UPSC Optional · 500 marks

Mathematics

Linear algebra, calculus, ODEs, mechanics, numerical analysis — deterministic scoring.

Five deep-dives: syllabus, booklist, paper analysis, strategy, PYQ trends (2021–2025).

What UPSC actually asked in Mathematics, 2021–2025

80 questions across 5 years, taken from the official papers. Every one has its own page with the directive word, marks, word limit and evaluation rubric.

Paper 1
40 questions · 2000 marks total
Paper 2
40 questions · 2000 marks total

Topics that came up

Linear algebra, calculus and 3D geometry · Differential equations, mechanics and vector calculus · Linear algebra and calculus · Abstract algebra, complex analysis and linear programming · Abstract algebra, real analysis and transportation problem · Analytical geometry and multivariable calculus · Analytical geometry, partial derivatives, linear algebra · Boolean functions, mechanics, partial differential equations

Directive words used most

solve (57) · prove (19) · derive (1) · examine (1) · trace (1) — see the directive words guide for how each one changes the answer you should write.

Mark distribution

80 questions at 50 marks

Browse all 80 Mathematics previous year questions →

Practice Mathematics answers, get AI feedback

Write an answer, upload it, and our evaluator scores it on content, structure, examples and directive-word fidelity — trained on UPSC-style marking.