Paper 1 · Non-Calculator (Core)
Specimen 2025 · 0580/01
Cambridge (CIE) · IGCSE
Mathematics 0580
Build confidence with numbers, algebra, geometry and data. Work through the methods, then apply them to problems.
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What you'll cover
- Number
- Algebra and graphs
- Coordinate geometry
- Geometry
- Mensuration
- Trigonometry
Published syllabus exam years: 2025, 2026, 2027, 2028, 2029, 2030. Confirm exam-series and centre availability with your school and Cambridge.
Your route through Mathematics
Explore nine areas, from number and algebra to geometry, probability and statistics.
Choose a pathway or review
Start the Number pathwayStart Algebra and graphsStart Coordinate geometryStart GeometryStart MensurationStart TrigonometryStart Transformations and vectorsStart ProbabilityStart Statistics
Check Coordinate geometry and plan a review
Check Geometry and plan a review
Check Mensuration and plan a review
Check Trigonometry and plan a review
Check Transformations and vectors and plan a review
View syllabus coverage
The nine syllabus areas
- 1 · Number19 sequenced lessons; 18 of 18 section entries have teaching and practice.
- 2 · Algebra and graphs21 sequenced lessons; 13 of 13 section entries have teaching and practice.
- 3 · Coordinate geometry10 sequenced teaching lessons; 7 of 7 section entries have teaching and practice. The mixed checkpoint recommends review lessons.
- 4 · Geometry15 sequenced teaching lessons; 8 of 8 section entries have teaching and practice. The mixed checkpoint recommends review lessons. Paper constructions are self-checked.
- 5 · Mensuration13 sequenced teaching lessons; 5 of 5 section entries have teaching and practice. A tier-specific mixed checkpoint suggests review lessons.
- 6 · Trigonometry13 sequenced teaching lessons; 6 of 6 section entries have teaching and practice. A tier-specific mixed checkpoint suggests review lessons.
- 7 · Transformations and vectors11 sequenced teaching lessons; 4 of 4 section entries have teaching and practice. A tier-specific mixed checkpoint suggests review lessons.
- 8 · Probability7 sequenced teaching lessons; 4 of 4 section entries have teaching and practice. A tier-specific mixed checkpoint suggests review lessons.
- 9 · Statistics13 sequenced teaching lessons; 7 of 7 section entries have teaching and practice. A tier-specific mixed checkpoint suggests review lessons.
Choose a pathway and work through the explanations and practice. All nine syllabus areas have teaching linked to all 72 Extended section entries, with Core requirements labelled. Mixed checkpoints help you choose what to revisit; they do not certify mastery or teacher verification.
Number: Lessons by syllabus section
- Number families and factorsC1.1 / E1.1
- Set relationshipsC1.2 / E1.2
- Powers and rootsC1.3 / E1.3
- Equivalent fractions, decimals and percentagesC1.4 / E1.4
- Numerical orderingC1.5 / E1.5
- Arithmetic operationsC1.6 / E1.6
- Index lawsC1.7 / E1.7
- Scientific notationC1.8 / E1.8
- Rounding and estimationC1.9 / E1.9
- Measurement boundsC1.10 / E1.10
- Ratios and proportional reasoningC1.11 / E1.11
- Rates and speedC1.12 / E1.12
- Percentage calculationsC1.13 / E1.13
- Calculator techniquesC1.14 / E1.14
- Time calculationsC1.15 / E1.15
- Money and currenciesC1.16 / E1.16
- Exponential changeE1.17 only
- Surd calculationsE1.18 only
Algebra and graphs: Lessons by syllabus section
- Algebraic language and substitutionC2.1 / E2.1
- Expansion, factorisation and completing the squareC2.2 / E2.2
- Algebraic fractionsE2.3 only
- Algebraic indicesC2.4 / E2.4
- Equations, simultaneous equations and formulasC2.5 / E2.5
- Inequalities and regionsC2.6 / E2.6
- SequencesC2.7 / E2.7
- Algebraic proportionE2.8 only
- Practical graphs and ratesC2.9 / E2.9
- Function graphs and graphical equationsC2.10 / E2.10
- Sketching curvesC2.11 / E2.11
- DifferentiationE2.12 only
- Functions, inverses and compositionE2.13 only
Coordinate geometry: Lessons by syllabus section
- Cartesian coordinatesC3.1 / E3.1
- Drawing linear graphsC3.2 / E3.2
- Gradients from a grid and two coordinatesC3.3 / E3.3
- Distance and midpointE3.4 only
- Equations of straight linesC3.5 / E3.5
- Parallel linesC3.6 / E3.6
- Perpendicular lines and bisectorsE3.7 only
Geometry: Lessons by syllabus section
- Geometrical terms, plane shapes, solids and circlesC4.1 / E4.1
- Measurement, three-side constructions and netsC4.2 / E4.2
- Scale drawings and three-figure bearingsC4.3 / E4.3
- Similar lengths, areas and volumesC4.4 / E4.4
- 2D symmetry and Extended 3D planes and axesC4.5 / E4.5
- Angle reasoning and polygon propertiesC4.6 / E4.6
- Core and Extended circle-angle theoremsC4.7 / E4.7
- Chord distances, bisectors and equal tangentsE4.8 only
Mensuration: Lessons by syllabus section
- Units and conversionsC5.1 / E5.1
- Perimeter and areaC5.2 / E5.2
- Circles, arcs and sectorsC5.3 / E5.3
- Surface areas and volumesC5.4 / E5.4
- Compound shapes and Extended frustaC5.5 / E5.5
Trigonometry: Lessons by syllabus section
- PythagorasC6.1 / E6.1
- Right triangles, bearings and Extended elevation/depressionC6.2 / E6.2
- Exact trigonometric valuesE6.3 only
- Graphs and all equation solutionsE6.4 only
- Sine rule, cosine rule, area and ambiguous casesE6.5 only
- Three-dimensional problemsE6.6 only
Transformations and vectors: Lessons by syllabus section
- Single Core and broader Extended transformationsC7.1 / E7.1
- Vector operationsE7.2 only
- Vector magnitudesE7.3 only
- Position vectors, ratios and collinearityE7.4 only
Probability: Lessons by syllabus section
- Single events, complements and Venn diagramsC8.1 / E8.1
- Relative and expected frequenciesC8.2 / E8.2
- Combined events and tree diagramsC8.3 / E8.3
- Conditional probabilityE8.4 only
Statistics: Lessons by syllabus section
- Classifying and tabulating dataC9.1 / E9.1
- Interpreting and comparing evidenceC9.2 / E9.2
- Averages, spread and Extended grouped dataC9.3 / E9.3
- Bar, pie, pictogram and stem-and-leaf diagramsC9.4 / E9.4
- Scatter diagrams and best-fit linesC9.5 / E9.5
- Cumulative frequency and percentilesE9.6 only
- Histograms and frequency densityE9.7 only
Learn
Lessons and worked examples
Your topic map
All subject practice Choose where to begin
Choose a lesson, try the practice and explain the idea without your notes. Your study checks help you decide what to review.
- 01
Number families and reciprocals
Learn the method · Practise with help · Try it yourself · Apply the idea
Not started - 02
Factors, multiples and prime building blocks
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Not started - 03
Sets and Venn diagrams
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Not started - 04
Powers and roots: reversing a process
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Not started - 05
Fractions, decimals and percentages as one quantity
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Not started - 06
Ordering numbers and interpreting inequalities
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Not started - 07
