How to prepare for Mathematics Optional?

I have extensively referred to the Prakash Rajpurohit’s Blog, which can be found here. I have nothing much new to add to whatever he has written. The sources and the way to attempt the paper wereΒ also mentioned quite well in the blog itself.

I have completed the whole syllabus – including for Paper II. However I have covered Mechanics and Fluid Dynamics from 10 markers point of view.

My Score in Mathematics:


My Correct Attempt:


In Paper II, for the question on Compound Pendulum using Hamilton’s equations, I had solved that for Simple Pendulum using the Hamilton’s equations. So I believe I would have received some partial marks for that problem. So my correct attempt would be around 242 in Paper II.

Also, unlike previous years, the scaling factor in Paper I is higher than that in Paper II. This is because Paper I was relatively difficult than Paper II. This shows that UPSC’s surprises are not just limited to GS but also to Optionals.

Lesson that I learnt: Give equal importance to both the papers and all the chapters.


66 thoughts on “How to prepare for Mathematics Optional?

  1. Sorry for troubling you..can u please share ur strategy for ethics coaching important for to write a good answer in ethics? Please provide as much detail like u gave for history and others..thanks in advance..


  2. Is case study important for answer writing..what is difference between examples and case study for paper 2 and paper 3? For example i wrote one example in my test series about food processing industry about my own experience of passighat in arunachal where oranges are left on road bcs if lack of food processing..can i write sich thing


    • You can write them if you feel they are relevant to the question that was asked. But you would have to be precise so as to not digress from the question and exceed the word limit.


  3. Did you referred IMS/ brilliant tutorials material for preparation?
    I mean if books suggested by Mr Rajpurohit and Kashish mittal are enough?


    • Yes I did take coaching at Analog IAS, Hyderabad for Mathematics and RC Reddy Study Circle for GS. But I feel that coaching for Mathematics and GS is not compulsory to score high marks as the exam has become very dynamic (the GS).


  4. Sir, Can you please share your strategy of preparation for the following topics in Mathematics Optional..
    Paper -1 : Calculus, Analytic Geometry, Dynamics & Statics
    Paper -2 : Modern Algebra, Real Analysis, Mechanics & Fluid Dynamics
    And after prelims how did you plan your revision strategy for Mathematics Optional

    I gave my mains attempt with mathematics optional this year and i scored 67 in paper 1 and 121 in paper 2.
    The above chapters are not in my comfort zone. Any help would be highly appreciated.

    Thank you.


    • There is no special strategy that I adopted. I only covered the relevant chapters from the sources as mentioned in Prakash Rajpurohit’s blog. It may seem a bit difficult to study these chapters, but they can be done. There is no special easier way to master these chapters, at least not that I’m aware of πŸ™‚

      I used to spend 3 hours everyday on my optional after Prelims.

      Even though these chapters may seem difficult, you should put in all the extra effort that it takes to master them. I feel its worth that effort because nothing is more sweet than some great marks in optional πŸ™‚


  5. Hi Saikanth Sir,
    First of all congratulations on your grand success.
    I was waiting for your interview on Mrunal from there i got this Blog. Sir i am considering Mathematics as my optional. Sir i have few doubts related to optional, Kindly reply to my doubts and if possible kindly provide me your email id or contact number so that i can get in touch with you:


    1. I am an Engineer working at L&T graduated in 2011 from a deemed university LPU. But my mathematics is good, as compare to any other subjects for optional as i have more interest in mathematics, currently the status of my maths is that i have forgotten almost all concepts of calculus and algebra, but if i give one reading then i know i can understand all of the. So my question is having such current situation should i go for maths or not? And i have not studied Real Analysis and some other subject from Part II of the syllabus during my graduation.

    2. I am working so obviously it will take more time to finish syllabus, so can you tell me how much time you took to complete the syllabus from scratch.

    3. Prakash raj purohit blog books are all mostly Indian authors, do we need to follow any foriegn author books, As i like reading the theory before jumping into calculatons, and theory is not there in indian authors books.

    4. Can you provide topic wise sources i know prakashraj has done a lot on this matter but still if you can elaborate it in more detail, than it will be really nice as i am not in delhi and i no connections to delhi, Living in Mysore.

    5. Which coaching material i should go for?

    6. Answer writing in mathematics: i have heard from ForumIAS that Answer writing style really matters in Mathematics also, Regarding Answer writing its like do we have to give Geometric Interpretation of things or real life examples, or if somehow we can relate it to social issue. if you can elaborate on that thatn i will be wonderful.
    7. Kindly share your notes of mathematics. And if you have created notes for GS on Evernote please share that also.

    Please respond to it.
    Looking forward for your response.

