The 14 topics of IGCSE Add Math (0606)

Functions

Domain and range, composite functions, inverse functions, modulus functions and their graphs, and one-one functions, with the exact working the 0606 mark scheme rewards.

Domain & Range · Composite Functions · Inverse Functions · Modulus Functions & Their Graphs · One-One Functions

Quadratic Functions

Completing the square, maximum/minimum and the vertex, the discriminant and nature of roots, quadratic inequalities, line–curve intersection and the range of a quadratic.

Completing the Square · Maximum/Minimum & the Vertex · Discriminant & Nature of Roots · Quadratic Inequalities · Line–Curve Intersection · Range of a Quadratic

Factors of Polynomials

The remainder theorem, the factor theorem, and factorising and solving cubic equations, a short topic where full marks are very gettable.

Remainder Theorem · Factor Theorem · Factorising & Solving Cubic Equations

Equations, Inequalities and Graphs

Solving modulus equations and inequalities of the form |ax + b|, graphs of modulus functions, and solving cubic inequalities and equations graphically.

Modulus Equations & Inequalities |ax+b| · Graphs of Modulus Functions · Solving Cubic Inequalities Graphically · Solving Equations Graphically

Simultaneous Equations

One linear and one non-linear (quadratic) equation, and finding points of intersection, the substitution method done the way examiners want to see it.

One Linear + One Non-Linear (Quadratic) · Points of Intersection

Logarithmic and Exponential Functions

Laws of logarithms, e^x and ln x, solving log and exponential equations, their graphs, and reducing relationships to linear form (y = ax^n and y = Ab^x).

Laws of Logarithms · e^x and ln x · Solving Log & Exponential Equations · Graphs of Log & Exponential Functions · Reducing Relationships to Linear Form

Straight-Line Graphs

Gradient, midpoint and length, the equation of a line, parallel and perpendicular lines, the perpendicular bisector, area of rectilinear figures, and converting to linear form.

Gradient, Midpoint & Length · Equation of a Line · Parallel & Perpendicular Lines · Perpendicular Bisector · Area of Rectilinear Figures · Converting to Linear Form

Coordinate Geometry of the Circle

The equation of a circle, centre and radius, intersections with lines, and tangents and circle properties, the topic newly added to the 2025–2027 syllabus.

Equation of a Circle · Centre & Radius · Intersections with Lines · Tangents & Circle Properties

Circular Measure

Radians, arc length, sector area and problem-solving, short, formula-driven, and one of the most reliable sources of marks in 0606.

Radians · Arc Length · Sector Area · Problem-Solving with Circular Measure

Trigonometry

Exact values and the unit circle, graphs of sin, cos and tan (amplitude and period), trig identities, the R-formula (a sinθ ± b cosθ), and solving trigonometric equations.

Exact Values & the Unit Circle · Graphs of sin, cos & tan · Trig Identities · The R-Formula (a sinθ ± b cosθ) · Solving Trigonometric Equations

Permutations and Combinations

The counting principle, factorials, nPr, nCr, and arrangements and selections, knowing which formula to use is most of the battle.

The Counting Principle · Factorials · Permutations (nPr) · Combinations (nCr) · Arrangements & Selections

Series

Binomial expansion with positive integer powers, arithmetic progressions, geometric progressions, and sum to infinity.

Binomial Expansion · Arithmetic Progressions · Geometric Progressions · Sum to Infinity

Vectors in Two Dimensions

Vector notation and magnitude, position vectors, velocity and relative velocity, and vector problem-solving.

Vector Notation & Magnitude · Position Vectors · Velocity & Relative Velocity · Vector Problem-Solving

Calculus

The largest topic in 0606: differentiation rules (product, quotient, chain), rates of change, tangents and normals, stationary points, integration, definite integrals and area under a curve, and kinematics.

Differentiation Rules (Product, Quotient, Chain) · Rates of Change & Connected Rates · Tangents & Normals · Stationary Points & the Second Derivative · Integration as the Reverse of Differentiation · Definite Integrals & Area Under a Curve · Kinematics (Displacement, Velocity, Acceleration)