Free Revision Checklist
Cambridge IGCSE Maths Revision Checklist
All 86 topics in the Cambridge IGCSE Mathematics (0580) syllabus, in order, with Core and Extended topics clearly marked. Rate each topic online, or download the PDF and tick it on paper. Free, with no sign-up.
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Your Exam at a Glance
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Cambridge IGCSE Mathematics
Your child sits one level: Core (the easier papers, top grade C) or Extended (the harder papers, grades A* to E). The school decides which. Core students sit Papers 1 and 3. Extended students sit Papers 2 and 4. One paper in each pair is non-calculator. Each student sits two papers, each worth half of the final grade. A list of formulas is printed in every paper, but some formulas must be learnt.
Core · Grades C–G
Paper 1Core · Non-Calculator1h 30m · 80 marks
Paper 3Core · Calculator1h 30m · 80 marks
Extended · Grades A*–E
Paper 2Extended · Non-Calculator2h · 100 marks
Paper 4Extended · Calculator2h · 100 marks
CoreGrades C–G · 53 topics
ExtendedGrades A*–E · all 86 topics
Interactive Checklist
How Confident Are You With Each Topic?
Next to each topic, tap Not Yet, Nearly or Confident. Your answers are saved on this phone or computer only, so use the same one each time and come back to update them every few weeks. Not Yet topics are the ones to revise first.
AllOn both Core and Extended papersExtendedOn Extended papers only
Number
20 topics- 1
Types of NumberNatural numbers, integers, primes, squares, cubes, factors, multiples, HCF, LCM, rational and irrational numbers
- 2
SetsVenn diagrams and set notation, such as n(A), ∈, A′, A ∩ B and A ∪ B
- 3
Powers and RootsSquares, square roots, cubes and cube roots
- 4
Fractions, Decimals and PercentagesUsing and converting between equivalent fractions, decimals and percentages
- 5
OrderingOrdering quantities and using =, ≠, >, <, ≥ and ≤
- 6
The Four OperationsCalculating with integers, fractions and decimals, including negatives and order of operations
- 7
IndicesIndex notation and the laws of indices, including zero and negative indices
- 8
Standard FormWriting and calculating with numbers in standard form
- 9
EstimationRounding to decimal places and significant figures, and estimating answers
- 10
Limits of AccuracyUpper and lower bounds of rounded values
- 11
Ratio and ProportionSimplifying ratios, sharing in a ratio and direct proportion
- 12
RatesAverage speed and other rates, including converting units
- 13
PercentagesPercentages of amounts, percentage increase and decrease, simple and compound interest
- 14
Using a CalculatorUsing a calculator efficiently and checking answers
- 15
Time and MoneyTime calculations, timetables and currency conversion
- 16
Fractional IndicesEvaluating and simplifying expressions with fractional indices
- 17
Bounds in CalculationsUpper and lower bounds of answers to calculations
- 18
Reverse PercentagesFinding the original amount after a percentage change
- 19
Exponential Growth and DecayProblems involving repeated percentage change
- 20
SurdsSimplifying surds and rationalising the denominator
Algebra and Graphs
22 topics- 21
Introduction to AlgebraUsing letters for numbers and substituting into expressions and formulae
- 22
Expanding and FactorisingSimplifying, expanding brackets and taking out common factors
- 23
Indices in AlgebraUsing the laws of indices with algebraic terms
- 24
Linear Equations and FormulaeSolving linear equations and changing the subject of simple formulae
- 25
Simultaneous Linear EquationsSolving a pair of linear equations
- 26
Linear InequalitiesSolving inequalities and showing them on a number line
- 27
SequencesContinuing sequences, spotting patterns and finding the nth term
- 28
Graphs in Practical SituationsTravel graphs, conversion graphs and other real-life graphs
- 29
Graphs of FunctionsDrawing tables of values and graphs of linear, quadratic and reciprocal functions
- 30
Sketching CurvesRecognising and sketching the shapes of common graphs
- 31
Harder Expanding and FactorisingExpanding products of brackets and factorising quadratics, including the difference of two squares
- 32
Algebraic FractionsSimplifying, adding, subtracting, multiplying and dividing algebraic fractions
- 33
Quadratic EquationsSolving by factorising, the quadratic formula and completing the square
- 34
Harder Simultaneous EquationsSolving a linear and a quadratic equation together
- 35
Rearranging Harder FormulaeChanging the subject when it appears more than once or inside a power or root
- 36
Inequalities and RegionsQuadratic inequalities and showing regions on a graph
