[Strategy] Mathematics : Strategy, Topicwise Booklist, Sample Answers for UPSC (Mains) Exam

MK Pandey Fast track to objective arithmetic
  1. Introduction: Maths as an optional subject
  2. General tips for preparation:
  3. General tips while attempting the paper:
  4. Paper 1: Topicwise Booklist
  5. Paper 2: Topicwise Booklist
  6. Model Answers for UPSC Maths Paper

I’m merely copy pasting the article of Prakash Rajpurohit (AIR 2/ CSE 2010).

Introduction: Maths as an optional subject

Before starting with the strategy I would like to answer a common question: What is the final score vis-à-vis correct attempt? It is true that there is heavy moderation of marks in science subjects especially in mathematics. But despite that it is possible to score very high. My final score and correct attempt paper wise is:

Year 2008 2009
Paper Paper I II Paper I Paper II
Correct Attempt (out of 300) 261 250 300 285
Marks Received (after scaling) 184 206 209 218

In the correct attempt I have counted only those answers which are absolutely correct. Paper I is relatively easy so the reduction is huge. Also do not confuse the term scaling down as only multiplication by a constant factor (some says scaling is 0.6 or 0.7). The statistical formulas are more complex and the subtraction part has larger weightage I guess (seeing the mark trends of all the students in last 2 years).
competition in maths is very tough, most of the candidates are from iit or from math background. scoring here is different from school/college as there is heavy moderation of marks.

General tips for preparation:

  • Need of coaching is a subjective matter. I did not take any.
  • For maths practice is appropriate word instead of revision.
  • While preparing one should not be bothered about the moderation/scaling. Target should be to score maximum possible marks.
  • study only those topics which are mentioned in the syllabus.
  • In Paper I try to cover all the topics. If time does not permit then cover dynamics and statics from 12 markers point of view.
  • In Paper II focus on the topics: Complex Analysis, Linear Programming, Partial Differential Equations and Numerical Analysis. Rest of the topics should be covered from 12 markers point of view.
  • it is not possible that you come across all the question before exam. what i do is try to finish the paper quickly and keep some time to think over them. for mechanics and dynamics see all the 12 markers which have come in last 10 years. try to cover the theory required to solve them. and practice few more examples related to that.
  • Make a fair copy and practice all the previous year questions in it.
  • Practice with pen and paper(Many aspirants take this point casually and just read the solved examples)
  • Do at least 3-4 papers in exam like conditions.

General tips while attempting the paper:

  • Ordering of questions does not matter. Attempt the questions which you know the best at the start.
  • Try to finish each question in the 75-80% of the allotted time. For example, a 15 marks question has allotted time of 9 minutes. Try to finish it in 7 minutes. Rest 2 minutes must be spent on revising the answer. Rechecking entire paper at the end may not be possible. Try to work out the answer quickly in rough space. All this is important because wrong answer may carry heavy penalty.
  • i did not write any theory, not even explained the terms in lagarange interpolation formula.. focus should be on getting the correct answer and that too quickly.
  • All the trivial calculations (like simple integration, algebraic and trigonometric manipulations) can be done in rough space to save time (I believe that showing them in answer might not carry any weightage).
  • I will also upload some of the answers which I wrote in the paper. In the next articles I will be sharing the detailed strategy for both the papers.

A major question that comes in the mind of an aspirant is whether she should go for selective or exhaustive preparation. I went for the exhaustive preparation, as most part of the syllabus was part of my graduation curriculum. But if time does not permit one can leave some topics from point of view of full 60 marks question. In this post I am giving topic wise preparation strategy.

Paper 1: Topicwise Booklist

  1. Calculus – Shanti Narayan – Course on Mathematical Analysis (S. Chand)
  2. Analytic Geometry – Shanti Narayan (S. Chand)
  3. Ordinary Differential Equations – M.D. Raisinghania (S. Chand)
  4. Statics – Krishna Series
  5. Dynamics – Krishna Series

Paper I Topics

  1. Linear Algebra Focus should on understanding the definition of various terms mentioned in the syllabus (like vector spaces, subspaces, linear dependence and so on). While answering questions explain all the steps.
  2. Calculus Single variable calculus is not a problem for candidates. Refer to chapters (book I mentioned in the booklist) that deal with continuity and differentiability for 2 variables. For double and triple integration also refer to that book. The solved examples from that book are sufficient. The relevant chapters are:12,13,15,16,17,18. Theory is not important , just understand the techniques through solved examples.
  3. Analytic Geometry Refer book by PN Chaterjee(Rajhans Publications). This book contains solved examples and all the questions are taken from this book.
  4. Ordinary Differential Equations In this topic it is better to make a sheet of all the formulas and techniques. Practice all the solved questions of the book I have mentioned.
  5. Dynamics and Statics Completing the Krishna Series books(do only topics mentioned in the syllabus) will be sufficient for attempting 60 marks question. Common Catenary, central orbits, constrained motion should be covered in depth(that is do all the solved examples).  For rest of the topics covering only few examples is sufficient.
  6. Vector Analysis In this topic make the formula sheet. And practice previous year questions. Regularly practice the derivations asked in the exam.

