AQA · GCSE · Mathematics
Course version: 8300 · Version from Sept 2015
Use compound units such as density and pressure
Full specification wording
Ratio, proportion and rates of change: use compound units such as density and pressure
A compound unit combines two or more measures, so its value is a rate.
Checked against the AQA 8300 specification (opens in a new tab) on .
- Point 13 of 21
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A compound unit combines two or more measures, so its value is a rate. Density compares mass with volume: density = mass ÷ volume, commonly in g/cm³ or kg/m³. Pressure compares force with area: pressure = force ÷ area, commonly in N/m² or pascals (Pa). To use these units, identify the two quantities, divide in the correct order, and keep units consistent. For example, a 240 g block of volume 30 cm³ has density 240 ÷ 30 = 8 g/cm³. A force of 60 N on an area of 4 m² gives pressure 60 ÷ 4 = 15 N/m². Rearranging finds a missing mass, volume, force or area. Converting units matters: 1 m³ = 1 000 000 cm³, so 8 g/cm³ = 8 000 kg/m³.
What earns the marks
- Selects the correct relationship: density = mass ÷ volume, or pressure = force ÷ area.
- Substitutes the given values with matching units before calculating.
- Calculates accurately, including correct use of a calculator where allowed.
- Interprets the result with the correct compound unit, such as g/cm³, kg/m³, N/m² or Pa.
- Rearranges the formula correctly when mass, volume, force or area is the unknown.
- Converts between compatible units, for example 1 m³ = 1 000 000 cm³, before comparing or calculating.
Common mistakes and how to put them right
Multiplying mass by volume instead of dividing.
Put it right: Density = mass ÷ volume.
Using pressure = area ÷ force.
Put it right: Pressure = force ÷ area.
Mixing units, such as grams with cubic metres, without converting.
Put it right: Convert to matching units first.
Writing the answer without a unit or with a single unit such as g.
Put it right: Give the compound unit, such as g/cm³.
Exam tips
- Write the formula before substituting numbers so the order of division is clear.
- Check that the units of the two quantities match the compound unit you will give.
- For a missing quantity, rearrange first and then substitute to reduce arithmetic slips.
- Estimate the size of the answer to check that a density or pressure value is reasonable.
Try the lesson
The start of the Ratio, proportion and rates of change: use compound units such as density and pressure lesson, made from checked teaching notes for this specification point.
Have a go first
A block of metal has a mass of 240 g and a volume of 30 cm³. Work out the density of the metal in grams per cubic centimetre.
Listen
A compound unit combines two or more measures, so its value is a rate. Density compares mass with volume: density = mass ÷ volume, commonly in g/cm³ or kg/m³. Pressure compares force with area: pressure = force ÷ area, commonly in N/m² or pascals (Pa). To use these units, identify the two quantities, divide in the correct order, and keep units consistent. For example, a 240 g block of volume 30 cm³ has density 240 ÷ 30 = 8 g/cm³. A force of 60 N on an area of 4 m² gives pressure 60 ÷ 4 = 15 N/m². Rearranging finds a missing mass, volume, force or area. Converting units matters: 1 m³ = 1 000 000 cm³, so 8 g/cm³ = 8 000 kg/m³. A strong answer earns marks for these points. Selects the correct relationship: density = mass ÷ volume, or pressure = force ÷ area. Substitutes the given values with matching units before calculating. Calculates accurately, including correct use of a calculator where allowed. Interprets the result with the correct compound unit, such as g/cm³, kg/m³, N/m² or Pa. A common slip: Multiplying mass by volume instead of dividing. Instead, density = mass ÷ volume. Exam tip: Write the formula before substituting numbers so the order of division is clear.
Watch it explained
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Read the described scene instead
A compound unit combines two or more measures, so its value is a rate. Density and pressure are common examples. This lesson shows how to choose the right relationship, keep units consistent, and interpret the answer with its compound unit. Pause briefly to think about what each measure compares. Density compares mass with volume. Density equals mass divided by volume, commonly in grams per cubic centimetre or kilograms per cubic metre. Pressure compares force with area. Pressure equals force divided by area, commonly in newtons per square metre or pascals. Notice the division order: the first quantity is divided by the second. To use these units, identify the two quantities, divide in the correct order, and keep units consistent. Write the formula before substituting numbers so the division order is clear. Check that the units match the compound unit you will give. For a missing quantity, rearrange first, then substitute. Pause here to think: a block has mass 240 grams and volume 30 cubic centimetres. What is its density? First write density equals mass divided by volume. Substitute 240 grams and 30 cubic centimetres. Then calculate 240 divided by 30, which equals 8. The density is 8 grams per cubic centimetre. Do not multiply mass by volume; density is mass divided by volume. Do not use pressure equals area divided by force; pressure is force divided by area. Avoid mixing units without converting; convert to matching units first. Give the compound unit, not a single unit such as grams. For pressure, write pressure equals force divided by area. A force of 60 newtons on 4 square metres gives 60 divided by 4, which equals 15 newtons per square metre. Converting units matters: 1 cubic metre equals 1 000 000 cubic centimetres, so 8 grams per cubic centimetre equals 8 000 kilograms per cubic metre. Remember: density is mass divided by volume, and pressure is force divided by area. Write the formula first, substitute with matching units, and give the compound unit. Rearrange before substituting when a quantity is missing. Check conversions before comparing or calculating.
Key words
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Compound unit
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Density
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Pressure
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Unit consistency
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See every definition
- Compound unit
- A unit that combines two or more measures, so its value is a rate.
- Density
- A comparison of mass with volume, calculated as mass ÷ volume, commonly in g/cm³ or kg/m³.
- Pressure
- A comparison of force with area, calculated as force ÷ area, commonly in N/m² or pascals (Pa).
- Unit consistency
- Keeping units consistent, including converting between compatible units such as 1 m³ = 1 000 000 cm³, before comparing or calculating.
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