The New Non-Calculator Era & General Verdict

The 2025 Additional Mathematics series marks a monumental shift in the syllabus structure, with Paper 1 operating under strict non-calculator conditions. This change significantly elevates the difficulty, turning relatively standard questions into high-stakes tests of mental math, rationalisation, and algebraic neatness. Paper 2 continues to permit calculators, but maintains a rigorous conceptual focus. Overall, this set of papers is highly demanding, placing a premium on students who can confidently manipulate logs, exponentials, and trigonometric identities without relying on technology.

Where the Marks are Won or Lost

As expected, Calculus dominates the mark distribution, accounting for over a quarter of the entire examination. Students secured excellent marks by demonstrating fluency in the product and quotient rules, as well as applying definite integration to shaded areas between curves. However, major marks were squandered on the Coordinate Geometry of the Circle (particularly Paper 2, Q11), where setting up equations for intersecting circles required advanced geometric reasoning and perfect coordinate manipulation under time pressure.

Examiner Pitfalls & Technical Slippage

Examiners highlighted several recurring mistakes that cost candidates dearly:

  • Integration Coefficients: In Paper 2 Q4(a)(ii), many failed to divide by the derivative of the inner function, missing the factor of \(-\frac{1}{3}\) during the integration of \(\frac{1}{4-3x}\).
  • Domain Restrictions in Functions: Many students struggled to define the range of the inverse function \(g^{-1}(x)\), forgetting that it is identical to the domain of the original function \(g(x) \ge 2\).
  • Logarithmic Base Changes: In Paper 1 Q9(a), converting \(\log_{25}x\) to base 5 was a significant stumbling block, with many executing incorrect fractional conversions.

Strategic Revision & Predictions

With Paper 1 now non-calculator, your preparation must adapt. Memorising exact trigonometric ratios (such as \(\sec 30^{\circ}\) or \(\tan 45^{\circ}\)) and perfecting logarithmic laws are no longer optional—they are foundational. Looking ahead, Non-Linear Simultaneous Equations was under-represented in this series and is highly likely to feature prominently in the next set. Focus on practicing multi-step coordinate geometry proofs and kinematic problems involving variable acceleration to secure your A*.