Paper 2: Topicwise Booklist

  1. Algebra Khanna and Bhambri
  2. Algebra- I. N. Herstein
  3. Elements of Real Analysis -MD. Raisinghania(S. Chand)
  4. Complex Analysis – Krishna Series
  5. Linear Programming -  Krishna Series
  6. Partial Differential Equations- M.D. Raisinghania + (Some portion of book on Boundary Value Problem by S. Chand)
  7. Numerical Analysis – Jain and Iynger
  8. Fluid Dynamics – M.D. Raisinghania
  9. Mechanics – Krishna Series (Rigid Dynamics vol.-1 and Vo.-II)
  10. For Linear Algebra and Vector Analysis, I could not find any books relevant to the exam. So I referred to Brilliant Tutorials material to practice questions.

Paper 2: Topics and Tips

  1. Algebra For the people who are totally new to this topic i would suggest that read the books i have mentioned 2-3 times. Then practice all the theorems and questions yourself 2-3 times.
  2. Real Analysis Cover chapters: 2- The Real Numbers(till page 24), 3-Neighbourhoods and Limit Point of a set(till page 11),  4 Countability of Sets(first 12 theorems and examples given at the end) 5,6,7(Regarding Sequence and series) 8. Real Functions. Limit and Continuity, 9,10,11,12,13,15,16. For the topics underlined cover the theorems also. For rest of the chapters solved examples are enough.
  3. Complex Analysis Cover this topic from any book. Practice this topic thoroughly.
  4. Linear Programming Practice is important. Improve upon the speed and accuracy for this topic.
  5. Partial Differential Equations Same as Ordinary Differential Equations.
  6. Numerical Analysis and Computer Programming Make the formula sheet for all the methods. Cover error analysis for newton raphson, lagrange interpolation, numerical integration. Draw flow chart and algorithm for all the numerical methods. Practice them regularly. For other topics i had M Morris Mano(this is digital electronics book). One can refer to the internet if she does not find the leftover topics in book.
  7. Mechanics and Fluid Dynamics For Mechanics focus on chapters of Lagrangian(cover it from Vol-II, Rigid Dyanamics-Krishna Series), Hamiltonian, Moment Of Inertia, D’Alembert’s principle. For Fluid Dynamics  cover topics mentioned in the syllabus. The book of MD Raisinghania covers syllabus from IAS exam perspective also.

My methodology was to first cover the topic from the books. Then practice previous year questions from that topic. I covered the topics in the order mentioned in the syllabus. However it does not matter much. After covering the entire syllabus I practiced last 3-4 year papers in exam like conditions.

Model Answers for UPSC Maths Paper

I have uploaded solutions to Q 1(a) and Q 7(a) of CSE-2009 paper-II attempted by me. Here they’re:

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अब तक 48 कमेंट्स लिखी गयी

  1. Abhishek says:

    Mrunal,the booklist is not there…

  2. Dishant says:

    Sir, what is meant by scaling? I mean Marks are given less in maths as compared to other subjects? why so,….

  3. vinay says:

    is knowledge of c and c++ important ??

  4. vivek says:

    i am a b.tech student but my medium is hindi. is there any difficulty if i take maths ??? i think mathematical terms are same in both hindi and english but what abt the theory part ????

  5. Ansar says:

    I have complete bsc maths,
    more detail for upsc maths optional, and answer wriitting models…

  6. rahul says:

    With reference to paper-I ,there are many books on calculus by Shanti Narayan( Around 8 books on various calculus topics).
    Which one should be referred ?

  7. sreya says:

    hi mrunal…i want mathematics notes for mains urgently….plz tell me a solution…

  8. Kunal Kumar says:

    Dear Mrunal,

    Is it possible to get mathematics notes of any topper by your team. Bcoz notes for mathematics is not easily available.

  9. Samir says:

    Hi Mrunal,

    You have mentioned two books for Algebra(Paper-II). Which books should be followed. Or it is like some topics from one book and some from other. Kindly elaborate.

  10. Rohit Singhal says:

    are calculators allowed during exam…??

    • Mrunal says:

      Yes Scientific (Non-programmable) calculators are allowed in UPSC mains exams.

  11. mridula says:

    is casio fx-991ms calculator allowed in the exam?

  12. Sumit Kansal says:

    Hello Mrunal,

    First of let me take this opportunity to thank you for providing such a platform for large of aspirants like me, esp ones who are short of guidance.
    My words can never match the blessings you would actually be getting by this effort of yours.

