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GCSE/Mathematics/Edexcel

G14Standard units of measure: length, area, volume, capacity, mass, time, money

Notes

Standard units of measure

Edexcel 1MA1 examines unit work across all six papers, but unit-conversion-heavy problems land on Papers 2F/2H. Foundation tier focuses on conversion within the metric system; Higher tier extends to compound units and rate problems.

Length

  • 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.
  • 1 km = 100 000 cm = 1 000 000 mm.

Area

  • 1 m² = 10 000 cm² (because 100 × 100).
  • 1 cm² = 100 mm² (because 10 × 10).
  • 1 km² = 1 000 000 m².

Common slip: students multiply linear conversions when they should square them.

Volume / Capacity

  • 1 m³ = 1 000 000 cm³.
  • 1 cm³ = 1 ml.
  • 1 litre = 1000 ml = 1000 cm³.
  • 1 m³ = 1000 litres.

Mass

  • 1 tonne = 1000 kg, 1 kg = 1000 g, 1 g = 1000 mg.

Time

  • 1 hour = 60 minutes, 1 minute = 60 seconds, 1 hour = 3600 seconds.
  • Decimal time: 0.5 h = 30 min, 0.25 h = 15 min, 1.5 h = 1h 30 min.

Money

  • £1 = 100p. Always state monetary answers to 2 decimal places (e.g. £4.50, not £4.5).

Common Edexcel mark-scheme phrasing

  • M1 for a correct conversion factor.
  • A1 for the converted value.
  • A1ft for follow-through if the student carried an arithmetic slip but used the right method.

Common mistakesCommon errors

  • Squaring or cubing wrong on area/volume conversions (1 m ≠ 100 cm² is the wrong reasoning).
  • Mixing up litres and ml (1 litre = 1000 ml, NOT 100 ml).
  • Reading 1.5 hours as 1 h 50 min (wrong — it is 1 h 30 min).
  • Stating money as £4.5 instead of £4.50.

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Practice questions

Try each before peeking at the worked solution.

  1. Question 15 marks

    Mixed unit conversions — Foundation

    Edexcel Paper 1F (non-calculator)

    (a) Convert 4500 mm to m. (1 mark)
    (b) Convert 2.5 litres to ml. (1 mark)
    (c) Convert 3 hours 15 minutes to minutes. (2 marks)
    (d) A book costs 450p. Write this in pounds. (1 mark)

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  2. Question 25 marks

    Area and volume conversions — Higher

    Edexcel Paper 1H — Higher

    (a) A rectangle has area 2.4 m². Convert this area to cm². (2 marks)
    (b) A cuboid has volume 750 000 cm³. Convert this volume to m³. (2 marks)
    (c) A water tank holds 1.8 m³. How many litres is this? (1 mark)

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  3. Question 35 marks

    Real-life unit problem — Foundation

    Edexcel Paper 2F (calculator)

    A swimming pool holds 60 m³ of water. Water is pumped in at a rate of 2.5 litres per second.

    (a) How many litres does the pool hold? (1 mark)
    (b) How many seconds does it take to fill? (2 marks)
    (c) Convert your answer to (b) into hours and minutes. (2 marks)

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Flashcards

G14 — Standard units of measure: length, area, volume, capacity, mass, time, money

7-card SR deck for Edexcel GCSE Mathematics (1MA1) — Leaves Batch 5 topic G14

7 cards · spaced repetition (SM-2)