    Thank you
    Abhinav Saxena
    my email ID:


    • Thanks Abhinav. Please find my responses:
      1. Its your decision and I can’t say whether you should choose Mathematics or not. When I started preparing for Mathematics I didn’t know most of these topics that you’ve mentioned. But still I chose Mathematics because I know that I have an interest in the subject and I can learn this subject. On the other hand, I’ve never studied the traditional optional subjects like Anthropology, Pub Ad, Pol Science etc., and so didn’t have the guts to take one of them an my optional.
      2. I started preparing on my optional after I left my job. It took me about 5-6 months to finish about 90% of the syllabus, along with some GS basics.
      3. I don’t know why you felt that there isn’t adequate theory in books by Indian authors. I did not face any such problem myself and I never referred to books by any foreign authors, as I didn’t find the need.
      4. I’ve already mentioned in my blog that I had referred only to Prakash Rajpurohit’s blog. And I find that to be extremely comprehensive and I have nothing new to add to that.
      5. I referred to IMS notes only for a few topics. But I feel they are not necessary, I’ve only used them because I’ve had them. In my opinion you don’t need any coaching or coaching material for Mathematics. Just try and cover the syllabus.
      6. Not at all man. Its mathematics. All you need to do is to solve mathematical problems. You don’t need to write anything more than what has been asked for. And you don’t need to give any real life examples, or social issues related stuff etc. You just have to write proper steps and a correct answer for the given problem πŸ™‚
      7. I didn’t prepare any notes for Mathematics, all I prepared was a few formula sheets so as to revise them quickly. Coming to my GS notes, I have written an exclusive post here –

      All the best!


  6. congrats on your splendid success in 1st attempt itself. Got hugely inspired after reading your interview on Mrunal. and then got this blog link (a goldmine for us !)
    Before jumping directly to the qstns, let me give you my short intro that should help you while answering my qstn.
    Computer science graduate –> working in s/w industry –> settled on Mathematics as optional.for CSE-2016 (1st attempt).

    I chose Mathematics mainly for two reasons : (don’t know if these are sufficient)
    (1.) Most important reason, I find myself incapable of writing long answers (say for 60 markers) that I’ve to do in humanities paper if I don’t select Maths. (though not a genuine reason but it’s true in my case).
    (2.) Huge scoring opportunity provided preparation is brilliant
    (2.) I’ve been decent in maths throughout my career, if not genius
    10th- got 91
    12th – 82
    B.Tech semesters – ‘E’ grade
    Cat – 91 percentile in quant
    (3.) Have decent interest.

    While after going through mock test answer sheets of at least four Maths topper-2014 I realized I can also write those kind of answers, I also got flooded with some doubts (and fear too) and worst of them is :

    (1.) How is IAS mathematics different from IIT/AIEEE/CAT Maths ? (in terms of unseen and brain storming qstns that we used to get in IIT/CAT)
    – considering the fact that correct attempt should be in the range of 220-250 in order to neutralize scaling monster,what might be the extent of unseen/tough/time-consuming/non-doable qstns that i won’t be able to attempt (just because i don’t know) in the exam hall even after finishing the syllabus, revising it and doing lots of mocks ?

    Awaiting for reply !!


      • Hahaha… Sorry mate, somehow missed it.
        UPSC mathematics is entirely different from IITJEE, CAT etc. It’s lot more theoretical and you must have got an idea of the same when you would have seen the syllabus. Don’t vacillate too much man, go for mathematics if you have an interest in the subject. And yes there are certain chapters which are a bit troublesome. But still you must complete the syllabus and attempt all questions correctly in the exam, then you’ll surely get one of the highest marks in all the optionals. If you don’t do these things, you’ll get very low marks because I don’t think there will be partial marking in Mathematics. Also please take a look at Nitish’s blog, a link to which can be found in my optionals page. All the best!


        • Thanks a lot sir for clearing the air. feeling much relieved now.
          one more doubt :
          what all chapters are you referring to when you say “certain chapters are a bit troublesome” ?
          are they “Abstract algebra and Real analysis” ?


          • The reason why I didn’t tell you that is because you might get intimidated by these chapters even before you study them. So don’t worry about that and complete the syllabus. 😊


              • one more doubt :
                After going through book list suggested by Nitish sir, I’m confused about which book should i select (say for calculus) as most of the books suggested by Nitish sir are different from what Prakash Rajpurohit sir has suggested in his blog.

                For calculus, Prakash sir has suggested ” Shanti Narayan – Course on Mathematical Analysis (S. Chand) ” but Nitish sir’s list is totally different. I checked reviews for this book on flipkart; there too, not so encouraging feedback for the same.

                similarly, for others topic too, I can see conflict in terms of books suggested.

                should I go as per Nitish sir’s book list considering current trend in maths question or Prakash’s sir book list is enough ?

                your take please.


  7. Hello Sir,
    I joined for public administration this june, and realizing that it would be a disaster for me, changed to maths after going through syllabus and previous papers. I dont want to join coaching but decided to give test series – IMS , ANALOG. I am planning to get postal material from Analog IAS, after reading ur interview. Is that material a necessity, or the books given in Prakash Raj Purohith Blog suffice the need of exam?


    • I have not taken any material from Analog IAS institute. I’ve attended only classes there and made my own notes. I don’t think that coaching is necessary for Mathematics optional and I think Prakash Rajpurohit’s blog is quite comprehensive and I feel that it should suffice.
      For more inputs you can refer to Nitish’s blog – I’ve put up a link in the Optionals page. All the best!


