📐
Maths Formulas Sheet
Essential maths formulas — algebra, sequences, areas, volumes, trigonometry, and calculus.
Algebra
| Quadratic formula | x = (−b ± √(b²−4ac)) / 2a |
| Perfect square | (a ± b)² = a² ± 2ab + b² |
| Difference of squares | a² − b² = (a + b)(a − b) |
Sequences
| Arithmetic nth term | aₙ = a + (n−1)d |
| Arithmetic sum | Sₙ = n/2 · (2a + (n−1)d) |
| Geometric nth term | aₙ = a·rⁿ⁻¹ |
| Geometric sum | Sₙ = a(rⁿ − 1)/(r − 1) |
Areas
| Circle | A = πr² |
| Triangle | A = ½ · b · h |
| Rectangle | A = l · w |
| Trapezium | A = ½(a + b)h |
Volumes
| Sphere | V = 4/3 · πr³ |
| Cylinder | V = πr²h |
| Cone | V = 1/3 · πr²h |
| Cuboid | V = l · w · h |
Trigonometry
| Identity | sin²θ + cos²θ = 1 |
| Tangent | tanθ = sinθ / cosθ |
| Sine rule | a/sinA = b/sinB = c/sinC |
| Cosine rule | c² = a² + b² − 2ab·cosC |
Coordinate geometry & calculus
| Distance | √((x₂−x₁)² + (y₂−y₁)²) |
| Midpoint | ((x₁+x₂)/2, (y₁+y₂)/2) |
| Gradient | m = (y₂−y₁)/(x₂−x₁) |
| Derivative of xⁿ | d/dx xⁿ = n·xⁿ⁻¹ |
| Integral of xⁿ | ∫xⁿ dx = xⁿ⁺¹/(n+1) + C |
📐Your quick maths reference
This maths formula sheet collects the essentials from algebra, sequences, mensuration (areas and volumes), trigonometry, and basic calculus. It's built for fast revision before tests — scan the topic you need and get the formula instantly.
💡Get more from formulas
- Understand where a formula comes from — derived formulas are far easier to remember than memorised ones.
- Practise substituting values so applying the formula under exam pressure becomes automatic.
- For geometry, always sketch the shape and label it before plugging into a formula.
💡 Frequently Asked Questions
Does this cover trigonometry and calculus?+
Yes — it includes the key trigonometric identities and rules, plus the basic differentiation and integration rules for powers of x.