Cambridge IGCSE Mathematics is a two-year course built on a small set of ideas that keep returning: exact number work, proportion, algebra, shape and data. If you understand how those ideas connect, a long syllabus becomes a map rather than a list.
This guide explains the codes, how the course is structured, how to study it, and the order in which to work through our topic modules.
Which Mathematics syllabus am I studying?
There are two main mathematics courses in this guide: Mathematics 0580 and International Mathematics 0607. They are separate Cambridge syllabuses. They share much of the same ground, but the syllabus content, calculator use and assessment design differ in places.
Your school or exam centre decides which one you are entered for, and the code appears on your paperwork. Check the 0580 syllabus page or the 0607 syllabus page for the year you sit. Our guides to 0580 and 0607 explain how to read them.
We also cover Additional Mathematics 0606 as a separate subject. See choosing your IGCSE maths route if you are unsure how the three relate.
How is the course structured?
Most students are entered for a Core or Extended route, and your school decides which. The topics are grouped in areas such as number, algebra, graphs, geometry and measures, and statistics and probability. The papers, durations and weightings differ by code and exam year, so read them on the Cambridge page rather than from memory.
Our modules mirror this structure. Each module has lessons with worked examples, a mistake to avoid, and self-check questions, then an original practice set. Use the syllabus and exam-year navigator to see which modules apply to your code and year.
How should I study Mathematics well?
Good study has three habits. They sound simple, but they change how quickly mistakes disappear.
- Work from your errors, not from the syllabus list. After each practice set, sort mistakes into three piles: did not know the method, knew it but chose wrongly, or slipped while calculating. Each pile needs a different fix.
- Write every step. Method marks belong to lines of working. Skipping lines makes errors invisible, including to you.
- Explain the method aloud. If you cannot say why a step is allowed, the idea is not yet secure. Saying “I divide both sides because…” catches a surprising number of gaps.
Here is a small example of the second habit.
Take 3x − 7 = 2x + 5.
A student writes “x = 12” with no working and is right. Another writes “x = −2” and is wrong. The first has nothing to check, and the second has nothing to learn from. With working, both can see that subtracting 2x gives x − 7 = 5, then adding 7 gives x = 12.
Use the non-calculator working trainer to practise writing exact steps, and the percentage-base explorer to see how a base changes a percentage answer. For revision planning, see the Mathematics revision route.
What is the topic map, in a sensible study order?
The order below follows how topics depend on each other. Begin with the first module, move down, and return to earlier modules whenever a later one exposes a gap.
Foundations: number and proportion
- Number sense and exact arithmetic: fractions, signs, factors and exact values. Everything else rests here.
- Percentages and changing bases: the base decides the answer.
- Ratio and proportional reasoning: sharing, scaling and comparing quantities.
- Rates, time and compound quantities: speed, density and other quantities built from two others.
- Indices, roots and standard form: the rules for powers, used throughout algebra and science.
- Non-calculator strategy: estimation and exact working, which protects accuracy.
- Precision, bounds and measurement: how rounding limits what you can claim.
Algebra and graphs
- Algebraic structure: expanding, factorising and recognising form.
- Equations and formulas: solving and rearranging.
- Simultaneous relationships: two conditions, two unknowns.
- Inequalities and feasible regions: ranges of values and shaded regions.
- Sequences and pattern rules: spotting and writing the rule.
- Graphs and transformations: reading and sketching graphs, and what changes a graph.
- Coordinate geometry: gradients, lines and midpoints.
- Functions and mappings: inputs, outputs, inverses and composites.
Shape, space and measure
- Angles and geometric reasoning: giving a reason for every angle.
- Similarity, congruence and scale: enlargements and proof of shape relationships.
- Constructions and loci: accurate drawing and regions.
- Area, perimeter and surface area: flat and curved shapes.
- Volume and capacity: solids and unit conversions.
- Right-triangle trigonometry: sine, cosine and tangent.
- Non-right triangles and bearings: sine and cosine rules, and direction problems.
- Vectors and transformations: movement described with numbers.
Probability and statistics
- Probability reasoning: outcomes, trees and conditional thinking.
- Statistics and distributions: averages, spread and comparing sets of data.
- Data displays and cumulative reasoning: histograms, cumulative frequency and what they show.
International Mathematics 0607 extras
- International Mathematics investigations
- International Mathematics modelling
- Graphic-display-calculator interpretation
The last three modules belong to 0607 learning, so check your syllabus before spending time on them.
What makes IGCSE Mathematics hard?
Four difficulties account for most stuck points. Each has a short guide.
- Calculator too early. Rounding in the middle of a question costs accuracy. See losing accuracy when using a calculator too early.
- Choosing a method in mixed questions. The skill is recognising the type of problem. See choosing the right method.
- Rearranging formulas. Knowing the formula is not the same as handling it. See rearranging a formula.
- Bounds and precision. Picking the wrong endpoint is common. See bounds answers with the wrong endpoints.
Weak foundations make all four worse. A shaky grasp of fractions or percentages turns into trouble with algebra, then with trigonometry, because each topic needs the one before it.
What does individual tuition add?
A guide and practice sets can teach the method. What they cannot do is watch you solve a question and notice the moment your reasoning bends. A teacher working one to one can ask you to explain a step, find the exact line that causes the error, and give a fresh example to test the fix.
That suits students whose mistakes repeat after honest practice, or whose foundations have a gap from earlier years. You can see how this works in online one-to-one Mathematics tuition, where we assign an experienced teacher and the first step is a paid one-hour trial starting from RM80. Whether it suits you is covered fairly in the comparison of ways to get help.