Spec Detail

Cambridge International → IGCSE → Mathematics → 0580 → cambridge-igcse-mathematics-0580-2025-2027:v1

Overview Papers Syllabus Content Sources Publishing API

Overview

4 Papers

91 Topics

82 Subtopics

489 Outcomes

9 Sources

1826 Paper-topic rules

Status published Locked

Version label: v1 | Years: 2025–2027 | Content hash: sha256:8fced804245f3a16fc675164eb3f1c0ad1a856db97ac9f35473681cd23308ce5 | Published: 2026-07-15T06:32:09+00:00 | Locked: 2026-07-15T06:32:09+00:00

`p1` Paper 1 - Non-calculator (Core)

Duration 90 min · Marks 80 · Weighting 50.00 · Structure flexible_structured_unstructured_core_non_calculator · Question count flexible_total_marks · Assembly exact_total_marks

Allowed styles: structured_response / top_level unsupported short_answer / part unsupported extended_structured / part unsupported long_text / part unsupported fill_in_the_blanks / part unsupported calculation_response / part unsupported graph_interpretation / part unsupported table_completion_as_text / part unsupported diagram_labeling / part unsupported canvas_drawing / part unsupported true_false / part unsupported error_correction / part unsupported matching / part unsupported sequence_ordering / part unsupported comparison / part unsupported math_numeric_response / part unsupported math_expression_response / part unsupported math_working_response / part unsupported algebraic_manipulation / part unsupported graph_plotting / part unsupported geometry_construction / part unsupported table_numeric_completion / part unsupported math_reasoning_proof / part unsupported statistics_chart_response / part unsupported probability_diagram_response / part unsupported transformation_vector_response / part unsupported diagram_math_response / part unsupported

Patterns: 5

`p2` Paper 2 - Non-calculator (Extended)

Duration 120 min · Marks 100 · Weighting 50.00 · Structure flexible_structured_unstructured_extended_non_calculator · Question count flexible_total_marks · Assembly exact_total_marks

Patterns: 5

`p3` Paper 3 - Calculator (Core)

Duration 90 min · Marks 80 · Weighting 50.00 · Structure flexible_structured_unstructured_core_calculator · Question count flexible_total_marks · Assembly exact_total_marks

Patterns: 5

`p4` Paper 4 - Calculator (Extended)

Duration 120 min · Marks 100 · Weighting 50.00 · Structure flexible_structured_unstructured_extended_calculator · Question count flexible_total_marks · Assembly exact_total_marks

