GCSE Maths Formulas Overview

Introduction

• Focus: Crossover formulas needed for both Foundation and Higher tier GCSE Maths exams.
• Note: Higher tier students also need these formulas.

Area Formulas

Rectangle

• Formula: Area = Length × Width
  • Example: Length = 3, Width = 8, Area = 24 cm²

Triangle

• Formula: Area = 0.5 × Base × Height
  • Perpendicular Height needed.
  • Example: Base = 10, Height = 7, Area = 35 cm²

Trapezium

• Formula: Area = 0.5 × (a + b) × Height
  • a and b are parallel sides.
  • Example: a = 8, b = 10, Height = 5, Area = 45 cm²

Parallelogram

• Formula: Area = Base × Height
  • Perpendicular Height needed.
  • Example: Base = 8, Height = 5, Area = 40 cm²

Circle

• Formula: Area = π × r²
  • Radius needed (half the diameter).
  • Example: Radius = 4, Area ≈ 50.3 cm²

Circumference of a Circle

• Formula: Circumference = π × Diameter or π × 2r
  • Example: Diameter = 6, Circumference ≈ 18.8 cm

Volume Formulas

Prisms

• Formula: Volume = Area of Cross-section × Length
  • Example: Triangular prism with Base = 6, Height = 4, Length = 10, Volume = 120 cm³

Cylinder

• Formula: Volume = π × r² × Height
  • Example: Radius = 3, Height = 8, Volume ≈ 226.2 cm³

Pythagoras Theorem

• Formula: a² + b² = c²
  • Applies to Right-angled triangles.
  • Example: a = 3, b = 4, c = 5

Trigonometric Ratios

Definitions

• Sine (Sin): Opposite / Hypotenuse
• Cosine (Cos): Adjacent / Hypotenuse
• Tangent (Tan): Opposite / Adjacent

Example

• Sin: Opposite = 5, Angle = 30°, Hypotenuse = 5 / sin(30°) = 10
• Cos: Hypotenuse = 8, Adjacent = cos(30°) × 8 ≈ 6.9

Measurement Formulas

Density

• Formula: Density = Mass / Volume
  • Example: Mass = 200g, Volume = 40 cm³, Density = 5 g/cm³

Speed

• Formula: Speed = Distance / Time
  • Example: Distance = 448 miles, Time = 8 hours, Speed = 56 mph

Pressure

• Formula: Pressure = Force / Area
  • Example: Force = 3500 N, Area = 5 m², Pressure = 700 N/m²

Conclusion

• These formulas are essential for both Foundation and Higher exams.
• For higher-only formulas, refer to the next video.