IAS Mathematics January 2026 Examination Analysis
The January 2026 IAS Mathematics exam series presented a robust test of algebraic precision, physical modeling, and statistical reasoning. Across Pure Mathematics (P1 and P2), Mechanics (M1), and Statistics (S1), candidates encountered several challenging multi-stage questions demanding not just mechanical recall, but deep conceptual flexibility.
Pure Mathematics: Algebraic Mastery and Geometric Proofs
In Pure Mathematics P1, core topics such as curve sketching, straight lines, and basic differentiation were highly accessible. However, the cubic function analysis in Question 10 and the coordinate geometry of triangles in Question 4 tested algebraic endurance. The integration question (Question 7) required finding a normal equation from a given derivative, which tripped up students who forgot to invert and negate the gradient of the tangent.
In Pure Mathematics P2, the optimization of the garden's perimeter (Question 7) stood out as a high-tier algebraic differentiator. Expressing the perimeter of a compound shape (rectangle + semicircle) in terms of a single variable required meticulous manipulation before applying calculus. Furthermore, the geometric series problem combined with trigonometric identities (Question 8) required students to recognize a quadratic in \( \sin\theta \) and solve for exact terms without reverting to decimals.
Mechanics M1: The Ultimate Test of Two-Stage Kinematics
Mechanics M1 continues to be the most demanding IAS unit. Question 8, a 16-mark connected particles problem, was the paper's climax. It required students to model two distinct phases of motion: first, where both particles accelerate, and second, where the hanging particle hits the ground and the table particle slides under friction alone. Many candidates lost marks by using the initial acceleration in the second phase or failing to use conservation of string length (greater than \( 2.4h \)) to draw a final inequality.
Moments (Question 7) also featured a non-uniform rod with moving supports. Students who struggled to write correct vertical resolution and moment equations struggled to find the ratio \( k \). In speed-time graphs (Question 5), a common pitfall was failing to match the final times of the car and the van on the same horizontal axis.
Statistics S1: Coding and Probability Rigor
In Statistics S1, standard representation of data (Stem & Leaf, Histogram) was highly accessible, but the regression coding (Question 3) and expected value calculations under the normal distribution (Question 6) proved challenging. For the jam jars problem, students had to standardise twice, solve simultaneous linear equations for the mean and standard deviation, and then apply these to a profit/loss expected value table—a multi-layered modeling task where arithmetic slips were heavily penalized.