Patterns: 6

1 Number

1.1 Types of number 6 outcomes
- C1.1.1 identify and use natural numbers, integers, prime numbers, square numbers, cube numbers, common factors and common multiples including HCF a... p1, p2, p3, p4
- C1.1.2 recognise and use rational and irrational numbers, reciprocals, set notation, Venn diagrams, ∪, ∩, A′ and n(A) p1, p2, p3, p4
- C1.1.3 apply types of number to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.1.1 identify and use natural numbers, integers, prime numbers, square numbers, cube numbers, common factors and common multiples including HCF a... p2, p4
- E1.1.2 recognise and use rational and irrational numbers, reciprocals, set notation, Venn diagrams, ∪, ∩, A′ and n(A) p2, p4
1.2 Sets 6 outcomes
- C1.2.1 use set language and notation for union, intersection, complement and number of elements p1, p2, p3, p4
- C1.2.2 solve problems using Venn diagrams and set notation in numerical and probability contexts p1, p2, p3, p4
- C1.2.3 apply sets to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.2.1 use set language and notation for union, intersection, complement and number of elements p2, p4
- E1.2.2 solve problems using Venn diagrams and set notation in numerical and probability contexts p2, p4
1.3 Powers and roots 6 outcomes
- C1.3.1 calculate squares, square roots, cubes, cube roots and other powers and roots p1, p2, p3, p4
- C1.3.2 use powers and roots in exact and approximate numerical problems p1, p2, p3, p4
- C1.3.3 apply powers and roots to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.3.1 calculate accurately squares, square roots, cubes, cube roots and other powers and roots p2, p4
- E1.3.2 use powers and roots in exact and approximate numerical problems p2, p4
1.4 Fractions, decimals and percentages 6 outcomes
- C1.4.1 convert between fractions, decimals and percentages p1, p2, p3, p4
- C1.4.2 calculate with fractions, terminating decimals, recurring decimals and percentages p1, p2, p3, p4
- C1.4.3 apply fractions, decimals and percentages to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.4.1 convert between fractions, decimals and percentages p2, p4
- E1.4.2 calculate accurately with fractions, terminating decimals, recurring decimals and percentages p2, p4
1.5 Ordering 6 outcomes
- C1.5.1 order quantities by size using =, ≠, >, <, ⩾ and ⩽ p1, p2, p3, p4
- C1.5.2 compare numbers written as fractions, decimals, percentages and in standard form p1, p2, p3, p4
- C1.5.3 apply ordering to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.5.1 order quantities by size using =, ≠, >, <, ⩾ and ⩽ p2, p4
- E1.5.2 compare numbers written as fractions, decimals, percentages and in standard form p2, p4
1.6 The four operations 6 outcomes
- C1.6.1 carry out the four operations with positive and negative integers, fractions and decimals p1, p2, p3, p4
- C1.6.2 apply the order of operations including brackets and powers p1, p2, p3, p4
- C1.6.3 apply the four operations to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.6.1 carry out the four operations with positive and negative integers, fractions and decimals p2, p4
- E1.6.2 apply the order of operations including brackets and powers p2, p4
1.7 Indices I 6 outcomes
- C1.7.1 use index notation for positive, zero and negative integer powers p1, p2, p3, p4
- C1.7.2 apply the laws of indices to numerical expressions p1, p2, p3, p4
- C1.7.3 apply indices i to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.7.1 use index notation for positive, zero and negative integer powers p2, p4
- E1.7.2 apply the laws of indices to numerical expressions p2, p4
1.8 Standard form 6 outcomes
- C1.8.1 write numbers in standard form A × 10^n where 1 ⩽ A < 10 p1, p2, p3, p4
- C1.8.2 calculate with numbers in standard form and interpret answers p1, p2, p3, p4
- C1.8.3 apply standard form to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.8.1 write numbers in standard form A × 10^n where 1 ⩽ A < 10 p2, p4
- E1.8.2 calculate accurately with numbers in standard form and interpret answers p2, p4
1.9 Estimation 6 outcomes
- C1.9.1 round values to a specified number of decimal places or significant figures p1, p2, p3, p4
- C1.9.2 estimate answers to calculations and check reasonableness p1, p2, p3, p4
- C1.9.3 apply estimation to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.9.1 round values to a specified number of decimal places or significant figures p2, p4
- E1.9.2 estimate answers to calculations and check reasonableness p2, p4
1.10 Limits of accuracy 6 outcomes
- C1.10.1 state upper and lower bounds for rounded measurements p1, p2, p3, p4
- C1.10.2 calculate limits of accuracy in practical problems p1, p2, p3, p4
- C1.10.3 apply limits of accuracy to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.10.1 state upper and lower bounds for rounded measurements p2, p4
- E1.10.2 calculate accurately limits of accuracy in practical problems p2, p4
1.11 Ratio and proportion 6 outcomes
- C1.11.1 divide a quantity in a given ratio and simplify ratios p1, p2, p3, p4
- C1.11.2 solve direct and inverse proportion problems p1, p2, p3, p4
- C1.11.3 apply ratio and proportion to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.11.1 divide a quantity in a given ratio and simplify ratios p2, p4
- E1.11.2 solve direct and inverse proportion problems p2, p4
1.12 Rates 6 outcomes
- C1.12.1 calculate average speed, distance, time, density and other compound measures p1, p2, p3, p4
- C1.12.2 interpret rates of change in practical situations p1, p2, p3, p4
- C1.12.3 apply rates to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.12.1 calculate accurately average speed, distance, time, density and other compound measures p2, p4
- E1.12.2 interpret rates of change in practical situations p2, p4
1.13 Percentages 6 outcomes
- C1.13.1 calculate percentage change, reverse percentages and repeated percentage change p1, p2, p3, p4
- C1.13.2 solve compound interest and depreciation problems p1, p2, p3, p4
- C1.13.3 apply percentages to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.13.1 calculate accurately percentage change, reverse percentages and repeated percentage change p2, p4
- E1.13.2 solve compound interest and depreciation problems p2, p4
1.14 Using a calculator 6 outcomes
- C1.14.1 use a scientific calculator efficiently and round answers appropriately p1, p2, p3, p4
- C1.14.2 interpret calculator displays and avoid premature rounding p1, p2, p3, p4
- C1.14.3 apply using a calculator to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.14.1 use a scientific calculator efficiently and round answers appropriately p2, p4
- E1.14.2 interpret calculator displays and avoid premature rounding p2, p4
1.15 Time 6 outcomes
- C1.15.1 calculate with units of time, timetables and time intervals p1, p2, p3, p4
- C1.15.2 solve problems involving the 12-hour and 24-hour clock p1, p2, p3, p4
- C1.15.3 apply time to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.15.1 calculate accurately with units of time, timetables and time intervals p2, p4
- E1.15.2 solve problems involving the 12-hour and 24-hour clock p2, p4
1.16 Money 6 outcomes
- C1.16.1 solve money problems involving profit, loss, discount, tax and exchange rates p1, p2, p3, p4
- C1.16.2 use ratio, percentage and calculator methods in financial contexts p1, p2, p3, p4
- C1.16.3 apply money to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.16.1 solve money problems involving profit, loss, discount, tax and exchange rates p2, p4
- E1.16.2 use ratio, percentage and calculator methods in financial contexts p2, p4
1.17 Exponential growth and decay 3 outcomes
- E1.17.1 model growth and decay using repeated percentage multipliers p2, p4
- E1.17.2 solve problems involving compound interest and depreciation p2, p4
- E1.17.3 interpret and justify results for exponential growth and decay in unfamiliar problem-solving contexts p2, p4
1.18 Surds 6 outcomes
- C1.18.1 simplify surds and rationalise simple denominators p1, p2, p3, p4
- C1.18.2 use exact surd forms in algebraic and geometrical problems p1, p2, p3, p4
- C1.18.3 apply surds to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E1.18.1 simplify surds and rationalise simple denominators p2, p4
- E1.18.2 use exact surd forms in algebraic and geometrical problems p2, p4

