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A-Level Maths Cheat Sheet

Updated: 5 days ago

This is absolutely not a cheat sheet... We do not endorse cheating at all! It's just a better name than "List of vital but forgettable equations for A Level Maths"


The Formula Book for Edexcel A-Level Maths and Further Maths can be seen here and downloaded here:

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Trigonometry


Cosine Rule

a² = b² + c² - 2bc cosA


Area of a Triangle

Area = ½ ab sinC


Radians

1° = π/180
1 rad = 180/π


Small Angle Approximations

sinθ ≈ θ
tanθ ≈ θ
cosθ ≈ 1 - θ²/2


Trig Identities

sin² θ + cos² θ ≡ 1
tan θ ≡ sin θ / cos θ
1 + tan² x ≡ sec² x
1 + cot² x ≡ cosec² x


Angle Addition Formulae

sin(A ± B) ≡ sinA cosB ± cosA sinB
cos(A ± B) ≡ cosA cos B ∓ sinA sinB
tan(A ± B) ≡ (tanA ± tanB) / (1 ∓ tanA tanB)


Double Angle Formulae

sin2A ≡ 2 sinA cosA
cos2A ≡ cos²A - sin²A ≡ 2cos²A - 1 ≡ 1 - 2sin²A
tan2A ≡ (2 tanA) / (1 - tan²A)


R-Addition Formula

a sinx ± b sinx can be expressed as R sin(x ± α)
a cosx ± b sinx can be expressed as R cos(x ∓ α)

Where:

  • R cos α = a

  • R sin α = b

  • R = √(a² + b²)


Differentiation & Integration

From First Principles:

Product Rule:

Quotient Rule:

Integration by Parts


Trigonometric Integration

∫ xⁿ dx = (xⁿ⁺¹) / (n+1) + c
e ˣ dx = e ˣ + c
∫ 1/x dx = ln|x| + c
∫ cos(x) dx = sin(x) + c
∫ sin(x) dx = -cos(x) + c
∫ tan(x) dx = ln|sec(x)| + c
∫ sec²(x) dx = tan(x) + c
∫ cosec(x) cot(x) dx = -cosec(x) + c
∫ cosec²(x) dx = -cot(x) + c
∫ sec(x) tan(x) dx = sec(x) + c
∫ f'(ax+b) dx = f(ax+b) / a + c


Series Expansions

The Binomial Expansion:

The Taylor Series:

The Maclaurin Expansion:

Common Expansions:


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