# Key Maths Formulas for GCSE Grade 5 Foundation

This page presents a comprehensive collection of essential mathematical formulas crucial for GCSE Grade 5 Foundation level. The formulas cover various topics including trigonometry, geometry, and physics-related calculations.

## Trigonometric Formulas

The page begins with important trigonometric formulas, which are fundamental for solving problems involving triangles and angles.

**Definition**: The Sine Rule is given as (sin A) / a = (sin B) / b = (sin C) / c, where A, B, and C are angles, and a, b, and c are the lengths of the sides opposite to these angles respectively.

**Definition**: The Cosine Rule is presented in two forms:

- a² = b² + c² - 2bc cos A
- cos A = (b² + c² - a²) / (2bc)
Where a, b, and c are side lengths, and A is the angle opposite side a.

**Highlight**: SOHCAHTOA is a mnemonic device for remembering the ratios in right-angled triangles:

- Sin θ = Opposite / Hypotenuse
- Cos θ = Adjacent / Hypotenuse
- Tan θ = Opposite / Adjacent

## Area Formulas

The guide provides formulas for calculating areas of various shapes, essential for **GCSE maths areas and volumes formulas worksheets**.

**Example**: Area of a rectangle = length × width
Area of a triangle = 1/2 × base × height
Area of a trapezium = 1/2 × (a + b) × height, where a and b are the parallel sides
Area of a parallelogram = base × height
Area of a circle = πr², where r is the radius

## Volume and Circumference Formulas

Formulas for calculating volumes of 3D shapes and circumference of circles are included, which are crucial for **GCSE maths areas and volumes formulas PDF** resources.

**Example**: Circumference of a circle = πd or 2πr, where d is diameter and r is radius
Volume of a prism = area of cross-section × length
Volume of a cylinder = πr² × height

## Physics-Related Formulas

The guide also covers formulas related to physics concepts, useful for interdisciplinary problem-solving.

**Definition**:
Density = mass / volume
Speed = distance / time
Pressure = force / area

## Pythagoras Theorem

**Highlight**: The Pythagoras Theorem states that in a right-angled triangle, a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

This comprehensive formula sheet serves as an excellent resource for students working on **GCSE maths grade 5 equations PDF** exercises and preparing for exams. It covers all the essential formulas needed for the foundation level, making it an invaluable tool for revision and problem-solving practice.