2 Algebra and graphs

2.1 Introduction to algebra 6 outcomes
- C2.1.1 use and apply introduction to algebra in routine mathematical contexts p1, p2, p3, p4
- C2.1.2 solve multi-step problems involving introduction to algebra and communicate working clearly p1, p2, p3, p4
- C2.1.3 apply introduction to algebra to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E2.1.1 extend and apply introduction to algebra in routine mathematical contexts p2, p4
- E2.1.2 solve multi-step problems involving introduction to algebra and communicate working clearly p2, p4
2.2 Algebraic manipulation 6 outcomes
- C2.2.1 expand brackets, factorise expressions and simplify algebraic expressions p1, p2, p3, p4
- C2.2.2 manipulate algebraic expressions including products of linear factors and quadratics p1, p2, p3, p4
- C2.2.3 apply algebraic manipulation to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E2.2.1 expand brackets, factorise expressions and simplify algebraic expressions p2, p4
- E2.2.2 manipulate algebraic expressions including products of linear factors and quadratics p2, p4
2.3 Algebraic fractions 6 outcomes
- C2.3.1 use and apply algebraic fractions in routine mathematical contexts p1, p2, p3, p4
- C2.3.2 solve multi-step problems involving algebraic fractions and communicate working clearly p1, p2, p3, p4
- C2.3.3 apply algebraic fractions to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E2.3.1 extend and apply algebraic fractions in routine mathematical contexts p2, p4
- E2.3.2 solve multi-step problems involving algebraic fractions and communicate working clearly p2, p4
2.4 Indices II 6 outcomes
- C2.4.1 use and apply indices ii in routine mathematical contexts p1, p2, p3, p4
- C2.4.2 solve multi-step problems involving indices ii and communicate working clearly p1, p2, p3, p4
- C2.4.3 apply indices ii to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E2.4.1 extend and apply indices ii in routine mathematical contexts p2, p4
- E2.4.2 solve multi-step problems involving indices ii and communicate working clearly p2, p4
2.5 Equations 6 outcomes
- C2.5.1 solve linear, quadratic and simultaneous equations by appropriate methods p1, p2, p3, p4
- C2.5.2 use formulae including the quadratic formula and rearrange formulae p1, p2, p3, p4
- C2.5.3 apply equations to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E2.5.1 solve linear, quadratic and simultaneous equations by appropriate methods p2, p4
- E2.5.2 use formulae including the quadratic formula and rearrange formulae p2, p4
2.6 Inequalities 6 outcomes
- C2.6.1 use and apply inequalities in routine mathematical contexts p1, p2, p3, p4
- C2.6.2 solve multi-step problems involving inequalities and communicate working clearly p1, p2, p3, p4
- C2.6.3 apply inequalities to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E2.6.1 extend and apply inequalities in routine mathematical contexts p2, p4
- E2.6.2 solve multi-step problems involving inequalities and communicate working clearly p2, p4
2.7 Sequences 6 outcomes
- C2.7.1 use and apply sequences in routine mathematical contexts p1, p2, p3, p4
- C2.7.2 solve multi-step problems involving sequences and communicate working clearly p1, p2, p3, p4
- C2.7.3 apply sequences to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E2.7.1 extend and apply sequences in routine mathematical contexts p2, p4
- E2.7.2 solve multi-step problems involving sequences and communicate working clearly p2, p4
2.8 Proportion 6 outcomes
- C2.8.1 use and apply proportion in routine mathematical contexts p1, p2, p3, p4
- C2.8.2 solve multi-step problems involving proportion and communicate working clearly p1, p2, p3, p4
- C2.8.3 apply proportion to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E2.8.1 extend and apply proportion in routine mathematical contexts p2, p4
- E2.8.2 solve multi-step problems involving proportion and communicate working clearly p2, p4
2.9 Graphs in practical situations 6 outcomes
- C2.9.1 use and apply graphs in practical situations in routine mathematical contexts p1, p2, p3, p4
- C2.9.2 solve multi-step problems involving graphs in practical situations and communicate working clearly p1, p2, p3, p4
- C2.9.3 apply graphs in practical situations to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E2.9.1 extend and apply graphs in practical situations in routine mathematical contexts p2, p4
- E2.9.2 solve multi-step problems involving graphs in practical situations and communicate working clearly p2, p4
2.10 Graphs of functions 6 outcomes
- C2.10.1 draw and interpret graphs of linear, quadratic, cubic, reciprocal and exponential functions p1, p2, p3, p4
- C2.10.2 use graphs to solve equations and estimate gradients p1, p2, p3, p4
- C2.10.3 apply graphs of functions to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E2.10.1 draw and interpret graphs of linear, quadratic, cubic, reciprocal and exponential functions p2, p4
- E2.10.2 use graphs to solve equations and estimate gradients p2, p4
2.11 Sketching curves 6 outcomes
- C2.11.1 sketch curves using key features including intercepts, turning points and asymptotes p1, p2, p3, p4
- C2.11.2 interpret the relationship between algebraic form and graphical shape p1, p2, p3, p4
- C2.11.3 apply sketching curves to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E2.11.1 sketch curves using key features including intercepts, turning points and asymptotes p2, p4
- E2.11.2 interpret the relationship between algebraic form and graphical shape p2, p4
2.12 Differentiation 6 outcomes
- C2.12.1 use dy/dx notation and differentiate simple powers of x p1, p2, p3, p4
- C2.12.2 apply differentiation to gradients, turning points and simple rate problems p1, p2, p3, p4
- C2.12.3 apply differentiation to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E2.12.1 use dy/dx notation and differentiate simple powers of x p2, p4
- E2.12.2 apply differentiation to gradients, turning points and simple rate problems p2, p4
2.13 Functions 6 outcomes
- C2.13.1 use function notation f(x), f⁻¹(x) and gf(x) p1, p2, p3, p4
- C2.13.2 find inverse and composite functions and interpret domains where required p1, p2, p3, p4
- C2.13.3 apply functions to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E2.13.1 use function notation f(x), f⁻¹(x) and gf(x) p2, p4
- E2.13.2 find inverse and composite functions and interpret domains where required p2, p4

