IGCSE Mathematics (0580): The Complete Guide for Parents and Students
Based on the official Cambridge syllabus for 2025–2027 · Last reviewed July 2026
Everything you need to navigate the IGCSE Maths syllabus, Core vs Extended explained, every topic mapped out, and a clear exam strategy for Papers 2 and 4.
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Cambridge IGCSE Mathematics (0580) is one of the most widely taken qualifications in international education, and for most students in Malaysia it is a core subject that shapes their options for A-Level, IB and university. This guide explains everything a parent or student needs to know: what the course covers, the complete list of topics, how the exams work, the command words that decide marks, and how the qualification is graded.
Quick answer
IGCSE Mathematics (0580) is a tiered qualification: Core (grades C–G) or Extended (grades A*–E). Students sit two written papers, including a non-calculator paper since 2025. The course has nine topic areas covering Number through to Statistics. Exam marks are decided as much by technique, showing working, reading command words, as by content knowledge.
Overview
What is IGCSE Mathematics (0580)?
Cambridge IGCSE Mathematics (syllabus code 0580) is the standard international mathematics qualification for students aged roughly 14 to 16, usually studied over Years 10 and 11. It builds fluency in mathematical techniques and understanding, and develops the reasoning, problem-solving and analytical skills students need for further study and everyday life.
A few essentials:
Tiered
Students follow either Core (grades C–G) or Extended (grades A*–E). Extended includes everything in Core plus additional material.
Study time
Approximately 130 guided learning hours, typically over Years 10 and 11.
Recognition
Internationally recognised, benchmarked as comparable to the UK GCSE, and accepted by Malaysian universities and the Ministry of Education.
Exam series
Available in the June and November series (March in some regions).
Related syllabus
Cannot be taken in the same series as Cambridge IGCSE (9–1) Mathematics (0980), International Mathematics (0607) or O Level Mathematics (4024).
New to IGCSE grading?
Our companion guide, The IGCSE Grading System Explained, covers A*–G, grade thresholds and what each grade means for your child’s next step.
The Most Important Decision
Core or Extended? Choosing the right tier
This is one of the most consequential decisions a family makes, because it sets a ceiling on the possible grade.
Core tier
Essential content
CDEFG
Grades C to G only. A Core candidate cannot be awarded above a C.
Best for: students confident in the essentials, not planning A-Level Math.
Extended tier
Core + additional content
A*ABCDE
Grades A* to E. The route for students targeting top grades.
Best for: anyone planning A-Level, IB or Additional Math (0606).
As a rule of thumb, students targeting a grade C or above, and those planning to take IGCSE Additional Mathematics (0606) or A-Level Math, should follow the Extended tier. A short diagnostic is the most reliable way to decide, since entering the wrong tier is a common and avoidable reason for underachievement.
Ready for more challenge?
Strong Extended students often go on to IGCSE Additional Mathematics (0606), which introduces calculus and advanced algebra and is excellent preparation for IB DP and A-Level.
The Exams
Exam format
All candidates take two written papers, each counting for 50% of the final grade. Since 2025, each tier includes a non-calculator paper, so both written fluency and calculator skill matter.
Tier
Papers
Duration
Marks
Calculator
Grades
Core
Paper 1 + Paper 3
1 hr 30 min each
80 each
None (P1); scientific (P3)
C–G
Extended
Paper 2 + Paper 4
2 hours each
100 each
None (P2); scientific (P4)
A*–E
Key exam rules
Calculators: algebraic and graphical calculators are not permitted. A scientific calculator (with trigonometric functions) is required for Paper 3 and Paper 4.
Working: candidates write answers on the question paper and must show all necessary working in the spaces provided. Marks are awarded for method, not just the final answer.
Accuracy: non-exact answers should be given to three significant figures (or one decimal place for angles in degrees) unless stated otherwise. Use the full calculator value of π or 3.142, and do not round early in calculations.
Instruments needed: a ruler, pair of compasses and protractor. Tracing paper may be requested.
The formula list: what is given, and what is not
Each paper provides a formula list on page 2. Knowing what is not given is a genuine exam advantage.
Provided on both tiers
Extended only (additional)
Not provided, must be memorised
Area of triangle; area & circumference of circle; curved surface area of cylinder & cone; surface area of sphere; volumes of prism, pyramid, cylinder, cone & sphere
Quadratic formula; sine rule; cosine rule; area of triangle = ½ ab sin C
Area of rectangle, parallelogram & trapezium; Pythagoras’ theorem; percentage, interest, speed and density relationships
The Syllabus
The complete list of topics
Cambridge IGCSE Mathematics is organised into nine topics. All candidates study all nine; Extended students go deeper within each. Click any topic to see the full content.
