4PM1/02R Jun 2022, Question 2: Connected Rates of Change and Small Changes
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 6 marks
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The question, in short
Concrete forms a cuboid with square base side x and height 3x; volume grows at 8 m³/s. Find the rate of increase of x in m/s when x = 2 metres.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 6 marks
- 1V = x² × 3x = 3x³
- 2dV/dx = 9x²
- 3dx/dt = dV/dt ÷ dV/dx = 8/(9x²)
- 4When x = 2: dx/dt = 8/(9 × 2²) = 8/36
- 5dx/dt = 2/9 m/s
Answer2/9 m/s
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