Cambridge International · IGCSE · 0580
Mathematics — Keywords & Key Terms — Definitions Glossary (2026)
Cambridge IGCSE Mathematics (0580 Extended)
Topic-by-topic keywords, key terms and definitions for precise exam language—separate from our revision checklists (topic coverage) and formula sheets (equations).
Keywords & Key Terms — definitions
Examiner-style keywords and definitions organised by syllabus topic. Terms are tagged Essential (start here), Core (typical exam standard), and Advanced for harder distinctions — tick each row when you can recall it. Your progress is saved in this browser for this list.
Cambridge International IGCSE Mathematics (0580)
Cambridge International IGCSE Mathematics (0580)
Cambridge IGCSE Mathematics (0580 Extended)
Aligned to Cambridge IGCSE Mathematics 0580 Extended content for 2026. Core (Core-only papers) omits some Extended topics — confirm whether you are entered for Core or Extended.
Mark schemes: Method marks are often awarded for a correct approach even if the final answer slips. Accuracy marks require correct rounding and exact forms when specified. Check whether the question asks for a particular degree of accuracy.
Active recall: 0 / 57 terms ticked
| Recalled | Topic | Level | Keyword | Definition |
|---|---|---|---|---|
| Working mathematically | Essential | Significant figures | Digits carrying meaning; leading zeros are not significant. | |
| Working mathematically | Core | Decimal places | Digits after the decimal point — round only at the end of working when asked. | |
| Working mathematically | Core | Estimation | Round numbers to one significant figure for a quick check of order of magnitude. | |
| Working mathematically | Core | Bounds of accuracy | A value given to nearest unit lies within ±0.5 of that unit. | |
| Working mathematically | Advanced | Upper and lower bounds | For calculations with rounded data, find max/min possible results. | |
| Number & algebra | Essential | Integer | Whole number (positive, negative or zero). | |
| Number & algebra | Essential | Rational number | Can be written as a/b with integers a, b (b ≠ 0). | |
| Number & algebra | Essential | Irrational number | Cannot be expressed as a simple fraction (e.g. √2, π). | |
| Number & algebra | Core | Prime factor | Prime number dividing another integer exactly. | |
| Number & algebra | Core | Highest common factor (HCF) | Largest integer dividing all given numbers. | |
| Number & algebra | Core | Lowest common multiple (LCM) | Smallest positive integer divisible by each given number. | |
| Number & algebra | Core | Standard form | A × 10ⁿ with 1 ≤ A < 10. | |
| Number & algebra | Core | Index laws | Rules for multiplying/dividing powers and raising powers to powers. | |
| Number & algebra | Core | Linear equation | Unknown to power 1 only; graph is a straight line. | |
| Number & algebra | Core | Simultaneous equations | Two equations in two unknowns — solve by substitution or elimination. | |
| Number & algebra | Core | Inequality | >, <, ≥, ≤ — solution often a range on a number line. | |
| Number & algebra | Core | Quadratic expression | ax² + bx + c; may factorise or use formula. | |
| Number & algebra | Advanced | Quadratic formula | x = (−b ± √(b² − 4ac)) / 2a for ax² + bx + c = 0. | |
| Number & algebra | Core | Completing the square | Rewrite x² + px as (x + p/2)² − (p/2)². | |
| Number & algebra | Core | Direct proportion | y = kx — graph through origin. | |
| Number & algebra | Core | Inverse proportion | y = k/x — product xy constant. | |
| Number & algebra | Core | Sequences | nth term rules for linear and quadratic patterns. | |
| Graphs & functions | Essential | Gradient | Steepness of a line; change in y ÷ change in x. | |
| Graphs & functions | Core | y-intercept | Value of y where graph crosses y-axis. | |
| Graphs & functions | Core | Parallel lines | Same gradient. | |
| Graphs & functions | Core | Perpendicular lines | Gradients multiply to −1 (non-vertical/horizontal case). | |
| Graphs & functions | Core | Sketch | Show correct shape, intercepts and key points — not necessarily to scale. | |
| Graphs & functions | Advanced | Graphical solution | Read intersection points to solve simultaneous equations. | |
| Geometry, mensuration & trigonometry | Essential | Angle | Measure of turn; degrees or radians. | |
| Geometry, mensuration & trigonometry | Core | Pythagoras’ theorem | Right-angled triangle: a² + b² = c² (c hypotenuse). | |
| Geometry, mensuration & trigonometry | Core | Similar triangles | Corresponding angles equal; sides in proportion. | |
