Function notation
f : x ↦ f(x); (f ∘ g)(x) = f(g(x)) Cambridge IGCSE 0606
📐 Cambridge IGCSE Additional Mathematics Formula Sheet 2026
Pure mathematics beyond core IGCSE: calculus, coordinate geometry, trigonometry, vectors, matrices, and probability — organised for Papers 1 & 2.
Functions & calculus Coordinate geometry Vectors & matrices
Our formula sheets are free to download — save this one as PDF for offline revision.
Aligned with the latest 2026 syllabus and board specifications. This sheet is prepared to match your exam board’s official specifications for the 2026 exam series.
Everything for Additional Mathematics in One Place
This sheet follows the breadth of Cambridge IGCSE Additional Mathematics (0606): algebraic fluency, graphical reasoning, differentiation and integration, and the quantitative skills examiners reward when you show clear structure.
📊
Polynomials, series & binomial expansions
📐
Full trigonometry and circular measure
🔢
Matrices, vectors & relative velocity
📈
Differentiation, integration & kinematics
Functions, roots & inequalities
Mappings, domain and range, composite and inverse functions, and quadratic inequalities.
Inverse function
Reflection in y = x; domain/range swap.
f⁻¹(f(x)) = x Discriminant (quadratic)
For ax² + bx + c = 0: Δ = b² − 4ac Quadratic roots
x = (−b ± √(b² − 4ac)) / (2a) Sum and product of roots
α + β = −b/a, αβ = c/a Linear & quadratic inequalities
Sketch graphs; critical values; test intervals.
Topic Focus
Exam technique
- State domain exclusions (e.g. division by zero) before manipulating expressions.
- For |ax + b| inequalities, split into cases or square both sides when both sides ≥ 0.
Indices, surds & logarithms
Laws of indices, rationalising denominators, and logarithmic identities.
Index laws
a^m × a^n = a^{m+n} (a^m)^n = a^{mn} a^{-m} = 1/a^m Surd conjugate
(a + √b)(a − √b) = a² − b
Log definition
If a^x = N then x = log_a N Log laws
log_a (xy) = log_a x + log_a y log_a (x/y) = log_a x − log_a y log_a (x^k) = k log_a x Change of base
log_a x = ln x / ln a Topic Focus
Accuracy
- Rationalise denominators with surds unless asked otherwise.
- Check log arguments stay positive.
Polynomials & series
Factor and remainder theorems, binomial expansion for positive integer n, and arithmetic/geometric progressions.
Remainder theorem
P(x) divided by (x − a) has remainder P(a) Factor theorem
(x − a) is a factor ⟺ P(a) = 0 Binomial (positive integer n)
C(n,r) = n! / (r!(n−r)!)
(a + b)^n = Σ_{r=0}^{n} C(n,r) a^{n−r} b^r Arithmetic progression
T_k = a + (k − 1)d S_n = n/2 (2a + (n − 1)d) = n/2 (a + l) Geometric progression
T_k = ar^{k−1} S_n = a(1 − r^n)/(1 − r) (r ≠ 1) Infinite sum (|r| < 1)
S_∞ = a / (1 − r) Topic Focus
Binomial
- Identify a and b so the first term is a^n; watch signs in (a − b)^n.
- C(n,r) row on calculator or Pascal’s triangle.
Coordinate geometry
Straight lines, perpendicular distances, and the circle.
Distance
√((x₂ − x₁)² + (y₂ − y₁)²) Midpoint
((x₁ + x₂)/2 , (y₁ + y₂)/2) Gradient
m = (y₂ − y₁)/(x₂ − x₁) Parallel / perpendicular
parallel: m₁ = m₂ perpendicular: m₁ m₂ = −1 Line forms
y − y₁ = m(x − x₁) ax + by + c = 0 Circle centre (a,b), radius r
(x − a)² + (y − b)² = r² General circle
x² + y² + 2gx + 2fy + c = 0; centre (−g, −f), r = √(g² + f² − c) Topic Focus
Tangents
- Tangent to circle: perpendicular from centre to tangent equals radius.
