IB Mathematics
Cheat Sheet

Quadratic Formula

$$x = rac{-b pm sqrt{b^2 - 4ac}}{2a}$$

For $ax^2 + bx + c = 0$

Sum of Geometric Series

$$S_n = rac{a(1-r^n)}{1-r}$$

For $r \neq 1$

Sum to Infinity

$$S_infty = rac{a}{1-r}$$

For $|r| < 1$

Power Rule

$$rac{d}{dx}x^n = nx^{n-1}$$

Chain Rule

$$rac{d}{dx}f(g(x)) = f'(g(x)) cdot g'(x)$$

Integration by Parts

$$int u , dv = uv - int v , du$$

Mean

$$ar{x} = rac{sum x_i}{n}$$

Standard Deviation

$$sigma = sqrt{rac{sum(x_i - ar{x})^2}{n}}$$

Normal Distribution

$$f(x) = rac{1}{sigmasqrt{2pi}} e^{-rac{1}{2}left(rac{x-mu}{sigma} ight)^2}$$