Cambridge IGCSE Mathematics 0580 PDF Syllabus 2025-2027

Syllabus Cambridge IGCSE™ Mathematics 0580 Use this syllabus for exams in 2025, 2026 and 2027. Exams are available in the June and November series. Exams are also available in the March series in India. Version 3 For the purposes of screen readers, any mention in this docum...

Syllabus Cambridge IGCSE™ Mathematics 0580 Use this syllabus for exams in 2025, 2026 and 2027. Exams are available in the June and November series. Exams are also available in the March series in India. Version 3 For the purposes of screen readers, any mention in this document of Cambridge IGCSE refers to Cambridge International General Certificate of Secondary Education. Why choose Cambridge International? Cambridge International prepares school students for life, helping them develop an informed curiosity and a lasting passion for learning. We are part of Cambridge University Press & Assessment, which is a department of the University of Cambridge. Our Cambridge Pathway gives students a clear path for educational success from age 5 to 19. Schools can shape the curriculum around how they want students to learn – with a wide range of subjects and flexible ways to offer them. It helps students discover new abilities and a wider world, and gives them the skills they need for life, so they can achieve at school, university and work. Our programmes and qualifications set the global standard for international education. They are created by subject experts, rooted in academic rigour and reflect the latest educational research. They provide a strong platform for learners to progress from one stage to the next, and are well supported by teaching and learning resources. Our mission is to provide educational benefit through provision of international programmes and qualifications for school education and to be the world leader in this field. Together with schools, we develop Cambridge learners who are confident, responsible, reflective, innovative and engaged – equipped for success in the modern world. Every year, nearly a million Cambridge students from 10 000 schools in 160 countries prepare for their future with the Cambridge Pathway. School feedback: ‘We think the Cambridge curriculum is superb preparation for university.’ Feedback from: Christoph Guttentag, Dean of Undergraduate Admissions, Duke University, USA Quality management Cambridge International is committed to providing exceptional quality. In line with this commitment, our quality management system for the provision of international qualifications and education programmes for students aged 5 to 19 is independently certified as meeting the internationally recognised standard, ISO 9001:2015. Learn more at www.cambridgeinternational.org/ISO9001 © Cambridge University Press & Assessment September 2022 Cambridge Assessment International Education is part of Cambridge University Press & Assessment. Cambridge University Press & Assessment is a department of the University of Cambridge. Cambridge University Press & Assessment retains the copyright on all its publications. Registered centres are permitted to copy material from this booklet for their own internal use. However, we cannot give permission to centres to photocopy any material that is acknowledged to a third party even for internal use within a centre. Contents Why choose Cambridge International?......................................................................... 2 1 Why choose this syllabus?......................................................................................... 4 2 Syllabus overview........................................................................................................ 7 Aims 7 Content overview 8 Assessment overview 9 Assessment objectives 10 3 Subject content..........................................................................................................12 Core subject content 12 Extended subject content 32 4 Details of the assessment........................................................................................ 57 Core assessment 58 Extended assessment 59 List of formulas – Core (Paper 1 and Paper 3) 60 List of formulas – Extended (Paper 2 and Paper 4) 61 Mathematical conventions 62 Command words 64 5 What else you need to know.................................................................................... 65 Before you start 65 Making entries 66 Accessibility and equality 66 After the exam 67 How students and teachers can use the grades 67 Grade descriptions 67 Changes to this syllabus for 2025, 2026 and 2027 68 Important: Changes to this syllabus For information about changes to this syllabus for 2025, 2026 and 2027, go to page 68. The latest syllabus is version 3, published May 2024.  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. 1 Why choose this syllabus? Key benefits Cambridge IGCSE is the world’s most popular international qualification for 14 to 16 year olds, although it can be taken by students of other ages. It is tried, tested and trusted. Students can choose from 70 subjects in any combination – it is taught by over 4500 schools in over 140 countries. Cambridge Our programmes balance a thorough knowledge and learner understanding of a subject and help to develop the skills learners need for their next steps in education or employment. Cambridge IGCSE Mathematics supports learners in building competency, confidence and fluency in their use of techniques and mathematical understanding. Learners develop a feel for quantity, patterns and relationships, as well as developing reasoning, problem-solving and analytical skills in a variety of abstract and real-life contexts. Cambridge IGCSE Mathematics provides a strong foundation of mathematical knowledge both for candidates studying mathematics at a higher level and those who will require mathematics to support skills in other subjects. The course is tiered to allow all candidates to achieve and progress in their mathematical studies. Our approach in Cambridge IGCSE Mathematics encourages learners to be: confident, in using mathematical language and techniques to ask questions, explore ideas and communicate responsible, by taking ownership of their learning, and applying their mathematical knowledge and skills so that they can reason, problem solve and work collaboratively reflective, by making connections within mathematics and across other subjects, and in evaluating methods and checking solutions innovative, by applying their knowledge and understanding to solve unfamiliar problems creatively, flexibly and efficiently engaged, by the beauty, patterns and structure of mathematics, becoming curious to learn about its many applications in society and the economy. School feedback: ‘The strength of Cambridge IGCSE qualifications is internationally recognised and has provided an international pathway for our students to continue their studies around the world.’ Feedback from: Gary Tan, Head of Schools and CEO, Raffles International Group of Schools, Indonesia Back to contents page www.cambridgeinternational.org/igcse 4  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Why choose this syllabus? International recognition and acceptance Our expertise in curriculum, teaching and learning, and assessment is the basis for the recognition of our programmes and qualifications around the world. The combination of knowledge and skills in Cambridge IGCSE Mathematics gives learners a solid foundation for further study. Candidates who achieve grades A* to C are well prepared to follow a wide range of courses including Cambridge International AS & A Level Mathematics. Cambridge IGCSEs are accepted and valued by leading universities and employers around the world as evidence of academic achievement. Many universities require a combination of Cambridge International AS & A Levels and Cambridge IGCSEs or equivalent to meet their entry requirements. UK NARIC*, the national agency in the UK for the recognition and comparison of international qualifications and skills, has carried out an independent benchmarking study of Cambridge IGCSE and found it to be comparable to the standard of the GCSE in the UK. This means students can be confident that their Cambridge IGCSE qualifications are accepted as equivalent to UK GCSEs by leading universities worldwide. * Due to the United Kingdom leaving the European Union, the UK NARIC national recognition agency function was re-titled as UK ENIC on 1 March 2021, operated and managed by Ecctis Limited. From 1 March 2021, international benchmarking findings are published under the Ecctis name. Learn more at www.cambridgeinternational.org/recognition School feedback: ‘Cambridge IGCSE is one of the most sought-after and recognised qualifications in the world. It is very popular in Egypt because it provides the perfect preparation for success at advanced level programmes.’ Feedback from: Managing Director of British School of Egypt BSE Back to contents page www.cambridgeinternational.org/igcse 5  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Why choose this syllabus? Supporting teachers We provide a wide range of resources, detailed guidance, innovative training and professional development so that you can give your students the best possible preparation for Cambridge IGCSE. To find out which resources are available for each syllabus go to our School Support Hub. The School Support Hub is our secure online site for Cambridge teachers where you can find the resources you need to deliver our programmes. You can also keep up to date with your subject and the global Cambridge community through our online discussion forums. Find out more at www.cambridgeinternational.org/support Support for Cambridge IGCSE Planning and Teaching and Learning and revision Results preparation assessment Example candidate Candidate Results Schemes of work Endorsed resources responses Service Specimen papers Online forums Past papers and Principal examiner Syllabuses Support for mark schemes reports for teachers Teacher guides coursework and Specimen paper Results Analysis speaking tests answers Sign up for email notifications about changes to syllabuses, including new and revised products and services at www.cambridgeinternational.org/syllabusupdates Professional development We support teachers through: Introductory Training – face-to-face or online Extension Training – face-to-face or online Enrichment Professional Development – face-to-face or online Find out more at www.cambridgeinternational.org/events Cambridge Professional Development Qualifications Find out more at www.cambridgeinternational.org/profdev Supporting exams officers We provide comprehensive support and guidance for all Cambridge exams officers. Find out more at: www.cambridgeinternational.org/eoguide Back to contents page www.cambridgeinternational.org/igcse 6  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. 2 Syllabus overview Aims The aims describe the purposes of a course based on this syllabus. The aims are to enable students to: develop a positive attitude towards mathematics in a way that encourages enjoyment, establishes confidence and promotes enquiry and further learning develop a feel for number and understand the significance of the results obtained apply their mathematical knowledge and skills to their own lives and the world around them use creativity and resilience to analyse and solve problems communicate mathematics clearly develop the ability to reason logically, make inferences and draw conclusions develop fluency so that they can appreciate the interdependence of, and connections between, different areas of mathematics acquire a foundation for further study in mathematics and other subjects. Cambridge Assessment International Education is an education organisation and politically neutral. The contents of this syllabus, examination papers and associated materials do not endorse any political view. We endeavour to treat all aspects of the exam process neutrally. Back to contents page www.cambridgeinternational.org/igcse 7  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Syllabus overview Content overview All candidates study the following topics: 1 Number 2 Algebra and graphs 3 Coordinate geometry 4 Geometry 5 Mensuration 6 Trigonometry 7 Transformations and vectors 8 Probability 9 Statistics Cambridge IGCSE Mathematics is tiered to enable effective differentiation for learners. The Core subject content is intended for learners targeting grades C–G, and the Extended subject content is intended for learners targeting grades A*–C. The Extended subject content contains the Core subject content as well as additional content. The subject content is organised by topic and is not presented in a teaching order. This content structure and the use of tiering allows flexibility for teachers to plan delivery in a way that is appropriate for their learners. Learners