SAT Math Formulas

$A = \pi r^2$

$C = 2\pi r$

$A = lw$

$A = \tfrac{1}{2}bh$

$c^2 = a^2 + b^2$

$x,\ x\sqrt{3},\ 2x$

$s,\ s,\ s\sqrt{2}$

$V = lwh$

$V = \pi r^2 h$

$V = \tfrac{4}{3}\pi r^3$

$V = \tfrac{1}{3}\pi r^2 h$

$V = \tfrac{1}{3}lwh$

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

$y = mx + b$

$y - y_1 = m(x - x_1)$

$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

$\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)$

$|x| = a \;\Rightarrow\; x = a \text{ or } x = -a \quad (a \ge 0)$

$a^2 - b^2 = (a-b)(a+b)$

$(a \pm b)^2 = a^2 \pm 2ab + b^2$

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

$D = b^2 - 4ac$

$x = -\dfrac{b}{2a};\quad y = a(x-h)^2 + k$

$y = a(x-p)(x-q)$

$x_1 + x_2 = -\dfrac{b}{a},\quad x_1 x_2 = \dfrac{c}{a}$

$a^m \cdot a^n = a^{m+n}$

$\dfrac{a^m}{a^n} = a^{m-n}$

$(a^m)^n = a^{mn}$

$a^{-n} = \dfrac{1}{a^n};\quad a^0 = 1 \ (a \ne 0)$

$a^{m/n} = \sqrt[n]{a^m}$

$\sqrt{ab} = \sqrt{a}\sqrt{b} \quad (a,b \ge 0)$

$y = a(1+r)^t \quad\text{/}\quad y = a(1-r)^t$

$f(x-h)+k$

$x\%\text{ of }y = \dfrac{x}{100}\cdot y$

$\dfrac{\text{new} - \text{old}}{\text{old}} \times 100\%$

$\text{mean} = \dfrac{\text{sum}}{\text{count}}$

$\dfrac{a}{b} = \dfrac{c}{d} \iff ad = bc$

$P = \dfrac{\text{favorable}}{\text{total}}$

$\sin = \dfrac{\text{opp}}{\text{hyp}},\ \cos = \dfrac{\text{adj}}{\text{hyp}},\ \tan = \dfrac{\text{opp}}{\text{adj}}$

$\sin^2\theta + \cos^2\theta = 1$

$\sin x = \cos(90° - x)$

$\text{radians} = \text{degrees} \times \dfrac{\pi}{180}$

$(x-h)^2 + (y-k)^2 = r^2$

$\dfrac{\text{arc}}{2\pi r} = \dfrac{\text{sector}}{\pi r^2} = \dfrac{\text{angle}}{360°}$