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How to Prepare UPSC Mains Mathematics Paper 2019


Today we are providing UPSC Civil Services  Mathematics Paper preparation tips & strategies. Now we will teach you strategy of “How to Prepare UPSC Civil Services Mathematics Paper 2019“. This post is aimed to help you in forming your strategy for Mathematics optional for Civil Services Exam, considering its various aspects.

How to Prepare UPSC Mains Mathematics Paper 2019

UPSC Mains Mathematics is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature.

To Prepare UPSC Civil Services Mathematics Paper for 2019, you need to follow below given steps.

Step 1 : Know the Syllabus – Mathematics Paper

UPSC MAINS MATHEMATICS SYLLABUS 2019. Get UPSC Mains Mathematics Syllabus, Paper structure & Applicable Topics covered in UPSC Mains Mathematics Syllabus. Earlier we’ve provided UPSC Mains Exam Pattern & Structure for 2018 & 2019 exams .

Read : UPSC Civil Services Mathematics Syllabus 2019

Step 2 : Select the Best Reference Books for Mathematics Paper

Civil Services Mathematics part (As part of GS or as optional) requires vast but focused reading. Apart from the IAS Books for Mathematics – Civil Services Prelims Exam, the below mentioned books can help.

Recommended Books for Mathematics – Civil Services Books – Mains Exam

  1. Linear Algebra
    Schaum Series (3000 solved problems book)
  2. Calculus and Real Analysis
    S.C Malik and Savita Arora Shanti Narayana
  3. 3-D Geometry
    P.N. Chatterjee
  4. Ordinary Differential Equations
    M.D. Raisinghania
    Ian Sneddon
  5. Vector Analysis
    A.R. Vasista
    Schuam Series
  6. Algebra
    Joseph A. Gallian
    Shramik Sen Upadhayay
  7. Complex Analysis
    Schuam Series
    J.N. Sharma
    Ponnu Swami
  8. Linear Programming
    Shanti Swarup
    Kanti Swarup
  9. Numerical Analysis
    Jain and Iyenger
    K. Shankar Rao
    S.S. Shasthry
  10. Computer Programming
    Raja Raman
  11. Dynamics & Statics
    A.R. Vasista
    M. Ray
  12. Mechanics and Fluid Dynamics
    M.D. Raisinghania
    R.K. Gupta
    J.K. Goyal and K.P. Gupta
CA CS CMA Free Lectures

Step 3 : Prepare Important Topics

The preparation for Mains must be over before you start with Preliminary preparation, as the Main exam syllabus covers nearly 75% of the requirements of the Preliminary examination.

If a student has not done graduation with Mathematics, the suggested strategy would be as follows.

(1) Surveying the syllabus of Mathematics carefully and identifying the completely unfamiliar areas.

(2)  Going through at least 2 basic books with a purpose to acquaint yourself with the unfamiliar areas.

You can consider the following books:(a) The NCERT Text Books for Mathematics–Std. XI and XII

(b) Mathematics for Degree Students

(3)  Doing a careful survey of the past 5 years’ Main Examination Question Papers and identifying the areas of significance.

(4)  Identifying the most fruitful areas:

(5)  If we see the Main Examination paper of last few years, then it is obvious that the UPSC can ask even a short note on a topic which is otherwise quite long in coverage.

How to Study Mathematics for IAS Mains

Study approach for Mathematics


This optional is meant for Patience and Calmness. We need to make different strategies for both paper.

There may be some questions out of the topics in the syllabus, prepare for these new topics also as these repeat regularly.

Also Check : UPSC Mains Mathematics Important Topics for 2019

Strategy for Paper I:

  1. Paper I being easier compared to Paper II, all the topics have to be covered in detail.
  2. For Analytical Geometry, read all the solved examples given in above mentioned books. Regularly revise particularly skew lines, sphere, cone and conicoids. In many problems you would have to remember how to start the problem i.e. you would have to mug the approach to solve specific problems.
  3. For Calculus, focus more on Calculus of many variables. This is well covered in Malik and Arora. Also many topics of Paper I and Paper II overlap, which can be prepared simultaneously from the above mentioned book.
  4. In Statics & Dynamics, try to solve all the problems. You can leave very complex problems which are usually given at the end of every chapter.
  5. Make formula sheet for every chapter and revise it regularly. Otherwise you might forget many formulas in exam.
  6. Practice makes perfect. Try solving problems with pen and paper with book closed, instead of just reading.

Strategy for Paper – 2:

  1. Usually Paper II is tough for many. Hence if you are able to master it, then you will able to score very high compared to others
  2. Abstract Algebra is a unique topic. Either you like the topic or you don’t. In first case it will be easy otherwise very tough. I loved the topic and did not read it from exam point of view. If you are finding it tough, I would suggest you to do it from 10 markers point of view. There is no point in spending a lot of time on Abstract Algebra as you won’t be rewarded proportionately. The same time could be used for studying other topics of Maths or GS, which would fetch much more marks. For 10 markers point of view, read books (a) and (b) mentioned above. Memorize all the theorems. Skip proofs of theorems which are big, particularly in Permutation groups, Cayley’s theorem, PID, Euclidean Domain and UFDs. On the other hand, if you are comfortable with Abstract algebra and want to do it in a detailed manner, I will shortly share various e-books, pdfs etc.
  3. For Real Analysis, Malik and Arora is the best. You can supplement it by MD Raisinghania. I felt it is better to leave the proofs. Focus more on Riemann Integral, Improper Integrals and Series and Sequences of functions.
  4. Linear Programming: I feel books for MBA like JK Sharma are written more clearly in Shanti Swarup Books
  5. PDE: Even though not mentioned in syllabus, Charpit’s method has to be covered as questions are regularly asked. For Boundary Value problems (heat equation etc.) first read from Grewal. For more types of problems you should refer to book (c) mentioned above in the booklist.
  6. Mechanics and Fluid Dynamics: From last year UPSC has started mixing questions from PDE, Numerical Analysis and Fluid & Rigid Dynamics. Therefore to score high it has become imperative to cover this topic. But the problem is the syllabus has been vaguely defined and there is confusion about which topics are there in syllabus. By analyzing past years question papers. I covered only the following topics. In Fluid dynamics cover Kinematics of Fluids in Motion, Equations of Motions of Inviscid Fluids, Sources and Sinks, Vortex Motion. No need to see proof of any theorems. From Navier Stokes equations, just try to see only solved examples. For Rigid Dynamics, cover those topics mentioned in booklist above.

Answer writing

  1. For Long answers-Introduction can be either indirect through some lines or quotes or direct with general explanation followed by exact definition.
  2. Thereafter topic need to be explained in short followed by establishing links with other chapters and focusing on the question again. Here give a pause,read the question again & think again. Diagrams can be used effectively.
  3. Ending of the answers should always be visionary/positive and solution based with example if needed or with some lines.
  4. There should be mixed use of paras and points. Examples should be quoted wherever possible but refrain from using one enterprise again & again.
  5. For short answers, write the basic definition and then directly hit the core.
  6. Ending should be solution based. For merit/demerit/feature use diagram or points.
  7. Test series can be joined for practice.

Step 4 : Prepare Previous Question papers

How much time it takes to prepare?

4-5 months, if you study Mathematics 12-15 hours per week. This should be enough. Also, it depends on how much can you recall your graduation concepts.

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