Slope Formula:
$~$\frac {(y_2-y_1)}{(x_2-x_1)}$~$= $~$\frac{\Delta y}{\Delta x}=\frac {rise}{run}$~$
Equation of a Line:
$~$y=mx+b$~$
Midpoint Formula:
($~$\frac {(x_1+x_2)}{2}$~$, $~$\frac {(y_1+y_2)}{2}$~$)
Distance Formula:
$~$\sqrt {(x_2-x_1)^2+(y_2-y_1)^2}$~$
Length of an Arc:
$~$L_{arc}=(2πr)(\frac {xº}{360})$~$
Area of an Arc Sector:
$~$L_{arc sector}=(πr^2)(\frac {xº}{360})$~$
Quadratic Formula:
$~$x=\frac {-b \pm \sqrt {b^2-4ac}}{2a}$~$
Completing the Square:
$~$ax^2+bx=0 \rightarrow a(x+d)^2+e=0$~$
$~$d=\frac{b}{2a}$~$
$~$e=c-\frac{b^2}{4a}$~$
Trigonometry:
$~$sin(x)=\frac {o}{h}$~$
$~$cos(x)=\frac {a}{h}$~$
$~$tan(x)=\frac{o}{a}$~$
Arithmetic Sequences:
$~$t_1, t_1+d, t_1+2d, …$~$
Geometric Sequences:
$~$t_1, t_1\cdot r, t_1\cdot r^2,…$~$
Exponent Rules:
$~$x^a\cdot{x^b}=x^{a+b}$~$
$~$(x^a)^b=x^{a\cdot{b}}$~$
$~$x^0=1$~$
$~$\frac {x^a}{x^b}=x^{a-b}$~$
$~$(xy)^a=x^a\cdot{y^a}$~$
$~$\sqrt{xy}=\sqrt{x} \cdot {\sqrt{y}}$~$
$~$x^{-b}=\frac {1}{x^b}$~$
Foil:
$~$(x+a)(x+b)=x^2+(b+a)x+ab$~$
Difference of Squares:
$~$a^2-b^2=(a+b)(a-b)$~$
Factoring:
$~$a^2+2ab+b^2=(a+b)(a+b)$~$
$~$a^2-2ab+b^2=(a-b)(a-b)$~$
Pythagorean Theorem:
$~$a^2+b^2=c^2$~$