3 Coordinate geometry

3.1 Coordinates 6 outcomes
- C3.1.1 use and apply coordinates in routine mathematical contexts p1, p2, p3, p4
- C3.1.2 solve multi-step problems involving coordinates and communicate working clearly p1, p2, p3, p4
- C3.1.3 apply coordinates to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E3.1.1 extend and apply coordinates in routine mathematical contexts p2, p4
- E3.1.2 solve multi-step problems involving coordinates and communicate working clearly p2, p4
3.2 Drawing linear graphs 6 outcomes
- C3.2.1 use and apply drawing linear graphs in routine mathematical contexts p1, p2, p3, p4
- C3.2.2 solve multi-step problems involving drawing linear graphs and communicate working clearly p1, p2, p3, p4
- C3.2.3 apply drawing linear graphs to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E3.2.1 extend and apply drawing linear graphs in routine mathematical contexts p2, p4
- E3.2.2 solve multi-step problems involving drawing linear graphs and communicate working clearly p2, p4
3.3 Gradient of linear graphs 6 outcomes
- C3.3.1 find and interpret the gradient of a straight line p1, p2, p3, p4
- C3.3.2 use y = mx + c to identify gradient and intercept p1, p2, p3, p4
- C3.3.3 apply gradient of linear graphs to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E3.3.1 find and interpret the gradient of a straight line p2, p4
- E3.3.2 use y = mx + c to identify gradient and intercept p2, p4
3.4 Length and midpoint 6 outcomes
- C3.4.1 use and apply length and midpoint in routine mathematical contexts p1, p2, p3, p4
- C3.4.2 solve multi-step problems involving length and midpoint and communicate working clearly p1, p2, p3, p4
- C3.4.3 apply length and midpoint to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E3.4.1 extend and apply length and midpoint in routine mathematical contexts p2, p4
- E3.4.2 solve multi-step problems involving length and midpoint and communicate working clearly p2, p4
3.5 Equations of linear graphs 6 outcomes
- C3.5.1 find equations of lines in the forms y = mx + c, ax + by = c and x = k p1, p2, p3, p4
- C3.5.2 use coordinate information to determine linear equations p1, p2, p3, p4
- C3.5.3 apply equations of linear graphs to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E3.5.1 find equations of lines in the forms y = mx + c, ax + by = c and x = k p2, p4
- E3.5.2 use coordinate information to determine linear equations p2, p4
3.6 Parallel lines 6 outcomes
- C3.6.1 recognise and use equal gradients for parallel lines p1, p2, p3, p4
- C3.6.2 solve coordinate geometry problems involving parallel lines p1, p2, p3, p4
- C3.6.3 apply parallel lines to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E3.6.1 recognise and use equal gradients for parallel lines p2, p4
- E3.6.2 solve coordinate geometry problems involving parallel lines p2, p4
3.7 Perpendicular lines 6 outcomes
- C3.7.1 recognise and use gradients whose product is -1 for perpendicular lines p1, p2, p3, p4
- C3.7.2 solve coordinate geometry problems involving perpendicular lines p1, p2, p3, p4
- C3.7.3 apply perpendicular lines to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E3.7.1 recognise and use gradients whose product is -1 for perpendicular lines p2, p4
- E3.7.2 solve coordinate geometry problems involving perpendicular lines p2, p4

