On this page we bring together everything you need for Mathematics Optional in the UPSC Civil Services Mains – the official syllabus, the year-wise question papers and topic-wise previous year questions (PYQs).
Paper I covers linear algebra, calculus, analytic geometry, ordinary differential equations, dynamics and statics, and vector analysis. Paper II covers algebra, real analysis, complex analysis, linear programming, partial differential equations, numerical analysis and computer programming, and mechanics and fluid dynamics.
Syllabus
The official UPSC syllabus for Paper I and Paper II, broken into numbered topics.
Open the syllabus →02Year-wise Question Papers
Every Mathematics Optional paper from 2008 to 2026, year by year, for Paper I and Paper II.
Open question papers →03Topic-wise PYQs
All previous year questions arranged under each syllabus topic, latest first.
Open topic-wise PYQs →How to use these PYQs
- Start with the syllabus. Read the official wording of each unit, so you know exactly what UPSC can ask.
- Go through recent years first. Questions from 2013 onwards follow the present 250-mark pattern and show what UPSC values today.
- Spot the repeats. Themes that come back across years deserve your deepest notes and best examples.
- Practise under exam conditions. Write answers within the word limit and time, then revise them after a week.
Preparing for Prelims too?
Our UPSC Prelims Topic-wise PYQ eBook covers every Prelims question with detailed explanations, so you can see exactly where UPSC asks from.
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Strengthen your GS papers
Our UPSC Mains Topic-wise & Year-wise PYQ eBook (2013–2026) maps every GS question to the syllabus, so you know what UPSC asks and how often.
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We classify every PYQ with care, but mistakes can slip in. If a question is in the wrong topic, has a typo, the wrong year, or is missing, let us know. We review every report and update the page.
Report an ErrorLast updated: 30 October 2026