Difficulty Verdict
This set of papers is classified as Medium-Hard (4 stars). While the early sections of both Papers 1 and 2 offer accessible marks through standard procedural questions (such as eigenvalues and hyperbolic derivatives), the long-structured questions on damped harmonic motion and the roots of unity require deep conceptual integration and advanced algebraic confidence.
Where the Marks Are
The largest mark allocations lie within Differential Equations (43 marks) and Complex Numbers (36 marks). Students who mastered coupled differential equations, the integration of rational functions for volumes of revolution, and the geometric applications of complex conjugates on Argand diagrams were able to secure more than half of the available marks on the papers.
Examiner Pitfalls & Lost Marks
- Angle Between Line and Plane (Vector Q10a): A common pitfall was failing to relate the line-plane angle correctly, with many using the cosine of the angle between the line direction and the plane normal instead of \(\sin \alpha = \cos \theta\).
- Polar Integration Limits (Q9b): Many students failed to recognize that for \(r^2 = 9\sin(2\theta)\), the integrand is only defined when \(\sin(2\theta) \ge 0\), resulting in incorrect integration bounds.
- Signs in Elastic String Equations (Q11a): Incorrect sign conventions for string tension forces on an inclined plane frequently prevented candidates from successfully deriving the simple harmonic motion equation.
Preparation Strategy & Predictions
Future candidates should focus intensely on coupled differential equations and second-order damped equations, which consistently carry significant weight. Practising the expansion of trigonometric functions in terms of exponential definitions remains vital for scoring high-tier marks in hyperbolic functions.