IGCSE Mathematics: Number (Cambridge 0580)

This guide covers the Core content of Topic 1 Number, for Cambridge IGCSE Mathematics 0580, 2025–2027 series. Extended-only content is not covered here. That means more than the two subtopics the syllabus marks “Extended content only” (C1.17 and C1.18): the Core and Extended statements for each subtopic have been compared item by item, and Extended-only additions inside subtopics that do have a Core version are excluded too — for example reverse percentages (E1.13 item 5), finding the bounds of the results of calculations (E1.10 item 2), fractional indices (E1.7), recurring decimals to fractions (E1.4) and three-set Venn diagrams (E1.2).

Where this fits in 0580

Number is the first of nine topics in 0580 and underpins nearly everything that follows — algebra, mensuration and statistics all assume fluent arithmetic, fraction and percentage work, and comfort converting between number forms. It is examined across all papers, not confined to one component.

Syllabus coverage

CAMBRIDGE IGCSE MATHEMATICS 0580 — TOPIC 1 NUMBER (CORE)

• C1.1 Types of number — natural numbers, integers, prime numbers, square and cube numbers, common factors and multiples, rational and irrational numbers, reciprocals
• C1.2 Sets — set language, notation and two-set Venn diagrams (n(A), A′, ∪, ∩)
• C1.3 Powers and roots — squares, square roots, cubes, cube roots, and other powers/roots, including recall of squares 1–15 and cubes 1–5 and 10
• C1.4 Fractions, decimals and percentages — proper/improper fractions, mixed numbers, decimals, percentages, and converting between them
• C1.5 Ordering — comparing quantities using =, ≠, >, <, ⩾, ⩽
• C1.6 The four operations — with integers, fractions and decimals, including correct order of operations and use of brackets
• C1.7 Indices I — positive, zero and negative integer indices and the rules of indices
• C1.8 Standard form — the form A × 10ⁿ, converting into and out of standard form, and calculating with it (Core candidates calculate with standard form only on Paper 3, the calculator paper)
• C1.9 Estimation — rounding to a specified accuracy, including decimal places and significant figures
• C1.10 Limits of accuracy — upper and lower bounds for data rounded to a specified accuracy (Core candidates are not expected to find the bounds of the results of calculations)
• C1.11 Ratio and proportion — simplifying ratios, dividing a quantity in a given ratio, proportional reasoning
• C1.12 Rates — common and other measures of rate, including average speed, density and population density
• C1.13 Percentages — percentage of a quantity, one quantity as a percentage of another, percentage increase/decrease, simple and compound interest (reverse percentages are Extended only, E1.13)
• C1.14 Using a calculator — efficient and accurate calculator use
• C1.15 Time — calculating with units of time, and the 24-hour and 12-hour clock
• C1.16 Money — calculating with money and converting between currencies

(C1.17 and C1.18 are Extended-only and not part of Core content.)

Worked examples

Prime factorisation, HCF and LCM. Writing a number as a product of primes underpins both. For 24 and 36:

24 = 2^3 x 3        36 = 2^2 x 3^2
HCF = lowest power of each common prime  = 2^2 x 3 = 12
LCM = highest power of every prime that appears = 2^3 x 3^2 = 72

Ratio. To share 180 in the ratio 2 : 3 : 4, first find the total number of parts (2 + 3 + 4 = 9), then divide:

180 / 9 = 20 per part   ->   40 : 60 : 80

If a question instead gives the difference between two shares, find the value of one part from that difference rather than the total.

Percentage increase. A price of $70 is increased by 20%. Using a multiplier is quicker and less error-prone than finding 20% and adding it on:

70 x 1.2 = $84

Working backwards from $84 to the original price (a reverse percentage) is Extended-only content (E1.13), so it is not examined on the Core papers.

Standard form. After multiplying or dividing two numbers in standard form, check the mantissa is still between 1 and 10, and renormalise if not — a common slip is leaving an answer as, say, 42 × 10⁵ instead of converting it to 4.2 × 10⁶.

Limits of accuracy. A mass given as 4.6 kg to 1 decimal place has been rounded to the nearest 0.1 kg, so the true value lies within half that interval either side:

4.55 <= mass < 4.65

The lower bound is 4.55 kg and the upper bound is 4.65 kg. At Core, the syllabus limits this to giving the bounds of the rounded value itself: “Candidates are not expected to find the bounds of the results of calculations which have used data rounded to a specified accuracy” (C1.10). Combining bounds through a calculation is Extended content (E1.10).

Sets, conversions, ordering, calculator use, time and money. These Core subtopics (C1.2, C1.4, C1.5, C1.14, C1.15 and C1.16) each have a worked example in the Number revision notes: two-set Venn diagrams and set notation, converting between fractions, decimals and percentages, ordering with =, ≠, >, <, ⩾ and ⩽, entering times and reading the calculator display, the 12-hour and 24-hour clock with timetables and time zones, and currency conversion. One example of each:

Venn: 30 students, 18 French, 14 Spanish, 5 neither
      both = 18 + 14 - (30 - 5) = 7
time: 09 47 to 13 22 = 13 min + 3 h + 22 min = 3 h 35 min
money: £1 = $1.28, so $500 = 500 / 1.28 = £390.63

How to approach it

Number is graded most heavily on accuracy under exam conditions rather than conceptual difficulty — the ideas themselves (fractions, ratios, percentages) are usually familiar from earlier years. The two places students lose marks are standard form manipulation (particularly negative indices) and multi-step rate/ratio word problems where the question buries the actual calculation inside real-world context. Working through several worded rate and ratio questions, and practising standard form calculations with a calculator (Core candidates meet them only on Paper 3, the calculator paper), closes most of the gap in this topic.

Self-test

1. Find the HCF and LCM of 24 and 36 using prime factors.
2. Share $200 in the ratio 3 : 5.
3. A price of $70 is increased by 20%. Find the new price using a multiplier.
4. State the bounds for a mass of 4.6 kg measured to 1 decimal place.

Answers: 1. HCF = 12, LCM = 72 (see the worked example above). 2. 8 parts of $25 each, giving $75 and $125. 3. 70 × 1.2 = $84. 4. 4.55 ≤ mass < 4.65.

For condensed recall notes on this topic, see the Number revision notes; for exam-style practice with full mark schemes, see the Number practice questions.

Official syllabus

Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027 — cambridgeinternational.org.