Key Summary & High-Yield Concept Takeaways
Curated by senior faculty at Hodu Academy for fast revision, formula derivations, and standard board & competitive exam marking schemes.
- ✓IGCSE Add Maths Syllabus Overview
- ✓Chapter-wise Key Formulas & Facts
- ✓Summary Tables & Units
- ✓Factor theorem: f(a)=0 ⇒ (x–a) is a factor of f(x)
IGCSE Additional Mathematics Formulas, Key Facts & Revision – 0606/4037
IGCSE Additional Mathematics (0606/4037) demands a sharp command of advanced algebra, calculus, trigonometry, coordinate geometry, and more. This Hodu Academy master page brings you everything you need: chapter-wise formulas, worked examples, common mistakes, revision tables, exam tips, and definitions—all mapped to the Cambridge Add Maths syllabus.
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Get in-depth explanations and walkthroughs for every chapter on our YouTube Add Maths Playlist. Perfect for visual learning and step-by-step guidance!
Table of Content
IGCSE Additional Mathematics Syllabus (0606/4037)
| Topic | Subtopics / Skills |
|---|---|
| Algebra | Equations, inequalities, polynomials, algebraic fractions, indices, surds, sequences & series |
| Functions | Composite/inverse functions, graphs, transformations |
| Quadratic Equations | Roots, factorization, graphs, nature of roots |
| Simultaneous Equations | Linear-quadratic, algebraic/graphical solutions |
| Logarithms & Exponentials | Laws of logs, solving exponential/log equations |
| Coordinate Geometry | Line equations, gradients, circle properties, distance |
| Trigonometry | Sine, cosine, tangent, identities, equations, graphs, sine/cosine rules, 3D |
| Matrices & Transformations | Matrix algebra, determinants, geometric transforms |
| Differentiation | First/second derivative, stationary points, curve sketching, applications |
| Integration | Indefinite/definite integrals, area under curves, applications |
| Vectors | Vector algebra, magnitude, direction, scalar product |
| Permutations, Combinations & Probability | Counting principles, probability rules, binomial theorem |
Chapter-wise Key Formulas & Facts
For each chapter, revise the formulas, then check the worked example and tips below.
1. Algebra
- Factor theorem: f(a)=0 ⇒ (x–a) is a factor of f(x)
- Remainder theorem: f(a) is the remainder when f(x) divided by (x–a)
- Indices laws: am × an = am+n; (am)n = amn
- Surds: Rationalise denominator as needed
Factorise completely: x³ – 4x² + x + 6
Solution: Try possible roots. x = –1 is a root (f(–1)=0). So, (x+1) is a factor.
Divide: (x+1)(x²–5x+6) = (x+1)(x–2)(x–3)
Common Mistakes & Exam Tips:
Solution: Try possible roots. x = –1 is a root (f(–1)=0). So, (x+1) is a factor.
Divide: (x+1)(x²–5x+6) = (x+1)(x–2)(x–3)
- Always test rational roots for polynomials.
- Don’t forget to fully factorise; check for quadratic factors.
- Be careful with negative and fractional indices.
2. Functions
- Function notation: f(x)
- Composite function: f(g(x))
- Inverse function: f–1(x)
If f(x) = 2x+3 and g(x) = x², find f(g(2)).
Solution: g(2) = 4. f(4) = 2×4+3 = 11.
Common Mistakes & Exam Tips:
Solution: g(2) = 4. f(4) = 2×4+3 = 11.
- Order matters: f(g(x)) ≠ g(f(x))!
- Careful when finding inverses: solve for x in terms of y, then swap.
3. Equations & Inequalities
- Linear, quadratic, cubic, absolute value equations
- Inequality symbols: <, >, ≤, ≥
- Quadratic inequalities: solve as equation then test intervals
Solve: x² – 5x + 6 > 0
Solution: Factor to (x–2)(x–3) > 0 ⇒ x < 2 or x > 3
Common Mistakes & Exam Tips:
Solution: Factor to (x–2)(x–3) > 0 ⇒ x < 2 or x > 3
- Always test regions between and outside roots for inequalities.
- Draw a sign chart if unsure.
4. Logarithms & Exponentials
- ax = y ⇒ logay = x
- loga(xy) = logax + logay
- loga(x/y) = logax – logay
- Change of base: logab = logcb / logca
Solve for x: 2x = 16.
Solution: 16 = 2⁴ ⇒ x = 4.
Common Mistakes & Exam Tips:
Solution: 16 = 2⁴ ⇒ x = 4.
- Don’t mix up bases—use change of base if needed.
- Watch out for log(0) or log(negative): undefined.
5. Quadratic Equations
- ax² + bx + c = 0: x = [–b ± √(b²–4ac)]/2a
- Sum of roots: –b/a; Product: c/a
- Discriminant: D = b²–4ac (nature of roots)
Find roots of x²–5x+6=0.
Solution: x = [5 ± √(25–24)]/2 = [5 ± 1]/2 ⇒ x = 3, 2
Common Mistakes & Exam Tips:
Solution: x = [5 ± √(25–24)]/2 = [5 ± 1]/2 ⇒ x = 3, 2
- Check discriminant for real/complex roots.
- Write both + and – solutions.
6. Simultaneous Equations
- Substitution, elimination, or matrix method
- For linear and/or quadratic pairs
Solve: x + y = 7; x – y = 1.
Solution: Add: 2x = 8 ⇒ x=4. Then y=3.
Common Mistakes & Exam Tips:
Solution: Add: 2x = 8 ⇒ x=4. Then y=3.
- Check your answer in both equations.
- For quadratic cases, expect two solutions.
