GCSE Maths Formula Sheet
📘 GCSE Maths Formula Sheet
Get the GCSE Maths Formula Sheet with all key formulas, from geometry to algebra, with detailed examples. Perfect for revision and exam preparation. Master essential maths concepts with this comprehensive guide to ace your GCSEs!
📐 Geometry Formulas
- Area of Circle: A = π × r²
Example: A = π × 5² = 78.54 cm² - Pythagoras' Theorem: a² + b² = c²
Example: √(3² + 4²) = 5 cm - Area of Triangle: A = ½ × base × height
Example: A = ½ × 10 × 6 = 30 cm² - Area of Parallelogram: A = base × height
Example: A = 8 × 5 = 40 cm² - Area of Trapezium: A = ½ × (a + b) × height
Example: A = ½ × (6 + 10) × 4 = 32 cm² - Volume of Prism: V = area of cross section × length
Example: V = 12 × 8 = 96 cm³ - Volume of Cylinder: V = π × r² × h
Example: V = π × 4² × 10 ≈ 502.65 cm³ - Volume of Cone: V = ⅓ × π × r² × h
Example: V = ⅓ × π × 3² × 9 = 25.13 cm³ - Volume of Sphere: V = 4/3 × π × r³
Example: V = 4/3 × π × 5³ = 523.6 cm³ - Surface Area of Sphere: A = 4 × π × r²
Example: A = 4 × π × 6² = 452.39 cm² - Surface Area of Cone: A = π × r × (r + l)
Example: A = π × 4 × (4 + 7) = 44.41 cm² - Surface Area of Cylinder: A = 2 × π × r × (r + h)
Example: A = 2 × π × 3 × (3 + 8) = 66.24 cm²
🧮 Algebra Formulas
- Compound Interest: A = P(1 + r/n)^(nt)
Example: ≈ 1104.71 - Simple Interest: I = P × r × t
Example: I = 1000 × 0.05 × 3 = 150 - Percentage Increase: New = Original × (1 + %)
Example: 200 × 1.1 = 220 - Percentage Decrease: New = Original × (1 - %)
Example: 500 × 0.8 = 400 - Expanding Brackets: a(b + c) = ab + ac
Example: 3(x + 2) = 3x + 6 - Factorizing Quadratics: ax² + bx + c = a(x + p)(x + q)
Example: x² + 5x + 6 = (x + 2)(x + 3)
📐 Trigonometry Formulas
- SOH CAH TOA:
Example: tan(θ) = 4/3 → θ ≈ 53.13° - Sine Rule: a/sinA = b/sinB = c/sinC
- Cosine Rule: c² = a² + b² − 2ab × cos(C)
📊 Probability & Statistics
- Probability: P(A) = favorable / total
Example: Rolling a 3 = 1/6 - Mean (Average): Sum / Count
Example: (5 + 10 + 15) / 3 = 10 - Standard Deviation: σ = √[(Σ(x - μ)²) / N]