Quadratic Formula: $x=\frac{\displaystyle -b \pm \sqrt{b^2-4ac}}{\displaystyle 2a}$ $\quad \text{where}\quad ax^2+bx+c=0$

Finance: $A=P(1+ni) \quad$ $A=P(1-ni) \quad$ $A=P(1-i)^n \quad$ $A=P(1+i)^n$ $F=\frac{\displaystyle x[(1+i)^n-1]}{\displaystyle i} \quad$ $P=\frac{\displaystyle x[1-(1+i)^{-n}]}{\displaystyle i}$

Sequences and Series: $T_n=a+(n-1)d \quad$ $S_n=\frac{\displaystyle n}{\displaystyle 2}[2a+(n-1)d]\quad$ $T_n=ar^{n-1} \quad$ $S_N=\frac{\displaystyle a(r^n-1)}{\displaystyle r-1}\: ; \, r \neq 1 \quad$ $S_\infty =\frac{\displaystyle a}{\displaystyle 1-r}\: -1<r<1$

First Principle: $f^\prime (x)=\lim\limits_{h \to 0}\frac{\displaystyle f(x+h)-f(x)}{\displaystyle h}$

Analytical Geometry: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \quad$ $M(\frac{\displaystyle x_1+x_2}{\displaystyle 2}\; ; \, \frac{\displaystyle y_1+y_2}{\displaystyle 2}) \quad$ $y=mx+c \quad$ $y-y_1=m(x-x_1) \quad$ $m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1} \quad$ $m=\tan{\theta}$ $(x-a)^2+(y-b)^2=r^2$

Trig Triangles, in $\Delta ABC$: $\frac{\displaystyle a}{\displaystyle \sin{A}} = \frac{\displaystyle b}{\displaystyle \sin{B}} = \frac{\displaystyle c}{\displaystyle \sin{C}}$ $a^2=b^2+c^2-2bc.\cos{A}$ area $\Delta ABC = \frac{\displaystyle 1}{\displaystyle 2} \, ab.\sin{C}$

Trig Compound Angles: $\sin{\alpha + \beta}=\sin{\alpha}\cos{\beta}+\cos{\alpha}\sin{\beta}$ $\sin{\alpha - \beta}=\sin{\alpha}\cos{\beta}-\cos{\alpha}\sin{\beta}$ $\cos{\alpha + \beta}=\cos{\alpha}\cos{\beta}-\sin{\alpha}\sin{\beta}$ $\cos{\alpha - \beta}=\cos{\alpha}\cos{\beta}+\sin{\alpha}\sin{\beta}$ $\cos{2\alpha}=\cos{\alpha}^2-\sin{\alpha}^2 \quad or \quad 1-2\sin{\alpha}^2 \quad or \quad 2\cos{\alpha}^2-1$ $\sin{2\alpha}=2\sin{\alpha}\cos{\alpha}$

Probability: $P(A)=\frac{\displaystyle n(A)}{\displaystyle n(S)}$ $P(A\; or\; B)=P(A)+P(B)-P(A\; and\; B)$

Statistics: $\bar x =\frac{\displaystyle \Sigma x}{\displaystyle n}$ $\sigma ^2 = \frac{\displaystyle \sum_{i=1}^{n}(x_i-\bar x)^2}{\displaystyle n}$ $\hat y=a+bx$ $b=\frac{\displaystyle \Sigma (x- \bar x)(y- \bar y)}{\displaystyle \Sigma (x- \bar x)^2}$