- Substitute line into circle → equal roots for tangency.
Circular measure & trigonometry
Radians, arc length, sector area, and full trigonometric toolkit.
Arc length
s = r θ (θ in radians) Sector area
A = ½ r² θ Pythagorean identity
sin² θ + cos² θ = 1 tan in terms of sin/cos
tan θ = sin θ / cos θ Sine rule
a / sin A = b / sin B = c / sin C Cosine rule
a² = b² + c² − 2bc cos A cos A = (b² + c² − a²)/(2bc) Area of triangle
½ ab sin C Heron: √(s(s−a)(s−b)(s−c)) Double angle (selection)
sin 2θ = 2 sin θ cos θ cos 2θ = cos² θ − sin² θ Topic Focus
Mode
- Ensure calculator in correct mode (radians vs degrees) to match the question.
- Oblique triangles: often sine or cosine rule.
Vectors (2D)
Position vectors, magnitude, unit vectors, and the scalar product.
Vector form
OP⃗ = p = xi + yj Magnitude
|p| = √(x² + y²) Unit vector
p̂ = p / |p| Scalar product
a · b = |a| |b| cos θ = a₁b₁ + a₂b₂ Parallel vectors
a = k b for scalar k Line equation
r = a + λ d Topic Focus
Geometry
- Perpendicular vectors: a · b = 0.
- Angle: cos θ = (a · b)/(|a||b|).
Matrices (0606 / FM Pure)
Addition, multiplication, determinants, and inverses for 2×2 matrices.
Product
Rows × columns; (AB)_{ij} = row i of A · column j of B.
Determinant (2×2)
det [[a,b],[c,d]] = ad − bc Inverse (2×2)
A⁻¹ = (1/det A) [[d, −b], [−c, a]] Simultaneous equations
AX = B ⇒ X = A⁻¹B when A invertible.
Topic Focus
Check
- det A = 0 ⇒ no unique inverse.
- Verify A A⁻¹ = I.
Differentiation
Gradients, tangents, stationary points, and basic kinematics.
First principles
f′(x) = lim_{h→0} (f(x+h) − f(x))/h Power rule
d/dx (x^n) = n x^{n−1} Chain rule
dy/dx = dy/du · du/dx Product rule
d/dx (uv) = u′v + uv′ Quotient rule
d/dx (u/v) = (u′v − uv′)/v² Stationary points
Solve f′(x) = 0; use f″(x) or sign change to classify Connected rates
dy/dt = dy/dx · dx/dt Topic Focus
Context
- Interpret derivative as gradient or rate of change with units.
- Sketch behaviour using stationary points and asymptotes.
Integration
Antiderivatives, definite integrals, and area under curves.
Fundamental link
If F′ = f then ∫ f(x) dx = F(x) + C Definite integral
∫_a^b f(x) dx = F(b) − F(a) Area under curve
∫_a^b y dx (y ≥ 0) Power rule (n ≠ −1)
∫ x^n dx = x^{n+1}/(n+1) + C Linear substitution
∫ f(ax + b) dx — adjust for constant factor.
Topic Focus
Area
- Area below axis contributes negatively unless using |y|.
- Between curves: ∫ (f − g) dx where f ≥ g.
Kinematics & relative velocity
Constant-acceleration equations and vector relative motion.
Constant acceleration
v = u + at s = ut + ½ at² v² = u² + 2as s = ½ (u + v) t Relative velocity
v_{A rel B} = v_A − v_B Interception
Equal position vectors at same time; or parallel relative velocity with aligned paths.
Topic Focus
Vectors
- Draw clear diagrams; resolve into components i, j.
- Check units (m s⁻¹, m s⁻²).
Permutations, combinations & probability
Counting arrangements and basic probability rules.
