Funatic Maths
Quadratic Formula:
x=b±b24ac2ax=\frac{\displaystyle -b \pm \sqrt{b^2-4ac}}{\displaystyle 2a} whereax2+bx+c=0\quad \text{where}\quad ax^2+bx+c=0
Finance:
A=P(1+ni)A=P(1+ni) \quad
A=P(1ni)A=P(1-ni) \quad
A=P(1i)nA=P(1-i)^n \quad
A=P(1+i)nA=P(1+i)^n
F=x[(1+i)n1]iF=\frac{\displaystyle x[(1+i)^n-1]}{\displaystyle i} \quad
P=x[1(1+i)n]iP=\frac{\displaystyle x[1-(1+i)^{-n}]}{\displaystyle i}
Sequences and Series:
Tn=a+(n1)dT_n=a+(n-1)d \quad
Sn=n2[2a+(n1)d]S_n=\frac{\displaystyle n}{\displaystyle 2}[2a+(n-1)d]\quad
Tn=arn1T_n=ar^{n-1} \quad
SN=a(rn1)r1;r1S_N=\frac{\displaystyle a(r^n-1)}{\displaystyle r-1}\: ; \, r \neq 1 \quad
S=a1r1<r<1S_\infty =\frac{\displaystyle a}{\displaystyle 1-r}\: -1<r<1
First Principle:
f(x)=limh0f(x+h)f(x)hf^\prime (x)=\lim\limits_{h \to 0}\frac{\displaystyle f(x+h)-f(x)}{\displaystyle h}
Analytical Geometry:
d=(x2x1)2+(y2y1)2d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \quad
M(x1+x22  ;y1+y22)M(\frac{\displaystyle x_1+x_2}{\displaystyle 2}\; ; \, \frac{\displaystyle y_1+y_2}{\displaystyle 2}) \quad
y=mx+cy=mx+c \quad
yy1=m(xx1)y-y_1=m(x-x_1) \quad
m=y2y1x2x1m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1} \quad
m=tanθm=\tan{\theta}
(xa)2+(yb)2=r2(x-a)^2+(y-b)^2=r^2
Trig Triangles, in ΔABC\Delta ABC:
asinA=bsinB=csinC\frac{\displaystyle a}{\displaystyle \sin{A}} = \frac{\displaystyle b}{\displaystyle \sin{B}} = \frac{\displaystyle c}{\displaystyle \sin{C}}
a2=b2+c22bc.cosAa^2=b^2+c^2-2bc.\cos{A}
area ΔABC=12ab.sinC\Delta ABC = \frac{\displaystyle 1}{\displaystyle 2} \, ab.\sin{C}
Trig Compound Angles:
sinα+β=sinαcosβ+cosαsinβ\sin{\alpha + \beta}=\sin{\alpha}\cos{\beta}+\cos{\alpha}\sin{\beta}
sinαβ=sinαcosβcosαsinβ\sin{\alpha - \beta}=\sin{\alpha}\cos{\beta}-\cos{\alpha}\sin{\beta}
cosα+β=cosαcosβsinαsinβ\cos{\alpha + \beta}=\cos{\alpha}\cos{\beta}-\sin{\alpha}\sin{\beta}
cosαβ=cosαcosβ+sinαsinβ\cos{\alpha - \beta}=\cos{\alpha}\cos{\beta}+\sin{\alpha}\sin{\beta}
cos2α=cosα2sinα2or12sinα2or2cosα21\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
sin2α=2sinαcosα\sin{2\alpha}=2\sin{\alpha}\cos{\alpha}
Probability:
P(A)=n(A)n(S)P(A)=\frac{\displaystyle n(A)}{\displaystyle n(S)}
P(A  or  B)=P(A)+P(B)P(A  and  B)P(A\; or\; B)=P(A)+P(B)-P(A\; and\; B)
Statistics:
xˉ=Σxn\bar x =\frac{\displaystyle \Sigma x}{\displaystyle n}
σ2=i=1n(xixˉ)2n\sigma ^2 = \frac{\displaystyle \sum_{i=1}^{n}(x_i-\bar x)^2}{\displaystyle n}
y^=a+bx\hat y=a+bx
b=Σ(xxˉ)(yyˉ)Σ(xxˉ)2b=\frac{\displaystyle \Sigma (x- \bar x)(y- \bar y)}{\displaystyle \Sigma (x- \bar x)^2}