CDS 2021 Mathematics - Syllabus, Exam Pattern, Preparation Tips, and Recommended Books

Updated On -

Mar 15, 2021

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Sudeshna Bhar

Exams Prepmaster

In the CDS 2021 exam, the Mathematics paper is important and must for the applicants of IMA, INA, and AFA whereas OTA candidates do not need to prepare for Mathematics Paper. Check CDS Exam Pattern

Among three sections in the CDS exam, the Mathematics section comprises 100 objective type question making a total of 100marks. The standard of the Mathematics section is Class 10th level.

Questions in Elementary Mathematics will be moderate in terms of difficulty level. Candidates are advised to solve as many previous years’ question papers to score good marks in this section.

Must Read: CDS 2021 English Syllabus, Exam Pattern, Preparation Tips, and Recommended Books

CDS 2021 Mathematics Preparation Highlights

  • CDS is a one-day Exam. The mathematics paper will be scheduled on the same day as the CDS Exam along with the English and General Knowledge paper.
  • This paper consists of 100 questions.
  • The duration of this paper is 2 hours.
  • The marking scheme of each question is 1 mark for each correct attempt and -0.33 for each wrong attempt.
  • There will be no deduction of marks for unattempted questions.

Check Here: CDS 2021 Selection Process

CDS 2021 Mathematics Syllabus


As per the declaration of UPSC, the syllabus of CDS Elementary Mathematics consists of 7 sections such as Number System, Elementary Number Theory, Algebra, Trigonometry, Geometry, Mensuration, and Statistics. To begin preparation, one can always start with NCERT Mathematics 9th and 10th standard books and it will also help to understand the steps and create your own shortcuts.

Number System

Natural numbers Integers Rational and Real Number
Additions Subtractions Multiplications
Square Roots Decimal fractions Unitary method
Time and Work Percentages Applications to simple and compound Interest
Ratio and Proportion Variations Profit and Loss
Time and distance Division Fundamental Operations

Elementary Number Theory

Division algorithm Prime and composite numbers
Tests of divisibility by 2, 3, 4, 5, 9 and 11 Multiples and factors
Factorization Theorem H.C.F. and L.C.M.
Euclidean algorithm Logarithms to base 10
Laws of logarithms Use of logarithmic tables


Basic Operations Simultaneous linear equations in two unknowns—analytical and graphical solutions
Simple Factors Simultaneous linear inequalities in two variables and their solutions
Remainder Theorem Practical problems leading to two simultaneous linear equations or inequalities in two variables or quadratic equations in one
Theory of Polynomials Set Language and set notation
HCF & LCM Relation between its roots and coefficients (Only real roots will be considered)
Solutions of quadratic equations Variable & their solutions
Law of Indices Rational Expressions and Conditional Identities
  • Trigonometry

    • Simple trigonometric identities
    • Use of trigonometric tables
    • Simple cases of heights and distances
  • Geometry

    • Lines and angles
    • Plane and plane figures
    • Properties of angles at a point
    • Sides and angles of a triangle
    • Congruence of triangles
    • Similar triangles
    • Concurrence of medians and altitudes
    • Properties of angles
    • Sides and diagonals of a parallelogram
    • Rectangle and square
    • Circles and its properties including tangents and normal and Loci
  • Mensuration

Areas of squares Rectangles
Parallelograms Triangle and Circle
Areas of figures which can be split up into smaller figures Surface area and volume of cuboids
Lateral Surface, Area and volume of spheres Volume of Right Circular Cones, cylinders and Surface
  • Statistics:

    • Collection and Tabulation of Statistical Data
    • Histograms
    • Measures of Central Tendency
    • Graphical Representation Frequency Polygons
    • Bar charts

Check Here: CDS 201 Eligibility Criteria in detail

CDS 2021 Expected Number of Questions

Number of Questions
Topics Level of difficulty Number of Questions
Number System Easy 20
Mensuration Moderate 13 - 15
Geometry Moderate to Difficult 11 - 15
Time, Speed and Distance Moderate 6
Simple Interest/ Compound interest Easy 2 - 5
Trigonometry Moderate 12
Algebra Moderate to Difficult 7 - 10
Percentage Easy-Moderate 2 - 4
Mixture Moderate 1
Time and Work Moderate 5
Ratio and Proportion Moderate 2
Profit and Loss Moderate 1
DI and DS Moderate 3
Statistics Easy 8

To know other sections, Check CDS 2021 syllabus and Exam Pattern

How to Prepare for CDS 2021 Mathematics

How to Prepare

To crack CDS, candidates should aim at least to obtain 65 marks in Elementary Mathematics Paper.

  • Number System

Any candidate preparing for CDS 2021, can easily expect 15 to 20 questions from this section. It can be said that approximately this section contains almost 15% of this paper. So candidates need to focus on every concept and method. Some easy tips to solve and prepare for Number system:

  • Candidates can use books of NCERT up to 10th class to clear the concept of the number system and it will help to complete the syllabus of the CDS number system as well.
  • Solve a minimum of 50 questions daily on this topic from easy to a high level of difficulty.
  • Candidates need to focus on questions related to HCF & LCM, finding the unit’s place and products of numbers.
  • Expected number of Questions:
    • Basics of number system: 5 Questions
    • LCM & HCF : 3 Questions
    • Surds & Indices : 2 Questions
    • BODMAS : 3 Questions
    • Factors: 4 Questions
  • Elementary Number Theory

The things you should be learning are the tricks of the sum of natural numbers, the sum of squares, the sum of cubes, tests of Divisibility and H.C.F AND L.C.M as well as few important formulas.

