formula sheet edexcel maths a level

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10-01-2025

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A-Level Maths can feel overwhelming, but mastering the core formulas is key to success. This comprehensive guide provides a structured overview of the essential formulas for Edexcel A-Level Maths, categorized for easy reference during your revision. Remember, understanding how to derive these formulas is as crucial as memorizing them.

Core Maths Formulae

This section covers fundamental formulas applicable across various A-Level Maths modules.

Algebra

• Quadratic Formula: For a quadratic equation of the form ax² + bx + c = 0, the solutions are given by: x = (-b ± √(b² - 4ac)) / 2a

• Factor Theorem: If P(x) is a polynomial, then (x - a) is a factor of P(x) if and only if P(a) = 0.

• Remainder Theorem: If P(x) is a polynomial divided by (x - a), the remainder is P(a).

• Laws of Indices:

  • a^m × aⁿ = a^m+n
  • a^m ÷ aⁿ = a^m-n
  • (a^m)ⁿ = a^mn
  • a⁰ = 1
  • a^-n = 1/aⁿ
  • a^1/n = ⁿ√a

• Laws of Logarithms: (Assuming base a)

  • log_a(xy) = log_ax + log_ay
  • log_a(x/y) = log_ax - log_ay
  • log_axⁿ = n log_ax
  • log_aa = 1
  • log_a1 = 0

Coordinate Geometry

• Distance between two points (x₁, y₁) and (x₂, y₂): √((x₂ - x₁)² + (y₂ - y₁)²)

• Midpoint of a line segment joining (x₁, y₁) and (x₂, y₂): ((x₁ + x₂)/2, (y₁ + y₂)/2)

• Equation of a straight line: y - y₁ = m(x - x₁), where m is the gradient and (x₁, y₁) is a point on the line.

• Gradient of a line passing through (x₁, y₁) and (x₂, y₂): (y₂ - y₁) / (x₂ - x₁)

Calculus Formulae

This section covers essential formulas for differentiation and integration.

Differentiation

• Derivative of xⁿ: nx^n-1

• Chain Rule: d/dx [f(g(x))] = f'(g(x))g'(x)

• Product Rule: d/dx [f(x)g(x)] = f'(x)g(x) + f(x)g'(x)

• Quotient Rule: d/dx [f(x)/g(x)] = [f'(x)g(x) - f(x)g'(x)] / [g(x)]²

Integration

• Integral of xⁿ: (xⁿ⁺¹)/(n+1) + C (where n ≠ -1 and C is the constant of integration)

• Integration by Substitution: A technique used to simplify integrals.

• Integration by Parts: ∫u(dv/dx)dx = uv - ∫v(du/dx)dx

Trigonometry Formulae

Mastering trigonometric identities and formulas is crucial for success in A-Level Maths.

• Trigonometric Identities:

  • sin²θ + cos²θ = 1
  • tanθ = sinθ / cosθ
  • secθ = 1/cosθ
  • cosecθ = 1/sinθ
  • cotθ = 1/tanθ

• Addition Formulae:

  • sin(A + B) = sinAcosB + cosAsinB
  • sin(A - B) = sinAcosB - cosAsinB
  • cos(A + B) = cosAcosB - sinAsinB
  • cos(A - B) = cosAcosB + sinAsinB
  • tan(A + B) = (tanA + tanB) / (1 - tanAtanB)
  • tan(A - B) = (tanA - tanB) / (1 + tanAtanB)

Further Modules (Specific Formulas)

The formulas listed above cover the core aspects of Edexcel A-Level Maths. However, further modules (such as Statistics and Mechanics) will require additional formulas specific to those areas. Consult your textbook and class notes for those.

This formula sheet is a valuable resource, but remember that rote memorization isn't enough. Practice applying these formulas to various problems to solidify your understanding and build confidence for your exams. Good luck!