A-level AQA Maths

• Laws of Indices


  • axa³ = ax+y
  • ax/ay = ax-y
  • (a*)y = a*y
• Trigonometry


  • Sine rule: sinA/sinB = sinC
  • Cosine rule: a² = b² + c² - 2bccosA
• Perimeter, Area and Volume

  • Perimeter: C = 2πr = πd
  • Area: A = πr²
  • Area of trapezium: A = 1/2(a + b)h
  • Arc length: s = rθ
  • Sector area: A = 1/2r²θ
• Laws of Logarithms


  • x=a⇒n=log x
  • log x + log y = log(xy)
  • log x - log y = log(x/y)
  • klog x = log(xk)
• Straight line equation


  y - y₁ = m(x - x₁)
• Perpendicular lines


  m₁ m₂ = -1
• Trigonometric Identities


  • sin²x + cos²x = 1
  • sec²x = 1 + tan²x
  • cosec²x = 1 + cot²x
  • sin2x = 2sinxcosx
  • cos2x = cos²x - sin²x
  • tan2x = 2tanx/(1 - tan²x)
• Sequences


  • Arithmetic: u₁ = a + (n-1)d
  • Geometric: u₁ = ar^(n-1)
• Differentiation


  • sinkx → kcos(kx)
  • coskx → -ksin(kx)
  • ekx → kekx
  • lnx → 1/x
• Chain rule: If y = f(g(x)), dy/dx = f'(g(x))g'(x)
• Integration


  • ∫sinkx dx = -1/k cos(kx) + c
  • ∫coskx dx = 1/k sin(kx) + c
  • ∫ekx dx = 1/k ekx + c
  • ∫1/x dx = ln|x| + c
• Product rule: The derivative of y = f(x)g(x), dy/dx = f'(x)g(x) + f(x)g'(x)
• Standard Normal variable


  Z = (X-μ)/σ where X~N(μ,σ²)
• Reverse Chain rule: [f'(g(x))g'(x)] = f(g(x)) + c
• Mechanics


  • v = dr/dt
  • a = dv/dt = d²r/dt²
  • F = ma
• Vectors: |xi + yj + zk| = √(x² + y² + z²)