OxfordAQA International GCSE Mathematics: Number (9260)

This guide covers Topic 1 Number, the first of four subject-content areas in OxfordAQA International GCSE Mathematics (9260), 120 guided learning hours. The qualification is tiered (Core, grades 1-5, and Extension, grades 4-9), and all content can be assessed on the Extension tier.

Where this fits in 9260

Number establishes the calculation fluency and understanding of ratio and proportion that underpin the other three content areas – Algebra, Geometry and measures, and Statistics and probability. This specification overlaps substantially with AQA’s UK GCSE Mathematics (8300) per the specification’s own administration section.

Syllabus coverage

OXFORDAQA INTERNATIONAL GCSE MATHEMATICS (9260) — TOPIC 1 NUMBER

• 1.1 Structure and calculation — the four operations applied to integers, decimals and fractions, and the correct order of operations
• 1.2 Fractions, decimal and percentages — converting between and calculating with fractions, decimals and percentages
• 1.3 Ratio and proportion — solving problems involving ratio, direct and inverse proportion

How to approach it

Structure and calculation (1.1) needs to be automatic before progressing, since errors in basic arithmetic and order of operations compound into every later topic area. Fractions, decimals and percentages (1.2) is tested heavily in applied, real-world contexts (such as percentage change and financial calculations), so practise converting fluently between all three forms rather than treating them as separate skills. Ratio and proportion (1.3) rewards being able to recognise whether a problem is direct or inverse proportion before setting up a solution method, since misidentifying the relationship is a common source of error on both tiers. Because all content can be assessed on the Extension tier, Core-tier candidates preparing to move up should treat this topic as a floor rather than a ceiling, and Extension candidates should expect number skills to reappear as supporting steps within algebra and statistics questions rather than only in standalone number questions. Working through varied practice questions across all three sub-topics, rather than relying on one question type, is the most reliable way to build the fluency this topic demands.

Official syllabus

OxfordAQA International GCSE Mathematics (9260) specification, Version 5.1, for exams May/June 2018 onwards — oxfordaqa.com.

Integers, primes and factorisation

Every integer greater than 1 is either prime or a product of primes, and that factorisation is unique. Writing numbers in prime factor form is the reliable route to HCF and LCM:

90  = 2 x 3^2 x 5
126 = 2 x 3^2 x 7

HCF = lowest power of each shared prime = 2 x 3^2       = 18
LCM = highest power of every prime seen = 2 x 3^2 x 5 x 7 = 630

Check with HCF x LCM = product of the numbers: 18 x 630 = 11 340 = 90 x 126.

Fractions, decimals and percentages

Convert freely between the three. To add or subtract fractions use a common denominator; to divide, multiply by the reciprocal.

Percentage work is fastest with multipliers:

increase of 12%  ->  x 1.12
decrease of 12%  ->  x 0.88
n years of compound growth at r%  ->  x (1 + r/100)^n

For a reverse percentage, divide by the multiplier. If a price after a 20% discount is $64, the original is 64 / 0.8 = $80 — not 64 x 1.2.

Ratio and proportion

Share a quantity in a given ratio by finding the value of one part. In direct proportion y = kx; in inverse proportion y = k/x. Find k from the given pair, then use it.

Best-buy and exchange-rate problems are proportion questions in disguise: reduce each option to a common unit before comparing.

Indices, standard form and surds

Index laws: multiplying adds indices, dividing subtracts, a power of a power multiplies, anything to the power zero is 1, a negative index is a reciprocal, a fractional index is a root.

Standard form is A x 10^n with 1 <= A < 10. Multiply by multiplying the numbers and adding the indices; divide by dividing and subtracting. Adjust if A leaves the range.

Surds are exact. Simplify by extracting square factors, and rationalise denominators by multiplying top and bottom by the surd or its conjugate.

Bounds and accuracy

A value rounded to a given accuracy lies within an interval. For a mass of 4.6 kg to 1 decimal place:

4.55 <= m < 4.65

When combining bounds: the greatest sum uses both upper bounds; the greatest difference uses upper minus lower; the greatest quotient uses upper divided by lower.

Worked example

A rectangle has length 12.4 cm and width 7.8 cm, each to 1 decimal place. Find the upper bound of the area.

Length: 12.35 <= l < 12.45
Width:   7.75 <= w <  7.85

Upper bound of area = 12.45 x 7.85 = 97.7325 cm^2

Use the upper bound of both because the quantities are multiplied — the reasoning changes for division.

Common mistakes

Multiplying rather than dividing in reverse percentage problems. Treating 1 as prime. Writing standard form as 15 x 10^4. Using the upper bound of the denominator when finding the greatest quotient. Rounding partway through instead of at the end. Adding fractions by adding numerators and denominators.

Quick revision checklist

• Write any integer as a product of primes and use it for HCF and LCM.
• Use multipliers for increase, decrease, reverse percentage and compound growth.
• Solve ratio, direct and inverse proportion problems.
• Apply all index laws and calculate in standard form.
• Simplify and rationalise surds.
• State bounds and combine them correctly for sums, differences, products and quotients.