

Area of a triangle (SAS Formula)


Area of a circle
A=πr^{2}

Curcumference of a circle

Lateral surface area of a cylinder
S = 2πrh

Total surface area of a cylinder
S = 2πrh + 2πr^{2}

Surface of a sphere
S = 4πr^{2}


Volume of a pyramid
 B = Area of Base

Volume of a cylinder
V = πr^{2}h

Volume of a cone
πr ^{2}h

Volume of a sphere
V = 4/3πr^{2}

Double angle identity for cos^{2}x
1/2 (1+cos2x)

Double angle identity for sin^{2}x^{}
1/2 (1cos2x)














cos2x (in terms of cosX and sinX)
cos^{2}x  sin^{2}x

cos2X (in terms of cosX)
2cos^{2}X1

cos2X (in terms of sinX)
1  2sin^{2}X




law of sines
a / sinA = b / sinB = c / sinC

Law of cosines
a^{2 }= b^{2} + c^{2} 2bccosA



log ( A / B )
log A  log B





Pythagorean Theorem
a^{2} + b^{2} = c^{2}

Distance between points ( x_{1}, y_{1 }) and ( x_{2}, y_{2} )

Slope of the line between points ( x_{1}, y_{1 }) and ( x_{2}, y_{2} )

PointSlope equation of a line
y  y_{1} = m( x x_{1} )

slope intercept equation of a line
y = mx + b

standard form of the equation of a line
Ax + Bx = C

Circle with center at point (h, k) and raduis r
( x  h )^{2} + ( y  k )^{2} = r^{2}

ellipse
Ax^{2} + By^{2} = C

Hyperbola
Ax^{2}  By^{2} = C

Hyperbola with axes as asymptotes
xy = k

Parabola (vertical axis of symmetry)
y = ax^{2} + bx + c

Parabola (horizontal axis of symmetry)
x = ay^{2} + by + c

Domain of a function
the set of all possible values of x for a functions

Range of a function
the set of all possible values of y for a function

function symmetric across the yaxis
f(x) = f(x)

Even functions
f(x) = f(x)

function symmetric through the origin
f(x) = f(x)

Odd Function
f(x) = f(x)

Quadratic formula (roots of y = ax^{2} +bx +c)

Inverse of a function
( f o f^{}^{1})(x) = x

To graph the inverse of a function...
reflect the graph of the function across the line y = x

To find the equation of the inverse of a function
interchange x and y, then solve the equation for y

If point ( a,b ) lies on the inverse function f^{1} then...
point ( b,a ) lies on function f

Inverse of y = e^{x}
y = ln x

Inverse of y = lnx
y = e^{x}

Line parallel to y = mx + b through point ( x_{1},y_{1} )
 y  y_{1} = m ( xx_{1} )
 or
 y = mx + b_{1}, where b_{1} = (y_{1}mx_{1})

Line perpendicular to y = mx + b through point ( x_{1},y_{1} )

