May 2025 IB DP Mathematics AA HL Exam Analysis

The May 2025 session of the Mathematics: Analysis and Approaches Higher Level exam stood out as a highly demanding series, matching the rigorous standards of the curriculum. Candidates faced sophisticated multi-step problems, particularly in the latter parts of Section B across Papers 1 and 2, and within the inquiry-based Paper 3.

Where the Marks Were Found

As is traditional for AA HL, Calculus was the dominant force, commanding 91 marks of the total 275. Key areas tested included solids of revolution (Paper 1, Q7), related rates of change (Paper 2, Q9), kinematics, and a major 21-mark differential equations problem (Paper 2, Q12) involving integrating factors and families of tangents. Number and Algebra followed closely with 73 marks, heavily supported by complex numbers (featuring a demanding locus and quartic root question in Paper 1, Q12) and sequences.

Examiner Pitfalls & Critical Areas
  • Complex Number Loci: In Paper 1, Q12, converting the argument condition \(\arg\left(\frac{z+p}{z-1}\right) = \frac{\pi}{4}\) into a cartesian equation tripped up many candidates who struggled with compound angle identities or algebraic division of complex numbers.
  • Related Rates of Change: In Paper 2, Q9, many candidates correctly set up the trigonometric equation but failed to apply the chain rule correctly when differentiating with respect to time, often forgetting that both \(\theta\) and \(x\) are functions of \(t\).
  • Induction on Compositions: In Paper 3, Q1, proving the general expression for the \(n\)-th self-composite of a linear function required exceptionally neat algebra and proper handling of geometric sums.
  • Integer Optimization Constraints: In Paper 3, Q2, students often struggled to transition from the pure calculus of finding maximum volume to the number-theory-style reasoning required to establish integer constraints.
Strategy for Success & Upcoming Predictions

To score highly in future sessions, students must master the integration of different topics—such as utilizing trigonometric identities inside complex numbers, and applying calculus to coordinate geometry. Our analysis suggests that areas like vector geometry (perpendicular lines and planes) and advanced probability models (such as conditional Bayes' theorem) will continue to feature as high-yield topics with structured, accessible marks if students practice standard algorithmic steps. Meanwhile, a thorough conceptual understanding of integrating factors and mathematical induction remains essential for securing the top-tier grades.