| Geometry, mensuration & trigonometry | Core | Congruent | Identical shape and size. | |
| Geometry, mensuration & trigonometry | Core | Sine rule | a/sin A = b/sin B = c/sin C. | |
| Geometry, mensuration & trigonometry | Core | Cosine rule | a² = b² + c² − 2bc cos A. | |
| Geometry, mensuration & trigonometry | Core | Area of triangle | ½ab sin C or ½ × base × height. | |
| Geometry, mensuration & trigonometry | Core | Circle | Circumference 2πr; area πr². | |
| Geometry, mensuration & trigonometry | Core | Arc length & sector area | Fraction of full circle using angle at centre. | |
| Geometry, mensuration & trigonometry | Core | Volume of prism | Cross-sectional area × length. | |
| Geometry, mensuration & trigonometry | Core | Volume of cylinder | πr²h. | |
| Geometry, mensuration & trigonometry | Core | Surface area | Total area of all faces — include units². | |
| Geometry, mensuration & trigonometry | Advanced | Circle theorems | Angle at centre twice angle at circumference; opposite angles of cyclic quadrilateral sum to 180°; angle in semicircle is 90°. | |
| Vectors & transformations | Essential | Vector | Quantity with magnitude and direction. | |
| Vectors & transformations | Core | Translation | Slide by column vector. | |
| Vectors & transformations | Core | Reflection | Mirror line given; equal distance from line. | |
| Vectors & transformations | Core | Rotation | Centre, angle, direction. | |
| Vectors & transformations | Core | Enlargement | Centre and scale factor; area scales by k². | |
| Vectors & transformations | Advanced | Column vector addition | Add top to top, bottom to bottom. | |
| Probability & statistics | Essential | Probability | Value from 0 (impossible) to 1 (certain). | |
| Probability & statistics | Core | Independent events | Outcome of one does not affect the other — multiply probabilities. | |
| Probability & statistics | Core | Mutually exclusive | Cannot both happen — add probabilities. | |
| Probability & statistics | Core | Mean | Sum of values ÷ number of values. | |
| Probability & statistics | Core | Median | Middle value when data ordered. | |
| Probability & statistics | Core | Mode | Most frequent value. | |
| Probability & statistics | Core | Range | Largest − smallest. | |
| Probability & statistics | Core | Cumulative frequency | Running total of frequencies — used for median and quartiles. | |
| Probability & statistics | Advanced | Histogram | Area represents frequency; frequency density = frequency ÷ class width. | |
| Probability & statistics | Core | Scatter diagram | Plot of paired data; correlation positive, negative or none. |
Pair this with our revision checklists, formula sheets hub and past paper finder.
Mathematics (0580) — Keywords & Key Terms FAQ
- What is on this Cambridge International IGCSE Mathematics keywords and key terms list?
- It is a topic-organised glossary of important mathematics terms with short, exam-style definitions aligned to Cambridge IGCSE Mathematics (0580 Extended) (0580). It is designed for “define”, “state”, “outline” and “explain” questions where precise vocabulary earns marks.
- How should I use this Mathematics glossary alongside past papers?
- Tick terms when you can recall them without reading the answer, then check your wording against mark schemes. Pair vocabulary practice with past papers for IGCSE Mathematics (0580) so you apply terms in context.
- Is this the same as a revision checklist or a formula sheet?
- No. Revision checklists help you track which syllabus topics you have covered and your confidence—separate pages on Tutopiya. Formula sheets summarise equations and quantitative relationships. This page is only a definitions and key-terms glossary for Mathematics. Use formula sheets for equations; use this list for precise terms and definitions.
- Can I download this Mathematics keywords and key terms list for free?
- Yes. After a quick free sign-up you can download a UTF-8 CSV (opens in Excel or Google Sheets) or open a print-friendly page and save as PDF. Browsing the list on the page is free.
- Is this Mathematics list aligned to the 0580 specification?
- Topic groupings and wording follow Cambridge IGCSE Mathematics (0580 Extended) for Cambridge International IGCSE. Always confirm final learning objectives and any regional options in your official specification and recent examiner reports for your exam session.
- Why focus on definitions instead of full notes?
- Mark schemes reward correct technical terms and clear links between ideas. A compact glossary lets you drill the exact language examiners expect for Mathematics at IGCSE, separate from longer notes or topic trackers.