Create Next App

📐Basic Shapes

Rectangle Area

A = l \times w

Length × Width

Rectangle Perimeter

P = 2(l + w)

2 × (Length + Width)

Triangle Area

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

Half × Base × Height

Square Area

A = s^2

Side × Side

⭕Circles

Circumference

C = \pi d = 2\pi r

π × diameter or 2π × radius

Area of Circle

A = \pi r^2

π × radius²

Arc Length

l = \frac{\theta}{360} \times 2\pi r

Fraction of circumference

Sector Area

A = \frac{\theta}{360} \times \pi r^2

Fraction of circle area

🔢Algebra

Difference of Squares

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

Factorising pattern

Perfect Square (add)

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

Expanding brackets

Perfect Square (subtract)

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

Expanding brackets

Quadratic Formula

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

Solves ax² + bx + c = 0

📈Straight Lines

Equation of a Line

y = mx + c

m = gradient, c = y-intercept

Gradient

m = \frac{y_2 - y_1}{x_2 - x_1}

Change in y ÷ Change in x

Midpoint

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

Average of coordinates

Distance

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

Using Pythagoras

📊Pythagoras & Trigonometry

Pythagoras Theorem

a^2 + b^2 = c^2

For right-angled triangles

SOH CAH TOA

\sin\theta = \frac{O}{H}, \cos\theta = \frac{A}{H}, \tan\theta = \frac{O}{A}

Trigonometric ratios

Sine Rule

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

For any triangle

Cosine Rule

a^2 = b^2 + c^2 - 2bc\cos A

For any triangle

Area of Triangle (Trig)

A = \frac{1}{2}ab\sin C

Using two sides and included angle

📦Volume & Surface Area

Cuboid Volume

V = l \times w \times h

Length × Width × Height

Prism Volume

V = A \times h

Cross-section area × Height

Cylinder Volume

V = \pi r^2 h

π × radius² × height

Cone Volume

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

⅓ × π × radius² × height

Sphere Volume

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

⁴⁄₃ × π × radius³

Sphere Surface Area

A = 4\pi r^2

4 × π × radius²

📊Statistics

Mean

\bar{x} = \frac{\sum x}{n}

Sum of values ÷ Number of values

Mean (Frequency)

\bar{x} = \frac{\sum fx}{\sum f}

For grouped data

Probability

P(A) = \frac{\text{favourable outcomes}}{\text{total outcomes}}

Basic probability

⚡Compound Measures

Speed

S = \frac{D}{T}

Distance ÷ Time

Density

D = \frac{M}{V}

Mass ÷ Volume

Pressure

P = \frac{F}{A}

Force ÷ Area