Formula Sheet

Algebra

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, \qquad \alpha + \beta = -\frac{b}{a}, \qquad \alpha\beta = \frac{c}{a} \]

\[ a^{m} a^{n} = a^{m+n}, \qquad \log_a(xy) = \log_a x + \log_a y, \qquad \log_a x = \frac{\log_b x}{\log_b a} \]

Coordinate geometry

\[ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}, \qquad m = \frac{y_2 - y_1}{x_2 - x_1} \]

\[ (x - a)^2 + (y - b)^2 = r^2 \]

Mensuration

\[ V_{\text{cone}} = \tfrac{1}{3}\pi r^2 h, \qquad V_{\text{sphere}} = \tfrac{4}{3}\pi r^3, \qquad A_{\text{sphere}} = 4\pi r^2 \]

Trigonometry

\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}, \qquad c^2 = a^2 + b^2 - 2ab\cos C \]

\[ \text{Area} = \tfrac{1}{2}ab\sin C \]

Statistics

\[ \bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i, \qquad \sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2}, \qquad z = \frac{x - \bar{x}}{\sigma} \]