Permutations (no repetition)
n! / (n − r)! = nP r Combinations
nC r = n! / (r!(n − r)!) With repetition (order matters)
n^r Probability
P(A) = favourable outcomes / total (equally likely) Complement
P(A′) = 1 − P(A) Independent events
P(A ∩ B) = P(A) P(B) Topic Focus
Structure
- Identify whether order matters (permutation) or not (combination).
- Use tree diagrams for multi-step problems.
How to Use This Formula Sheet
Boost your Cambridge exam confidence with these proven study strategies from our tutoring experts.
✍️
Show Layout
Examiners expect factorisation, formula quotes, or a short sketch before you jump to a final answer — especially for inequalities and coordinate geometry.
🎯
Watch Radians
Arc length and sector formulas use radians; convert or set your calculator mode to match the question.
🧮
Check Domains
For logarithms, surds, and composite functions, state restrictions (e.g. x > 0) before manipulating expressions.
🧠
Link Topics
Questions often combine calculus with graphs or coordinate geometry — rehearse moving between algebraic and graphical forms.
Formula sheet FAQ
Quick answers about this free PDF, how to use it for exam revision, and how it relates to your official syllabus.
Is the Cambridge IGCSE Additional Mathematics Formula Sheet 2026 free to download as a PDF?
Yes. This Tutopiya formula sheet is free to use and you can download it as a PDF from this page for offline revision. There is no payment or account required for the PDF download.
What Mathematics topics and equations does this formula sheet cover?
This page groups key Mathematics formulas in one place for revision. Comprehensive Cambridge IGCSE Additional Mathematics (0606) formula sheet for 2026: functions, polynomials, trigonometry, vectors, matrices, calculus, kinematics, and counting & probability. Always cross-check with your official syllabus and past papers for your exam session.
Can I use this instead of the official exam formula booklet in the exam?
No. In the exam you must follow only what your exam board allows in the hall—usually the official formula booklet or data sheet where provided. This page is a revision and teaching aid, not a replacement for board-issued materials.
Who is this formula sheet for (Secondary)?
It is written for students preparing for assessments at Secondary in Mathematics, including classroom revision, homework support, and independent study. Teachers and tutors can also share it as a quick reference.
How should I revise with this formula sheet?
Work through past paper questions, quote the correct formula before substituting values, and check units and notation every time. Pair this sheet with timed practice and mark schemes so you see how examiners expect working to be set out.
Where can I get more help with Mathematics revision?
Explore Tutopiya’s study tools, past paper finder, and revision checklists linked from our tools hub, or book a trial lesson with a subject specialist for personalised support alongside this formula reference.
Tighten Your 0606 Exam Technique
Work with tutors who specialise in Cambridge Additional Mathematics: past-paper walkthroughs, non-routine problems, and feedback on written communication.
More Tutopiya study tools
Pair this formula sheet with past papers, revision checklists, and planners — all free on our study tools hub.
- All study tools Browse the full hub: calculators, planners, past papers, and more.
- Past paper finder Search past papers by board, subject, and year.
- Revision checklists Topic-by-topic checklists for IGCSE & A Level (2026 syllabi).
- Study planner Build schedules and stay on track before exams.
- Past paper error log Log mistakes from papers and review them systematically.
- Score tracker Track marks and grades across past paper sittings.
- Topic & paper planner Plan revision by topic and tie it to past papers.
- GPA calculator Convert IGCSE, GCSE, and A Level grades to GPA-style summaries.
- The Tutopiya Test Quick diagnostic to see where you stand.
- IGCSE resources Practice questions, notes, and guides for Cambridge & Edexcel IGCSE.
Aligned with the spirit of Cambridge IGCSE Additional Mathematics (0606) assessment objectives; always follow your current syllabus and formula booklet in the exam hall.
Some topics (e.g. matrices) appear in 0606; confirm against your teaching group’s final syllabus version.