(a)]^b = exp(ab)
exp(a) = 1/exp(a)
Domain: all real numbers
Range: all positive numbers 
Secant, Cosecant, CotangentSecant: 1/cos(x)
Cosecant = 1/sin(x)
Cotangent = 1/tan(x) = cos(x)/sin(x) 
Trigonometric Identitiescos^{2}x + sin^{2}x = 1
tan^{1}x = arctan x
cot(x) = 1/tan x
e^{10} = cos x + isin x 
  Basic FactsTotal human population: 7 billion
USA population: 300 million
Distance from NY to LA: 2500 miles
Distance to the moon: 2.4E5 miles
Distance to the Sun: 1E8 miles
Distance around the equator: 2.5E4 miles
Area of the US: 4E6 square miles
Surface area of the Earth: 2E8 square miles 
Distance Between PointsThe distance between two points on the plane is based on the Pythagorean Theorem
AB = sqrt((XaXb)^{2} +(Ya  Yb)^{2})
A=(Xa,Ya) B=(Xb,Yb) 
Function VariablesDomain = valid inputs to function
Range = what can the function produce
Zeros or Roots = where is f(x)=0
Intersections = Where is f(x) = g(x)
Local maximum is largest value around itself
Local minimum is smallest value around itself
Global is largest overall 
LogarithmsLogarithms are the functional inverses of the exponential
y = b^x is equivalent to logb(y) = x
log(mn) = log(m) + log(n)
log(m^n) = nlog(m)
log(1/m) = log(m)
loga(m) = logb(m)/logb(a)
exp(a)exp(b) = exp(ab)
exp(a) = 1/exp(a)
e^{2.3 = 10, e}12 = e^{2.3*5.2 = (e}2.3)^{5.2 = 10}5.2 = 2E5 
SineSine is the y component as theta spins
Domain is all real numbers
Range 1</ y </ 1
Maxima at pi/2 + 2kpi, Minima at 3pi/2 + 2kpi
Zeros at kpi
Period 2pi 
CosineCosine is the x component as theta spins
Domain is all real numbers
Range is 1</ y </ 1
Max is 2kpi, Minima (2k + 1)pi
Zeros at pi/2 + kpi
Period is 2pi 
TangentTangent is the slope of the line with angle theta
Domain is all real numbers except pi/2 + kpi
Range is all real numbers
No max or min. asymptotes at undefined points
Zeros at kpi
Period is pi 

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