Where the marks went
The biggest scorer, about 10% of all marks across the 14 years.
About 9% of marks, with a steady 70 marks or so most years.
About 9% of marks, with strong recurring topics in 2D motion and sources and sinks.
How the marks are split
By question size, 15-mark questions carried 39% of marks, 10-mark questions 31% and 20-mark questions 20%. Paper I and Paper II carry half each.
Highest-weightage topics
Linear Transformations, Rank and Nullity (Linear Algebra); Double and Triple Integrals (Calculus); the Sphere (Analytic Geometry); the Simplex Method (Linear Programming); Second Order Variable Coefficients and First Order Integrating Factors (Ordinary Differential Equations); Partial Derivatives, Maxima and Minima (Real Analysis); and 2D and Axisymmetric Motion (Mechanics and Fluid Dynamics).
How to use the PYQ analysis
Cover the topics that carried the most marks before the rest.
Solve the past questions of a topic right after you finish it.
Practise 10, 15 and 20-mark answers to the time limit.
Open the full PYQ analysisSign up
Also see the UPSC Maths Optional guide for the syllabus, trends and toppers' strategies, and the Antim Paryas test series.
The questions come from official UPSC papers; copyright of the original questions rests with the Union Public Service Commission. The analysis is by PiCraft.
Questions answered
Which years does the UPSC Maths Optional PYQ analysis cover?
All Mathematics optional questions from 2013 to 2026: 854 questions and 11,200 marks, each tagged to its syllabus topic.
Which subject carries the most marks in UPSC Maths Optional?
Ordinary Differential Equations is the biggest scorer at about 10% of all marks, followed by Calculus and Mechanics and Fluid Dynamics at about 9% each.
How are the marks split by question size?
Across 2013 to 2026, 15-mark questions carried 39% of marks, 10-mark questions 31% and 20-mark questions 20%. Paper I and Paper II each carry 50%.
Which topics should I study first?
The analysis ranks topics by marks. The highest are Linear Transformations, Rank and Nullity; Double and Triple Integrals; the Sphere; the Simplex Method; and two Ordinary Differential Equations topics.
Are the UPSC questions official?
The questions are from official UPSC Civil Services Mathematics papers. Copyright of the original questions rests with the Union Public Service Commission. The analysis is by PiCraft.