Numbers and the number system: Integers to Percentages for Edexcel IGCSE Mathematics Specification A: Methods and Worked Examples

The number system topics are the foundation your entire IGCSE maths grade is built on. Master them here with worked examples and exam-ready techniques.

Numbers and the number system is the first section of the Pearson Edexcel IGCSE Mathematics Specification A syllabus, and it is there for a reason. Every algebraic equation you solve, every geometric calculation you perform, and every statistical measure you compute depends on your ability to handle integers, fractions, decimals, powers, and percentages confidently. This set of edexcel igcse mathematics specification a revision notes covers the first six topics in the section: Integers, Fractions, Decimals, Powers and roots, Set language and notation, and Percentages.

These topics are examined heavily across both papers of the 4MA1 exam. If you are looking for edexcel igcse mathematics specification a notes that will actually help you in the exam, this is a strong place to start.

Integers

An integer is any whole number, positive, negative, or zero. The igcse specification expects you to work confidently with directed numbers, place value, and the hierarchy of operations (BIDMAS/BODMAS).

Prime factorisation, HCF and LCM

Finding the highest common factor (HCF) and lowest common multiple (LCM) of two numbers is one of the most reliable question types in the edexcel exam. The method is always the same: break each number into its prime factors, then pick what you need.

A common mistake is confusing HCF and LCM. Remember: the HCF is always smaller than or equal to the smaller number, and the LCM is always at least as large as the larger number. If your HCF comes out bigger than one of the original numbers, you have mixed them up.

Fractions

You need to add, subtract, multiply and divide fractions and mixed numbers fluently. The edexcel igcse exam will not give you fraction questions in isolation at Higher tier, but fractions appear inside algebra, probability, and ratio questions constantly.

When multiplying fractions, multiply numerators together and denominators together. When dividing, flip the second fraction and multiply. The most frequent error students make is forgetting to convert mixed numbers to improper fractions before multiplying or dividing.

Decimals

Decimal work overlaps heavily with fractions and percentages. You should be able to convert freely between all three representations. The specification also requires you to order decimals, which sounds straightforward but catches students who do not align decimal places properly.

At Higher tier, you need to convert recurring decimals into fractions. Here is the standard method:

The key is choosing the right multiplier. If one digit recurs, multiply by 10. If two digits recur, multiply by 100. If three digits recur, multiply by 1000. Match the multiplier to the length of the repeating block.

Powers and roots

This topic covers square numbers, cube numbers, index notation, index laws, and at Higher tier, surds and fractional/negative powers. The index laws are essential throughout the rest of the course.

For Higher tier students, rationalising the denominator is a skill worth drilling. To rationalise 1/sqrt(3), multiply top and bottom by sqrt(3) to get sqrt(3)/3. For expressions like 1/(3 + sqrt(2)), multiply top and bottom by (3 - sqrt(2)) to eliminate the surd from the denominator.

Set language and notation

Set notation and Venn diagrams are tested across both tiers, though Higher tier goes further into subsets, algebraic set definitions, and using n(A) notation. At Foundation, you need to understand union, intersection, complement, and how to read and draw Venn diagrams.

Venn diagram questions commonly appear alongside probability. Make sure you fill in the intersection first, then subtract to find the "only" regions, and finally use the universal set total to find the "neither" region.

Percentages

Percentages are among the most commonly examined topics in the edexcel igcse. The specification covers simple percentage calculations, percentage increase and decrease, reverse percentages, compound interest, and repeated percentage change (Higher).

The most common mistake with reverse percentages is applying the percentage to the reduced amount instead of recognising that the reduced amount represents a percentage of the original. If a price has been increased by 15%, the new price is 115% of the original, not 100% + 15% of the new price.

Common mistakes across number topics

• BIDMAS errors: Forgetting that multiplication and division are done left to right, not "multiplication always before division." The same applies to addition and subtraction. 8 - 3 + 2 = 7, not 3.
• Negative number arithmetic: -3 x -4 = 12 (positive), but -3 x 4 = -12. Students sometimes treat the sign as optional in multi-step calculations.
• Rounding too early: In compound interest and repeated percentage change questions, keep full calculator precision until the final answer. Rounding intermediate values changes the final result, and examiners check for this.
• Forgetting to simplify fractions: If the mark scheme says "give your answer in its simplest form" and you write 36/99 instead of 4/11, you lose the final accuracy mark.

Self-check questions

Test yourself on these. Cover the answers and try each one before checking.

1. Find the HCF and LCM of 36 and 90. (Answer: HCF = 18, LCM = 180)
2. Calculate 3 1/2 x 2 2/3. (Answer: 7/2 x 8/3 = 56/6 = 28/3 = 9 1/3)
3. Convert 0.272727... to a fraction in its simplest form. (Answer: 3/11)
4. Simplify 2⁵ x 2^-2 / 2². (Answer: 2¹ = 2)
5. A house increases in value by 5% each year. It is worth 200,000 pounds today. What will it be worth in 3 years? (Answer: 200,000 x 1.05³ = 231,525 pounds)
6. After a 12% pay rise, a worker earns 33,600 pounds. What was the original salary? (Answer: 33,600 / 1.12 = 30,000 pounds)

Exam patterns across number topics

Number questions on the edexcel exam often combine several of these sub-topics within a single multi-mark problem. A question might ask you to find a fraction of a quantity, then express the answer as a percentage, then apply a percentage increase. Treating each step as its own mini-problem keeps the working organised and makes it easier to pick up method marks even if the final answer goes wrong.

At Foundation tier, expect the number questions to be more direct: calculate this percentage, simplify this fraction, find these factors. At Higher tier, the same skills appear but wrapped in context or combined with algebra. Reverse percentage problems, for instance, often sit inside a word problem that also involves ratio or proportion.

If you scored well on all six, your number foundations are solid. If any gave you trouble, revisit the relevant worked examples above and try similar numbers and the number system: integers to percentages edexcel igcse practice questions from past papers. These edexcel igcse mathematics specification a explained concepts will appear across both papers, so the time you invest here pays off throughout the entire igcse 4ma1 numbers and the number system: integers to percentages section and beyond.

Use the Green Bridge CBT platform for more edexcel igcse mathematics specification a practice questions on each of these sub-topics, organised so you can drill your weak spots and track improvement over time.