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Exam questions · Maths · Ratio and Proportion

Units, Conversions and Scale

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

    (a) Change 4.5 km to metres. (1 mark) (b) Change 2750 ml to litres. (1 mark)

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    Model answer

    (a) \(4.5 \times 1000 = 4500\) m. (b) \(2750 \div 1000 = 2.75\) litres.

    Mark scheme

    • (a) 4500 m — B1
    • (b) 2.75 litres — B1
  2. 2 Work out [3 marks]

    A cake needs 125 g of butter. Maria has a 2 kg block of butter. Work out how many cakes she can make.

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    Model answer

    \(2\text{ kg} = 2000\) g, and \(2000 \div 125 = 16\) cakes.

    Mark scheme

    • 2 kg changed to 2000 g — M1
    • \(2000 \div 125\) — M1
    • 16 — A1
  3. 3 Work out [5 marks]

    The diagram shows a scale drawing of the floor of a living room. The scale is 1 cm represents 2 m. (a) Work out the real length of the room. (1 mark) (b) Work out the real width of the room. (1 mark) Carpet costs \(\pounds 15\) per square metre. (c) Work out the cost of carpet to cover the whole floor. (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 area is \(12 \times 7 = 84\) m\(^2\), so the cost is \(84 \times 15 = \pounds 1260\).

    Mark scheme

    • (a) 12 m — B1
    • (b) 7 m — B1
    • (c) \(12 \times 7 = 84\) — M1
    • (c) \(84 \times 15\) — M1
    • (c) \(\pounds 1260\) — A1
  4. 4 Work out [3 marks]

    A map has a scale of \(1 : 25\,000\). Two villages are 6.4 cm apart on the map. Work out the real distance between the villages in kilometres.

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    Model answer

    \(6.4 \times 25\,000 = 160\,000\) cm. This is \(1600\) m, which is 1.6 km.

    Mark scheme

    • \(6.4 \times 25\,000\) — M1
    • \(160\,000\) cm or \(1600\) m — M1
    • 1.6 km — A1
  5. 5 Work out [3 marks]

    A rectangle measures 2.5 m by 40 cm. Work out the area of the rectangle in cm\(^2\).

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    Model answer

    \(2.5\text{ m} = 250\) cm, so the area is \(250 \times 40 = 10\,000\) cm\(^2\).

    Mark scheme

    • 2.5 m changed to 250 cm, or 40 cm changed to 0.4 m — M1
    • \(250 \times 40\) — M1
    • \(10\,000\) cm\(^2\) — A1
  6. 6 Change [4 marks]

    (a) Change 3.5 m\(^2\) to cm\(^2\). (2 marks) (b) Change \(4\,000\,000\) cm\(^3\) to m\(^3\). (2 marks)

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    Model answer

    (a) \(1\text{ m}^2 = 100 \times 100 = 10\,000\) cm\(^2\), so \(3.5 \times 10\,000 = 35\,000\) cm\(^2\). (b) \(1\text{ m}^3 = 1\,000\,000\) cm\(^3\), so \(4\,000\,000 \div 1\,000\,000 = 4\) m\(^3\).

    Mark scheme

    • (a) \(3.5 \times 10\,000\) or \(350 \times 100\) — M1
    • (a) \(35\,000\) — A1
    • (b) \(4\,000\,000 \div 1\,000\,000\) — M1
    • (b) 4 — 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\(^3\).