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GCSE Maths · Higher · Chapter 5: Ratio and proportion · Lesson 2

Compound measures

Grades 4–7About 40 minutesCalculator allowed33 marks
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NameClassDate
A

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

  1. A1
    Needed today

    Write 2 hours 15 minutes in hours, as a decimal.

    [1 mark]
    Answer
  2. A2
    Last lesson

    Share £66 in the ratio . Find the larger share.

    [1 mark]
    Answer
  3. A3
    From chapter 3

    A line of best fit is . Estimate when .

    [1 mark]
    Answer
  4. A4
    Key Stage 3

    Write out of as a percentage.

    [1 mark]
    Answer
B

Example, then your turn

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

A cyclist rides 33 km at an average speed of 12 km/h. How long does the ride take? Give your answer in hours and minutes.

Hint Time distance speed. Then turn the decimal part of an hour into minutes.
  1. B1

    A coach travels 189 km at an average speed of 54 km/h. How long does the journey take? Give your answer in hours and minutes.

    [2 marks]
    Answer hours minutes
Example 2

A block of metal has a mass of 702 g and a volume of 90 cm³. Work out its density.

Hint Density mass volume.
  1. B2

    A piece of glass has a mass of 375 g and a volume of 150 cm³. Work out its density.

    [2 marks]
    Answer
C

Practice

Grades 5–6
  1. C1

    A train travels 95 km in 1 hour 15 minutes. Work out its average speed in km/h.

    [2 marks]
    Answer
  2. C2

    Write a speed of 12 m/s in km/h.

    [2 marks]
    Answer
  1. C3

    Aluminium has a density of 2.7 g/cm³. Work out the mass of 250 cm³ of aluminium.

    [2 marks]
    Answer
  2. C4

    A crate weighs 840 N. It stands on the floor on its base, which is 0.7 m by 0.5 m. Work out the pressure on the floor, in N/m².

    [2 marks]
    0.7 m0.5 m
    Not drawn accurately
    Answer
  3. C5

    150 cm³ of a metal with density 8 g/cm³ is melted together with 250 cm³ of a metal with density 4 g/cm³. Work out the density of the mixture.

    [3 marks]
    Answer
  4. C6

    A tank is a cuboid. Water flows in at 12 litres per minute. How many minutes does it take to fill the empty tank? ( litre cm³)

    [3 marks]
    80 cm60 cm50 cm
    Not drawn accurately
    Answer
D

Exam-style questions

Grades 6–7
  1. D1

    Kai says, "A journey of 2.3 hours takes 2 hours 30 minutes."

    Explain why Kai is wrong, and give the correct time in hours and minutes.

    [2 marks]
  1. D2

    Ana leaves home at 08:50. She drives 150 km at an average speed of 60 km/h, stops for 40 minutes, then drives a further 90 km at an average speed of 45 km/h.

    (a)

    Work out the time she arrives.

    [3 marks]
    Answer
    (b)

    Work out her average speed for the whole trip, including the stop. Give your answer to 1 decimal place.

    [3 marks]
    Answer
    Total for D2: 6 marks
E

Extension

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

  1. E1

    A solid cube is made of metal with a density of 8 g/cm³. It stands on the floor and exerts a pressure of 4000 N/m². Take the force to be 10 N for each kilogram of mass. Work out the length of a side of the cube.

    [3 marks]
    Hint 1 · What to try

    Call the side cm. Write the mass, the force and the area of the base in terms of .

    Hint 2 · The first line

    Mass g kg, so the force is N. The base is cm², which is m².

    Hint 3 · The full method

    Pressure . So and cm.

    Answer
F

How did it go?

Colour one circle on each line.
Not yetNearlyYes
I can use speed, distance and time, and write a time in hours and minutes.
I can use density and pressure, and change between units.

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