All students cover
Types of number: natural numbers, integers, primes, square & cube numbers, HCF, LCM, rational & irrational numbers, reciprocals, prime factorisation
Sets: set language, notation and Venn diagrams
Powers and roots: squares, cubes and roots; recall of key values
Fractions, decimals and percentages: using and converting between all three
Ordering: using =, ≠, >, <, ≥ and ≤
The four operations with integers, fractions and decimals, including negative numbers and order of operations
Indices: positive, zero and negative integer indices and the rules of indices
Standard form: writing, converting and calculating
Estimation and limits of accuracy: rounding, estimating, upper and lower bounds
Ratio, proportion and rates: simplifying, proportional reasoning, average speed, exchange rates
Percentages: finding percentages, percentage change, simple and compound interest
Calculator use, time and money: 24- and 12-hour clock, timetables, currency conversion
Extended students also cover Extended
Three-set Venn diagrams and additional set notation
Recurring decimals, including converting them to fractions
Fractional indices
Bounds of the results of calculations
Reverse percentages and repeated percentage change
Exponential growth and decay
Surds: simplifying and rationalising the denominator
All students cover
Introduction to algebra: substitution into expressions and formulas
Algebraic manipulation: simplifying, expanding brackets, factorising by common factors
Indices in algebra and their rules
Equations: linear equations, simultaneous linear equations, changing the subject of simple formulas
Inequalities: representing on a number line
Sequences: nth term of linear, simple quadratic and simple cubic sequences
Graphs in practical situations: travel and conversion graphs
Graphs of functions: linear, quadratic and simple reciprocal; solving equations graphically
Sketching curves: linear and quadratic
Extended students also cover Extended
Expanding more than two brackets; full range of factorising including quadratics and difference of two squares
Completing the square
Algebraic fractions and simplifying rational expressions
Quadratic and non-linear simultaneous equations
Linear inequalities in two variables and defining regions
Exponential sequences; direct and inverse proportion in algebraic form
Kinematics: distance–time and speed–time graphs, distance as area under a graph
Advanced graphs of functions: turning points, roots, symmetry and asymptotes
Differentiation: gradients, stationary points, maxima and minima
Functions: notation, domain and range, inverse and composite functions
All students cover
Cartesian coordinates and drawing straight-line graphs
Finding the gradient of a line from a grid
Interpreting and obtaining the equation of a line in the form y = mx + c
Finding the equation of a line parallel to a given line
Extended students also cover Extended
Finding a gradient from the coordinates of two points
Length and midpoint of a line segment
Equations of lines in different forms
Perpendicular lines, including perpendicular bisectors
All students cover
Geometrical vocabulary: angles, triangles, quadrilaterals, polygons, simple solids and circles
Relationships between areas and volumes of similar shapes and solids
Symmetry properties of solids and angle properties of irregular polygons
Full set of circle theorems: angle at centre, angles in the same segment, cyclic quadrilaterals, alternate segment theorem
Further circle properties: equal chords, perpendicular bisector of a chord, tangents from an external point
All students cover
Using and converting metric units
Perimeter and area of rectangles, triangles, parallelograms and trapeziums
Circumference and area of circles; arc length and sector area
Surface area and volume of cuboids, prisms, cylinders, spheres, pyramids and cones
Calculations involving compound shapes and parts of shapes
Extended students also cover Extended
Minor and major sectors
More advanced compound and partial solids (e.g. frustum)
All students cover
Pythagoras’ theorem
Sine, cosine and tangent ratios for right-angled triangles
Solving two-dimensional problems including bearings
Extended students also cover Extended
Angles of elevation and depression
Exact trigonometric values
Graphs of sine, cosine and tangent; solving trigonometric equations
Sine and cosine rules for non-right-angled triangles, including area = ½ ab sin C
Pythagoras and trigonometry in three dimensions, including angle between a line and a plane
All students cover
Recognising, describing and drawing reflections, rotations, enlargements and translations
Extended students also cover Extended
Combinations of transformations and negative scale factors
Vectors in two dimensions: adding, subtracting and multiplying by a scalar
Magnitude of a vector
Vector geometry: position vectors, parallel lines, collinear points and geometric reasoning
All students cover
Probability scale from 0 to 1; probability of a single event
P(not happening) = 1 − P(happening)
Relative and expected frequencies
Combined events using sample space diagrams, Venn diagrams and tree diagrams
Extended students also cover Extended
Probability notation
Combined events with and without replacement
Conditional probability using Venn diagrams, tree diagrams and tables
All students cover
Classifying and tabulating data; reading, interpreting and comparing data
Mean, median, mode and range
Bar charts, pie charts, pictograms and stem-and-leaf diagrams
Scatter diagrams, correlation and line of best fit
Extended students also cover Extended
Quartiles and interquartile range
Estimating the mean of grouped data; identifying the modal class
Cumulative frequency diagrams: estimating median, quartiles and percentiles
Histograms with frequency density
Exam Technique
Command words, and why they decide marks
Cambridge uses a fixed set of command words in its questions. Each tells the student exactly what kind of answer is expected. Reading them correctly is one of the simplest ways to avoid losing marks.