      • Sir could you tell me the chapters in which you prepared theorems for? And sir, are the standard of questions equivalent to the IIT – JEE entrance or is it of AIEEE standard or some where between the two or even lower as that of EAMCET?


  8. Congrats on your success. I have also taken maths as an optional. I have already prepared booklist with the help of Prakashraj Purohit blog & Dias website. So how can i mail you that list so that you can once review & give your best opinion. For practice what should i do? which classes paper would be good for maths? Pls guide me.


  9. Hello sir,

    1 Doubt

    For ordinary and partial differential equations (paper 1+ paper 2), I’m covering M.D.Raisinghania as suggested by praskash sir and Nithish sir. But even after going through previous years question papers and syllabus,I’m in doubt regarding some of the chapters from that book whether those chapters are relevant or not.

    Though below listed chapters seem irrelevant to me at the moment, after your suggestion I’ll update to-do list of chapters accordingly. I’ll be doing Laplace transform and Boundary value problems from other source.


    part-1:: chapter-4, part-3 – extraneous loci
    chapter-8 – ordinary simultaneous differential equations
    chapter -11 – applications of differential equation
    part-2 :: all chapters are irrelevant (will be doing laplace transform from other source)

    part-3 :: chapter-4, homogeneous linear partial differential equations with constant coefficient
    chapter-5 , non-homogeneous linear partial differential equations with constant coefficient
    chapter -9 , monge’s method
    chapter -10 transport equation


  10. Hello sir, congratulations…
    sir, i was very good in maths… topped my school in 10th and 12th with 95+ marks each time. But when i entered mechanical engg i kind of got distracted from studies and studied just a night prior to my exams and hence don’t have any base of engg maths. Now i want to ask you, how much is the maths here related to that of engg and also how much time does a personal generally take to complete maths, if he is starting form scratch, like me ?
    It will be a great help from your side sir πŸ™‚


    • There is not so much of engineering math. I did my eng in computer science and engineering and I hardly knew the topics mentioned in the syllabus. Take a look at the syllabus to get an idea. If you have an appetite for mathematics then you should do well with this optional. All the best.


  11. Hello Saikanth,

    Congrats !! I would like to know for the below query

    -> How did you seggregate previous questions in topic wise, do we have any book available for this, or you just downloaded and solve the previous year problems on your own ?

    Best Regards,
    Bhargava Tadi


  12. I have some doubts whether the following topics are in syllabus or not:
    analytical solid geometry,,krishna series:
    1.the paraboloids
    2.generating lines
    3.the plane section of the conicoids
    4.confocal conicoids

    differential geometry….krishna series
    does the whloe first chapter upto 131 pages in syllabus

    complex analysis
    do we need to cover contours like rectangular contours as well

    does CHARPITS METHOD is in syllabus


  13. Hello Sir! πŸ™‚
    Can you please tell me
    1)whether i should remember theorem’s proof also as there are too much of them. For eg: i have started with Linear Algebra and Matrices and it have a lot of theorems and proofs. Do we need to know the proofs also and remember them?
    2) i have seen in examination some question which are like having no ” integers, real numbers” in them and looks like they have to be proved by assumption. How to tackle that questions?
    3) i have started preparing for maths from 15th jan 2015 as i was not comfortable with History but i find maths intersting. But there are many topics in which i’m weak. Also, i’ve not studied maths from last 3 years i guess. So dont remember integration, differentiation now! How much time should i give to maths daily? so that i cant finish it near sep-oct!! and can utilize november in revising whole syllabus. πŸ™‚
    Thanking you in advance Sir πŸ™‚


  14. Hai.. I have few doubts regarding maths optional… In analytic geometry where should I stop.. At tangents and normals for conics or the generating lines for conics… I study with shantinarayan.. Also I have same problems with abstract algebra. Don’t know where to stop.. Kindly give a suggestion


  15. Sir, if you can please upload ims main material for maths, it will be of great help for the students who cant afford buying these books.

    Congrats and All the best for serving our nation. Jai Hind!!!


  16. Hi Mr.Saikanth,
    1) Are there any maths test series with solutions available in the market?
    2) Are the previous year test series question papers available in ashok nagar ?
    Thank you for your time.


  17. Hello Mr.Saikanth ,
    I am thinking of taking maths as my optional . I am confused because if the optionals are removed in 2017 or 2018 , then all the hours I spend on Maths ( which are going to be way more than others spend on their optionals , since its huge ) will be futile and which is supposed to an advantage( like high scoring or efforts proportional to final score ) will turn against me .
    1) Do you think Maths can be completed in 5-6 months time for someone who is good at math ( btech from IIT and good at math during JEE times) ?
    2) Is there lot of mugging up to do in maths .. like theorems and proofs ?
    3) What do you think ( guess ) about the future of optionals ? ( scrapping immediately or after 3–4 yrs gap )
    Thank you for your time.
    All the best !


  18. Hi Mr.Saikanth ,
    How is the coaching for maths in analog IAS ? Do you think it’s good ? Or is IMS better than analog for maths?
    Thank you.


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