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.
