Examination Overview

The January 2026 Further Pure Mathematics F1 (WFM01/01) paper offered a fair but algebraically intensive test of candidates' skills. With a total of 75 marks distributed across 10 structured questions, the paper demands not only high logical precision but also robust algebraic stamina. The overall difficulty is rated at a 3.6 out of 5, representing a standard yet challenging paper typical of recent series.

Where the Marks are Won and Lost

A significant portion of the marks resides within the Coordinate Systems chapter, specifically through a parabola problem in Question 4 and a rectangular hyperbola analysis in Question 9. In these questions, candidates who maintained algebraic discipline secured high marks, whereas minor sign errors in tangent/normal equations quickly cascaded into lost accuracy marks. Another critical area was Complex Numbers (Questions 2 and 7), where finding the exact modulus of \(z\) required rationalising with a variable parameter \(k\).

Examiner Pitfalls & Misconceptions

  • Recurrence Relation Induction: In Question 10, many candidates struggled with the inductive step for the second-order recurrence relation. A common pitfall was failing to establish both base cases (\(n=1\) and \(n=2\)) or assuming \(u_{k+1}\) without using strong induction.
  • Matrix Multiplication Order: In Question 3, showing \(A = B^{-1}B^{-1}\) from \(BAB = I\) required multiplying by \(B^{-1}\) on correct sides. Many candidates incorrectly commuted matrices, neglecting the non-commutative nature of matrix algebra.
  • Directrix Distances: In Question 4(b), candidates frequently forgot to add the shift of \(a = 2\) when calculating the shortest distance from the midpoint \(M\) to the directrix \(x = -2\), instead only finding the \(x\)-coordinate of \(M\).

Preparation Strategy & Future Predictions

To excel in future sittings, students must practice algebraic flexibility. When preparing for matrix transformations, ensure you are comfortable with the determinant's geometric meaning (\(\text{Area of } T' = |\det(C)| \times \text{Area of } T\)). For series summation, pay close attention to index shifts (e.g., evaluating \(\sum_{r=13}^{48} u_r\) instead of simple limits). Since linear interpolation was omitted in this series in favour of interval bisection and Newton-Raphson, it is highly overdue and extremely likely to feature in upcoming papers.