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CDS Mathematics Syllabus

Combined Defence Services (UPSC)

15
Topics
141
Sub-topics
100
Questions

Mathematics is one of 3 sections in the CDS syllabus. It has 15 topics and 141 sub-topics, tested in CDS Paper I (Math), with about 100 questions (300 marks). Algebra, Trigonometry, Geometry, Calculus, Per CDS Official Notification.

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CDS Mathematics: topic-wise syllabus

  1. 1

    Algebra

    ~3 marks

    Sets, Relations, Functions, Per CDS Official Notification

    • Sets, Relations, Functions, Venn Diagrams
    • Complex Numbers, Quadratic Equations, Polynomials
    • Sequences and Series — AP, GP, HP, Sum of n terms
    • Binomial Theorem, Permutation-Combination, Probability
    • Matrices and Determinants, Linear Algebra, System of Equations
    • Logarithms, Partial Fractions, Induction, Mathematical Reasoning
    • Boolean Algebra, Logic Gates, Number Theory
  2. 2

    Trigonometry & Geometry

    ~3 marks

    Trigonometric Functions, 2D/3D, Per CDS Official Notification

    • Trigonometric Ratios, Identities, Equations, Inverse Trig
    • Heights and Distances, Properties of Triangles
    • Coordinate Geometry — Straight Lines, Circles, Conic Sections
    • 2D Geometry — Triangles, Quadrilaterals, Polygons, Circles
    • 3D Geometry — Lines, Planes, Spheres, Cylinders, Cones
    • Vectors and 3D Geometry, Dot Product, Cross Product
    • Mensuration, Areas, Volumes, Surface Area
  3. 3

    Calculus & Statistics

    ~3 marks

    Differentiation, Integration, Statistics, Per CDS Official Notification

    • Limits, Continuity, Differentiability, Derivatives
    • Applications of Derivatives — Maxima, Minima, Rate of Change
    • Integration — Definite, Indefinite, Areas, Applications
    • Differential Equations — First Order, First Degree
    • Statistics — Mean, Median, Mode, Standard Deviation, Variance
    • Probability — Conditional, Bayes Theorem, Random Variables
    • Vectors, Matrices, Determinants — Advanced Applications
  4. 4

    Arithmetic (MBA Quant)

    ~3 marks

    Number System, Percentages, Profit-Loss, SI-CI

    • Number System, HCF-LCM, Indices, Surds, Simplification, Approximation
    • Percentages, Profit-Loss, Discount, SI-CI, Growth Rate, Population Growth
    • Ratio, Proportion, Mixture-Alligation, Partnership, Ages
    • Time-Work, Work-Wages, Pipes & Cisterns, Efficiency
    • Time-Speed-Distance, Trains, Boats, Races, Clocks, Calendar
    • Averages, Mixture Problems, Alligation, Allegation Method
    • Mensuration, Geometry, Coordinate Geometry, Trigonometry
    • Data Interpretation — Tables, Bar, Pie, Line, Caselet, Data Sufficiency
    • Modern Math — Permutation, Combination, Probability, Sets, Functions
    • Commercial Math — Stocks, Shares, Dividends, Brokerage, GST, True Discount
  5. 5

    Algebra (MBA Quant)

    ~3 marks

    Equations, Functions, P&C, Probability

    • Linear Equations, Quadratic Equations, Polynomials, Identities
    • Functions, Graphs, Inequalities, Logarithms, Modulus, Domain, Range
    • Sequences and Series, AP, GP, HP, Sum of n terms, Special Series
    • Permutation, Combination, Binomial Theorem, Probability
    • Matrices, Determinants, Linear Programming, System of Equations
    • Set Theory, Relations, Functions, Venn Diagrams, Cardinality
    • Trigonometry — Ratios, Identities, Heights and Distances, Equations
    • Coordinate Geometry — Lines, Circles, Conics, Distance, Slope
    • Calculus — Limits, Derivatives, Integrals, Maxima, Minima, Applications
    • Statistics — Mean, Median, Mode, Variance, Skewness, Correlation, Regression
  6. 6

    Data Interpretation

    ~3 marks

    Charts, Tables, Caselets, Data Sufficiency

    • Table DI — Direct, Calculation-Based, Multi-Step
    • Bar Graph DI — Single, Double, Stacked, Comparison
    • Pie Chart DI — Sector Angle, Percentage, Comparison, Multiple Pie
    • Line Graph DI — Trend, Multiple Lines, Comparison, Growth Rate
    • Caselet DI — Story-Based, Multi-Step, Verbal Reasoning with Data
    • Data Sufficiency — Two-Statement, Three-Statement, Multi-Condition
    • Comparison DI — Ratio, Percentage, Difference, Growth Rate
    • Missing Data DI — Find the Missing Value, Estimate, Calculate
    • Quant-Based DI — Averages, Ratios in Data, Business Scenarios, HR Data
    • Radar, Web, Mixed Chart DI, Business Scenarios — Revenue, Cost, Profit, Market Share
  7. 7

