O-LevelAdditional MathematicsTrigonometryMay/June 2018Paper 2 Q128 Marks
In this question all lengths are in centimetres. The volume of a cone of height h and base radius r is given by V = ⅓πr²h. It is known that sin (π/12) = (√6 - √2)/4, cos (π/12) = (√6 + √2)/4, tan (π/12) = 2 - √3. A water cup is in the shape of a cone with its axis vertical. The diagrams show the cup and its cross-section. The vertical angle of the cone is π/6 radians. The depth of water in the cup is h. The surface of the water is a circle of radius r. [Figure 12.1]
📋 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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