    Not to say, i am also one of those lakhs of aspirants who dream the next to impossible ( cracking the Mother of Exams :) )
    I do now and will in future need guidance of people like you.

    One information regarding this article i need is, that can you suggest some solved previous year papers of mathematics mains by any publisher. As i could not find a single publication . Would be great help.

    Also as i am thinking to take mathematics as one of my optional, i need guidance of someone who has taken the same optional. Can you suggest anyone who is approachable ?

    Thanks again for the great platform !!

    Keep Going !!
    God Bless !!

    • Mrunal says:

      sorry no idea on math solved papers.
      I had tried R.T.I route also, but UPSC stonewalled it, now appeal pending before CIC.

  13. Swarup says:

    I am searching solid geometry book of P.N. Chaterjee of Rajhans Publications. Can any one tell me from where can I get that book ?

  14. Manu says:

    I am doing master of computer applications and my degree is bca,,, isn’t der any problem for me in appearing for the ias exam no,,,

  15. anil says:

    is it possible for a bsc graduate in physics, chemistry and maths (Pass course) to opt. for maths optional and actually crack it. please reply

  16. vinay says:

    can i take ias exam in hindi besides mathematics

  17. Avinash says:

    i want to know which books should i refer for previously solved paper of ssc(1997-2012)

  18. raju says:

    Hi Mrunal,
    it’s my first turn, is it possible to prepare for maths(2 paper)+philosophy(2 paper)+GK(3 papers) in next 6 months, if i didn’t ever prepare before?

  19. puspol mondal says:

    can you give me full syllabus of math(optional) for upsc main

  20. veerendra says:

    please tell me about availability of mathematics optional material

  21. sunil tyagi says:

    Please provide strategy for physics also.

  22. Varun says:

    I have one doubt…As here they said ordering of question doesn’t matter…is this apply to sub-parts of questions as well?

    I mean suppose we attempt question no 1 and B part(say 1.B) first and then after any question no with any part(say 2.C),,is this matter here ??

    Please help me out..I’ll highly be thankful to you

  23. Minu says:

    hello sir,
    I am minu i have completed bsc maths. I am going do pg degreee. I want to go classes for ias coaching. I have searched more classes there are not taking classes for maths can you suggest me where the classes going on for maths coaching sir………………………………. please consider it sir

  24. raju says:

    Hi can u tell me best book for boolean-algebra?

  25. durga says:

    am doing bsc.maths,i need more details regarding maths optional.
    i need previous question papers and i want to know whether maths is a good optional and whether it is difficult when compared to other subjects as optional…

  26. prabuddh says:

    Dear Sir,

    Help us in uppcs main exam in mathematics and social works. need syllabus and main exam paper.

  27. rahul nimse says:


  28. Anuj says:

    Hi Mrunal,
    I have a question
    Who can choose MAths as an optional for mains

    can i choose it
    i has always score above 90+ from 6th-12th
    during Btech 1st and 2nd year above 80+
    in competitive exam like SSC-cgl has scored above 90% in maths section both mains and pre
    or the maths in CSE mains is totally different and do had to study from a whole new level(scratch).

    • Varun says:

      No doubt this Math has nothing to do with 10 11 12th…..But if yours basic are strong enough then you should defintely go for it…You can score well…Math will be a better option for you..

  29. kiran says:

    sir,,,,,nice to meet u.basically i am from maths background.but now i am in little confuse.which one is the better option for civils either public admin or maths.plz guide me.as early as possible thank you ……

  30. Rupesh Kumar says:

    Hello Mrunal Ji,

    First of all,i would like to thank you for providing such a great platform for ias aspirants. I have MATH as my optional subject.

    Could you please tell me where i can buy UPSC(Main) Mathematics solved Question Paper.



  31. M.Vasim says:

    I need Maths 2013 paper…..

    please upload asap……

  32. trivedi devdatt says:

    thank you very very much. god bledd you,sir.

  33. NIKITA says:

    thnx alot sir..

  34. Test_taker says:

    I have had opted for maths as one of the optionals for mains 2013 prior to notification, but since number of optionals was reduced, I didn’t appear with maths. I have good quality notes of a classes based in delhi with standard textbooks for almost each chapter, most of which are brand new. I am ready to offer the textbooks and notes at a good discount. I stay in Mumbai and anyone interested can contact me on [email protected].

  35. sumanth says:

    what are the books do you have for the topics LINEAR PROGRAMING, numerical analysis and for applied maths chapters.if i could have the opportunity to know the list of books for the above chapters i would like to bye them.

  36. neha says:

    which chapters to cover in partial differential equation from m.d.rajsinghania

  37. deepak says:

    sir which chapters should be cover for vector from shanti narayan?

  38. Dhimaan says:

    I have not found any solved (or unsolved,for that matter) Maths optional papers in book form.I guess they are not published by any publisher.Would be grateful if somebody could help me with finding the previous 10 years (or more) papers.

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