Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed

Number

Place value, fractions, decimals, indices, standard form, bounds, surds and sets — the arithmetic bedrock of both papers, and nearly a fifth of all marks by itself.

Every lesson here ends the same way: learn it, teach it to an AI pupil who asks the awkward question, then defend it against the thinker with the strongest claim on it — free · no account needed.

8 modules of Pearson Edexcel International GCSE Mathematics (1 Higher Tier), each explained in full — what it is, why it works, when a question is asking for it, the mistakes that cost marks and worked examples — with five graded questions marked on your own device. Completely free.

The modules in Number

Integers, Place Value & Ordering

Negative numbers, the order of operations, and putting any mix of numbers in order — the arithmetic everything else stands on. Place value says every digit's worth depends on WHERE it sits: in 3.596 the 9 means nine hundredths.

When a question is asking for it: Every time you touch a calculation. Learn Integers, Place Value & Ordering →

Fractions & Mixed Numbers

Adding, multiplying and dividing fractions with certainty — and the bar-model picture that makes worded fraction problems fall open. A fraction is a division waiting to happen: 3/8 is 3 ÷ 8, and also '3 parts of a whole cut into 8'.

When a question is asking for it: Any exact-answer arithmetic (fractions never round), any 'what fraction of…' or 'a tank is 5/8 full' problem, and inside almost every other topic: probability, ratio, algebraic fractions and gradients all lean on this… Learn Fractions & Mixed Numbers →

Decimals & Recurring Decimals

Multiplying and dividing decimals without a wobble, and the Higher-tier trick that turns any recurring decimal into an exact fraction. Decimal arithmetic is whole-number arithmetic plus place-value bookkeeping: 4.7 × 0.06 is 47 × 6 with the decimal point placed by counting decimal places.

When a question is asking for it: Money and measurement arithmetic without a calculator; 'given 468 × 23 = 10 764, write down…' questions (pure place-value); and any 'write 0.4̇5̇ as a fraction' question… Learn Decimals & Recurring Decimals →

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. An index counts repeated multiplication: 3⁴ = 3×3×3×3.

When a question is asking for it: Simplifying any product or quotient of powers, evaluating things like 27^(2/3) or 5⁻², and inside standard form, surds and algebra — the index laws are the grammar those topics are written in. Learn Powers, Roots & Index Laws →

Standard Form

Writing enormous and tiny numbers as a×10ⁿ, and calculating with them confidently — the physicist's notation, on both papers. Standard form writes any number as a × 10ⁿ where 1 ≤ a < 10.

When a question is asking for it: Whenever a question says 'give your answer in standard form', in astronomy/atoms contexts, and whenever multiplying or dividing very large/small quantities — the index laws do the heavy lifting: multiply the front… Learn Standard Form →

Rounding, Estimation & Bounds

Significant figures, one-significant-figure estimates that sanity-check everything, and the upper and lower bounds of a rounded measurement. Rounding keeps the significant part of a number (0.04962 → 0.050 to 2 s.f.).

When a question is asking for it: 'Estimate' in a question ALWAYS means round to 1 s.f. Learn Rounding, Estimation & Bounds →

Surds (Higher Tier)

Exact answers with square roots: simplifying √48, expanding surd brackets, and rationalising denominators. Higher Tier. A surd is a root left unevaluated because its decimal never ends: √3 exactly, rather than 1.732… approximately.

When a question is asking for it: Whenever a question says 'give your answer in surd form' or 'exact value' — a decimal there usually loses the final accuracy mark even when numerically right, although correct working can still earn method marks. Learn Surds →

Sets & Venn Diagrams

Set notation, intersections and unions, and the counting arguments that solve 'how many study both?' problems in two lines. A set is a collection with a membership rule.

When a question is asking for it: Any 'in a class of 30, 18 do French and 14 do Spanish…' problem; probability questions built on Venn diagrams (Higher); and whenever a question uses the symbols ∩, ∪, ′ or n( ) directly. Learn Sets & Venn Diagrams →

The mistakes that cost marks in Number

One from each module — the error examiners see most, with the module that puts it right.

• "0.45 is bigger than 0.5 because 45 > 5." Length of digits is not size — line up place values: 0.50 vs 0.45. (Integers, Place Value & Ordering)
• Adding tops and bottoms: 1/2 + 1/3 is NOT 2/5. (2/5 is smaller than 1/2 — the answer got smaller by adding, which should ring an alarm.) (Fractions & Mixed Numbers)
• "Multiplying always makes numbers bigger." Multiplying by anything below 1 SHRINKS: 4.7 × 0.06 is far less than 4.7. (Decimals & Recurring Decimals)
• "Anything to the power 0 is 0." It's 1 (for any non-zero base) — the dividing-down pattern demands it (and the divide law proves it: aⁿ ÷ aⁿ = a⁰ = 1). (Powers, Roots & Index Laws)
• Writing 18 × 10³ as standard form. The front number must satisfy 1 ≤ a < 10 — re-zoom: 18 × 10³ = 1.8 × 10⁴. (Standard Form)
• "The upper bound of 5.6 (to 1 d.p.) is 5.7." It's 5.65 — half the rounding unit, not the whole unit. (Rounding, Estimation & Bounds)
• √(a + b) = √a + √b. False: √(9+16) = 5, but √9 + √16 = 7. Roots split over MULTIPLICATION only. (Surds)
• Adding group sizes to get the union: 18 + 14 = 32 in a class of 30 isn't a contradiction — it's a double-counted overlap of 2… plus anyone in neither. The overlap subtraction fixes it. (Sets & Venn Diagrams)

Where Number sits in the specification

Content area 1 of 4MA1, sub-topics 1.1, 1.3, 1.2, 1.4, 1.9, 1.8, 1.5. Incandio is aligned to the specification and is not published by Pearson; the numbers are given so you can check every module against your own copy.

• 1.1 — Integers
• 1.3 — Decimals (recurring → fraction: Higher)
• 1.2 — Fractions
• 1.4 — Powers and roots — surds (Higher)
• 1.9 — Standard form
• 1.8 — Degree of accuracy (bounds calculations: Higher)
• 1.5 — Set language and notation

How Number is mastered on Incandio

Every module above ends the same way: five questions that climb Grade 6 → 9+, then you teach the method back to Ember, an AI pupil who asks the awkward question, and defend it against the mathematician with the strongest claim on it. Exam Ready carries 82 authored exam-style questions across this strand, marked on Incandio.

All of Incandio Mathematics · The 4MA1 specification · Exam Ready