The receipts
How we know.
Every claim on this site that sounds like a number was measured, not guessed. This page is where we show the work — in full, on this page, not behind an email you have to wait for.
We catalogued every sub-part of all 26 maths-optional papers from 2013 to 2025 — 804 in total — solving each one and verifying the mathematics with code. Every solution was classified against a map of the syllabus's testable areas.
Then we ran a blind test. We built our coverage map from 2013–2024 alone, held back the 2025 paper entirely, and asked: could a student prepared only on the older papers attempt the unseen one? The answer was yes — a strategic candidate could reach the full attemptable marks on both 2025 papers, choosing optimally among the optional questions. In thirteen years, only a single genuinely new topic ever appeared, and it sat in a question you could skip.
That is the whole idea behind our method: the maths-optional syllabus is finite, and here is the map that proves it.
Maths Optional
The 13-year coverage map.
Every one of 804 sub-parts, sorted into the 13 syllabus areas UPSC itself uses — the same 13 you'd plan a study calendar around. Bar length is how often an area was tested, not a promise about how it will be marked next year.
26 papers · 13 years (2013–2025) · 804 sub-parts classified.
Paper I 431 · 53.6%
Paper II 373 · 46.4%
The one exception: 2025-P1-Q4c-ii, the quotient space V/W (dim P₄/P₂) — matched no atom in the 2013–2024 map. 8 marks, in a skippable question.
13 years, 13 syllabus areas — 804 sub-parts, mapped.
Sub-part count = how often this area was tested, 2013–2025 (not a marks-weighted score share, not a prediction of future papers).
CSAT · Quantitative
Three families, most of the paper.
Ten years of CSAT quant (2016–2025), 444 questions, counted by hand by a math-and-statistics house — not estimated from a syllabus document. Every family, every count, visible; nothing merged away to make the chart tidier.
- Arithmetic & numeracy 128 · 28.8%
- Number properties 100 · 22.5%
- Logical-quant reasoning 96 · 21.6%
- Counting & combinatorics 45 · 10.1%
- Data sufficiency 35 · 7.9%
- Statement validity 35 · 7.9%
- Data interpretation 5 · 1.1%
Data interpretation: 5 of 444 — about 1%
Ten years of CSAT. Five DI questions. The pie-and-bar-chart drilling most aspirants over-invest in is the rarest thing on the paper.
Three question-families carry 73% of every CSAT quant mark.
10 years of CSAT (2016–2025), 444 quant questions. Uniform marking (2.5 marks each, no partial credit) means share of questions = share of marks, exactly.
CSAT · Comprehension & reasoning
Seven types. Not a vocabulary test.
The same discipline, applied to the half of CSAT most aspirants fear the most — because it feels unmeasurable. It isn't. Every one of 284 verbal-reasoning questions solved so far sorts into one of seven recurring types, and every trap we found was built by twisting the passage's own logic, never by hiding a hard word in it.
- Which inference the passage forces 89 · 31%
- Which unstated premise the argument needs 81 · 29%
- The passage's load-bearing thesis 51 · 18%
- What the passage literally says 21 · 7%
- The stance the text commits the author to 19 · 7%
- What the passage asserts (vs. merely raises) 9 · 3%
- Free-standing deduction — no passageno passage 14 · 5%
Classification (what type of question this is) is settled for all 284. Official-answer verification is complete for 2021–2025 (145 items); for 2016–2020 (139 items) it rests on our own blind-derived reading or a recalled key, pending primary-source confirmation — those years are excluded from anything we score for money.
Seven question-types. Zero vocabulary tests. Ten years.
270 of these are genuine reading-comprehension questions — a passage, then a question that turns on reading it precisely. The other 14 are free-standing logic puzzles with no passage at all (statement-and-conclusion, does-it-follow). Both families are held to the same standard: the key must be provable — from the passage’s own lines, or from the stated premises — never from outside knowledge, and never from a word’s dictionary meaning.
Zero of 284 questions ask you to know a word’s meaning. Every trap is built by twisting the passage’s logic — not by hiding a hard word in it.
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