Overview
This lecture covers the essential crossover formulas required for passing the GCSE Maths exam, including area, volume, and key mathematical relationships.
Area Formulas
- Area of rectangle = length × width.
- Area of triangle = ½ × base × height (perpendicular height).
- Area of trapezium = ½ × (a + b) × height, where a and b are parallel sides.
- Area of parallelogram = base × perpendicular height.
- Area of circle = π × (radius)².
Circle Properties
- Circumference of a circle = π × diameter or 2 × π × radius.
Volume Formulas
- Volume of a prism = area of cross-section × length.
- Volume of cylinder = π × (radius)² × height.
Pythagoras’ Theorem & Trigonometry
- Pythagoras’ theorem: a² + b² = c² for right-angled triangles (c is hypotenuse).
- Sine ratio: sin(θ) = opposite / hypotenuse.
- Cosine ratio: cos(θ) = adjacent / hypotenuse.
- Tangent ratio: tan(θ) = opposite / adjacent.
- Use inverse sine, cosine, or tangent to find angles.
Units
- Area answers in cm² or appropriate squared units.
- Volume answers in cm³ or appropriate cubed units.
- Circumference and other lengths in cm or appropriate linear units.
Key Terms & Definitions
- Rectangle — Four-sided figure with opposite sides equal and all angles 90°.
- Parallelogram — Four-sided figure with opposite sides parallel and equal.
- Trapezium — Four-sided figure with one pair of parallel sides.
- Radius — Distance from center to edge of a circle.
- Diameter — Distance across a circle through the center (2 × radius).
- Circumference — Perimeter or distance around a circle.
- Prism — Solid object with uniform cross-section along its length.
- Hypotenuse — Longest side of a right-angled triangle, opposite the right angle.
- Opposite, Adjacent — Sides of a triangle defined relative to a specific angle.
Other Key Formulas
- Density = mass ÷ volume.
- Speed = distance ÷ time.
- Pressure = force ÷ area.
Action Items / Next Steps
- Review higher-tier formulas if taking the higher GCSE paper.
- Practice using each formula with sample questions.
- Memorize the key trigonometric ratios and exact values for common angles.