Linear algebra, calculus, ODEs, mechanics, numerical analysis — deterministic scoring.
Five deep-dives: syllabus, booklist, paper analysis, strategy, PYQ trends (2021–2025).
Five long-form articles. Read in order or jump to what you need.
The official Mathematics syllabus decoded topic by topic — what each line really means, how UPSC asks it, and where to draw the boundaries of your preparation.
The exact reading order topppers follow for Mathematics — NCERT base, core standard books, supplementary reference, notes strategy and what to skip.
A paper-pattern analysis of Mathematics — question structure, sectional weightage, marks distribution, difficulty trends and recurring themes over the last 5 years.
A realistic month-wise preparation strategy for Mathematics — reading, notes, answer writing, revision and mock tests, with time allocations by topic.
Year-by-year analysis of Mathematics Mains PYQs from 2021-2025 — topic distribution, repeated themes, difficulty shift and what it signals for the next cycle.
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.
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
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.
80 questions at 50 marks
Browse all 80 Mathematics previous year questions →Write an answer, upload it, and our evaluator scores it on content, structure, examples and directive-word fidelity — trained on UPSC-style marking.