Topic explanation
Density & Pressure Problems is part of the Ratio, Proportion & Rates of Change strand in GCSE Maths. Rearrange ρ = m/V and pressure = force/area in multi-step exam contexts.
Exam papers from AQA, Edexcel, OCR assess fluency (short questions) and reasoning (multi-mark). Practise reading command words (“show that”, “hence”, “give your answer in the form…”) before you rearrange algebra or interpret a result.
Key formulas & rules
- Ratio scaling: multiply all parts by the same factor to match a total
- Speed = distance ÷ time; density = mass ÷ volume; pressure = force ÷ area
- Compound growth/decay: multiplier (1 ± r) applied for n periods
Common mistakes
- Arithmetic and sign errors when simplifying expressions involving density & pressure problems.
- Not answering in the required form (fraction vs decimal, surd vs rounded).
- Missing a final sentence that interprets the result in context when the question is applied.
Exam tips
- Underline key words in the question: “exact”, “integer”, “give reasons”.
- Estimate or use inverse operations to sanity-check answers when a calculator is allowed.
- Use StudyVector practice filtered to “Speed, Density & Pressure” to drill exam-style questions on this skill.
Practice questions
Exam-style questions aligned to your board. Open full practice for worked feedback and your next best question.
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