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Unit Conversions - Edexcel GCSE Higher Maths

Typically 2-4 marks per paper asked directly, plus the conversions buried inside other questions · Spec 1MA1

Spec reference R1 on Edexcel's 1MA1 syllabus asks you to change freely between related standard units, and it names them: time, length, area, volume and capacity, mass, together with the compound units built from those, such as speed, rates of pay, prices, density and pressure. At Foundation level most of that is a one-mark instruction to shift a decimal point. At Higher tier it becomes a question about dimension. One metre is 100 centimetres, but one square metre is 100×100=10000100 \times 100 = 10000 square centimetres and one cubic metre is 100×100×100=1000000100 \times 100 \times 100 = 1000000 cubic centimetres. Those two facts carry most of the marks this topic is worth.

Edexcel sets it in two shapes. The bare instruction, 'Change 2.5 m2^2 to cm2^2', is worth 2 marks and has been on papers of both tiers for years; 250 is the answer it was built to collect, and it collects plenty of them. The other shape hides the conversion inside a longer question: a cuboid with one edge in metres and another in millimetres, a capacity wanted in litres when the volume came out in cubic centimetres, or two speeds quoted in different units with 'which is faster' underneath. Any of the three papers can carry it. Paper 1 is non-calculator, so the numbers there are chosen to keep the arithmetic to a shift of the decimal point, while Papers 2 and 3 take the currency questions, where a rate such as £1 = €1.16 reduces the whole thing to one multiplication or one division and the mark rests entirely on which of the two you choose.

Two lines of working protect most of these marks. Write the conversion factor down as a statement about one unit before you use it: 1 m2^2 = 10000 cm2^2, 1 cm3^3 = 1000 mm3^3, 1 litre = 1000 cm3^3. Then say, in words, whether the answer should be a bigger number or a smaller one, because a smaller unit always needs more of them, and that one check catches every reversed division. For a compound unit, convert the top and the bottom separately and combine at the end instead of reaching for a half-remembered multiplier. And keep the power on the conversion factor, never on the measurement: converting 7 m2^2 means 7×10027 \times 100^2, and the 7 is never squared.

Worked example

The floor of a room is a rectangle measuring 4.2 m by 3.5 m. One tin of floor sealant covers 30 000 cm2^2. Work out the smallest number of tins needed to seal the whole floor.
[4 marks]
  1. Area of the floor =4.2×3.5=14.7= 4.2 \times 3.5 = 14.7 m2^2.
    M1: area worked out in the units the room was given in
  2. 1 m2^2 is 100×100=10000100 \times 100 = 10000 cm2^2, so the floor is 14.7×10000=14700014.7 \times 10000 = 147000 cm2^2.
    M1: multiplying by the squared factor; multiplying by 100 here is the error the mark is placed to catch
  3. Tins needed =14700030000=4.9= \frac{147000}{30000} = 4.9.
    M1: dividing floor area by coverage with both quantities in cm2^2
  4. You cannot buy 0.9 of a tin, so 5 tins are needed.
    A1: 5; rounding 4.9 down to 4 leaves part of the floor unsealed

Practice questions

These are original questions in Edexcel 1MA1 Higher style. The opening set is straight metric conversion of length, mass and capacity; the bulk of the bank is the squared and cubed work on areas and volumes, which is where the Higher marks sit; the later questions convert a speed, a flow rate, a rate of pay and a currency, or run backwards from a converted answer to the measurement it came from. Every answer is exact unless the question states a rounding.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

  1. Question 1 Warm-up [1 mark]
    Change 3.6 km into metres.
  2. Question 2 Exam pace [3 marks]
    Change 3.5 m2^2 into cm2^2, and change 3.5 m3^3 into cm3^3.
  3. Question 3 Exam pace [1 mark]
    To change an area from mm2^2 into cm2^2, you divide by which number?
    Answer options for question 3
  4. Question 4 Exam pace [1 mark]
    To change a speed from km/h into m/s, what do you do?
    Answer options for question 4
  5. Question 5 Stretch [3 marks]
    A pump moves 4500 cm3^3 of water every second. Work out the rate at which it pumps, in litres per minute.
  6. Question 6 Stretch [4 marks]
    A water tank is a cuboid measuring 80 cm by 50 cm by 1.2 m. Water flows into the empty tank at 15 litres per minute. Work out how long it takes to fill the tank, in minutes.

