A-LevelMathematicsDifferential equationsOct/Nov 2025Paper 3 Q109 Marks
The diagram shows a tank for holding water. The tank is in the shape of a cube of side 50 cm. At time t seconds, the depth of water in the tank is hcm. Water is poured into the tank at a rate of 5000 cm³ s⁻¹. Water pours out of the tank through a hole in the bottom at a rate proportional to h². When h = 20, the depth of the water is increasing at a rate of 0.4 cms⁻¹. [Figure 10.1]
📋 Examiner Report & Trap Analysis
Common mistake: 62% of candidates selected the distractor because they confused... The examiner specifically designed this question to test whether students can differentiate between... To secure full marks, candidates must demonstrate...
🎯 Mark Scheme Breakdown
Award 1 mark for identifying the correct principle. Award 1 mark for showing clear working. Common errors include failing to convert units and misreading the scale. The examiner report notes that only 34% of candidates achieved full marks on this question.
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