Math Formula Cheat Sheet (Year 0-11)

Formula sheet covering basic arithmetic, geometry, algebra, trigonometry, and finance for Year 0-11.

Fraction Addition Formula

$$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$

Percentage Formula

$$\text{Percentage} = (\frac{\text{part}}{\text{whole}}) \times 100$$

Rectangle (Area and Perimeter)

$A = l \times w$ and $P = 2(l + w)$

Square (Area and Perimeter)

$A = a^2$ and $P = 4a$

Triangle Area

$$A = \frac{1}{2} \times b \times h$$

Parallelogram Area

$$A = b \times h$$

Trapezium Area

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

Circle (Area and Circumference)

$A = \pi r^2$ and $C = 2\pi r$

Cube Volume

$$V = a^3$$

Cuboid Volume

$$V = l \times w \times h$$

Cylinder Volume

$$V = \pi r^2 h$$

Sphere Volume

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

Linear Equation

$$y = mx + b$$

Quadratic Formula

$$ax^2 + bx + c = 0 \Rightarrow x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Factorisation of Difference of Squares

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

Factorisation of Square of a Sum

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

Index Multiplication Law

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

Power of a Power Law

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

Distance Formula

$$d = \sqrt{(x - x)^2 + (y - y)^2}$$

Midpoint Formula

$$M = (\frac{x + x}{2}, \frac{y + y}{2})$$

Slope Formula

$$m = \frac{y - y}{x -}$$

Sine Ratio

$$\sin(\theta) = \frac{\text{opp}}{\text{hyp}}$$

Cosine Ratio

$$\cos(\theta) = \frac{\text{adj}}{\text{hyp}}$$

Tangent Ratio

$$\tan(\theta) = \frac{\text{opp}}{\text{adj}}$$

Pythagoras Theorem

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

Common Triangles

$3-4-5$ and $5-12-13$

Arithmetic Mean

$$\text{Mean} = \frac{\text{sum}}{n}$$

Median

The middle value in a set of data.

Mode

The most frequent value in a set of data.

Range

$$\text{max} - \text{min}$$

Probability

$$\text{Probability} = \frac{\text{favourable}}{\text{total}}$$

Z-score Formula

$$z = \frac{x - \mu}{o}$$

Ratios

$$a:b = \frac{a}{b}$$

Speed Formula

$$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$

Distance Formula (from Speed)

$$\text{Distance} = \text{Speed} \times \text{Time}$$

Time Formula

$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$

Simple Interest Formula

$$SI = \frac{P \times R \times T}{100}$$

Compound Interest Formula

$$A = P(1 + \frac{R}{100})^T$$

Square Numbers Ending in 5 trick

$$(n \times (n + 1))25$$