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Exam questions · Maths · Ratio and Proportion

Units, Conversions and Scale

  • 6 exam questions
  • 19 marks
  • 9 quick checks
  1. 1 Convert [2 marks]

    (a) Convert 0.45 km to metres. [1 mark] (b) Convert 5.2 kg to grams. [1 mark]

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    Model answer

    (a) \(0.45 \times 1000 = 450\) m. (b) \(5.2 \times 1000 = 5200\) g.

    Mark scheme

    • (a) 450 m — B1
    • (b) 5200 g — B1
  2. 2 Calculate [2 marks]

    A bag of rice has a mass of 1.5 kg. Calculate how many 60 g portions can be made from the bag.

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    Model answer

    \(1.5\text{ kg} = 1500\) g, and \(1500 \div 60 = 25\) portions.

    Mark scheme

    • 1500 g seen, or \(1500 \div 60\) — M1
    • 25 — A1
  3. 3 Calculate [5 marks]

    The diagram shows a scale drawing of a living room. The scale is 1 cm represents 2 m. (a) Calculate the real length of the room. [1 mark] (b) Calculate the real width of the room. [1 mark] A rug has an area of 21 m\(^2\). (c) What percentage of the floor of the room is covered by the rug? [3 marks]

    A floor plan of a living room measuring 6 cm by 3.5 cm on the drawing, with the scale 1 cm represents 2 m.
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    Model answer

    (a) \(6 \times 2 = 12\) m. (b) \(3.5 \times 2 = 7\) m. (c) The floor area is \(12 \times 7 = 84\) m\(^2\), so the rug covers \(\dfrac{21}{84} = \dfrac{1}{4} = 25\%\).

    Mark scheme

    • (a) 12 m — B1
    • (b) 7 m — B1
    • (c) \(12 \times 7 = 84\) — M1
    • (c) \(\dfrac{21}{84}\) or \(21 \div 84\) — M1
    • (c) 25% — A1
  4. 4 Calculate [3 marks]

    A plan of a field has a scale of \(1 : 5000\). The field is 4.5 cm long on the plan. Calculate the real length of the field in metres.

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    Model answer

    \(4.5 \times 5000 = 22\,500\) cm, which is 225 m.

    Mark scheme

    • \(4.5 \times 5000\) — M1
    • \(22\,500\) cm — M1
    • 225 m — A1
  5. 5 Calculate [3 marks]

    A water tank has a volume of 2.4 m\(^3\). 1 m\(^3\) is 1000 litres. Calculate the volume of the tank in litres, and the number of 20-litre buckets needed to fill it.

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    Model answer

    \(2.4 \times 1000 = 2400\) litres. The number of buckets is \(2400 \div 20 = 120\).

    Mark scheme

    • \(2.4 \times 1000\) — M1
    • 2400 litres — A1
    • 120 buckets — B1
  6. 6 Convert [4 marks]

    (a) Convert 5 m\(^2\) to cm\(^2\). [2 marks] (b) Convert \(15\,000\) mm\(^2\) to cm\(^2\). [2 marks]

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    Model answer

    (a) \(1\text{ m}^2 = 10\,000\) cm\(^2\), so \(5 \times 10\,000 = 50\,000\) cm\(^2\). (b) \(1\text{ cm}^2 = 100\) mm\(^2\), so \(15\,000 \div 100 = 150\) cm\(^2\).

    Mark scheme

    • (a) \(5 \times 10\,000\) — M1
    • (a) \(50\,000\) — A1
    • (b) \(15\,000 \div 100\) — M1
    • (b) 150 — A1

Quick check

  1. 1

    Change 3.6 km to metres.

    1. A3600 m
    2. B360 m
    3. C36 m
    4. D36 000 m
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    A: 3600 m

    Multiply by 1000: \(3.6 \times 1000 = 3600\).

  2. 2

    Change 2450 g to kilograms.

    1. A24.5 kg
    2. B0.245 kg
    3. C2450 kg
    4. D2.45 kg
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    D: 2.45 kg

    Divide by 1000: \(2450 \div 1000 = 2.45\).

  3. 3

    Change 0.75 litres to millilitres.

    1. A75 ml
    2. B7.5 ml
    3. C750 ml
    4. D7500 ml
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    C: 750 ml

    Multiply by 1000: \(0.75 \times 1000 = 750\).

  4. 4

    Change 250 cm to metres.

    1. A25 m
    2. B2.5 m
    3. C0.25 m
    4. D2500 m
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    B: 2.5 m

    Divide by 100: \(250 \div 100 = 2.5\).

  5. 5

    A map has a scale of \(1 : 50\,000\). Two towns are 4 cm apart on the map. What is the real distance?

    1. A2 km
    2. B200 km
    3. C20 km
    4. D0.2 km
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    A: 2 km

    \(4 \times 50\,000 = 200\,000\) cm. Divide by 100 to get 2000 m, then by 1000 to get 2 km.

  6. 6

    A scale drawing uses 1 cm to represent 2 m. A line on the drawing is 7 cm. How long is it in real life?

    1. A3.5 m
    2. B9 m
    3. C140 m
    4. D14 m
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    D: 14 m

    Multiply by the scale: \(7 \times 2 = 14\) m.

  7. 7

    A cake uses 250 g of flour. How many cakes can be made from a 2 kg bag?

    1. A80
    2. B125
    3. C8
    4. D500
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    C: 8

    \(2\text{ kg} = 2000\) g, and \(2000 \div 250 = 8\).

  8. 8

    How many cm\(^2\) are in 1 m\(^2\)?

    1. A100
    2. B10 000
    3. C1000
    4. D1 000 000
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    B: 10 000

    A square metre is a square of side 100 cm, so its area is \(100 \times 100 = 10\,000\) cm\(^2\).

  9. 9

    Change 5 m\(^3\) to cm\(^3\).

    1. A5 000 000 cm\(^3\)
    2. B500 000 cm\(^3\)
    3. C500 cm\(^3\)
    4. D5000 cm\(^3\)
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    A: 5 000 000 cm\(^3\)

    \(1\text{ m}^3 = 100^3 = 1\,000\,000\) cm\(^3\), so \(5\text{ m}^3 = 5\,000\,000\) cm\(^3\).