- 37
Harder SequencesFinding the nth term of quadratic, cubic and exponential sequences
- 38
Direct and Inverse ProportionForming and using equations for direct and inverse proportion
- 39
Speed-Time GraphsAcceleration, deceleration and distance as the area under the graph
- 40
Harder Graphs and TangentsCubic and exponential graphs, solving equations graphically and estimating gradients with tangents
- 41
FunctionsFunction notation, composite functions and inverse functions
- 42
DifferentiationDifferentiating axⁿ, finding gradients and turning points, and deciding if they are maximum or minimum points
Coordinate Geometry
7 topics- 43
CoordinatesPlotting and reading points in all four quadrants
- 44
Drawing Linear GraphsDrawing straight-line graphs from their equations
- 45
Gradient of Linear GraphsFinding the gradient of a straight line
- 46
Equations of Straight LinesUsing and finding equations in the form y = mx + c
- 47
Parallel LinesFinding the equation of a line parallel to another
- 48
Length and MidpointFinding the length and midpoint of a line segment
- 49
Perpendicular LinesFinding the gradient and equation of a perpendicular line
Geometry
9 topics- 50
Geometrical TermsCorrect names for angles, lines, triangles, quadrilaterals, polygons, circles and solids
- 51
Geometrical ConstructionsConstructing triangles, bisectors and nets with a ruler and compasses
- 52
Scale Drawings and BearingsUsing scales and measuring and calculating bearings
- 53
SimilarityCalculating lengths in similar shapes
- 54
SymmetryLine and rotational symmetry of 2D shapes
- 55
AnglesAngle facts, angles in parallel lines and angles in polygons
- 56
Circle Theorems IThe first set of circle theorems, such as the angle in a semicircle and tangent properties
- 57
Similar Areas and VolumesUsing the relationship between lengths, areas and volumes of similar shapes
- 58
Circle Theorems IIThe full set of circle theorems, including cyclic quadrilaterals and the alternate segment theorem
Mensuration
5 topics- 59
Units of MeasureConverting units of length, area, volume, mass and capacity
- 60
Area and PerimeterRectangles, triangles, parallelograms, trapezia and compound shapes
- 61
Circles, Arcs and SectorsCircumference and area of circles, arc lengths and sector areas
- 62
Surface Area and VolumeCuboids, prisms, cylinders, spheres, pyramids and cones
- 63
Compound Shapes and Parts of ShapesAreas and volumes of shapes made from or cut from simpler ones
Trigonometry
6 topics- 64
Pythagoras' TheoremFinding a missing side in a right-angled triangle
- 65
Right-Angled TrigonometryUsing sine, cosine and tangent, including angles of elevation and depression
- 66
Exact Trigonometric ValuesExact values of sin, cos and tan for 0°, 30°, 45°, 60° and 90° where they exist
- 67
Trigonometric FunctionsGraphs of sine, cosine and tangent and solving simple trigonometric equations
- 68
Non-Right-Angled TrianglesThe sine rule, the cosine rule and area = ½ab sin C
- 69
3D Pythagoras and TrigonometryLengths and angles in 3D shapes
Transformations and Vectors
5 topics- 70
TransformationsReflection, rotation, translation and enlargement
- 71
Harder TransformationsEnlargement with fractional and negative scale factors, and combined transformations
- 72
Vectors in Two DimensionsColumn vectors, adding, subtracting and multiplying by a scalar
- 73
Magnitude of a VectorFinding the length of a vector
- 74
Vector GeometryUsing vectors to find paths and prove geometric results
Probability
4 topics- 75
Introduction to ProbabilityThe probability scale and the probability of an event not happening
- 76
Relative and Expected FrequenciesEstimating probabilities from experiments and predicting outcomes
- 77
Combined EventsSample space diagrams, Venn diagrams and tree diagrams
- 78
Conditional ProbabilityProbabilities that depend on a previous outcome
Statistics
8 topics- 79
Classifying DataTypes of data and collecting data
- 80
Interpreting DataReading and drawing conclusions from tables and charts
- 81
Averages and RangeMean, median, mode and range, including from frequency tables
- 82
Charts and DiagramsBar charts, pie charts, pictograms and stem-and-leaf diagrams
- 83
Scatter DiagramsCorrelation and lines of best fit
- 84
Averages and Measures of SpreadEstimated mean from grouped data, quartiles and the interquartile range
- 85
Cumulative FrequencyDrawing and using cumulative frequency diagrams
- 86
HistogramsDrawing and interpreting histograms with unequal class widths
Core and Extended labels follow the Cambridge IGCSE Mathematics (0580) syllabus for 2025 to 2027.
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