Command word
What it asks the student to do
Calculate
Work out from given facts, figures or information
Work out
Calculate, with or without a calculator
Show (that)
Provide structured evidence that leads to a given result, every step must be shown
Determine
Establish with certainty
Give / State / Write
Give an answer from a source, from memory, or in a specific form
Write down
Give an answer without significant working
Describe
Give the characteristics and main features
Explain
Set out reasons or say why and how, with supporting evidence
Sketch
Make a simple freehand drawing showing the key features
Plot
Mark points accurately on a graph
Construct
Make an accurate drawing using ruler and compasses
Why this matters
“Write down” expects a quick answer with no working, while “Show that” expects every step of the reasoning. A student who treats them the same will lose method marks even when the final answer is right. Training students to read and respond to command words is a core part of good exam preparation.
Results
How IGCSE Math is graded
Cambridge IGCSE Mathematics is reported on the standard A* to G scale, with U meaning ungraded. A* is the highest and G the lowest classified grade. Core candidates can achieve C to G; Extended candidates can achieve A* to E.
Grades are set using grade thresholds decided after each exam series, so the exact marks needed vary from session to session. This is why understanding the PUM (Percentage Uniform Mark) is useful, it shows where within a grade band a student landed.
Full grading guide
For the full picture, including how grade boundaries are set, what a “pass” really means and what each grade signals to universities, read The IGCSE Grading System Explained.
How to Do Well
Five things that actually move grades
1
Master both papers
With a non-calculator paper in each tier, students need fluent written methods as well as calculator skill. The non-calculator paper rewards exact-value techniques that pure calculator practice never develops.
2
Learn the formula list, and what is not on it
Knowing which formulas are provided (and which must be memorised, like the area of a trapezium or Pythagoras’ theorem) prevents easy lost marks on every paper.
3
Answer the command word
Read whether a question says “show that”, “write down” or “explain”, and respond accordingly. Show full working where expected, even when the method seems obvious.
4
Practise past papers under timed conditions
This is the single most effective way to build accuracy, pacing and mark-scheme awareness. Students who understand the content but haven’t done past papers regularly tend to underperform on exam day.
5
Understand, don’t memorise
Questions often combine topics and appear in unfamiliar contexts. Real understanding holds up where rote learning fails, especially for the Extended-tier problem-solving questions that carry the most marks.
This is exactly what we teach.
Brainiac’s small-group IGCSE Math classes are built around mark-scheme mastery and past-paper practice. Our holiday crash courses are designed to close gaps and sharpen exam technique quickly.
Students beginning 0580 should have followed the Cambridge Lower Secondary programme or an equivalent framework.
Group award
A strong set of IGCSEs including Mathematics can count toward the Cambridge ICE (International Certificate of Education) group award.
Retakes
Candidates can retake the whole qualification as many times as they wish.
Private candidates
Private candidates can enter for this syllabus.
Assessment objectives
Extended papers weight reasoning (AO2) more heavily than Core, roughly 50–60% vs 30–40%, meaning Extended students are rewarded for clear communication and problem-solving, not just correct answers.
Questions
Frequently asked questions
Is IGCSE Math hard?
▾
It is challenging but very achievable with good teaching and consistent practice. The bigger factor is usually exam technique: showing working, using correct notation and answering the command word, rather than the difficulty of the content itself.
What is the difference between Core and Extended?
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Core covers the essentials and is graded C to G. Extended covers the Core plus additional, more demanding content and is graded A* to E. Students aiming for top grades or moving on to A-Level, IB or Additional Math should take Extended.
Do students need a calculator?
▾
Yes, a scientific calculator for Paper 3 (Core) and Paper 4 (Extended). But calculators are not allowed on Paper 1 or Paper 2, so mental and written methods matter just as much.
How is IGCSE Math different from Additional Mathematics (0606)?
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0580 is the standard IGCSE Math qualification all students take. Additional Mathematics (0606) is a separate, harder qualification for high-ability students that introduces calculus and advanced algebra. Many students take both, and 0606 is excellent preparation for IB DP and A-Level Math.
How many topics are there?
▾
Nine: Number, Algebra and graphs, Coordinate geometry, Geometry, Mensuration, Trigonometry, Transformations and vectors, Probability, and Statistics. All candidates study all nine; Extended students go deeper within each.
What grade does my child need for A-Level or IB?
▾
Requirements vary by school and course, but a grade C is a common minimum and top A-Level and IB courses usually expect a B or above, which means taking the Extended tier. For more on grades, see The IGCSE Grading System Explained.
Sources & note: This guide is based on the official Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027 (Cambridge Assessment International Education). Syllabus content, exam formats and grade thresholds can change, always check the latest official syllabus for your child’s exam series at the Cambridge International website. This is general information, not official examination guidance.
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