A-Math 'Formula Bible'
The advanced reference for A-Math excellence. Every identity and calculus rule you need for Paper 1 & 2.
The A-Math Formula Bible is an advanced reference for Secondary 3 and 4 students taking O-Level Additional Mathematics (Syllabus 4049). It covers every identity, rule, and formula across Algebra & Logarithms, Trigonometric Identities, Calculus (Differentiation and Integration), and Coordinate Geometry & Binomial Theorem. Designed to match the cognitive flow of actual O-Level questions.
Algebra & Logarithms
- • Discriminant (b²-4ac): >0 (2 roots), =0 (equal), <0 (no real roots)
- • Sum of Roots (α+β) = -b/a | Product (αβ) = c/a
- • Log Laws: log(AB) = logA + logB | log(A/B) = logA - logB | log(Aⁿ) = nlogA
- • Change of Base: logₐb = (log꜀b) / (log꜀a)
- • Indices: aᵐ × aⁿ = aᵐ⁺ⁿ | (aᵐ)ⁿ = aᵐⁿ | a⁻ⁿ = 1/aⁿ
Trigonometry Identities
- • sin²A + cos²A = 1 | 1 + tan²A = sec²A | 1 + cot²A = cosec²A
- • Double Angle: sin2A = 2sinAcosA | cos2A = cos²A - sin²A = 2cos²A - 1
- • Addition Formula: sin(A±B) = sinAcosB ± cosAsinB
- • R-Formula: a sinθ ± b cosθ = R sin(θ ± α)
Calculus (Differentiation)
- • Power Rule: d/dx(axⁿ) = anxⁿ⁻¹
- • Product Rule: u v' + v u' | Quotient Rule: (v u' - u v') / v²
- • Chain Rule: dy/dx = (dy/du) × (du/dx)
- • Trig: d/dx(sin x) = cos x | d/dx(cos x) = -sin x | d/dx(tan x) = sec²x
- • Stationary Points: dy/dx = 0 (Max if d²y/dx² < 0, Min if d²y/dx² > 0)
Calculus (Integration)
- • ∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ -1)
- • ∫ (1/x) dx = ln|x| + C
- • ∫ eᵏˣ dx = (1/k)eᵏˣ + C
- • ∫ sin kx dx = -(1/k)cos kx + C | ∫ cos kx dx = (1/k)sin kx + C
- • Area under curve = ∫[a to b] y dx
Coordinate Geometry & Binomial
- • Distance Formula: √[(x₂-x₁)² + (y₂-y₁)²]
- • Perpendicular Lines: m₁ × m₂ = -1
- • Binomial Theorem: (a+b)ⁿ = aⁿ + ⁿC₁aⁿ⁻¹b + ... + ⁿCᵣaⁿ⁻ʳbʳ + ... + bⁿ
- • Linear Law: Transform non-linear to Y = mX + c
Frequently Asked Questions
What A-Math topics does this formula sheet cover?▾
It covers 45 formulas across 5 domains: Algebra & Logarithms (Discriminant, Sum/Product of Roots, Log Laws, Change of Base, Indices), Trigonometry Identities (Pythagorean, Double Angle, Addition Formula, R-Formula), Calculus Differentiation (Power, Product, Quotient, Chain rules), Calculus Integration (Polynomial, Exponential, Trigonometric), and Coordinate Geometry & Binomial Theorem.
How is this different from the E-Math checklist?▾
The E-Math checklist covers Elementary Mathematics (Syllabus 4048) and is a self-assessment tool. This A-Math Formula Bible covers Additional Mathematics (Syllabus 4049) — a separate, more advanced syllabus — and is designed as a rapid-recall reference sheet for exam preparation.
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