Difficulty Verdict

The January 2026 Pure Mathematics (XPM01) series is a fair yet testing assessment. While the early questions in both papers provide accessible marks, the later questions introduce algebraic friction and multi-step reasoning. P1 is dominated by algebraic manipulation and graphing, whereas P2 demands sophisticated logical links between sequences, trigonometry, and calculus optimization.

Where the Marks Are

The core of both papers lies in high-yield topics. In P1, Algebra and Functions constitutes nearly half of the marks (34 out of 75), covering quadratics, inequalities, indices, surds, and transformations. In P2, the weight is shared across Sequences and Series (21 marks) and Trigonometry. Mastering circular coordinate geometry and optimization equations accounts for a critical portion of the remaining marks, making standard algebra skills the foundation of scoring well.

Examiner Pitfalls

  • The Calculator Trap: The instruction 'Solutions relying on calculator technology are not acceptable' was heavily enforced. In WMA11/01A Q1(b) and Q2(i), candidates who wrote down roots or index solutions without showing intermediate factoring or exponent matching scored zero.
  • Integral Transformations: In WMA12/01A Q3(b), many candidates struggled to relate the transformed integral \( \int_{-2}^6 (2x + \sqrt{4x+8})\,dx \) to their trapezium rule result for \( \int_{-2}^6 \sqrt{x+2}\,dx \). Successful candidates split the integral and recognized that \( \sqrt{4x+8} = 2\sqrt{x+2} \).
  • Circle Geometry Coordinates: Finding the coordinates of point \( W \) in WMA12/01A Q6(d) via diametrical relationships or vector steps proved highly challenging, with many making sign slips or failing to construct a clear geometric path.

Strategy and Preparation

To excel, students must move away from calculator dependency. Ensure all quadratic solving, simultaneous equations, and surd simplifications show detailed intermediate steps. Furthermore, focus on proving formulas from scratch, such as setting up perimeters and areas of composite shapes in optimization questions.

Upcoming Predictions

With exponential modeling absent from this set (only standard log equations were featured), a contextual exponential growth or decay modeling question is highly anticipated for the next session. Trigonometric proof is also overdue for a more prominent role.