are expected to use techniques listed in the content and apply them to solve problems with or without the use of a calculator, as appropriate. Back to contents page www.cambridgeinternational.org/igcse 8  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Syllabus overview Assessment overview All candidates take two components. Candidates who have studied the Core subject content, or who are expected to achieve a grade D or below, should be entered for Paper 1 and Paper 3. These candidates will be eligible for grades C to G. Candidates who have studied the Extended subject content, and who are expected to achieve a grade C or above, should be entered for Paper 2 and Paper 4. These candidates will be eligible for grades A* to E. Candidates should have a scientific calculator for Paper 3 and Paper 4. Calculators are not allowed for Paper 1 and Paper 2. Please see the Cambridge Handbook at www.cambridgeinternational.org/eoguide for guidance on use of calculators in the examinations. Core assessment Core candidates take Paper 1 and Paper 3. The questions are based on the Core subject content only: Paper 1: Non-calculator (Core) Paper 3: Calculator (Core) 1 hour 30 minutes 1 hour 30 minutes 80 marks 50% 80 marks 50% Structured and unstructured questions Structured and unstructured questions Use of a calculator is not allowed A scientific calculator is required Externally assessed Externally assessed Extended assessment Extended candidates take Paper 2 and Paper 4. The questions are based on the Extended subject content only: Paper 2: Non-calculator (Extended) Paper 4: Calculator (Extended) 2 hours 2 hours 100 marks 50% 100 marks 50% Structured and unstructured questions Structured and unstructured questions Use of a calculator is not allowed A scientific calculator is required Externally assessed Externally assessed Information on availability is in the Before you start section. Back to contents page www.cambridgeinternational.org/igcse 9  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Syllabus overview Assessment objectives The assessment objectives (AOs) are: AO1 Knowledge and understanding of mathematical techniques Candidates should be able to: recall and apply mathematical knowledge and techniques carry out routine procedures in mathematical and everyday situations understand and use mathematical notation and terminology perform calculations with and without a calculator organise, process, present and understand information in written form, tables, graphs and diagrams estimate, approximate and work to degrees of accuracy appropriate to the context and convert between equivalent numerical forms understand and use measurement systems in everyday use measure and draw using geometrical instruments to an appropriate degree of accuracy recognise and use spatial relationships in two and three dimensions. AO2 Analyse, interpret and communicate mathematically Candidates should be able to: analyse a problem and identify a suitable strategy to solve it, including using a combination of processes where appropriate make connections between different areas of mathematics recognise patterns in a variety of situations and make and justify generalisations make logical inferences and draw conclusions from mathematical data or results communicate methods and results in a clear and logical form interpret information in different forms and change from one form of representation to another. Back to contents page www.cambridgeinternational.org/igcse 10  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Syllabus overview Weighting for assessment objectives The approximate weightings allocated to each of the assessment objectives (AOs) are summarised below. Assessment objectives as a percentage of the Core qualification Assessment objective Weighting in IGCSE % AO1 Knowledge and understanding of mathematical techniques 60–70 AO2 Analyse, interpret and communicate mathematically 30–40 Total 100 Assessment objectives as a percentage of the Extended qualification Assessment objective Weighting in IGCSE % AO1 Knowledge and understanding of mathematical techniques 40–50 AO2 Analyse, interpret and communicate mathematically 50–60 Total 100 Assessment objectives as a percentage of each component Assessment objective Weighting in components % Paper 1 Paper 2 Paper 3 Paper 4 AO1 Knowledge and understanding of mathematical 60–70 40–50 60–70 40–50 techniques AO2 Analyse, interpret and communicate mathematically 30–40 50–60 30–40 50–60 Total 100 100 100 100 Back to contents page www.cambridgeinternational.org/igcse 11  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. 3 Subject content This syllabus gives you the flexibility to design a course that will interest, challenge and engage your learners. Where appropriate you are responsible for selecting resources and examples to support your learners’ study. These should be appropriate for the learners’ age, cultural background and learning context as well as complying with your school policies and local legal requirements. Learners should pursue an integrated course that allows them to fully develop their skills and understanding both with and without the use of a calculator. Candidates study either the Core subject content or the Extended subject content. Candidates aiming for grades A* to C should study the Extended subject content. A List of formulas is provided on page 2 of the examination papers for candidates to refer to during the examinations. Please note that not all required formulas are given; the ‘Notes and examples’ column of the subject content will indicate where a formula is given in the examination papers and when a formula is not given, i.e. knowledge of a formula is required. Core subject content 1 Number C1.1 Types of number Notes and examples Identify and use: Example tasks include: natural numbers convert between numbers and words, e.g. integers (positive, zero and negative) six billion is 6 000 000 000 10 007 is ten thousand and seven prime numbers express 72 as a product of its prime factors square numbers find the highest common factor (HCF) of two cube numbers numbers common factors find the lowest common multiple (LCM) of two common multiples numbers. rational and irrational numbers reciprocals. Back to contents page www.cambridgeinternational.org/igcse 12  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 1 Number (continued) C1.2 Sets Notes and examples Understand and use set language, notation and