J560 · 2.03, 5.01–5.03Ratio & ProportionFoundation & HigherGrades 3–6

Compound Measures

Kilometres per hour, grams per cubic centimetre, newtons per square metre: each of these units combines two measurements. They are $\textbf{compound measures}$ , and the three that GCSE tests — speed, density and pressure — all share the same structure, so learning one pattern handles all three.

45 min Ratio & Proportion

The big picture

Each compound measure is one quantity divided by another: speed is distance per unit time, density is mass per unit volume, pressure is force per unit area. The unit tells you the formula — "km per hour" is km ÷ hours.

Most lost marks come from units, not formulas: a time in minutes used in km/h, or a mass in kilograms with a volume in cm³. OCR questions frequently include a conversion step deliberately.

GCSE Maths - How to Use Conversion Graphs (2026/27 exams)Curated by Kepler, not produced by us. Watch it, then read the notes below.

Open on YouTube

Before you start

Try a short calculation from the preceding topic without the notes.
Check the tier and grade band shown in this lesson.

Watch, pause, try

Video by Cognito. The video’s own board label is retained; follow the specification reference and scope notes on this lesson for assessed content.

Viewing focus: Use speed $=$ distance ÷ time and rearrange it

After watching, attempt these questions before opening the answers. You can also use the written lesson below.

After watching 1: A car travels 150 km in 2 hours. What is its average speed?

Show answer and reasoning

75 km/h. $150 \div 2$ .

After watching 2: A 30 g object has volume 12 cm³. What is its density?

Show answer and reasoning

2.5 g/cm³. $30 \div 12$ .

What you'll learn

Use speed $=$ distance ÷ time and rearrange it
Use density $=$ mass ÷ volume and pressure $=$ force ÷ area
Convert between units of time and compound units
Solve multi-step problems combining compound measures

Speed

Speed $= \dfrac{\text{distance}}{\text{time}}$ , so distance $=$ speed × time and time $=$ distance ÷ speed.

Times must match the unit of speed. 36 minutes is $\tfrac{36}{60} = 0.6$ hours.

Average speed for a whole journey is total distance ÷ total time.

s = \dfrac{d}{t}

Speed.

Example 1A train travels 45 km in 36 minutes. Find its average speed in km/h.

136 minutes

= 0.6

hours.

2Speed

= 45 \div 0.6

Answer75 km/h

Your turnSame method, new numbers — try it before moving on.

A coach travels 150 km in 2 hours 30 minutes. Find its average speed in km/h.

Your answer

Tip — Never write 1 h 15 min as 1.15 hours. It is $1\tfrac{15}{60} = 1.25$ hours.

Density

Density $= \dfrac{\text{mass}}{\text{volume}}$ , measured in g/cm³ or kg/m³.

Rearranged: mass $=$ density × volume, volume $=$ mass ÷ density.

\rho = \dfrac{m}{V}

Density.

Example 1Aluminium has density 2.7 g/cm³. Find the mass of a block measuring 2 cm by 4 cm by 5 cm.

1Volume

= 2 \times 4 \times 5 = 40

cm³.

2Mass

= 2.7 \times 40

Answer108 g

Your turnSame method, new numbers — try it before moving on.

A block measures 3 cm by 2 cm by 5 cm and has density 8 g/cm³. Find its mass, in grams.

Your answer

Pressure

Pressure $= \dfrac{\text{force}}{\text{area}}$ , measured in N/m² (pascals, Pa) or N/cm².

The same force on a smaller area gives a greater pressure — why a knife cuts and snowshoes stop you sinking.

P = \dfrac{F}{A}

Pressure.

Example 1A box weighing 600 N rests on a face of area 0.25 m². Find the pressure on the floor.

P = \dfrac{600}{0.25}

Answer2400 N/m²

Why this works

All three formulas have the form "top ÷ bottom" with the compound unit written "top per bottom". If you remember the unit, you have the formula.

Converting compound units

Convert each part of the unit separately. $72$ km/h $= \dfrac{72\,000 \text{ m}}{3600 \text{ s}} = 20$ m/s.

For area and volume units, the conversion factor is squared or cubed: $1$ m³ $= 1\,000\,000$ cm³, so $3$ g/cm³ $= 3\,000\,000$ g/m³ $= 3000$ kg/m³.

Example 1400 cm³ of a liquid of density 0.8 g/cm³ is mixed with 600 cm³ of a liquid of density 1.1 g/cm³. Find the density of the mixture.

