The IGCSE Add Math glossary

24 terms from the Cambridge 0606 syllabus, defined in plain English. Every definition links to the full topic or exam guide so you can go deeper.

Syllabus

Additional Mathematics (0606): The Cambridge IGCSE course (syllabus code 0606) covering early A Level topics (calculus, trigonometry, logarithms, vectors) sat at 16. Examined in two papers with no Core/Extended tiers. Full guide

Non-calculator paper (Paper 1): Paper 1 of 0606 is sat without a calculator and is worth 50% of the grade. It rewards exact-value work with surds, fractions and $\pi$ rather than decimals. Full guide

Command word: The instruction verb that tells you what the examiner wants: 'show that', 'hence', 'find', 'prove'. The command word sets how much working the mark scheme expects. Full guide

Method mark (M): A mark awarded for using a correct method, even if the final number is wrong. In 0606 most marks in a question are method marks, which is why showing working matters more than the answer. Full guide
Accuracy mark (A): A mark awarded for a correct result that depends on the method mark before it. Lose the M mark and the A mark usually falls with it, so accuracy marks are never independent. Full guide
Independent mark (B): A mark awarded for a correct stated result on its own, with no method required, for example quoting an exact value or a correct coordinate. Full guide

Discriminant: The expression $b^2 - 4ac$ from a quadratic $ax^2 + bx + c$ . Its sign tells you how many real roots exist: positive gives two, zero gives one repeated, negative gives none. Full guide
Completing the square: Rewriting a quadratic as $a(x + p)^2 + q$ . It exposes the vertex $(-p,\ q)$ directly and is the reliable route to maximum/minimum values on the non-calculator paper. Full guide
Factor theorem: If $f(a) = 0$ then $(x - a)$ is a factor of the polynomial $f(x)$ . It is the standard first step for factorising and solving cubics in 0606. Full guide
Surd: An irrational root left in exact form, such as $\sqrt{2}$ or $3\sqrt{5}$ . Paper 1 expects answers kept as surds rather than rounded decimals. Full guide

Logarithm: The inverse of exponentiation: if $a^x = y$ then $\log_a y = x$ . 0606 tests the laws of logs, change of base, and solving exponential equations. Full guide
Function (domain and range): A rule mapping each input to one output. The domain is the set of allowed inputs; the range is the set of outputs produced. 0606 tests composite and inverse functions on these. Full guide
Modulus function: Written $\lvert f(x)\rvert$ , it returns the size of a value regardless of sign. Solving modulus equations and sketching $y = \lvert f(x)\rvert$ graphs are common 0606 tasks. Full guide

Radian: The angle measure where a full turn is $2\pi$ . Arc length $r\theta$ and sector area $\tfrac{1}{2}r^2\theta$ formulae only work when $\theta$ is in radians, not degrees. Full guide
R-formula: Rewriting $a\sin\theta \pm b\cos\theta$ as a single $R\sin(\theta \pm \alpha)$ or $R\cos(\theta \pm \alpha)$ . It is the standard method for solving combined trig equations and finding maxima. Full guide
Exact value: A value left in precise form (a fraction, surd or multiple of $\pi$ ) rather than a rounded decimal. The unit circle gives exact values for key angles like $30^\circ$ , $45^\circ$ and $60^\circ$ . Full guide

Binomial expansion: Expanding $(a + b)^n$ using binomial coefficients $\binom{n}{r}$ . 0606 asks for specific terms or coefficients without expanding the whole bracket. Full guide
Arithmetic and geometric progressions: An arithmetic progression adds a fixed common difference each term; a geometric progression multiplies by a fixed common ratio. 0606 tests nth-term and sum formulae, including sum to infinity. Full guide

Permutation vs combination: A permutation $\left({}^nP_r\right)$ counts arrangements where order matters; a combination $\left({}^nC_r\right)$ counts selections where it does not. Choosing the right one is most of the marks. Full guide

Gradient function: The derivative $\frac{dy}{dx}$ , which gives the gradient of a curve at any point. Setting it to zero locates stationary points. Full guide
Stationary point: A point where $\frac{dy}{dx} = 0$ : a maximum, minimum or point of inflexion. The second derivative $\frac{d^2y}{dx^2}$ classifies which: negative for a maximum, positive for a minimum. Full guide
Tangent and normal: The tangent is the straight line touching a curve at a point with the curve's gradient there; the normal is perpendicular to it, with gradient $-1 \div$ (the tangent's gradient). Full guide
Definite integral: An integral evaluated between two limits, written with the bracketed antiderivative then $F(b) - F(a)$ . It gives the area under a curve between those limits. Full guide

Position vector and relative velocity: A position vector locates a point from the origin; relative velocity is one object's velocity as seen from another. Both appear in 0606 vector problems set in two dimensions. Full guide