Pearson Edexcel International GCSE Mathematics · specification 4MA1 · Paper 1F | Whole paper: Number, Algebra, Geometry, Statistics · Free · no account needed
Integers, place value and decimals (4MA1 specification)
The arithmetic everything else rests on: integers, place value, decimal notation, fractions and the conversions between them.
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The 6 Incandio pages that teach this — each explained in full, then proved in marked questions, taught back to an AI pupil and defended in a debate. Completely free.
- Integers, Place Value & Ordering — Negative numbers, the order of operations, and putting any mix of numbers in order — the arithmetic everything else stands on.
- Fractions & Mixed Numbers — Adding, multiplying and dividing fractions with certainty — and the bar-model picture that makes worded fraction problems fall open.
- Decimals & Recurring Decimals — Multiplying and dividing decimals without a wobble, and the Higher-tier trick that turns any recurring decimal into an exact fraction.
- Powers, Roots & Index Laws — What indices really mean — including the zero, negative and fractional ones that look strange until you see the pattern they complete.
- Surds — Exact answers with square roots: simplifying √48, expanding surd brackets, and rationalising denominators. Higher Tier.
- Sets & Venn Diagrams — Set notation, intersections and unions, and the counting arguments that solve 'how many study both?' problems in two lines.
The teaching route this belongs to: Number — the lessons in order, with every gate.
Specification coverage
1 Numbers and the number system — statements 1.1–1.5 (Foundation and Higher Tier)
Assessment objectives: AO1. Suggested learning time: 45 minutes.
Required knowledge
- Understand and use integers, both positive and negative
- Understand place value
- Use decimal notation
- Convert between fractions, decimals and percentages
- Order numbers, including negatives and decimals
Required skills
- Convert fluently between the three forms without a calculator
- Order a mixed list of fractions, decimals and percentages
How it is examined
- Structured questions building from a routine start to a multi-step finish
- Problem-solving questions with no method given
- 'Show that' and reasoning questions where the working IS the answer
Common mistakes
- Comparing decimals by length — thinking 0.45 is bigger than 0.5 because it has more digits.
- Ordering negatives forwards. −7 is smaller than −2.
- Converting to different forms and then comparing the mixed set anyway. Convert everything to ONE form first.
This page maps the specification. The pages above teach it, and the Mathematics modules hold the whole course — completely free.