Difficulty Verdict
The 2021 paper is rated as moderately difficult (4 stars). While Section A(1) and A(2) followed historical trends closely, Section B pushed the boundaries of algebraic complexity. In particular, the coordinate geometry of circles in Question 19 and the 3D folding problem in Question 18 served as significant hurdles for high-achieving students.
Where the Marks Are
Standard questions in Section A, such as indices (Q1), change of subject (Q2), and factorization (Q3), provided quick, accessible marks. Candidates who mastered basic statistical measures (Q9 and Q11) and linear programming setup (Q16) secured a solid foundation of passing marks. The core of the differentiation, however, lies in the final sub-parts of Section B questions, which carried heavy weightings for precision and algebraic proofs.
Examiner Pitfalls & Weaknesses
- Premature Rounding: In sequence questions (Q17) involving logarithms, many candidates rounded off intermediate values too early, resulting in inaccurate final integer answers for \( k \).
- Lack of Rigor in Geometric Proofs: In Q14(b), candidates often asserted similarity of 3D cones without verifying the ratio of corresponding linear dimensions, losing crucial method marks.
- Incomplete Conditions for Quadrilaterals: In Q19(c)(iii), to determine if STUV was a rectangle, many candidates only proved opposite sides were parallel or equal, completely forgetting to test the perpendicularity of adjacent sides.
Preparation Strategy
Future candidates should prioritize algebraic precision under time pressure. Practicing completing the square with parametric coefficients (as seen in Q19) and strengthening the logical flow of geometric proofs are vital. Do not merely memorize formulas; understand the geometric definitions behind properties like orthocentres and tangent circles.