4 Geometry

4.1 Geometrical terms 6 outcomes
- C4.1.1 use and apply geometrical terms in routine mathematical contexts p1, p2, p3, p4
- C4.1.2 solve multi-step problems involving geometrical terms and communicate working clearly p1, p2, p3, p4
- C4.1.3 apply geometrical terms to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E4.1.1 extend and apply geometrical terms in routine mathematical contexts p2, p4
- E4.1.2 solve multi-step problems involving geometrical terms and communicate working clearly p2, p4
4.2 Geometrical constructions 6 outcomes
- C4.2.1 use and apply geometrical constructions in routine mathematical contexts p1, p2, p3, p4
- C4.2.2 solve multi-step problems involving geometrical constructions and communicate working clearly p1, p2, p3, p4
- C4.2.3 apply geometrical constructions to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E4.2.1 extend and apply geometrical constructions in routine mathematical contexts p2, p4
- E4.2.2 solve multi-step problems involving geometrical constructions and communicate working clearly p2, p4
4.3 Scale drawings 6 outcomes
- C4.3.1 use and apply scale drawings in routine mathematical contexts p1, p2, p3, p4
- C4.3.2 solve multi-step problems involving scale drawings and communicate working clearly p1, p2, p3, p4
- C4.3.3 apply scale drawings to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E4.3.1 extend and apply scale drawings in routine mathematical contexts p2, p4
- E4.3.2 solve multi-step problems involving scale drawings and communicate working clearly p2, p4
4.4 Similarity 6 outcomes
- C4.4.1 use and apply similarity in routine mathematical contexts p1, p2, p3, p4
- C4.4.2 solve multi-step problems involving similarity and communicate working clearly p1, p2, p3, p4
- C4.4.3 apply similarity to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E4.4.1 extend and apply similarity in routine mathematical contexts p2, p4
- E4.4.2 solve multi-step problems involving similarity and communicate working clearly p2, p4
4.5 Symmetry 6 outcomes
- C4.5.1 use and apply symmetry in routine mathematical contexts p1, p2, p3, p4
- C4.5.2 solve multi-step problems involving symmetry and communicate working clearly p1, p2, p3, p4
- C4.5.3 apply symmetry to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E4.5.1 extend and apply symmetry in routine mathematical contexts p2, p4
- E4.5.2 solve multi-step problems involving symmetry and communicate working clearly p2, p4
4.6 Angles 6 outcomes
- C4.6.1 use and apply angles in routine mathematical contexts p1, p2, p3, p4
- C4.6.2 solve multi-step problems involving angles and communicate working clearly p1, p2, p3, p4
- C4.6.3 apply angles to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E4.6.1 extend and apply angles in routine mathematical contexts p2, p4
- E4.6.2 solve multi-step problems involving angles and communicate working clearly p2, p4
4.7 Angle properties 6 outcomes
- C4.7.1 use and apply angle properties in routine mathematical contexts p1, p2, p3, p4
- C4.7.2 solve multi-step problems involving angle properties and communicate working clearly p1, p2, p3, p4
- C4.7.3 apply angle properties to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E4.7.1 extend and apply angle properties in routine mathematical contexts p2, p4
- E4.7.2 solve multi-step problems involving angle properties and communicate working clearly p2, p4
4.8 Circle theorems 6 outcomes
- C4.8.1 use angle properties of circles including cyclic quadrilaterals and tangents p1, p2, p3, p4
- C4.8.2 apply circle theorems in geometrical reasoning p1, p2, p3, p4
- C4.8.3 apply circle theorems to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E4.8.1 use angle properties of circles including cyclic quadrilaterals and tangents p2, p4
- E4.8.2 apply circle theorems in geometrical reasoning p2, p4
4.9 Loci 6 outcomes
- C4.9.1 use and apply loci in routine mathematical contexts p1, p2, p3, p4
- C4.9.2 solve multi-step problems involving loci and communicate working clearly p1, p2, p3, p4
- C4.9.3 apply loci to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E4.9.1 extend and apply loci in routine mathematical contexts p2, p4
- E4.9.2 solve multi-step problems involving loci and communicate working clearly p2, p4
4.10 Bearings 6 outcomes
- C4.10.1 use and apply bearings in routine mathematical contexts p1, p2, p3, p4
- C4.10.2 solve multi-step problems involving bearings and communicate working clearly p1, p2, p3, p4
- C4.10.3 apply bearings to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E4.10.1 extend and apply bearings in routine mathematical contexts p2, p4
- E4.10.2 solve multi-step problems involving bearings and communicate working clearly p2, p4
4.11 Geometrical reasoning 6 outcomes
- C4.11.1 use and apply geometrical reasoning in routine mathematical contexts p1, p2, p3, p4
- C4.11.2 solve multi-step problems involving geometrical reasoning and communicate working clearly p1, p2, p3, p4
- C4.11.3 apply geometrical reasoning to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E4.11.1 extend and apply geometrical reasoning in routine mathematical contexts p2, p4
- E4.11.2 solve multi-step problems involving geometrical reasoning and communicate working clearly p2, p4
4.12 Three-dimensional geometry 6 outcomes
- C4.12.1 use and apply three-dimensional geometry in routine mathematical contexts p1, p2, p3, p4
- C4.12.2 solve multi-step problems involving three-dimensional geometry and communicate working clearly p1, p2, p3, p4
- C4.12.3 apply three-dimensional geometry to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E4.12.1 extend and apply three-dimensional geometry in routine mathematical contexts p2, p4
- E4.12.2 solve multi-step problems involving three-dimensional geometry and communicate working clearly p2, p4

