1MA1 · R1, R11Ratio, Proportion & Rates of ChangeFoundation & 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 $compound measures$ , 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. Edexcel questions frequently include a conversion step deliberately.

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 $= \frac{distance}{time}$ , so distance $=$ speed × time and time $=$ distance ÷ speed.

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

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

s = \frac{d}{t}

Speed.

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 $1 \frac{15}{60} = 1.25$ hours.

Density

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

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

ρ = \frac{m}{V}

Density.

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 $= \frac{force}{area}$ , 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 = \frac{F}{A}

Pressure.

P = \frac{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 $= \frac{72 000 m}{3600 s} = 20$ m/s.

For area and volume units, the conversion factor is squared or cubed: $1$ m³ $= 1000000$ cm³, so $3$ g/cm³ $= 3000000$ g/m³ $= 3000$ kg/m³.

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

speed = \frac{distance}{time}

Speed.

density = \frac{mass}{volume}

Density.

pressure = \frac{force}{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.

10 0^{3} = 1000000

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.

0 / 0 first-time correct Streak 0Best at this level: 0

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Real past-paper questions on Compound Measures, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.

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Compound Measures

Speed

Density

Pressure

Converting compound units

Practise it the way it is examined

Skill drill

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Related topics

Compound Measures

Speed

Density

Pressure

Converting compound units

Practise it the way it is examined

Skill drill

Practise this topic

Related topics