Venn diagrams are limited to two sets. Venn diagrams to describe sets. The following set notation will be used: n(A) Number of elements in set A A′ Complement of set A Universal set A∪B Union of A and B A∩B Intersection of A and B. Example definition of sets: A = {x: x is a natural number} B = {a, b, c, …} C = {x: a ⩽ x ⩽ b}. C1.3 Powers and roots Notes and examples Calculate with the following: Includes recall of squares and their corresponding squares roots from 1 to 15, and recall of cubes and their corresponding roots of 1, 2, 3, 4, 5 and 10, e.g.: square roots Write down the value of 169. cubes 3 2 Work out 5 # 8. cube roots other powers and roots of numbers. C1.4 Fractions, decimals and percentages Notes and examples 1 Use the language and notation of the following in Candidates are expected to be able to write appropriate contexts: fractions in their simplest form. proper fractions Candidates are not expected to use recurring improper fractions decimal notation. mixed numbers decimals percentages. 2 Recognise equivalence and convert between Candidates are not expected to demonstrate the these forms. conversion of a recurring decimal to a fraction and vice versa. C1.5 Ordering Notes and examples Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, >, < , ⩾ and ⩽. Back to contents page www.cambridgeinternational.org/igcse 13  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 1 Number (continued) C1.6 The four operations Notes and examples Use the four operations for calculations with Includes: integers, fractions and decimals, including correct negative numbers ordering of operations and use of brackets. improper fractions mixed numbers practical situations, e.g. temperature changes. C1.7 Indices I Notes and examples 1 Understand and use indices (positive, zero and e.g. find the value of 7 –2. negative integers). 2 Understand and use the rules of indices. e.g. find the value of 2–3 × 24, (23)2, 23 ÷ 24. C1.8 Standard form Notes and examples 1 Use the standard form A × 10n where n is a positive or negative integer and 1 ⩽ A < 10. 2 Convert numbers into and out of standard form. 3 Calculate with values in standard form. Core candidates are expected to calculate with standard form only on Paper 3. C1.9 Estimation Notes and examples 1 Round values to a specified degree of accuracy. Includes decimal places and significant figures. 2 Make estimates for calculations involving e.g. write 5764 correct to the nearest thousand. numbers, quantities and measurements. e.g. by writing each number correct to 1 significant 41.3 3 Round answers to a reasonable degree of figure, estimate the value of. 9.79 # 0.765 accuracy in the context of a given problem. C1.10 Limits of accuracy Notes and examples Give upper and lower bounds for data rounded to a e.g. write down the upper bound of a length specified accuracy. measured correct to the nearest metre. Candidates are not expected to find the bounds of the results of calculations which have used data rounded to a specified accuracy. Back to contents page www.cambridgeinternational.org/igcse 14  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 1 Number (continued) C1.11 Ratio and proportion Notes and examples Understand and use ratio and proportion to: give ratios in their simplest form e.g. 20 : 30 : 40 in its simplest form is 2 : 3 : 4. divide a quantity in a given ratio use proportional reasoning and ratios in e.g. adapt recipes; use map scales; determine best context. value. C1.12 Rates Notes and examples 1 Use common measures of rate. e.g. calculate with: hourly rates of pay exchange rates between currencies flow rates fuel consumption. 2 Apply other measures of rate. e.g. calculate with: pressure density population density. Required formulas will be given in the question. 3 Solve problems involving average speed. Knowledge of speed/distance/time formula is required. e.g. A cyclist travels 45 km in 3 hours 45 minutes. What is their average speed? Notation used will be, e.g. m/s (metres per second), g/cm3 (grams per cubic centimetre). C1.13 Percentages Notes and examples 1 Calculate a given percentage of a quantity. 2 Express one quantity as a percentage of another. 3 Calculate percentage increase or decrease. 4 Calculate with simple and compound interest. Formulas are not given. Percentage calculations may include: deposit discount profit and loss (as an amount or a percentage) earnings percentages over 100%. Back to contents page www.cambridgeinternational.org/igcse 15  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 1 Number (continued) C1.14 Using a calculator Notes and examples 1 Use a calculator efficiently. e.g. know not to round values within a calculation and to only round the final answer. 2 Enter values appropriately on a calculator. e.g. enter 2 hours 30 minutes as 2.5 hours or 2° 30’ 0’’. 3 Interpret the calculator display appropriately. e.g. in money 4.8 means $4.80; in time 3.25 means 3 hours 15 minutes. C1.15 Time Notes and examples 1 Calculate with time: seconds (s), minutes (min), 1 year = 365 days. hours (h), days, weeks, months, years, including the relationship between units. 2 Calculate times in terms of the 24-hour and In the 24-hour clock, for example, 3.15 a.m. will be 12-hour clock. denoted by 03 15 and 3.15 p.m. by 15 15. 3 Read clocks and timetables. Includes problems involving time zones, local times and time differences. C1.16 Money Notes and examples 1 Calculate with money. 2 Convert from one currency to another. C1.17 Extended content only. C1.18 Extended content only. Back to contents page www.cambridgeinternational.org/igcse 16  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 2 Algebra and graphs C2.1 Introduction to algebra Notes and examples 1 Know that letters can be used to represent generalised numbers. 2 Substitute numbers into expressions and formulas. C2.2 Algebraic manipulation Notes and examples 1 Simplify expressions by collecting like terms. Simplify means give the answer in its simplest form, e.g. 2a + 3b + 5a – 9b = 7a – 6b. 2 Expand products of algebraic expressions. e.g. expand 3x(2x – 4y). Includes products of two brackets involving one variable, e.g. expand (2x + 1)(x – 4). 3 Factorise by extracting common factors. Factorise means factorise fully, e.g. 9x2 + 15xy = 3x(3x + 5y). C2.3 Extended content only. C2.4 Indices II Notes and examples 1 Understand and use indices (positive, zero and e.g. 2x = 32. Find the value of x. negative). 