5 Mensuration

5.1 Measures 6 outcomes
- C5.1.1 use and apply measures in routine mathematical contexts p1, p2, p3, p4
- C5.1.2 solve multi-step problems involving measures and communicate working clearly p1, p2, p3, p4
- C5.1.3 apply measures to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E5.1.1 extend and apply measures in routine mathematical contexts p2, p4
- E5.1.2 solve multi-step problems involving measures and communicate working clearly p2, p4
5.2 Perimeter and area 6 outcomes
- C5.2.1 use and apply perimeter and area in routine mathematical contexts p1, p2, p3, p4
- C5.2.2 solve multi-step problems involving perimeter and area and communicate working clearly p1, p2, p3, p4
- C5.2.3 apply perimeter and area to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E5.2.1 extend and apply perimeter and area in routine mathematical contexts p2, p4
- E5.2.2 solve multi-step problems involving perimeter and area and communicate working clearly p2, p4
5.3 Circles, arcs and sectors 6 outcomes
- C5.3.1 use and apply circles, arcs and sectors in routine mathematical contexts p1, p2, p3, p4
- C5.3.2 solve multi-step problems involving circles, arcs and sectors and communicate working clearly p1, p2, p3, p4
- C5.3.3 apply circles, arcs and sectors to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E5.3.1 extend and apply circles, arcs and sectors in routine mathematical contexts p2, p4
- E5.3.2 solve multi-step problems involving circles, arcs and sectors and communicate working clearly p2, p4
5.4 Surface area 6 outcomes
- C5.4.1 use and apply surface area in routine mathematical contexts p1, p2, p3, p4
- C5.4.2 solve multi-step problems involving surface area and communicate working clearly p1, p2, p3, p4
- C5.4.3 apply surface area to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E5.4.1 extend and apply surface area in routine mathematical contexts p2, p4
- E5.4.2 solve multi-step problems involving surface area and communicate working clearly p2, p4
5.5 Volume 6 outcomes
- C5.5.1 use and apply volume in routine mathematical contexts p1, p2, p3, p4
- C5.5.2 solve multi-step problems involving volume and communicate working clearly p1, p2, p3, p4
- C5.5.3 apply volume to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E5.5.1 extend and apply volume in routine mathematical contexts p2, p4
- E5.5.2 solve multi-step problems involving volume and communicate working clearly p2, p4
5.6 Compound measures and problem-solving contexts 6 outcomes
- C5.6.1 use and apply compound measures and problem-solving contexts in routine mathematical contexts p1, p2, p3, p4
- C5.6.2 solve multi-step problems involving compound measures and problem-solving contexts and communicate working clearly p1, p2, p3, p4
- C5.6.3 apply compound measures and problem-solving contexts to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E5.6.1 extend and apply compound measures and problem-solving contexts in routine mathematical contexts p2, p4
- E5.6.2 solve multi-step problems involving compound measures and problem-solving contexts and communicate working clearly p2, p4

6 Trigonometry

6.1 Pythagoras’ theorem 6 outcomes
- C6.1.1 use and apply pythagoras’ theorem in routine mathematical contexts p1, p2, p3, p4
- C6.1.2 solve multi-step problems involving pythagoras’ theorem and communicate working clearly p1, p2, p3, p4
- C6.1.3 apply pythagoras’ theorem to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E6.1.1 extend and apply pythagoras’ theorem in routine mathematical contexts p2, p4
- E6.1.2 solve multi-step problems involving pythagoras’ theorem and communicate working clearly p2, p4
6.2 Right-angled triangle trigonometry 6 outcomes
- C6.2.1 use and apply right-angled triangle trigonometry in routine mathematical contexts p1, p2, p3, p4
- C6.2.2 solve multi-step problems involving right-angled triangle trigonometry and communicate working clearly p1, p2, p3, p4
- C6.2.3 apply right-angled triangle trigonometry to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E6.2.1 extend and apply right-angled triangle trigonometry in routine mathematical contexts p2, p4
- E6.2.2 solve multi-step problems involving right-angled triangle trigonometry and communicate working clearly p2, p4
6.3 Sine rule 6 outcomes
- C6.3.1 use the sine rule to find sides and angles p1, p2, p3, p4
- C6.3.2 solve ambiguous and contextual triangle problems using trigonometry p1, p2, p3, p4
- C6.3.3 apply sine rule to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E6.3.1 use the sine rule to find sides and angles p2, p4
- E6.3.2 solve ambiguous and contextual triangle problems using trigonometry p2, p4
6.4 Cosine rule 6 outcomes
- C6.4.1 use the cosine rule to find sides and angles p1, p2, p3, p4
- C6.4.2 solve contextual triangle problems using trigonometry p1, p2, p3, p4
- C6.4.3 apply cosine rule to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E6.4.1 use the cosine rule to find sides and angles p2, p4
- E6.4.2 solve contextual triangle problems using trigonometry p2, p4
6.5 Area of triangle using trigonometry 6 outcomes
- C6.5.1 use and apply area of triangle using trigonometry in routine mathematical contexts p1, p2, p3, p4
- C6.5.2 solve multi-step problems involving area of triangle using trigonometry and communicate working clearly p1, p2, p3, p4
- C6.5.3 apply area of triangle using trigonometry to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E6.5.1 extend and apply area of triangle using trigonometry in routine mathematical contexts p2, p4
- E6.5.2 solve multi-step problems involving area of triangle using trigonometry and communicate working clearly p2, p4
6.6 Three-dimensional trigonometry 6 outcomes
- C6.6.1 use and apply three-dimensional trigonometry in routine mathematical contexts p1, p2, p3, p4
- C6.6.2 solve multi-step problems involving three-dimensional trigonometry and communicate working clearly p1, p2, p3, p4
- C6.6.3 apply three-dimensional trigonometry to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E6.6.1 extend and apply three-dimensional trigonometry in routine mathematical contexts p2, p4
- E6.6.2 solve multi-step problems involving three-dimensional trigonometry and communicate working clearly p2, p4