    English

    ~3 marks

    Verbal Ability, Grammar, Vocabulary, RC

    • Reading Comprehension — Factual, Inferential, Critical, Editorial, Business
    • Cloze Test, Fill in the Blanks, Sentence Completion
    • Spotting Errors, Sentence Correction, Sentence Improvement
    • Para Jumbles, Sentence Rearrangement, Paragraph Completion
    • Vocabulary — Synonyms, Antonyms, One-Word Substitutes, Idioms, Phrasal Verbs
    • Grammar — Tenses, Voice, Narration, Prepositions, Articles, Modals
    • Word Usage, Foreign Words, Root Words, Etymology, Confusables
    • Essay Writing, Letter Writing, Email Writing, Report, Précis
    • Business Reading — Business News, Annual Reports, Strategies, Case Studies
    • Critical Reading — Argument Analysis, Flaw Identification, Strengthen/Weaken
  8. 8

    Logical Reasoning

    ~3 marks

    Puzzles, Arrangements, Logic, Decisions

    • Seating Arrangement — Linear, Circular, Square, Rectangular, Hexagonal
    • Floor/Ladder Puzzles, Box Puzzles, Scheduling (Day/Month/Year)
    • Venn Diagrams, Sets, Family Tree, Blood Relations, Direction
    • Number Series, Letter Series, Coding-Decoding, Pattern Recognition
    • Syllogisms, Statement-Conclusion, Assumption, Inference, Course of Action
    • Critical Reasoning, Paradox, Brainteasers, Logic Games
    • Decision Making, Selection, Prioritization, Optimization, Negotiation
    • Data Sufficiency, Input-Output, Scheduling, Ranking
    • Verbal Reasoning — Analogies, Classification, Odd-Man-Out, Series
    • Visual Reasoning, Pattern Completion, Embedded Figures, Mirror, Water
  9. 9

    Reading Comprehension

    ~3 marks

    Factual, Inferential, Critical, Business

    • Factual Reading Comprehension — Direct Information, Recall
    • Inferential Reading Comprehension — Logic, Reasoning, Implications
    • Critical Reading Comprehension — Argument Analysis, Tone, Stance
    • Literary Reading Comprehension — Fiction, Poetry, Drama
    • Business Reading Comprehension — Business News, Annual Reports, Strategies
    • Editorial and Opinion-Based Passages, Critical Thinking, Perspective
    • Scientific and Technical Passages, Business Jargon, Industry Terminology
    • Passage-based Vocabulary, Main Idea, Title, Theme, Inference Questions
    • Comparative Reading — Comparing Two Passages, Synthesis, Critical Comparison
    • Speed Reading, Skimming, Scanning, Active Reading, Time Management
  10. 10

    Verbal Ability

    ~3 marks

    Grammar, Vocabulary, Para Jumbles

    • Grammar — Tenses, Voice, Narration, Subject-Verb Agreement
    • Vocabulary — Synonyms, Antonyms, One-Word Substitutes, Idioms, Phrasal Verbs
    • Sentence Correction, Error Spotting, Sentence Improvement
    • Para Jumbles, Sentence Rearrangement, Paragraph Completion
    • Cloze Test, Fill in the Blanks, Sentence Completion
    • Word Usage, Foreign Words, Root Words, Etymology, Confusables
    • Spelling, Punctuation, Capitalization, Common Errors
    • Verbal Analogies, Classification, Odd-Man-Out, Verbal Series
    • Critical Reasoning, Paradox, Brainteasers, Logic Games
    • Business Writing — Memo, Report, Email, Letter, Précis, Summary
  11. 11

    Arithmetic

    ~3 marks

    Number System, Percentages, Profit-Loss, SI-CI

    • Number System, HCF-LCM, Indices, Surds, Simplification, Approximation
    • Percentages, Profit-Loss, Discount, SI-CI, Growth Rate, Population Growth
    • Ratio, Proportion, Mixture-Alligation, Partnership, Ages
    • Time-Work, Work-Wages, Pipes & Cisterns, Efficiency
    • Time-Speed-Distance, Trains, Boats, Races, Clocks, Calendar
    • Averages, Mixture Problems, Alligation, Allegation Method
    • Mensuration, Geometry, Coordinate Geometry, Trigonometry
    • Data Interpretation — Tables, Bar, Pie, Line, Caselet, Data Sufficiency
    • Modern Math — Permutation, Combination, Probability, Sets, Functions
    • Commercial Math — Stocks, Shares, Dividends, Brokerage, GST, True Discount
  12. 12