2 Understand and use the rules of indices. e.g. simplify: (5x 3) 2 12a 5 ÷ 3a –2 6x 7y 4 × 5x –5y. Knowledge of logarithms is not required. C2.5 Equations Notes and examples 1 Construct simple expressions, equations and e.g. write an expression for a number that is 2 more formulas. than n. Includes constructing linear simultaneous equations. 2 Solve linear equations in one unknown. Examples include: 3 Solve simultaneous linear equations in two 3x + 4 = 10 unknowns. 5 – 2x = 3(x + 7). 4 Change the subject of simple formulas. e.g. change the subject of formulas where: the subject only appears once there is not a power or root of the subject. Back to contents page www.cambridgeinternational.org/igcse 17  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 2 Algebra and graphs (continued) C2.6 Inequalities Notes and examples Represent and interpret inequalities, including on a When representing and interpreting inequalities on number line. a number line: open circles should be used to represent strict inequalities () closed circles should be used to represent inclusive inequalities (⩽, ⩾) e.g. – 3 ⩽ x < 1 x –3 –2 –1 0 1 C2.7 Sequences Notes and examples 1 Continue a given number sequence or pattern. e.g. write the next two terms in this sequence: 1, 3, 6, 10, 15, … , … 2 Recognise patterns in sequences, including the term-to-term rule, and relationships between different sequences. 3 Find and use the nth term of the following sequences: (a) linear (b) simple quadratic e.g. find the nth term of 2, 5, 10, 17 (c) simple cubic. C2.8 Extended content only. C2.9 Graphs in practical situations Notes and examples 1 Use and interpret graphs in practical situations e.g. interpret the gradient of a straight-line graph as including travel graphs and conversion graphs. a rate of change. 2 Draw graphs from given data. e.g. draw a distance–time graph to represent a journey. Back to contents page www.cambridgeinternational.org/igcse 18  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 2 Algebra and graphs (continued) C2.10 Graphs of functions Notes and examples 1 Construct tables of values, and draw, recognise and interpret graphs for functions of the following forms: ax + b ± x2 + ax + b a x (x ≠ 0) where a and b are integer constants. 2 Solve associated equations graphically, including e.g. find the intersection of a line and a curve. finding and interpreting roots by graphical methods. C2.11 Sketching curves Notes and examples Recognise, sketch and interpret graphs of the following functions: (a) linear (b) quadratic. Knowledge of symmetry and roots is required. Knowledge of turning points is not required. C2.12 Extended content only. C2.13 Extended content only. Back to contents page www.cambridgeinternational.org/igcse 19  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 3 Coordinate geometry C3.1 Coordinates Notes and examples Use and interpret Cartesian coordinates in two dimensions. C3.2 Drawing linear graphs Notes and examples Draw straight-line graphs for linear equations. Equations will be given in the form y = mx + c (e.g. y = –2x + 5), unless a table of values is given. C3.3 Gradient of linear graphs Notes and examples Find the gradient of a straight line. From a grid only. C3.4 Extended content only. C3.5 Equations of linear graphs Notes and examples Interpret and obtain the equation of a straight-line Questions may: graph in the form y = mx + c. use and request lines in the forms y = mx + c x=k involve finding the equation when the graph is given ask for the gradient or y-intercept of a graph from an equation, e.g. find the gradient and y-intercept of the graph with the equation y = 6x + 3. Candidates are expected to give equations of a line in a fully simplified form. C3.6 Parallel lines Notes and examples Find the gradient and equation of a straight line e.g. find the equation of the line parallel to parallel to a given line. y = 4x – 1 that passes through (1, –3). C3.7 Extended content only. Back to contents page www.cambridgeinternational.org/igcse 20  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 4 Geometry C4.1 Geometrical terms Notes and examples 1 Use and interpret the following geometrical Candidates are not expected to show that two terms: shapes are congruent. point vertex line parallel perpendicular bearing right angle acute, obtuse and reflex angles interior and exterior angles similar congruent scale factor. 2 Use and interpret the vocabulary of: Includes the following terms: triangles Triangles: special quadrilaterals equilateral polygons isosceles nets scalene simple solids. right-angled. Quadrilaterals: square rectangle kite rhombus parallelogram trapezium. Polygons: regular and irregular polygons pentagon hexagon octagon decagon. continued Back to contents page www.cambridgeinternational.org/igcse 21  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 4 Geometry (continued) C4.1 Geometrical terms (continued) Notes and examples Simple solids: cube cuboid prism cylinder pyramid cone sphere (term ‘hemisphere’ not required) face surface edge. 3 Use and interpret the vocabulary of a circle. Includes the following terms: centre radius (plural radii) diameter circumference semicircle chord tangent arc sector segment. C4.2 Geometrical constructions Notes and examples 1 Measure and draw lines and angles. A ruler should be used for all straight edges. Constructions of perpendicular bisectors and angle bisectors are not required. 2 Construct a triangle, given the lengths of all e.g. construct a rhombus by drawing two triangles. sides, using a ruler and pair of compasses only. Construction arcs must be shown. 3 Draw, use and interpret nets. Examples include: draw nets of cubes, cuboids, prisms and pyramids use measurements from nets to calculate volumes and surface areas. Back to contents page www.cambridgeinternational.org/igcse 22  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 4 Geometry (continued) C4.3 Scale drawings Notes and examples 1 Draw and interpret scale drawings. A ruler must be used for all straight edges. 