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DfE statement R1 · Ratio, proportion and rates of change

Converting between standard and compound units

Both tiersEither paper

Converting between standard and compound units is content statement R1 of the DfE GCSE mathematics subject content, in the ratio, proportion and rates of change area. It is on both tiers, and it appears on both the calculator and the non-calculator papers. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.

What the specification says

The DfE subject content for GCSE mathematics states, verbatim: "Change freely between related standard units (e.g. time, length, area, volume/capacity, mass) and compound units (e.g. speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts." (statement R1). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.

— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement R1

Tier

Both tiers. This statement is Foundation content, which means Higher students are examined on it too — Higher is Foundation plus more, never instead of it.

Calculator

This turns up on both the non-calculator and the calculator papers, so practise it both ways — the written method for Paper 1 and the efficient calculator route for Papers 2 and 3.

Common mistakes

  • Converting area and volume with the linear factor: 1 cm² is 100 mm², and 1 m³ is 1 000 000 cm³.
  • Multiplying where you should divide. Going from a large unit to a small one gives a bigger number.
  • Converting km/h to m/s by dividing by 3600 only, and forgetting to multiply by 1000 first.

Sample questions (10 of 30)

R1 · Converting between standard and compound unitsQuestion 1 of 10 · 0 correct
Practice mode· no pressure · hints available

Ratio, proportion and rates of change

R1

Beginner

A watering can holds 4500 cm³ of water. Given that 1 litre = 1000 cm³, work out the capacity of the watering can in litres.

💡 Hints:
Foundation worksheetHigher worksheetFoundation ratio, proportion and rates of change practiceHigher ratio, proportion and rates of change practice

Nearby statements

R2Scale factors, scale diagrams and mapsR3One quantity as a fraction of another

Questions people ask

Is converting between standard and compound units on Foundation or Higher?

Both. It is Foundation content, so it can be asked on either tier.

Can I use a calculator for converting between standard and compound units?

It depends on the paper. Paper 1 is non-calculator; Papers 2 and 3 allow one, and this topic is asked on both kinds.

What is the single most common mistake here?

Converting area and volume with the linear factor: 1 cm² is 100 mm², and 1 m³ is 1 000 000 cm³.

Are these past paper questions?

No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.

Back to Ratio, proportion and rates of change at Foundation or at Higher.

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