    Algebra

    ~3 marks

    Equations, Functions, P&C, Probability

    • Linear Equations, Quadratic Equations, Polynomials, Identities
    • Functions, Graphs, Inequalities, Logarithms, Modulus, Domain, Range
    • Sequences and Series, AP, GP, HP, Sum of n terms, Special Series
    • Permutation, Combination, Binomial Theorem, Probability
    • Matrices, Determinants, Linear Programming, System of Equations
    • Set Theory, Relations, Functions, Venn Diagrams, Cardinality
    • Trigonometry — Ratios, Identities, Heights and Distances, Equations
    • Coordinate Geometry — Lines, Circles, Conics, Distance, Slope
    • Calculus — Limits, Derivatives, Integrals, Maxima, Minima, Applications
    • Statistics — Mean, Median, Mode, Variance, Skewness, Correlation, Regression
  13. 13

    Data Interpretation

    ~3 marks

    Charts, Tables, Caselets, Data Sufficiency

    • Table DI — Direct, Calculation-Based, Multi-Step
    • Bar Graph DI — Single, Double, Stacked, Comparison
    • Pie Chart DI — Sector Angle, Percentage, Comparison, Multiple Pie
    • Line Graph DI — Trend, Multiple Lines, Comparison, Growth Rate
    • Caselet DI — Story-Based, Multi-Step, Verbal Reasoning with Data
    • Data Sufficiency — Two-Statement, Three-Statement, Multi-Condition
    • Comparison DI — Ratio, Percentage, Difference, Growth Rate
    • Missing Data DI — Find the Missing Value, Estimate, Calculate
    • Quant-Based DI — Averages, Ratios in Data, Business Scenarios, HR Data
    • Radar, Web, Mixed Chart DI, Business Scenarios — Revenue, Cost, Profit, Market Share
  14. 14

    Verbal Ability

    ~3 marks

    Grammar, Vocabulary, Reading, Writing

    • Reading Comprehension — Factual, Inferential, Critical, Editorial, Business
    • Cloze Test, Fill in the Blanks, Sentence Completion
    • Spotting Errors, Sentence Correction, Sentence Improvement
    • Para Jumbles, Sentence Rearrangement, Paragraph Completion
    • Vocabulary — Synonyms, Antonyms, One-Word Substitutes, Idioms, Phrasal Verbs
    • Grammar — Tenses, Voice, Narration, Prepositions, Articles, Modals
    • Word Usage, Foreign Words, Root Words, Etymology, Confusables
    • Essay Writing, Letter Writing, Email Writing, Report, Précis
    • Business Reading — Business News, Annual Reports, Strategies, Case Studies
    • Critical Reading — Argument Analysis, Flaw Identification, Strengthen/Weaken
  15. 15

    Logical Reasoning

    ~3 marks

    Puzzles, Arrangements, Logic, Decisions

    • Seating Arrangement — Linear, Circular, Square, Rectangular, Hexagonal
    • Floor/Ladder Puzzles, Box Puzzles, Scheduling (Day/Month/Year)
    • Venn Diagrams, Sets, Family Tree, Blood Relations, Direction
    • Number Series, Letter Series, Coding-Decoding, Pattern Recognition
    • Syllogisms, Statement-Conclusion, Assumption, Inference, Course of Action
    • Critical Reasoning, Paradox, Brainteasers, Logic Games
    • Decision Making, Selection, Prioritization, Optimization, Negotiation
    • Data Sufficiency, Input-Output, Scheduling, Ranking
    • Verbal Reasoning — Analogies, Classification, Odd-Man-Out, Series
    • Visual Reasoning, Pattern Completion, Embedded Figures, Mirror, Water

Frequently asked questions

What topics are in the CDS Mathematics syllabus?

Mathematics for CDS has 15 topics: Algebra, Trigonometry & Geometry, Calculus & Statistics, Arithmetic (MBA Quant), Algebra (MBA Quant), Data Interpretation, English, Logical Reasoning, Reading Comprehension, Verbal Ability and 5 more, with 141 sub-topics in all.

How many questions come from Mathematics in CDS?

About 100 questions (300 marks) in CDS Paper I (Math). Always check the latest notification, as numbers can change.

Which Mathematics topics matter most for CDS?

By weightage in the syllabus data: Algebra (~3 marks), Trigonometry & Geometry (~3 marks), Calculus & Statistics (~3 marks).

How do I practise CDS Mathematics on Topicly?

Pick a topic above and study it your way — step-by-step chat, a quiz, a formula sheet or a voice call with Sia. Topicly tracks each sub-topic so you know what's left. It's free to start.

Compiled from official notifications for study purposes. Always confirm with the conducting body's latest notification.