2 Use and interpret three-figure bearings. Bearings are measured clockwise from north (000° to 360°). e.g. find the bearing of A from B if the bearing of B from A is 025°. Includes an understanding of the terms north, east, south and west. e.g. point D is due east of point C. C4.4 Similarity Notes and examples Calculate lengths of similar shapes. C4.5 Symmetry Notes and examples Recognise line symmetry and order of rotational Includes properties of triangles, quadrilaterals and symmetry in two dimensions. polygons directly related to their symmetries. C4.6 Angles Notes and examples 1 Calculate unknown angles and give simple Knowledge of three-letter notation for angles is explanations using the following geometrical required, e.g. angle ABC. Candidates are expected properties: to use the correct geometrical terminology when sum of angles at a point = 360° giving reasons for answers. sum of angles at a point on a straight line = 180° vertically opposite angles are equal angle sum of a triangle = 180° and angle sum of a quadrilateral = 360°. 2 Calculate unknown angles and give geometric explanations for angles formed within parallel lines: corresponding angles are equal alternate angles are equal co-interior angles sum to 180° (supplementary). 3 Know and use angle properties of regular Includes exterior and interior angles, and angle polygons. sum. Back to contents page www.cambridgeinternational.org/igcse 23  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 4 Geometry (continued) C4.7 Circle theorems Notes and examples Calculate unknown angles and give explanations Candidates will be expected to use the geometrical using the following geometrical properties of circles: properties listed in the syllabus when giving angle in a semicircle = 90° reasons for answers. angle between tangent and radius = 90°. C4.8 Extended content only. Back to contents page www.cambridgeinternational.org/igcse 24  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 5 Mensuration C5.1 Units of measure Notes and examples Use metric units of mass, length, area, volume Units include: and capacity in practical situations and convert mm, cm, m, km quantities into larger or smaller units. mm2, cm2, m2, km2 mm3, cm3, m3 ml, l g, kg. Conversion between units includes: between different units of area, e.g. cm2 ↔ m2 between units of volume and capacity, e.g. m3 ↔ litres. C5.2 Area and perimeter Notes and examples Carry out calculations involving the perimeter and Except for area of a triangle, formulas are not area of a rectangle, triangle, parallelogram and given. trapezium. C5.3 Circles, arcs and sectors Notes and examples 1 Carry out calculations involving the Answers may be asked for in terms of π. circumference and area of a circle. Formulas are given in the List of formulas. 2 Carry out calculations involving arc length and sector area as fractions of the circumference and area of a circle, where the sector angle is a factor of 360°. C5.4 Surface area and volume Notes and examples Carry out calculations and solve problems involving Answers may be asked for in terms of π. the surface area and volume of a: The following formulas are given in the List of cuboid formulas: prism curved surface area of a cylinder cylinder curved surface area of a cone sphere surface area of a sphere pyramid volume of a prism cone. volume of a pyramid volume of a cylinder volume of a cone volume of a sphere. The term prism refers to any solid with a uniform cross-section, e.g. a cylindrical sector. Back to contents page www.cambridgeinternational.org/igcse 25  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 5 Mensuration (continued) C5.5 Compound shapes and parts of shapes Notes and examples 1 Carry out calculations and solve problems Answers may be asked for in terms of π. involving perimeters and areas of: compound shapes parts of shapes. 2 Carry out calculations and solve problems involving surface areas and volumes of: compound solids parts of solids. e.g. find the volume of half of a sphere. Back to contents page www.cambridgeinternational.org/igcse 26  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 6 Trigonometry C6.1 Pythagoras’ theorem Notes and examples Know and use Pythagoras’ theorem. C6.2 Right-angled triangles 1 Know and use the sine, cosine and tangent Angles will be given in degrees and answers should ratios for acute angles in calculations involving be written in degrees, with decimals correct to one sides and angles of a right-angled triangle. decimal place. 2 Solve problems in two dimensions using Knowledge of bearings may be required. Pythagoras’ theorem and trigonometry. C6.3 Extended content only. C6.4 Extended content only. C6.5 Extended content only. C6.6 Extended content only. Back to contents page www.cambridgeinternational.org/igcse 27  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 7 Transformations and vectors C7.1 Transformations Notes and examples Recognise, describe and draw the following Questions will not involve combinations of transformations: transformations. A ruler must be used for all straight 1 Reflection of a shape in a vertical or horizontal edges. line. 2 Rotation of a shape about the origin, vertices or midpoints of edges of the shape, through multiples of 90°. 3 Enlargement of a shape from a centre by a scale Positive and fractional scale factors only. factor. JN x 4 Translation of a shape by a vector KK OO. y LP C7.2 Extended content only. C7.3 Extended content only. C7.4 Extended content only. Back to contents page www.cambridgeinternational.org/igcse 28  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 8 Probability C8.1 Introduction to probability Notes and examples 1 Understand and use the probability scale from Probability notation is not required. 0 to 1. Probabilities should be given as a fraction, decimal or percentage. Problems may require using information from tables, graphs or Venn diagrams (limited to two sets). 2 Calculate the probability of a single event. 3 Understand that the probability of an event e.g. The probability that a counter is blue is 0.8. not occurring = 1 – the probability of the event What is the probability that it is not blue? occurring. C8.2 Relative and expected frequencies Notes and examples 1 Understand relative frequency as an estimate of e.g. use results of experiments with a spinner to probability. estimate the probability of a given outcome. 2 Calculate expected frequencies. e.g. use probability to estimate an expected value from a population. Includes understanding what is meant by fair, bias and random. C8.3 Probability of combined events Notes and examples Calculate the probability of combined events using, Combined events will only be with replacement. where appropriate: sample space diagrams Venn diagrams Venn diagrams will be limited to two sets. tree diagrams. In tree diagrams, outcomes will be written at the end of the branches and probabilities by the side of the branches. C8.4 Extended content only. Back to contents page www.cambridgeinternational.org/igcse 29  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 9 Statistics C9.1 Classifying statistical data Notes and examples Classify and tabulate statistical data. e.g. tally tables, two-way tables. C9.2 Interpreting statistical data Notes and examples 1 Read, interpret and draw inferences from tables and statistical diagrams. 