All 14 topics of Cambridge IGCSE Additional Mathematics 0606 in syllabus order. Both papers cover the whole syllabus; Paper 1 is non-calculator, so every worked example shows the exact working. Lessons are arriving topic by topic, starting with Functions.
Domain and range, function notation, the modulus of a function, inverse and composite functions, and the graph of a function against its inverse.
Completing the square for the maximum or minimum, sketching and range, the discriminant for roots and for lines meeting curves, equations and inequalities.
The remainder and factor theorems, factorising cubics and solving cubic equations.
Modulus equations and inequalities, equations in quadratic form, and cubic graphs, their moduli and cubic inequalities.
Solving a linear and a non-linear equation together by substitution or elimination.
The graphs of e^x and ln x and their asymptotes, the laws of logarithms with change of base, and solving a^x = b.
Equations of lines, parallel and perpendicular lines, midpoints, lengths and perpendicular bisectors, and reducing a relationship to straight-line form.
The equation of a circle in either form, a circle meeting a line, tangents, and two circles.
Radians, arc length and sector area, including compound shapes.
All six trigonometric functions, amplitude and period, graphs of a sin bx + c and its family, the Pythagorean identities, equations and proofs.
Telling arrangements from selections, n!, nPr and nCr, and arrangement and selection problems.
The binomial theorem and its general term, arithmetic and geometric progressions, and the sum to infinity.
Vector notation, position and unit vectors, magnitude and vector arithmetic, and velocities, including particles that collide.
Derivatives of standard functions with the chain, product and quotient rules, tangents, stationary points, rates of change, integration, areas and kinematics.
Additional Maths is the best preparation for AS & A Level Mathematics 9709: functions, the discriminant, logarithms, radians and calculus all reappear in Pure 1.
Maths olympiad practice: feeder, national and international problems with hints, a timed drill, dates and how to apply.