1Masses:

0.8 \times 400 = 320

g and

1.1 \times 600 = 660

2Total mass 980 g, total volume 1000 cm³.

Answer0.98 g/cm³

Your turnSame method, new numbers — try it before moving on.

Convert 72 km/h into m/s.

Your answer

Tip — The density of a mixture is not the average of the two densities. Find total mass and total volume, then divide.

Think like an examiner

Show unit conversions as a separate step.
Include units in every answer.
For mixtures or multi-stage journeys, work with totals.

Compound measures

\text{speed} = \tfrac{\text{distance}}{\text{time}}

Speed.

\text{density} = \tfrac{\text{mass}}{\text{volume}}

Density.

\text{pressure} = \tfrac{\text{force}}{\text{area}}

Pressure.

Watch out for these

Using 36 minutes as 0.36 hours.

36 minutes is

36 \div 60 = 0.6

hours.

Averaging densities to get the density of a mixture.

Divide total mass by total volume.

Converting 1 m³ to 100 cm³.

100^{3} = 1\,000\,000

cm³.

Mixing kg and g in a density calculation.

Use consistent units throughout.

Stretch yourself

Ella drives 120 km at an average speed of 80 km/h, then 90 km at an average speed of 60 km/h. Find her average speed for the whole journey.

Hint — Find the time for each part first. Average speed is total distance over total time.

Questions students ask

What is a compound measure?

A measure made from two others, such as speed (distance and time) or density (mass and volume).

How do I remember the formulas?

Read the unit: "grams per cubic centimetre" means grams ÷ cm³.

What is a pascal?

One newton per square metre, the SI unit of pressure.

Key takeaways

Speed = distance ÷ time; density = mass ÷ volume; pressure = force ÷ area.
The unit "A per B" tells you the formula A ÷ B.
Convert times to hours, and match units before calculating.
Area and volume conversions square or cube the factor.
Use totals for average speeds and mixed densities.

Exam-style questions

Practise it the way it is examined

3 original questions · 7 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.

Question 1Grade 32 marks

A car travels for 2 hours 15 minutes at an average speed of 48 km/h. How far does it travel?[2]

Question 2Grade 52 marks

A force of 750 N acts on an area of 0.3 m². Work out the pressure.[2]

Question 3Grade 63 marks

300 cm³ of metal A (density 7 g/cm³) and 200 cm³ of metal B (density 9 g/cm³) are combined. Work out the density of the alloy.[3]

Unlimited practice

Skill drill

A new question every time, marked instantly, with a full worked solution. Aim for a streak of five, then move up a level.

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Explore further

OCR J560 official specification (opens in a new tab)
Check the assessed scope and practical or mathematical requirements.
Read or explore this topic (opens in a new tab)
An external explanation or interactive activity to use alongside the lesson. It may include extension material.

Return to this tomorrow

Close the notes and answer from memory. Revisit any explanation you cannot yet reconstruct.

How long does a 140 km journey take at 56 km/h?
A force of 90 N acts on 0.03 m². What is the pressure?
Convert 54 km/h to m/s.
A metal has density 8 g/cm³. What is the mass of 0.002 m³ of it?

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

Browse practice topics

Related lessons

All 5 lessons

Compound Measures

Kilometres per hour, grams per cubic centimetre, newtons per square metre: each of these units combines two measurements. They are

\textbf{compound measures}

, and the three that GCSE tests — speed, density and pressure — all share the same structure, so learning one pattern handles all three.

45 min Ratio & Proportion

Watch, pause, try

Video by Cognito. The video’s own board label is retained; follow the specification reference and scope notes on this lesson for assessed content.

Viewing focus: Use speed

=

distance ÷ time and rearrange it

After watching, attempt these questions before opening the answers. You can also use the written lesson below.

After watching 1: A car travels 150 km in 2 hours. What is its average speed?

Show answer and reasoning

75 km/h. $150 \div 2$ .

After watching 2: A 30 g object has volume 12 cm³. What is its density?

Show answer and reasoning

2.5 g/cm³. $30 \div 12$ .

Practise it the way it is examined

Question 1Grade 32 marks

A car travels for 2 hours 15 minutes at an average speed of 48 km/h. How far does it travel?[2]

Question 2Grade 52 marks

A force of 750 N acts on an area of 0.3 m². Work out the pressure.[2]

Question 3Grade 63 marks

300 cm³ of metal A (density 7 g/cm³) and 200 cm³ of metal B (density 9 g/cm³) are combined. Work out the density of the alloy.[3]