Arithmetic operations and the order of calculation
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Not started - 08
Index laws from repeated factors
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Not started - 09
Standard form and calculations at different scales
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Not started - 10
Rounding, estimation and sensible accuracy
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Not started - 11
Measurement bounds and the limits of accuracy
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Not started - 12
Ratios and proportional reasoning in context
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Not started - 13
Rates, average speed and compound measures
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Not started - 14
Percentages, interest and recovering the original
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Not started - 15
Calculator techniques and interpreting the display
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Not started - 16
Time calculations, timetables and time differences
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Not started - 17
Money calculations and currency conversions
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Not started - 18
Exponential growth and decay models
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Not started - 19
Surds and rationalising a denominator
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Not started - 20
Algebraic language and substitution
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Not started - 21
Collecting terms and expanding brackets
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Not started - 22
Factorising quadratics and grouped expressions
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Not started - 23
Completing the square and locating a turning point
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Not started - 24
Algebraic fractions and excluded values
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Not started - 25
Algebraic indices and equal-base equations
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Not started - 26
Constructing and solving linear equations
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Not started - 27
Linear simultaneous equations and modelling
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Not started - 28
Quadratic equations with three solving methods
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Not started - 29
Rearranging formulas and repeated subjects
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Not started - 30
Fractional equations and checking forbidden roots
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Not started - 31
Simultaneous linear and non-linear equations
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Not started - 32
Inequalities and intervals on a number line
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Not started - 33
Inequality regions and boundary lines
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Not started - 34
Sequences from differences, powers and ratios
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Not started - 35
Direct and inverse proportion as equations
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Not started - 36
Travel graphs, rates and area under speed
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Not started - 37
Tables, function graphs and graphical solutions
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Not started - 38
Sketching curves from roots, symmetry and asymptotes
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Not started - 39
Differentiation, tangents and stationary points
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Not started - 40
Functions, domains, inverses and composition
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Not started - 41
Coordinates, axes and a point's position
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Not started - 42
Drawing straight-line graphs from an equation
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Not started - 43
Reading a gradient from the grid
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Not started - 44
Gradient from two stated coordinates
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Not started - 45
Distance between two points
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Not started - 46
Midpoints and a missing endpoint
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Not started - 47
Line equations from a graph or a point
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Not started - 48
Rearranging general line equations
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Not started - 49
Parallel lines and their equations
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Not started - 50
Perpendicular lines and perpendicular bisectors
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Not started - 51
Coordinate geometry mixed checkpoint
Understand the idea · See an example · Check yourself
Not started - 52
Geometrical language and plane shapes
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Not started - 53
Solids and circle vocabulary
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Not started - 54
Measuring angles and constructing triangles
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Not started - 55
Nets that fold into solids
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Not started - 56
Scale drawings and real distances
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Not started - 57
Three-figure bearings and return directions
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Not started - 58
Similar lengths and matching triangles
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Not started - 59
Similar areas and volumes
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Not started - 60
Line and rotational symmetry
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Not started - 61
Symmetry planes and axes in solids
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Not started - 62
Angles, triangles and parallel lines
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Not started - 63
Interior and exterior polygon angles
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Not started - 64
Semicircle angles and tangent radii
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Not started - 65
Central angles, cyclic shapes and tangent chords
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Not started - 66
Chord distances and equal tangent lengths
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Not started - 67
- 68
Metric units, square units and capacity
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Not started - 69
Perimeter and perpendicular area
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Not started - 70
Trapezium areas and missing dimensions
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Not started - 71
Circle circumference and area
