Number for OxfordAQA IGCSE Mathematics: Methods and Worked Examples

Why Number carries so much weight in OxfordAQA IGCSE Mathematics

Ask any teacher which section of oxfordaqa igcse mathematics number work students underestimate, and the answer is usually the same: Number. It looks straightforward on the specification page, but a dense cluster of skills sits inside it, and those skills are the building blocks for algebra, geometry and statistics questions later on the same paper. Get standard form or percentage change wrong here and the error tends to ripple forward into whatever calculation depends on it. This is a igcse 9260 number deep dive built to close that gap: full explanations, worked examples, common mistakes, and a set of self-check questions at the end.

The Number section of the syllabus covers three named topics: structure and calculation, fractions/decimals/percentages, and ratio and proportion. All three are examined regularly and in combination with other topics, so treat this as a foundation to master rather than a box to tick early in the year. This oxfordaqa igcse mathematics explained page is written so you can work through each topic once, properly, rather than skimming three separate revision guides that each cover half the picture.

Structure and calculation

This topic is the widest of the three, covering ordering, the four operations, powers and roots, standard form, sets, and rounding and estimation. Each sub-skill sounds simple in isolation; the exam usually tests two or three of them together.

Order of operations and notation

OxfordAQA expects fluency with the symbols =, ≠, <, >, ≤, ≥, including placing values on a number line, and with conventional priority of operations: brackets, powers and roots, then multiplication and division, then addition and subtraction. A calculator will apply this order automatically, but you are still expected to predict what it should output, which is where careless bracket placement costs marks.

Powers, roots and standard form

You need positive integer powers and their associated roots (square, cube and higher), the index laws for multiplication and division, and at Extension, fractional powers. Standard form work asks you to write and interpret numbers as A × 10ⁿ, where 1 ≤ A < 10 and n is an integer, and to read standard form correctly off a calculator display, which does not always show the ×10ⁿ the way a textbook does.

Prime factors, factors and multiples

You are expected to know and use even, odd and prime numbers, factors, multiples, common factors, common multiples, the highest common factor, the lowest common multiple, and prime factorisation written in index (product) form. Writing a number as a product of its prime factors is a skill in itself: divide repeatedly by the smallest prime that fits, and keep going until only 1 remains.

Index laws build on this directly: when multiplying powers of the same base, add the indices; when dividing, subtract them. a^m × aⁿ = a^m+n, and a^m ÷ aⁿ = a^m-n. At Extension, this extends to fractional indices, where a^1/2 means the square root of a and a^1/3 means the cube root of a.

Sets and Venn diagrams

You should be comfortable with set notation n(A), A′, A ∩ B, A ∪ B, and ξ, and with using Venn diagrams to solve problems involving two or three sets. The most common error here is misreading which region a shaded area represents; always label every region with its count or description before answering the question underneath it.

Rounding, estimation and bounds

Rounding to a stated number of decimal places or significant figures, estimating an answer before a full calculation, and (at Extension) working with upper and lower bounds for measurements are all tested regularly. A bounds question typically gives you a measurement rounded to a given accuracy and asks for the largest or smallest possible value of a calculation using that measurement.

Fractions, decimals and percentages

This topic asks you to move fluently between the three representations, and to apply percentages to real contexts: percentage change, simple interest, and compound interest.

• Convert between fractions, terminating decimals and percentages (and, at Extension, recurring decimals).
• Express one quantity as a fraction or percentage of another, including cases where the fraction exceeds 1 or the percentage exceeds 100%.
• Solve percentage change problems: increase, decrease, simple interest and compound interest.
• At Extension, work backwards from a final value in reverse percentage problems, and apply the compound interest formula directly.

The compound interest formula is worth memorising precisely: value of investment = P(1 + r/100)ⁿ, where P is the amount invested, r is the percentage rate of interest, and n is the number of years.

A reverse percentage question works in the opposite direction: you are given the value after a percentage change and asked to find the original value. Divide by the multiplier rather than trying to subtract the percentage back off the final amount, which is the single most common error on this question type.

Ratio and proportion

Ratio and proportion questions test whether you can move between ratio notation, fraction notation, and real-world sharing and rate problems.

1. Simplify a ratio to its lowest terms, and understand the link between ratio notation and fractions.
2. Divide a quantity in a given ratio.
3. Apply ratio to worded problems, including recipes, mixing and scaling.
4. Use common measures of rate, including pay calculations and best-buy comparisons.
5. Solve direct and inverse proportion problems, including repeated proportional change, and at Extension, exponential growth and decay.

Distinguishing direct from inverse proportion is a recurring sticking point. In direct proportion, both quantities increase or decrease together (double one, double the other). In inverse proportion, one quantity increases as the other decreases (double one, halve the other), which is typical of speed and time problems for a fixed distance.

Common mistakes across Number topics

How to use this for revision

Treat this page as one part of a wider set of oxfordaqa igcse mathematics revision notes: read the explanation, close the page, and redo each worked example from memory before checking it against the version above. Good oxfordaqa igcse mathematics notes are ones you have rebuilt yourself, not ones you have only read. Once each worked example above is comfortable, move on to full oxfordaqa igcse mathematics practice questions drawn from past papers, and time yourself against the paper's actual duration rather than working topic by topic indefinitely.

Self-check questions

1. Write 63,000 in standard form.
2. A quantity is measured as 15 kg to the nearest kg. State the upper and lower bounds.
3. A price of $150 is reduced by 20% and then increased by 20%. Is the result $150? Explain your answer.
4. Find the compound interest earned on $5,000 invested at 3% per year for 2 years.
5. Divide $540 in the ratio 4:5.
6. Two variables are inversely proportional. If one doubles, what happens to the other?
7. Write 504 as a product of its prime factors.
8. Two shops sell the same brand of juice: 1.5 litres for $2.10, or 2 litres for $2.60. Which is the better buy?
9. A rectangle has sides measured as 6 cm and 4 cm, both correct to the nearest cm. Find the upper bound for its area.

If any of these nine questions felt unfamiliar, that is exactly the number oxfordaqa igcse content worth revisiting before you tackle algebra, because every one of the four syllabus sections leans on Number being solid first.