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Exam questions · Maths · Ratio and Proportion

Units, Conversions and Scale

  • 6 exam questions
  • 17 marks
  • 9 quick checks
  1. 1 Change [2 marks]

    (a) Change 6.5 m to centimetres. [1 mark] (b) Change 3200 g to kilograms. [1 mark]

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    Model answer

    (a) \(6.5 \times 100 = 650\) cm. (b) \(3200 \div 1000 = 3.2\) kg.

    Mark scheme

    • (a) 650 cm — B1
    • (b) 3.2 kg — B1
  2. 2 Work out [2 marks]

    A bottle holds 1.5 litres of juice. How many 250 ml glasses can be completely filled from the bottle?

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    Model answer

    \(1.5\text{ litres} = 1500\) ml, and \(1500 \div 250 = 6\) glasses.

    Mark scheme

    • 1500 ml seen, or \(1500 \div 250\) — M1
    • 6 — A1
  3. 3 Work out [5 marks]

    The diagram shows a scale drawing of a living room. The scale is 1 cm to 2 m. (a) Work out the real length of the room. [1 mark] (b) Work out the real perimeter of the room. [2 marks] (c) Work out the real area of the room. [2 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) The real width is \(3.5 \times 2 = 7\) m, so the perimeter is \(2 \times (12 + 7) = 38\) m. (c) The area is \(12 \times 7 = 84\) m\(^2\).

    Mark scheme

    • (a) 12 m — B1
    • (b) Real width 7 m, or \(12 + 7 + 12 + 7\) — M1
    • (b) 38 m — A1
    • (c) \(12 \times 7\) — M1
    • (c) 84 m\(^2\) — A1
  4. 4 Work out [3 marks]

    A map has a scale of \(1 : 20\,000\). A path is 9 cm long on the map. Work out the real length of the path in kilometres.

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    Model answer

    \(9 \times 20\,000 = 180\,000\) cm. This is 1800 m, which is 1.8 km.

    Mark scheme

    • \(9 \times 20\,000\) — M1
    • \(180\,000\) cm or \(1800\) m — M1
    • 1.8 km — A1
  5. 5 Work out [2 marks]

    1 gallon is approximately 4.5 litres. A tank holds 36 litres of water. Approximately how many gallons does it hold?

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    Model answer

    \(36 \div 4.5 = 8\) gallons.

    Mark scheme

    • \(36 \div 4.5\) — M1
    • 8 gallons — A1
  6. 6 Change [3 marks]

    (a) Change 0.2 m\(^2\) to cm\(^2\). [2 marks] (b) Change \(3\,000\,000\) cm\(^3\) to m\(^3\). [1 mark]

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    Model answer

    (a) \(1\text{ m}^2 = 10\,000\) cm\(^2\), so \(0.2 \times 10\,000 = 2000\) cm\(^2\). (b) \(3\,000\,000 \div 1\,000\,000 = 3\) m\(^3\).

    Mark scheme

    • (a) \(0.2 \times 10\,000\) or \(20 \times 100\) — M1
    • (a) 2000 — A1
    • (b) 3 — B1

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\(^3\).