7 Transformations and vectors

7.1 Reflections 6 outcomes
- C7.1.1 use and apply reflections in routine mathematical contexts p1, p2, p3, p4
- C7.1.2 solve multi-step problems involving reflections and communicate working clearly p1, p2, p3, p4
- C7.1.3 apply reflections to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E7.1.1 extend and apply reflections in routine mathematical contexts p2, p4
- E7.1.2 solve multi-step problems involving reflections and communicate working clearly p2, p4
7.2 Rotations 6 outcomes
- C7.2.1 use and apply rotations in routine mathematical contexts p1, p2, p3, p4
- C7.2.2 solve multi-step problems involving rotations and communicate working clearly p1, p2, p3, p4
- C7.2.3 apply rotations to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E7.2.1 extend and apply rotations in routine mathematical contexts p2, p4
- E7.2.2 solve multi-step problems involving rotations and communicate working clearly p2, p4
7.3 Translations 6 outcomes
- C7.3.1 use and apply translations in routine mathematical contexts p1, p2, p3, p4
- C7.3.2 solve multi-step problems involving translations and communicate working clearly p1, p2, p3, p4
- C7.3.3 apply translations to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E7.3.1 extend and apply translations in routine mathematical contexts p2, p4
- E7.3.2 solve multi-step problems involving translations and communicate working clearly p2, p4
7.4 Enlargements 6 outcomes
- C7.4.1 use and apply enlargements in routine mathematical contexts p1, p2, p3, p4
- C7.4.2 solve multi-step problems involving enlargements and communicate working clearly p1, p2, p3, p4
- C7.4.3 apply enlargements to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E7.4.1 extend and apply enlargements in routine mathematical contexts p2, p4
- E7.4.2 solve multi-step problems involving enlargements and communicate working clearly p2, p4
7.5 Combined transformations 6 outcomes
- C7.5.1 use and apply combined transformations in routine mathematical contexts p1, p2, p3, p4
- C7.5.2 solve multi-step problems involving combined transformations and communicate working clearly p1, p2, p3, p4
- C7.5.3 apply combined transformations to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E7.5.1 extend and apply combined transformations in routine mathematical contexts p2, p4
- E7.5.2 solve multi-step problems involving combined transformations and communicate working clearly p2, p4
7.6 Vectors 6 outcomes
- C7.6.1 use and apply vectors in routine mathematical contexts p1, p2, p3, p4
- C7.6.2 solve multi-step problems involving vectors and communicate working clearly p1, p2, p3, p4
- C7.6.3 apply vectors to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E7.6.1 extend and apply vectors in routine mathematical contexts p2, p4
- E7.6.2 solve multi-step problems involving vectors and communicate working clearly p2, p4
7.7 Vector geometry 6 outcomes
- C7.7.1 use and apply vector geometry in routine mathematical contexts p1, p2, p3, p4
- C7.7.2 solve multi-step problems involving vector geometry and communicate working clearly p1, p2, p3, p4
- C7.7.3 apply vector geometry to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E7.7.1 extend and apply vector geometry in routine mathematical contexts p2, p4
- E7.7.2 solve multi-step problems involving vector geometry and communicate working clearly p2, p4

8 Probability

8.1 Probability language and scale 6 outcomes
- C8.1.1 use and apply probability language and scale in routine mathematical contexts p1, p2, p3, p4
- C8.1.2 solve multi-step problems involving probability language and scale and communicate working clearly p1, p2, p3, p4
- C8.1.3 apply probability language and scale to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E8.1.1 extend and apply probability language and scale in routine mathematical contexts p2, p4
- E8.1.2 solve multi-step problems involving probability language and scale and communicate working clearly p2, p4
8.2 Single-event probability 6 outcomes
- C8.2.1 use and apply single-event probability in routine mathematical contexts p1, p2, p3, p4
- C8.2.2 solve multi-step problems involving single-event probability and communicate working clearly p1, p2, p3, p4
- C8.2.3 apply single-event probability to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E8.2.1 extend and apply single-event probability in routine mathematical contexts p2, p4
- E8.2.2 solve multi-step problems involving single-event probability and communicate working clearly p2, p4
8.3 Combined events 6 outcomes
- C8.3.1 use and apply combined events in routine mathematical contexts p1, p2, p3, p4
- C8.3.2 solve multi-step problems involving combined events and communicate working clearly p1, p2, p3, p4
- C8.3.3 apply combined events to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E8.3.1 extend and apply combined events in routine mathematical contexts p2, p4
- E8.3.2 solve multi-step problems involving combined events and communicate working clearly p2, p4
8.4 Relative frequency 6 outcomes
- C8.4.1 use and apply relative frequency in routine mathematical contexts p1, p2, p3, p4
- C8.4.2 solve multi-step problems involving relative frequency and communicate working clearly p1, p2, p3, p4
- C8.4.3 apply relative frequency to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E8.4.1 extend and apply relative frequency in routine mathematical contexts p2, p4
- E8.4.2 solve multi-step problems involving relative frequency and communicate working clearly p2, p4
8.5 Tree diagrams 6 outcomes
- C8.5.1 use and apply tree diagrams in routine mathematical contexts p1, p2, p3, p4
- C8.5.2 solve multi-step problems involving tree diagrams and communicate working clearly p1, p2, p3, p4
- C8.5.3 apply tree diagrams to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E8.5.1 extend and apply tree diagrams in routine mathematical contexts p2, p4
- E8.5.2 solve multi-step problems involving tree diagrams and communicate working clearly p2, p4
8.6 Venn diagrams and sets in probability 6 outcomes
- C8.6.1 use and apply venn diagrams and sets in probability in routine mathematical contexts p1, p2, p3, p4
- C8.6.2 solve multi-step problems involving venn diagrams and sets in probability and communicate working clearly p1, p2, p3, p4
- C8.6.3 apply venn diagrams and sets in probability to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E8.6.1 extend and apply venn diagrams and sets in probability in routine mathematical contexts p2, p4
- E8.6.2 solve multi-step problems involving venn diagrams and sets in probability and communicate working clearly p2, p4