  • Algebra

17 - 20 questions out of 100 questions come from Algebra. Basic operations, simple factors, and remainder theorems are good topics to start algebra preparation. Some tips and tricks for solving algebra problems in a faster way:

  • First, you should choose the easy methods especially when you are practising at home.
  • Sometimes in the case of a lot of questions, taking variables might help as well as it can provide you with a shortcut way of solving the problem in less time than it usually takes.
  • You must remember all the important formulas in algebra. At least you need to remember the logic behind the formulas so that in time of need you can just use the logic instead of wasting time during the Exam.
  • To master this topic, do practice several different familiar types of questions. Once you start solving similar topics and solve previous years’ questions, it will give a rough idea of your progress and the logic behind the problems.

Check CDS 2021 Preparation Tips

  • Trigonometry

Around 10-15 questions were asked from the trigonometry section in the CDS Mathematics paper. Thus, the weightage of trigonometry in the UPSC CDS exam is around 12-15%. Some basic tips that you can follow while preparing for mathematics:

  • Though trigonometric ratios have more importance, you should know the trigonometric identities as well.
  • In height and distance questions, you should keep in mind the form of angle (angle of elevation or angle of depression) given in the particular question.
  • Practice Language-based questions that will help you with Height and Distance problems.
  • Geometry

Geometry is one of the most important sections of Mathematics. 15 - 20 questions come in the CDS Mathematics paper from the geometry section. The geometry section can be divided into three subsections like Co-ordinate geometry; Properties of lines and Angles; and Properties of Triangles, Circles, Rectangles, Squares, etc.

  • Some of the topics that need to be practised parallelly along with coordinate geometry are circles, parallel lines, and triangles out of which congruence and similarity of triangles are quite stressed.
  • Write the geometry formulas down on a piece of paper and stick them onto the wall where you can see them regularly. It’ll help you memorize them.
  • If you are stuck with a geometry question, don’t waste your time trying to solve it right away. Instead, get on with the others and come back to the question when you are done with the rest.
  • Mensuration

Mensuration actually deals with the problems related to Measurements which include columns, areas, lengths, etc. From this topic, 13 to 15 questions are expected in the CDS II 2021 Exam.

  • Clear your concepts about 2D and 3D dimensions and the shapes related to them.
  • Most of the measurements are in decimals or require complex calculations. Due to rush, one can easily miscalculate them or make silly mistakes.
  • Questions that involve the calculation of fencing, flooring, painting cost, etc usually require an increase or decrease of percentage in the measuring meter mentioned in the question or one figure inscribed within another figure, etc.
  • Always remember the most important and essential formulas. Most of the time, formulas can shorten the calculation or sometimes even simplify the problem also.

Check Complete UPSC CDS 2021 Exam Dates

  • Statistics

In CDS II 2021, a maximum of 8 questions can be expected from Statistics. It is quite easy if you have a clear concept. Statistics can be divided into three parts: Common Statistics Terms, Frequency Distribution and Data Interpretations.

  • In Common Statistics Terms, candidates should prepare for Mean, Median, Mode, Variance, and Standard deviation.
  • In the case of Frequency Distribution, candidates basically need to understand some important components like Class, Class limit, Class Frequency, and Mean of frequency distribution etc.
  • Data Representation refers to a given set of data in various forms like a pie chart, tabular form, bar chart, etc. There is no fixed formula for data representation. These types of questions basically require average, percentage, ratio, and other types of calculation for the given data.

Previous Years’ Questions of CDS Mathematics

Previous Years’ Papers

Previous years’ questions papers are one of the main keys to crack the CDS 2021 Exam. Click on link “ Download” to download to previous years’ question papers of CDS Mathematics:

Name of Years Link
CDS I 2021 Download
CDS II 2020 Download
CDS I 2020 Download
CDS II 2019 Download
CDS I 2019 Download
CDS II 2018 Download
CDS I 2018 Download
CDS II 2017 Download
CDS I 2017 Download
CDS II 2016 Download
CDS I 2016 Download
CDS II 2015 Download
CDS I 2015 Download
CDS II 2014 Download
CDS I 2014 Download

Recommended Books for CDS 2021 Mathematics

Recommended Books

These days candidates can always go for online books and mock tests that are provided by numerous websites. But to complete the syllabus of the CDS Mathematics Paper, candidates are advised to use the following books for reference and they need to practice it regularly. For SSB interview, candidates will also require these books for Verbal and Non-verbal reasoning.

Name of Books Author/Publisher
Quantitative Aptitude for Competitive Examination Dr R. S. Aggarwal(S.Chand Publication)
Mathematics for CDS Examination Dr R. S. Aggarwal(S.Chand Publication)
Pathfinder for CDS Examination Arihant Publication
Quicker Mathematics M.Tyra
Numerical Ability Dilhan Publications



Ques. What is the level of maths in CDS?

Ans. Overall, the CDS Mathematics paper is difficult to crack in comparison with the English paper. Mathematics paper needs to be understood and not to be memorized. No shortcut will help you crack mathematics.

Ques. Is Mathematics paper mandatory for CDS candidates?

Ans. For IMA, INA and AFA candidates, the total marks are 300 including Mathematics paper having 100 marks and they need to have at least 20 % of minimum qualifying marks in each subject including Mathematics. But for OTA candidates, this paper is not mandatory. They need to give CDS of 200 marks including English and GK.

Ques. When will be the mathematics paper held?

Ans. As it is declared by UPSC that CDS is a one-day examination, on the declared date by UPSC, all three papers will be held.

Ques. Is the Mathematics paper held online or offline?

Ans. Like the other two papers, CDS Mathematics will be in offline mode. You have to use a black ball pen to bubble the correct option among the four given options for each question.

*The article might have information for the previous academic years, please refer the official website of the exam.