Sheet № 40 · Foundation + Higher · AQA · Edexcel · OCR
Compound Measures: Density & Pressure –
Compound measures combine two or more different units into a single measurement — and in GCSE Maths, the two you need to know inside out are density and pressure. These questions appear on both Foundation and Higher papers across AQA, Edexcel and OCR, and they reward students who can rearrange formulas confidently and keep units consisten
§Key definitions
Step 1:
Write the formula: Density = Mass ÷ Volume.
Step 2:
Substitute: Density = 540 ÷ 200 = 2.7.
Step 3:
Write the answer with units: 2.7 g/cm³.
§Formulas to memorise
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\text{Mass} = \text{Density} \times \text{Volume}
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
\text{Pressure} = \frac{\text{Force}}{\text{Area}}
\text{Force} = \text{Pressure} \times \text{Area}
\text{Area} = \frac{\text{Force}}{\text{Pressure}}
V = \pi r^2 h = \pi \times 5^2 \times 12 = 300\pi = 942.478 \text{ cm}^3
M = 8.9 \times 942.478 = 8,388.05 \text{ g}
Worked example
See example below.
A metal block has a mass of 540 g and a volume of 200 cm³. Calculate the density of the metal.
⚠ Common mistakes
- ✗Mixing up the formula. Students sometimes put volume on top or mass on the bottom. Remember: Density = Mass ÷ Volume — the "heavier" quantity (mass) is on top.
- ✗Unit mismatches. If mass is in kilograms and volume in cm³, your density will not be in standard units. Convert before dividing.
- ✗Forgetting compound units. Writing "2.7" without "g/cm³" loses the units mark.
- ✗Confusing density and pressure formulas. They have the same structure but use different quantities. Read the question to determine which formula applies.
- ✗Not calculating area correctly. In pressure questions, students sometimes use length instead of area. Pressure requires a two-dimensional measurement (cm², m²).
✦ Exam tips
- →State the formula at the start. Even if you make a calculation error, the formula earns method marks.
- →Set out conversions clearly. If you need to convert kg to g (×1000) or m² to cm² (×10,000), write it as a separate line.
- →Combined questions on Higher papers may give you a 3D shape, ask you to find the volume, then use the volume to find mass or pressure. Work through each step methodically.
- →Read the units in the question. Sometimes the question gives density in kg/m³ but lengths in cm — you will need to convert.
- →Pressure questions may involve weight. Remember: Weight = mass × g (where g = 9.8 N/kg or 10 N/kg as stated in the question).