Unit Overview

Number

CIE IGCSE Mathematics· 5 min read 📊 Number underpins every 0580 paper (Paper 1/Paper 3 Core, Paper 2/Paper 4 Extended), all written structured questions — there is no multiple-choice

1. Unit at a glance

This unit builds sequentially from basic number fundamentals to practical, exam-focused applications. You will start with core classification and calculation rules before moving to more abstract concepts like indices and surds, then apply all these skills to solve real-world problems involving money, time and growth.

All concepts in this unit are tested across every paper type, so mastering these foundational skills will directly improve your performance in algebra, geometry and statistics topics later in the course.

Work through the following subtopics in order to build your knowledge incrementally:

Types of Number, Factors & Powers

Learn to classify number types, calculate factors, multiples, HCF, LCM and apply basic power rules.

★⏱ 10 min

Sets & Venn Diagrams

Understand set notation, represent number groups using Venn diagrams and solve set operation problems.

★★⏱ 12 min

Fractions, Decimals & the Four Operations

Master addition, subtraction, multiplication and division of fractions, decimals and mixed numbers.

★★⏱ 15 min

Indices, Standard Form & Surds

Apply indices laws, convert between standard and ordinary form, and simplify surd expressions.

★★★⏱ 18 min

Estimation & Limits of Accuracy

Estimate calculation results and calculate upper/lower bounds for measured values.

★★★⏱ 12 min

Ratio, Proportion & Rates

Simplify ratios, solve direct/inverse proportion problems and calculate unit rates for real contexts.

★★⏱ 15 min

Percentages, Interest & Growth/Decay

Calculate percentage changes, simple/compound interest and solve growth/decay problems.

★★★⏱ 16 min

Time, Money & Using a Calculator

Convert time units, calculate currency values and use a scientific calculator efficiently for exam problems.

★⏱ 8 min

2. Common Pitfalls

Wrong move:

Confusing HCF and LCM when solving word problems

Why:

HCF is the largest number that divides both values, while LCM is the smallest number both values divide into, so mixing them leads to incorrect answers

Correct move:

Use prime factor trees: HCF uses the lowest power of common primes, LCM uses the highest power of all primes present

Wrong move:

Rounding intermediate calculation values when solving multi-step percentage or proportion problems

Why:

Premature rounding introduces small errors that accumulate, leading to answers outside the allowed exam tolerance range

Correct move:

Keep all intermediate values in your calculator memory, only round your final answer to the required number of significant figures

Wrong move:

Forgetting the $1 \leq A < 10$ rule when writing numbers in standard form

Why:

Standard form requires the leading number to be between 1 (inclusive) and 10 (exclusive), so values outside this range are marked incorrect in exams

Correct move:

Adjust the power of 10 to ensure your leading coefficient is always within the required 1 to 10 range

3. Quick Reference Cheatsheet

Concept	Key Formula/Rule
HCF/LCM	HCF = product of lowest powers of shared prime factors; LCM = product of highest powers of all prime factors
Indices Rules	$a^{m} \times a^{n} = a^{m + n}$ , $a^{m} \div a^{n} = a^{m - n}$ , $(a^{m})^{n} = a^{mn}$
Standard Form	$A \times 1 0^{n}$ where $1 \leq A < 10$ and $n$ is an integer
Percentage Change	$Percentage Change = \frac{New Value - Original Value}{Original Value} \times 100%$
Compound Interest	$A = P (1 + \frac{r}{100})^{n}$ where $P$ = principal, $r$ = rate, $n$ = time periods
Limits of Accuracy	Upper bound = measured value + $\frac{1}{2}$ precision; Lower bound = measured value - $\frac{1}{2}$ precision
Inverse Proportion	If $y \propto \frac{1}{x}$ , then $x y = k$ where $k$ is the constant of proportionality

What's Next

Start your learning for this unit with the first subtopic on Types of Number, Factors & Powers, where you will build the foundational number classification skills you need for all subsequent lessons. Once you have completed all subtopics in this Number unit, you will move on to the Algebra unit, which builds directly on the calculation and rule application skills you have mastered here. Make sure to attempt all end-of-subtopic practice questions to reinforce your knowledge before progressing.

→Types of Number, Factors & Powers