Maths

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What: CDS Elementary Mathematics — 100 questions in 2 hours, covering arithmetic, algebra, trigonometry, geometry, mensuration, and statistics.
Why it matters: Maths is one of three sections in the CDS-I and CDS-II written exams. The cut-off is decided largely by your Maths score.
Key fact: CDS Maths has 25 syllabus topics. Number System, Time-Speed-Distance, Trigonometry, and Mensuration carry the highest weightage — together over 50% of the paper.

CDS Maths (officially: Elementary Mathematics) is one of the three written papers in the UPSC Combined Defence Services examination conducted by the Union Public Service Commission. The paper carries 100 marks across 100 MCQs to be answered in 2 hours. The syllabus, drawn from the Class 10 NCERT level, spans arithmetic, algebra, trigonometry, geometry, mensuration, and statistics.

This hub page is your single launchpad for CDS Maths preparation on Defence Road. Every one of the 25 syllabus topics has its own detailed notes page with worked examples, PYQ analysis, shortcuts, and a CDS-specific FAQ.

Full Syllabus & Weightage

The table below shows typical CDS Maths paper composition by topic-block.

Block	Topics	Approx. Questions
Arithmetic	Number System, HCF/LCM, Decimal Fractions, Power/Roots, Percentage, Ratio, Average, SI/CI, P/L, TSD, Time/Work, Logarithm	30–40
Algebra & Sets	Basic Ops, Linear Eq, Quadratic Eq, Set Theory	10–15
Trigonometry	Functions/Identities, Height/Distance	8–12
Mensuration & Geometry	Area/Perimeter, Volume/SA, Lines/Angles, Triangles, Quadrilateral/Polygon, Circles	25–35
Statistics	Mean, Median, Mode, Graphs	2–4

Arithmetic Chapters (12 topics)

Build the arithmetic base first — it carries 30-40 marks per paper

Number System — divisibility, primes, Euclid, remainders.
HCF and LCM — bell-tolling, cutting, polynomial pairs.
Decimal Fractions — terminating vs recurring, conversion.
Power and Roots — exponents, surds, rationalisation.
Percentage — successive change, population, election.
Ratio and Proportion — componendo, partnership, alligation.
Average — arithmetic, weighted, harmonic.
Simple and Compound Interest — difference identity, doubling time.
Profit and Loss — successive discount, false weight.
Time, Speed and Distance — trains, boats, circular tracks.
Time and Work — combined rate, pipes, efficiency.
Logarithm — laws, change of base, characteristic.

Algebra & Sets (4 topics)

Algebra runs through equations and identities — 10-15 marks per paper

Basic Operations and Factorisation — identities, factor theorem, Sophie-Germain.
Linear Equations — substitution, elimination, consistency.
Quadratic Equations — discriminant, Vieta's formulas.
Set Theory — inclusion-exclusion, De Morgan.

Trigonometry (2 topics)

Trigonometry is the single largest geometry-block head — 8-12 marks per paper

Trigonometry Functions and Identities — six ratios, Pythagorean identities.
Height and Distance — angles of elevation and depression.

Mensuration & Geometry (6 topics)

Pure formula recall plus diagram-reading — 25-35 marks per paper

Area and Perimeter — basic shapes, Heron, sector.
Volume and Surface Area — 3D solids, melt-and-recast.
Lines and Angles — parallel-transversal, linear pair.
Triangles and Properties — Pythagoras, similarity, congruence.
Quadrilateral and Polygon — property table, angle sums.
Circles — inscribed angle, tangent, cyclic quadrilateral.

Statistics (1 topic)

Closing chapter — 2-4 marks per paper

Statistics — mean, median, mode, range, empirical relation.

Preparation Strategy

Phase 1 — Arithmetic (4-5 weeks). Build percentage, ratio, average, and TSD fluency first — these are the highest-yield chapters and unlock several others (SI/CI, P/L, mixtures all depend on percentage and ratio).

Phase 2 — Algebra (2-3 weeks). Cover identities and factorisation, then linear and quadratic equations. Set theory closes this block.

Phase 3 — Trigonometry (2 weeks). Memorise the standard angle table and the three Pythagorean identities. Master the Height and Distance archetypes.

Phase 4 — Geometry (3-4 weeks). Build property tables for quadrilaterals and polygons. Drill triangles (Pythagoras triples and similarity). Practice circle theorems.

Phase 5 — Mock testing (2-3 weeks). Take timed CDS papers. Track which chapter still leaks marks and drill specifically.

Test Yourself with CDS Maths Mocks

Once you have a couple of chapters under your belt, the fastest way to improve is timed practice. Take CDS Maths mock tests covering all 25 syllabus topics.

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Frequently Asked Questions

What is the format of the CDS Maths paper?

100 MCQs in 2 hours, total 100 marks. Negative marking of 1/3 mark per wrong answer. The paper is conducted as part of both CDS-I (held in February) and CDS-II (held in September) exams.

What level is CDS Maths?

Class 10 NCERT level. The syllabus covers arithmetic, algebra (up to quadratic equations), trigonometry, geometry, mensuration, and statistics. No calculus, no advanced algebra.

Which CDS Maths topics carry the highest weightage?

Number System, Time-Speed-Distance, Trigonometry, Mensuration (Area + Volume), and Triangles together cover over 50% of the paper. Build these first.

Is the same Maths syllabus tested in OTA?

OTA candidates do not write the Maths paper. CDS-OTA (Officers Training Academy) candidates appear for English and General Knowledge only. Maths is required for IMA, Naval Academy, and Air Force Academy candidates.

How should I prepare for CDS Maths?

Start with arithmetic (4–5 weeks), then algebra (2–3 weeks), then trigonometry (2 weeks), then geometry (3–4 weeks), and close with statistics. Finish with 2–3 weeks of timed mock practice. Each topic page on Defence Road has its own detailed strategy.

What is the cut-off for CDS Maths?

The cut-off varies by exam cycle. Historically, scoring 60–70 out of 100 in Maths puts you safely above the sectional cut-off. Aim higher to compensate for negatives in other sections.

Where do I start preparing?

Pick a chapter from the arithmetic block — Number System or Percentage are good entry points. Read the chapter page, drill the worked examples, take a chapter-level mock, then move on.