Mathematics and Learning Centre Reference Notes

Fundamental mathematical formulas and definitions covering coordinate geometry, trigonometry, finance, and basic measurements based on classroom lecture notes.

Gradient (Rise/Run)

$$\frac{\text{rise}}{\text{run}}$$

Gradient (Coordinates)

$\frac{y_2 - y_1}{x_2 - x_1}$ or $\frac{y_1 - y_2}{x_1 - x_2}$

Percentage change

$$\frac{\text{change}}{\text{original}} \times 100$$

Compound Interest

$$v = P(1 + \frac{R}{100})^n$$

Annually

1x a year

Biannually

2x a year

Quarterly

4x a year

Simple interest

$P \times R \times T$ (Principal, Rate, Time)

Pythagoras Theorem

$c^2 = a^2 + b^2$ where $c$ is the hypotenuse.

$$\sin \theta$$

$$\frac{\text{Opp}}{\text{Hyp}}$$

$$\cos \theta$$

$$\frac{\text{Adj}}{\text{Hyp}}$$

$$\tan \theta$$

$$\frac{\text{Opp}}{\text{Adj}}$$

SOH-CAH-TOA

A mnemonic for trigonometric ratios where Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, and Tangent is Opposite over Adjacent.

Length of line segment

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

Midpoint

$$(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$$

Area of trapezium

$$\frac{1}{2} \times (a + b) \times h$$

Speed

$$\frac{\text{distance}}{\text{time}}$$