2 Compare sets of data using tables, graphs and e.g. compare averages and ranges between two statistical measures. data sets. 3 Appreciate restrictions on drawing conclusions from given data. C9.3 Averages and range Notes and examples Calculate the mean, median, mode and range Data may be in a list or frequency table, but will not for individual data and distinguish between the be grouped. purposes for which these are used. C9.4 Statistical charts and diagrams Notes and examples Draw and interpret: (a) bar charts Includes composite (stacked) and dual (side-by- (b) pie charts side) bar charts. (c) pictograms (d) stem-and-leaf diagrams Stem-and-leaf diagrams should have ordered data with a key. (e) simple frequency distributions. Back to contents page www.cambridgeinternational.org/igcse 30  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 9 Statistics (continued) C9.5 Scatter diagrams Notes and examples 1 Draw and interpret scatter diagrams. Plotted points should be clearly marked, for example as small crosses (×). 2 Understand what is meant by positive, negative and zero correlation. 3 Draw by eye, interpret and use a straight line of A line of best fit: best fit. should be a single ruled line drawn by inspection should extend across the full data set does not need to coincide exactly with any of the points but there should be a roughly even distribution of points either side of the line over its entire length. C9.6 Extended content only. C9.7 Extended content only. Back to contents page www.cambridgeinternational.org/igcse 31  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content Extended subject content 1 Number E1.1 Types of number Notes and examples Identify and use: Example tasks include: natural numbers convert between numbers and words, e.g. integers (positive, zero and negative) six billion is 6 000 000 000 10 007 is ten thousand and seven prime numbers express 72 as a product of its prime factors square numbers find the highest common factor (HCF) of two cube numbers numbers common factors find the lowest common multiple (LCM) of two common multiples numbers. rational and irrational numbers reciprocals. E1.2 Sets Notes and examples Understand and use set language, notation and Venn diagrams are limited to two or three sets. Venn diagrams to describe sets and represent The following set notation will be used: relationships between sets. n(A) Number of elements in set A ∈ “… is an element of …” ∉ “… is not an element of …” A′ Complement of set A ∅ The empty set Universal set A⊆B A is a subset of B A⊈B A is not a subset of B A∪B Union of A and B A∩B Intersection of A and B. Example definition of sets: A = {x: x is a natural number} B = {(x, y): y = mx + c} C = {x: a ⩽ x ⩽ b} D = {a, b, c, …}. E1.3 Powers and roots Notes and examples Calculate with the following: Includes recall of squares and their corresponding squares roots from 1 to 15, and recall of cubes and their corresponding roots of 1, 2, 3, 4, 5 and 10, e.g.: square roots Write down the value of 169. cubes 3 2 Work out 5 # 8. cube roots other powers and roots of numbers. Back to contents page www.cambridgeinternational.org/igcse 32  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 1 Number (continued) E1.4 Fractions, decimals and percentages Notes and examples 1 Use the language and notation of the following in Candidates are expected to be able to write appropriate contexts: fractions in their simplest form. proper fractions Recurring decimal notation is required, e.g. improper fractions 0.17o = 0.1777f mixed numbers o o = 0.1232323f 0.123 decimals 0. 123 = 0.123123f percentages. 2 Recognise equivalence and convert between Includes converting between recurring decimals these forms. and fractions and vice versa, e.g. write 0.17o as a fraction. E1.5 Ordering Notes and examples Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, >, < , ⩾ and ⩽. E1.6 The four operations Notes and examples Use the four operations for calculations with Includes: integers, fractions and decimals, including correct negative numbers ordering of operations and use of brackets. improper fractions mixed numbers practical situations, e.g. temperature changes. E1.7 Indices I Notes and examples 1 Understand and use indices (positive, zero, Examples include: negative, and fractional). 1 62 = 6 1 4 16 4 = 16 find the value of 7 –2, 81 2 , 8 1 - 32. 2 Understand and use the rules of indices. e.g. find the value of 2–3 × 24, (23)2, 23 ÷ 24. E1.8 Standard form Notes and examples 1 Use the standard form A × 10n where n is a positive or negative integer and 1 ⩽ A < 10. 2 Convert numbers into and out of standard form. 3 Calculate with values in standard form. Back to contents page www.cambridgeinternational.org/igcse 33  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 1 Number (continued) E1.9 Estimation Notes and examples 1 Round values to a specified degree of accuracy. Includes decimal places and significant figures. 2 Make estimates for calculations involving e.g. write 5764 correct to the nearest thousand. numbers, quantities and measurements. e.g. by writing each number correct to 1 significant figure, estimate the value of 41.3. 3 Round answers to a reasonable degree of 9.79 # 0.765 accuracy in the context of a given problem. E1.10 Limits of accuracy Notes and examples 1 Give upper and lower bounds for data rounded e.g. write down the upper bound of a length to a specified accuracy. measured correct to the nearest metre. 2 Find upper and lower bounds of the results of Example calculations include: calculations which have used data rounded to a calculate the upper bound of the perimeter specified accuracy. or the area of a rectangle given dimensions measured to the nearest centimetre find the lower bound of the speed given rounded values of distance and time. E1.11 Ratio and proportion Notes and examples Understand and use ratio and proportion to: give ratios in their simplest form e.g. 20 : 30 : 40 in its simplest form is 2 : 3 : 4. divide a quantity in a given ratio use proportional reasoning and ratios in e.g. adapt recipes; use map scales; determine best context. value. Back to contents page www.cambridgeinternational.org/igcse 34  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 1 Number (continued) E1.12 Rates Notes and examples 1 Use common measures of rate. e.g. calculate with: hourly rates of pay exchange rates between currencies flow rates fuel consumption. 