9 Statistics

9.1 Classifying statistical data 6 outcomes
- C9.1.1 use and apply classifying statistical data in routine mathematical contexts p1, p2, p3, p4
- C9.1.2 solve multi-step problems involving classifying statistical data and communicate working clearly p1, p2, p3, p4
- C9.1.3 apply classifying statistical data to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E9.1.1 extend and apply classifying statistical data in routine mathematical contexts p2, p4
- E9.1.2 solve multi-step problems involving classifying statistical data and communicate working clearly p2, p4
9.2 Interpreting statistical data 6 outcomes
- C9.2.1 use and apply interpreting statistical data in routine mathematical contexts p1, p2, p3, p4
- C9.2.2 solve multi-step problems involving interpreting statistical data and communicate working clearly p1, p2, p3, p4
- C9.2.3 apply interpreting statistical data to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E9.2.1 extend and apply interpreting statistical data in routine mathematical contexts p2, p4
- E9.2.2 solve multi-step problems involving interpreting statistical data and communicate working clearly p2, p4
9.3 Averages and range / measures of spread 6 outcomes
- C9.3.1 use and apply averages and range / measures of spread in routine mathematical contexts p1, p2, p3, p4
- C9.3.2 solve multi-step problems involving averages and range / measures of spread and communicate working clearly p1, p2, p3, p4
- C9.3.3 apply averages and range / measures of spread to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E9.3.1 extend and apply averages and range / measures of spread in routine mathematical contexts p2, p4
- E9.3.2 solve multi-step problems involving averages and range / measures of spread and communicate working clearly p2, p4
9.4 Statistical charts and diagrams 6 outcomes
- C9.4.1 use and apply statistical charts and diagrams in routine mathematical contexts p1, p2, p3, p4
- C9.4.2 solve multi-step problems involving statistical charts and diagrams and communicate working clearly p1, p2, p3, p4
- C9.4.3 apply statistical charts and diagrams to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E9.4.1 extend and apply statistical charts and diagrams in routine mathematical contexts p2, p4
- E9.4.2 solve multi-step problems involving statistical charts and diagrams and communicate working clearly p2, p4
9.5 Scatter diagrams 6 outcomes
- C9.5.1 use and apply scatter diagrams in routine mathematical contexts p1, p2, p3, p4
- C9.5.2 solve multi-step problems involving scatter diagrams and communicate working clearly p1, p2, p3, p4
- C9.5.3 apply scatter diagrams to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E9.5.1 extend and apply scatter diagrams in routine mathematical contexts p2, p4
- E9.5.2 solve multi-step problems involving scatter diagrams and communicate working clearly p2, p4
9.6 Cumulative frequency diagrams 6 outcomes
- C9.6.1 draw and interpret cumulative frequency diagrams p1, p2, p3, p4
- C9.6.2 estimate median, quartiles and interquartile range p1, p2, p3, p4
- C9.6.3 apply cumulative frequency diagrams to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E9.6.1 draw and interpret cumulative frequency diagrams p2, p4
- E9.6.2 estimate median, quartiles and interquartile range p2, p4
9.7 Histograms 6 outcomes
- C9.7.1 draw and interpret histograms with unequal class widths p1, p2, p3, p4
- C9.7.2 use frequency density to calculate frequencies and compare distributions p1, p2, p3, p4
- C9.7.3 apply histograms to structured Cambridge IGCSE Mathematics problems p1, p2, p3, p4
- E9.7.1 draw and interpret histograms with unequal class widths p2, p4
- E9.7.2 use frequency density to calculate accurately frequencies and compare distributions p2, p4

Type	Title	URL	Confidence
official_syllabus Official source	Cambridge IGCSE Mathematics 0580 syllabus for examination in 2025, 2026 and 2027	https://www.cambridgeinternational.org/Images/6624...	official_component_structure
official_subject_page	Cambridge IGCSE Mathematics 0580 subject page	https://www.cambridgeinternational.org/programmes-...	official_subject_page
official_syllabus_update	Cambridge IGCSE Mathematics 0580 2025-2027 syllabus update	https://www.cambridgeinternational.org/Images/7097...	official_update_notice
official_past_paper	Official Cambridge past paper sample: 569920 June 2024 Mark Scheme Paper 21		official_past_paper_sample
official_past_paper	Official Cambridge past paper sample: 569924 June 2024 Question Paper 21		official_past_paper_sample
official_past_paper	Official Cambridge past paper sample: 663664 2025 Specimen Paper 2		official_past_paper_sample
official_past_paper	Official Cambridge past paper sample: 663672 2025 Specimen Paper 2 Mark Scheme		official_past_paper_sample
official_past_paper	Official Cambridge past paper sample: 671437 June 2024 Mark Scheme Paper 41		official_past_paper_sample
official_past_paper	Official Cambridge past paper sample: 671439 June 2024 Question Paper 41		official_past_paper_sample

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Syllabus Content

1 Number

2 Algebra and graphs

3 Coordinate geometry

4 Geometry

5 Mensuration

6 Trigonometry

7 Transformations and vectors

8 Probability

9 Statistics

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