IGCSE Maths Notes (0580)
12 free chapter notes with diagrams, worked examples and quizzes, plus night-before sheets.
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Maths clicks when every method comes with a picture and a worked example. These chapter notes cover the Cambridge IGCSE Mathematics (0580) course from number toolkit to statistics. Each one opens with a 30-second summary, builds the idea step by step with diagrams, and ends with questions you can check yourself.
12 chapter notes
- 1Number toolkitThe foundations of every IGCSE Maths paper: types of number, primes with HCF and LCM, Venn diagrams, fractions, rounding and bounds, index laws, standard form and surds, with every step shown.~20 min read · Core + Extended
- 2Ratio, percentages & moneyRatio, proportion, speed, percentages, interest and exchange rates: the everyday maths that fills IGCSE Paper 1 and Paper 3, taught with bar models, multipliers and full worked examples.~21 min read · Core + Extended
- 3Algebraic manipulationCollect, expand, factorise, simplify and rearrange with confidence. Area models, FOIL arrows and step-by-step flow charts show why every algebra rule works, not just what to do.~18 min read · Core + Extended
- 4Equations & inequalitiesSolve linear, simultaneous and quadratic equations and inequalities with confidence. Balance diagrams, graphs and step-by-step methods show you what each answer really means.~21 min read · Core + Extended
- 5Sequences, functions & graphsSpot patterns and write the nth term, use function machines, sketch and read every graph shape, and meet the gradient of a curve and differentiation, all with clear pictures.~18 min read · Core + Extended
- 6Coordinate geometryGradient, y = mx + c, midpoints, lengths and parallel and perpendicular lines, all built from one picture: the gradient triangle. Learn to write the equation of any straight line in four steps.~25 min read · Core + Extended
- 7Geometry & circle theoremsEvery angle rule in one place: lines, parallel lines, triangles, polygons, symmetry, congruence, similarity, constructions and all the circle theorems. Each rule has a picture, a worked example and the exact reason to write in the exam.~31 min read · Core + Extended
- 8Mensuration — area & volumeConvert units, find area and perimeter, then master circles, arcs, sectors, prisms, cylinders, cones, spheres and frustums. Every formula is explained with a picture so you understand where it comes from.~28 min read · Core + Extended
- 9Pythagoras & trigonometryRight-angled triangles first (Pythagoras, SOH CAH TOA, bearings), then the sine rule, cosine rule, 3D problems and trig graphs. Every method is shown on a labelled diagram, so you can see which rule to pick.~34 min read · Core + Extended
- 10Transformations & vectorsReflection, rotation, translation and enlargement, then vectors: column vectors, addition, magnitude and vector geometry. Every transformation is drawn on a grid so you can see exactly what moves where.~29 min read · Core + Extended
- 11ProbabilityFrom the probability scale to tree diagrams and conditional probability. Every method is drawn with sample space tables, tree diagrams and Venn diagrams, so you can see why you multiply for AND and add for OR.~21 min read · Core + Extended
- 12StatisticsAverages, frequency tables, charts and scatter graphs, then the Extended topics: quartiles, cumulative frequency, box plots and histograms. Every method has a diagram and a worked example, so you can see what to do before you try it.~34 min read · Core + Extended
Night-before sheets
- ★Maths Formula & Method SheetEvery formula you must be able to write down from memory, drawn where a picture helps, plus the first move for the most common question types. One sheet for the night before.
- ★Maths Exam Traps & Last-Night ChecklistThe 30 mistakes that lose the most marks in IGCSE Maths, grouped by topic, plus command words, calculator habits and a checklist for the night before.
Frequently asked questions
Are these IGCSE Maths notes free?
Yes. Every chapter note is free to read online and to save as a PDF. They are free to share with friends, but not to sell.
Do the notes cover both Core and Extended?
Yes, in one note. Extended-only material carries an EXTENDED tag, so Core students can skip it.
Which syllabus do the notes follow?
Cambridge IGCSE Mathematics (0580).
How do I download a note as a PDF?
Tap Download PDF at the top of any note. The PDF file saves straight to your phone or computer, ready to print or revise offline.
How should I use these notes?
Read a chapter note, do the quick check, practise a paper with the Paper Generator, then finish with the night-before sheet.
Who writes the notes?
Riyaz Shaikh ("Riyaz Sir"), a Mumbai-based mentor with 15+ years of experience teaching IGCSE, IB and A Level one-to-one.
Message Riyaz Sir: one-to-one IGCSE Maths mentoring, online or in Mumbai.