2 Apply other measures of rate. e.g. calculate with: pressure density population density. Required formulas will be given in the question. 3 Solve problems involving average speed. Knowledge of speed/distance/time formula is required. e.g. A cyclist travels 45 km in 3 hours 45 minutes. What is their average speed? Notation used will be, e.g. m/s (metres per second), g/cm3 (grams per cubic centimetre). E1.13 Percentages Notes and examples 1 Calculate a given percentage of a quantity. 2 Express one quantity as a percentage of another. 3 Calculate percentage increase or decrease. 4 Calculate with simple and compound interest. Problems may include repeated percentage change. Formulas are not given. 5 Calculate using reverse percentages. e.g. find the cost price given the selling price and the percentage profit. Percentage calculations may include: deposit discount profit and loss (as an amount or a percentage) earnings percentages over 100%. E1.14 Using a calculator Notes and examples 1 Use a calculator efficiently. e.g. know not to round values within a calculation and to only round the final answer. 2 Enter values appropriately on a calculator. e.g. enter 2 hours 30 minutes as 2.5 hours or 2° 30’ 0’’. 3 Interpret the calculator display appropriately. e.g. in money 4.8 means $4.80; in time 3.25 means 3 hours 15 minutes. Back to contents page www.cambridgeinternational.org/igcse 35  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 1 Number (continued) E1.15 Time Notes and examples 1 Calculate with time: seconds (s), minutes (min), 1 year = 365 days. hours (h), days, weeks, months, years, including the relationship between units. 2 Calculate times in terms of the 24-hour and In the 24-hour clock, for example, 3.15 a.m. will be 12-hour clock. denoted by 03 15 and 3.15 p.m. by 15 15. 3 Read clocks and timetables. Includes problems involving time zones, local times and time differences. E1.16 Money Notes and examples 1 Calculate with money. 2 Convert from one currency to another. E1.17 Exponential growth and decay Notes and examples Use exponential growth and decay. e.g. depreciation, population change. Knowledge of e is not required. E1.18 Surds Notes and examples 1 Understand and use surds, including simplifying Examples include: expressions. 20 = 2 5 200 − 32 = 6 2. 2 Rationalise the denominator. Examples include: 10 =2 5 5 1 1+ 3 =. −1 + 3 2 Back to contents page www.cambridgeinternational.org/igcse 36  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 2 Algebra and graphs E2.1 Introduction to algebra Notes and examples 1 Know that letters can be used to represent generalised numbers. 2 Substitute numbers into expressions and formulas. E2.2 Algebraic manipulation Notes and examples 1 Simplify expressions by collecting like terms. Simplify means give the answer in its simplest form, e.g. 2a2 + 3ab – 1 + 5a2 – 9ab + 4 = 7a2 – 6ab + 3. 2 Expand products of algebraic expressions. e.g. expand 3x(2x – 4y), (3x + y)(x – 4y). Includes products of more than two brackets, e.g. expand (x – 2)(x + 3)(2x + 1). 3 Factorise by extracting common factors. Factorise means factorise fully, e.g. 9x2 + 15xy = 3x(3x + 5y). 4 Factorise expressions of the form: ax + bx + kay + kby a2 x2 − b2y2 a2 + 2ab + b2 ax2 + bx + c ax3 + bx2 + cx. 5 Complete the square for expressions in the form ax2 + bx + c. E2.3 Algebraic fractions Notes and examples 1 Manipulate algebraic fractions. Examples include: x +x–4 3 2 2x – 3(x –5) 3 2 3a × 9a 4 10 3a ÷ 9a 4 10 1 +x+1. x–2 x–3 e.g. x2 – 2x. 2 Factorise and simplify rational expressions. x2 – 5x + 6 Back to contents page www.cambridgeinternational.org/igcse 37  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 2 Algebra and graphs (continued) E2.4 Indices II Notes and examples 1 Understand and use indices (positive, zero, e.g. solve: negative and fractional). 32x = 2 5x + 1 = 25x. 2 Understand and use the rules of indices. e.g. simplify: − 2 1 3x 4 # 3 x 2 2 12 ' − 2 5 x 2x J 5N3 2x KK OO. L3P Knowledge of logarithms is not required. E2.5 Equations Notes and examples 1 Construct expressions, equations and formulas. e.g. write an expression for the product of two consecutive even numbers. Includes constructing simultaneous equations. 2 Solve linear equations in one unknown. Examples include: 3x + 4 = 10 5 – 2x = 3(x + 7). 3 Solve fractional equations with numerical and Examples include: linear algebraic denominators. x =4 2x + 1 2 + 3 =1 x + 2 2x – 1 x = 3. x+2 x–6 4 Solve simultaneous linear equations in two unknowns. 5 Solve simultaneous equations, involving one With powers no higher than two. linear and one non-linear. 6 Solve quadratic equations by factorisation, Includes writing a quadratic expression in completing the square and by use of the completed square form. quadratic formula. Candidates may be expected to give solutions in surd form. The quadratic formula is given in the List of formulas. 7 Change the subject of formulas. e.g. change the subject of a formula where: the subject appears twice there is a power or root of the subject. Back to contents page www.cambridgeinternational.org/igcse 38  Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027. Subject content 2 Algebra and graphs (continued) E2.6 Inequalities Notes and examples 1 Represent and interpret inequalities, including on When representing and interpreting inequalities on a number line. a number line: open circles should be used to represent strict inequalities () closed circles should be used to represent inclusive inequalities (⩽, ⩾). e.g. – 3 ⩽ x < 1 x –3 –2 –1 0 1 2 Construct, solve and interpret linear inequalities. Examples include: 3x < 2x + 4 –3 ⩽ 3x – 2 < 7. 3 Represent and interpret linear inequalities in two The following conventions should be used: variables graphically. broken lines should be used to represent strict inequalities () solid lines should be used to represent inclusive inequalities (⩽, ⩾) shading should be used to represent unwanted regions (unless otherwise directed in the question). e.g. y x