A-LevelFurther MathematicsCalculus (Parametric & Polar Curves)Oct/Nov 2016Paper 1 Q1214 Marks
Answer only one of the following two alternatives. OR A curve C has parametric equations x = 1 − 3t², y = t(1 – 3t²), for 0 ≤ t ≤ 1/√3. Show that (dx/dt)² + (dy/dt)² = (1+9t²)². Hence find (i) the arc length of C, (ii) the surface area generated when C is rotated through 2π radians about the x-axis. Use the fact that t = y/x to find a cartesian equation of C. Hence show that the polar equation of C is r = sec θ(1 – 3 tan²θ), and state the domain of θ. Find the area of the region enclosed between C and the initial line.
📋 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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