7. Sequences & Series
- Arithmetic: nth term a + (n–1)d; Sum Sₙ = n/2 [2a + (n–1)d]
- Geometric: nth term arn–1; Sum Sₙ = a(1–rⁿ)/(1–r)
- Sum to infinity: S∞ = a/(1–r), |r| < 1
Find the sum of the first 5 terms: 3, 6, 12, ...
Solution: Geometric, a=3, r=2. S₅ = 3(1–2⁵)/(1–2) = 3(1–32)/–1 = 3(–31)/–1 = 93.
Common Mistakes & Exam Tips:
Solution: Geometric, a=3, r=2. S₅ = 3(1–2⁵)/(1–2) = 3(1–32)/–1 = 3(–31)/–1 = 93.
- Watch out for n vs n–1 in formulas.
- Check if the series is arithmetic or geometric.
8. Coordinate Geometry
- Gradient: m = (y₂–y₁)/(x₂–x₁)
- Midpoint: [(x₁+x₂)/2, (y₁+y₂)/2]
- Distance: √[(x₂–x₁)² + (y₂–y₁)²]
- Equation of line: y=mx+c
Find the midpoint between (2,3) and (6,7).
Solution: [(2+6)/2, (3+7)/2] = (4,5)
Common Mistakes & Exam Tips:
Solution: [(2+6)/2, (3+7)/2] = (4,5)
- Don’t mix up x and y when applying formulas.
- Check if gradient is positive or negative.
9. Trigonometry
- SOHCAHTOA: sinθ = opp/hyp, cosθ = adj/hyp, tanθ = opp/adj
- sin²θ + cos²θ = 1
- Sine rule: a/sinA = b/sinB = c/sinC
- Cosine rule: c² = a² + b² – 2ab cosC
- Area: (1/2)ab sinC
Solve for x: sinx = 0.5, 0 ≤ x ≤ 180°.
Solution: x = 30°, 150°
Common Mistakes & Exam Tips:
Solution: x = 30°, 150°
- Remember to check if your calculator is in degrees!
- Use correct range for inverse functions.
10. Calculus (Differentiation & Integration)
- d/dx xⁿ = n xn–1
- Product rule: d(uv)/dx = u dv/dx + v du/dx
- Quotient rule: d(u/v)/dx = (v du/dx – u dv/dx)/v²
- Chain rule: d/dx f(g(x)) = f'(g(x)) × g'(x)
- ∫xⁿ dx = xn+1/(n+1) + C
- Area under curve = definite integral between bounds
Differentiate y = 3x² + 5x.
Solution: dy/dx = 6x + 5.
Common Mistakes & Exam Tips:
Solution: dy/dx = 6x + 5.
- Don’t forget to use the chain rule for nested functions.
- Add +C for indefinite integrals.
11. Vectors
- Vector notation: a = (a₁, a₂)
- Magnitude: |a| = √(a₁² + a₂²)
- Unit vector: a/|a|
- Scalar product: a · b = |a||b|cosθ
Find magnitude of (3,4).
Solution: |a| = √(3²+4²) = 5.
Common Mistakes & Exam Tips:
Solution: |a| = √(3²+4²) = 5.
- Always sketch vectors for clarity.
- Direction matters for subtraction!
12. Matrices & Transformations
- Matrix multiplication: AB ≠ BA (in general)
- Determinant 2x2: ad–bc for [[a,b],[c,d]]
- Inverse: A–1 = (1/detA) × adjA
- Transformation: matrix × vector
Find det([[2,3],[4,5]]).
Solution: (2×5)-(3×4) = 10-12 = –2.
Common Mistakes & Exam Tips:
Solution: (2×5)-(3×4) = 10-12 = –2.
- Order matters in multiplication.
- Inverse exists only if determinant ≠ 0.
13. Permutations, Combinations & Probability
- n! = n × (n–1) × ... × 1
- nCr = n! / [r!(n–r)!]
- P(A or B) = P(A) + P(B) – P(A and B)
- P(A and B) = P(A) × P(B) for independent
- Permutations: order matters, Combinations: order doesn’t
How many ways to choose 2 from 5? (order doesn’t matter)
Solution: 5C2 = 10.
Common Mistakes & Exam Tips:
Solution: 5C2 = 10.
- Use the right formula: permutation for order, combination for selection.
- Check if events are independent or not.
Summary Table: Key Add Maths Formulas
| Topic | Formula / Fact |
|---|---|
| Quadratic Equation | x = [–b ± √(b²–4ac)]/2a |
| Binomial Expansion | (a + b)n = Σ nCr × an–r × br |
| Derivative of xⁿ | d/dx xⁿ = n xn–1 |
| Sine Rule | a/sinA = b/sinB = c/sinC |
| Area of triangle (Trig.) | (1/2)ab sinC |
| Integration | ∫xn dx = xn+1/(n+1) + C |
Key Definitions
- Composite function: Applying one function to the result of another: f(g(x))
- Determinant: Special number calculated from a square matrix
- Permutation: An arrangement of objects in order
- Combination: Selection of objects without regard to order
- Derivative: Slope of a function at a point
- Integral: Area under a curve
FAQs on Add Maths
- Q1. Is Add Maths much harder than IGCSE Maths?
Yes, it’s a step up—especially with calculus, advanced trigonometry, and algebra. But with consistent practice and formula revision, you’ll master it! - Q2. Do I need to show all working?
Yes. Even if you use a calculator for checking, always show your method to get full marks. - Q3. Are these formulas enough for the exam?
This page covers all high-yield formulas. For more details and extra practice, visit the topic pages linked above. - Q4. Can I use this for Edexcel/O Level Additional Maths?
Most concepts and formulas overlap, but always check your syllabus for any variations.
Bookmark Hodu Academy Add Maths Resources for quick revision, topic pages, and worked examples for every chapter!