Common mistakes examiners see

  • Using the length factor on an area, so 7 m2^2 is written as 700 cm2^2 instead of 70 000 cm2^2, and 2.5 m2^2 comes out as 250.

    Write the factor as a statement about one unit before you touch the measurement: 1 m2^2 is a square 100 cm by 100 cm, so it is 10 000 cm2^2. Then multiply by 10 000. Sketching that unit square with 100 along each edge takes five seconds and settles the argument.

  • Using the length factor on a volume, so 8 m3^3 becomes 800 cm3^3 rather than 8 000 000 cm3^3, or 0.5 m3^3 is answered as 50 cm3^3.

    Cube the factor: 1 m3^3 is 100 cm by 100 cm by 100 cm, which is 1 000 000 cm3^3. Any figure in cubic metres is multiplied by a million to reach cubic centimetres, so if your answer has not grown by six digits you have used the wrong factor.

  • Squaring the measurement instead of the factor, converting 7 m2^2 by working out 72=497^2 = 49, or by finding 700 and then squaring that to get 490 000.

    The power belongs to the conversion factor. Converting 7 m2^2 to cm2^2 is 7×10027 \times 100^2, and the 7 stays as it is. Read the calculation to yourself as 'seven lots of ten thousand' and the wrong version stops looking plausible.

  • Multiplying when the unit is getting larger, turning 45 000 cm2^2 into 450 000 000 m2^2, or changing €522 into pounds at £1 = €1.16 by multiplying to get £605.52 instead of dividing to get £450.

    Settle the direction in words first. A larger unit means fewer of them, so the number must shrink; a smaller unit means more of them, so the number must grow. On a currency question, one pound buys more than one euro, so a euro amount converted into pounds is always the smaller figure.

  • Converting only one half of a compound unit, so 285 km/h is turned into 0.079 m/s by dividing by 3600 alone, or into 285 000 m/s by multiplying by 1000 alone.

    Treat the numerator and the denominator as two separate conversions and write both lines down: 285 km/h is 285 000 metres per hour, and one hour is 3600 seconds, so the speed is 285 000 divided by 3600. The same routine handles a rate of pay in pence per minute or a flow rate in cubic metres per hour, and it removes the guesswork about a single multiplier.

Frequently asked questions

Why is 1 square metre 10 000 square centimetres and not 100?
A square metre is a square whose sides are one metre long, and each of those sides is 100 cm. The square therefore holds 100 rows of 100 centimetre squares, which is 10 000 cm2^2. Volume works the same way with a third dimension: a cubic metre holds 100 layers of 100 by 100 centimetre cubes, so it is 1 000 000 cm3^3.
Are the metric conversions given in the Edexcel maths exam?
No. The Exam Aid formulae sheet issued with 1MA1 papers for the 2025 to 2027 series carries the trapezium and prism formulae, the circle formulae, the quadratic formula, Pythagoras and the trigonometric rules, compound interest and two probability rules. No conversion factor is on it, so 1 kg = 1000 g, 1 litre = 1000 cm3^3, 1 m2^2 = 10 000 cm2^2 and 1 m3^3 = 1 000 000 cm3^3 all have to be recalled. A question needing an imperial equivalent, such as miles to kilometres, normally states it in the stem.
How do you convert litres into cubic metres?
Divide by 1000. A litre is 1000 cm3^3 and a cubic metre is 1 000 000 cm3^3, so one cubic metre holds 1000 litres. A 250 litre water butt is therefore 0.25 m3^3, and going the other way a 0.4 m3^3 tank holds 400 litres.
How many marks are unit conversions worth on Edexcel Higher?
Asked directly, a conversion is 1-2 marks, and questions of that kind account for roughly 2-4 marks per paper. The larger contribution is indirect, inside a mensuration question that mixes metres and centimetres, a best-buy comparison across two currencies, or a compound-measure calculation where the units have to be matched before the formula is used. Those are the cheapest marks on the paper to win back, because the mathematics around them was already right.

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