What is the ELEMENTARY MATHEMATICS Syllabus of CSD Examinations

What is the ELEMENTARY MATHEMATICS Syllabus of CDS Examinations

CDS ( Combined Defence Service ) is conducted two times in a year by the UPSC  ( Union Public Service Commission ) for a needs into the Indian Military Academy, the Indian Naval Academy, the Indian Air Force Academy and The Officer Training Academy. In CDS examination you should write with black ball pen the name of the centre and subject in English or Hindi.

In CDS examination there are three subjects

  • English
  • General Knowledge
  • Mathematics

Elementary Mathematics Syllabus

The examination of the Mathematics syllabus is divided into the various topics they are:-

  • Algebra
  • Trigonometry
  • Geometry
  • Arithmetic
  • Mensuration
  • Statistics



Basic Operations, simple factors, Remainder Theorem, H.C.F., L.C.M., Theory of polynomials, solutions of quadratic equations, the relation between its roots and coefficients (Only real roots to be considered). Simultaneous linear equations in two unknowns—analytical and graphical solutions. Simultaneous linear inequations in two variables and their solutions. Practical problems are leading to two simultaneous linear equations or inequations in two variables or quadratic equations in one variable & their solutions. Set language and set notation, rational expressions and conditional identities, Laws of indices.


Sine ×, cosine ×, Tangent × when 0° < × <90° Values of sin ×, cos × and tan ×, for × = 0°, 30°, 45°, 60° and 90°

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


Lines and angles, Plane and plane figures, Theoremson (i) Properties of angles at a point, (ii) Parallel lines, (iii) Sides and angles of a triangle, (iv) Congruency of triangles, (v) Similar triangles, (vi) Concurrence of medians and altitudes, (vii) Properties of angles, sides and diagonals of a parallelogram, rectangle and square, (viii) Circles and its properties including tangents and normal, (ix) Loci


Number System — Natural numbers, Integers, Rational and Real numbers. Fundamental operations, addition, Subtraction, multiplication, division, Square roots, Decimal fractions. Unitary method, time and distance, time and work, percentages, applications to simple and compound interest, profit and loss, ratio and proportion, variation.

Elementary Number Theory—Division algorithm. Prime and composite numbers. Tests of divisibility by 2, 3, 4, 5, 9 and 11. Multiples and factors. Factorisation Theorem. H.C.F. and L.C.M. Euclidean algorithm. Logarithms to base 10, laws of logarithms, use of logarithmic tables.


Areas of squares, rectangles, parallelograms, triangle and circle. Areas of figures which can be split up into these figures (Field Book), Surface area and volume of cuboids, lateral surface and volume of right circular cones and cylinders, surface area and volume of spheres.


Collection and tabulation of statistical data, Graphical representation frequency polygons, histograms, bar charts, pie charts, etc. Measures of central tendency.

Examination Instruction

  1. The maximum marks given to the written examination and to the interviews will be equal for each course i.e. the maximum marks allotted to the written examination and to the interviews will be 300, 300,300 and 200 each for admission to the Indian Military Academy, Indian Naval Academy, Air Force Academy and Officers’ Training Academy respectively.
  2. The papers in all the subjects will consist of objective type questions only. The question papers (Test Booklets) of General Knowledge and Elementary Mathematics will be set bilingually in Hindi as well as English
  3. In the question papers, wherever necessary, questions involving the metric system of Weights and Measures only will be set.
  4. Candidates must write the papers in their own hand. In no circumstances will they be allowed the help of a scribe to write answers for them.
  5. The Commission has discretion to fix qualifying marks in any or all the subjects of the examination.
  6. The candidates are not permitted to use calculator for answering objective type papers (Test Booklets). They should not therefore, bring the same inside the Examination Hall.

Examination hall advice

Articles permitted inside Examination Hall

Clip board or hard board (on which nothing is written)a good quality Black Ball Pen for marking responses on the Answer Sheet. Answer Sheet and sheet for rough work will be supplied by the invigilator.

Articles not permitted inside Examination Hall

Do not bring any article into the Examination Hall or other than that thing like books, notes, loose sheets, electronic or any other type of calculators, mathematical and drawing instruments, Log Tables, stencils of maps, slide rules, Test Booklets and rough sheets pertaining to earlier session(s) etc.

Mobiles, phones, Bluetooth, pagers or any other communication devices are not allowed inside the premises where the examination is being conducted. Any infringement of these instructions shall entail disciplinary action including ban from future examinations. Candidates are advised in their own interest not to bring any of the banned items including mobile phones/Bluetooth/pagers to the venue of the examination, as arrangements for safekeeping cannot be assured. Candidates are advised not to bring any valuable/costly items to the Examination Halls, as safe keeping of the same cannot be assured. Commission will not be responsible for any loss in this regard.

Negative marketing


  1. There are four alternatives for the answer to every question. For each question for which a wrong answer has been given by the candidate. One third (0.33) of the marks assigned to that question will be deducted as penalty.
  2. If a candidate given more than one answer, it will be treated as a wrong answer even if one of the given answers happens to be correct and there will be same penalty as above for that question.
  3. If a question is left blank i.e. no answer is given by the candidate, there will be no penalty for that question.

Unfair means strictly prohibited

No candidate shall copy from the papers of any other candidate nor permit his papers to be copied nor give nor attempt to give nor obtain nor attempt to obtain irregular assistance of any description.

In Examination Hall

No candidate should misbehave in any manner or create disorderly scene in the Examination Hall or harass the staff employed by the Commission for the conduct of the examination. Any such misconduct will be severely penalised.



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