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Not started - 72
Arc lengths and sector boundaries
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Not started - 73
Cuboids, prisms and exposed faces
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Not started - 74
Cylinder volume and surface area
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Not started - 75
Pyramid volume and triangular faces
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Not started - 76
Cone volume, slant height and surface area
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Not started - 77
Spheres and hemispheres
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Not started - 78
Compound areas and outside perimeters
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Not started - 79
Compound solids and hidden join faces
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Not started - 80
Frusta from similar cones
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Not started - 81
- 82
Pythagoras and the hypotenuse
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Not started - 83
Sine, cosine and tangent for missing sides
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Not started - 84
Inverse ratios for right-triangle angles
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Not started - 85
Two-dimensional routes and right-triangle models
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Not started - 86
Angles of elevation and depression
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Not started - 87
Exact trigonometric values
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Not started - 88
Trigonometric graphs over one full turn
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Not started - 89
All solutions of trigonometric equations
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Not started - 90
Sine rule and opposite pairs
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Not started - 91
Cosine rule for sides and angles
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Not started - 92
Triangle area from an included angle
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Not started - 93
The ambiguous sine-rule case
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Not started - 94
Three-dimensional triangles and line–plane angles
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Not started - 95
- 96
Translations and column vectors
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Not started - 97
Reflections in horizontal and vertical lines
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Not started - 98
Rotations and a stated centre
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Not started - 99
Positive and fractional enlargements
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Not started - 100
Reflections in diagonal mirror lines
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Not started - 101
Negative enlargement factors
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Not started - 102
Combinations and the order of transformations
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Not started - 103
Vector addition, subtraction and scalar multiples
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Not started - 104
Vector magnitude and unit directions
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Not started - 105
Position vectors and division of a segment
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Not started - 106
Parallel and collinear vector arguments
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Not started - 107
Transformations and vectors mixed checkpoint
Understand the idea · See an example · Check yourself
Not started - 108
Probability scales and complementary events
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Not started - 109
Relative frequency and expected outcomes
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Not started - 110
Sample spaces for combined experiments
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Not started - 111
Two-event Venn diagrams and overlap
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Not started - 112
Tree diagrams with replacement
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Not started - 113
Tree diagrams without replacement
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Not started - 114
Conditional probability and a restricted group
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Not started - 115
- 116
Classifying data and two-way tables
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Not started - 117
Interpreting and comparing statistical evidence
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Not started - 118
Mean, median, mode and range
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Not started - 119
Averages from an ungrouped frequency table
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Not started - 120
Quartiles and interquartile range
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Not started - 121
Estimated means and modal classes for grouped data
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Not started - 122
Bar charts and honest scales
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Not started - 123
Pie charts and pictogram keys
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Not started - 124
Ordered stem-and-leaf diagrams
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Not started - 125
Dual and stacked bar charts
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Not started - 126
Scatter diagrams and lines of best fit
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Not started - 127
Cumulative frequency curves and percentiles
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Not started - 128
Histograms with unequal class widths
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Not started - 129
- 130
- 131
- 132
- 133
Coordinate geometry and stationary points
Understand the idea · See an example · Check yourself
Not started - 134
Geometry, circle theorems and similarity
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Not started - 135
- 136
- 137
- 138
These checks record your study activity and self-assessment, not a mastery score. Check the course coverage map for available lessons and remaining topics.
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Topic tests: Easy, Normal and Difficult
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Browse 72 topics →IGCSE Mathematics 0580 · Extended Practice Paper 1
25 questions · 120 min · Timed practice
IGCSE Mathematics 0580 · Mixed Skills Mini
6 questions · 40 min · Timed practice
Official papers
Historical and specimen papers may follow a different syllabus. Check the year and component before practising.
Paper 2 · Non-Calculator (Extended)
Specimen 2025 · 0580/02
Paper 3 · Calculator (Core)
Specimen 2025 · 0580/03
Paper 4 · Calculator (Extended)
Specimen 2025 · 0580/04
Paper 1 · Core · Timezone 1
June 2024 · 0580/11
Paper 2 · Extended · Timezone 1
June 2024 · 0580/21