Maths Optional Strategy (Bhavesh Mishra, Rank 58)

Why Maths?

Simply because it is one of the best performing optional subject in UPSC.

  1. Extremely high scoring: If you get your maths optional right then you will make it to the final list. This year Nitish K (Rank 8 ) has got a mind boggling 346 marks.
  2. Certainty: If you have attempted your paper well then you are sure that you will get good marks. For example this year just by attempting 400 marks paper you could get a decent 260+ marks. Even if you don’t get good marks in first attempt you can be sure that you will increase your marks in subsequent attempt.
  3. Fun: Mathematics is a delightful subject and therefore doing maths takes you away from somewhat boring humanities.
  4. Good Impression: The fact that you have taken Maths makes a good impression on interview board members (it happened in my case !). They are very pleased to see that you have opted for a tough optional.
  5. Easy paper: The difficulty level of paper is quite moderate and almost all questions are directly picked from the standard textbooks.

Who should take it?

Anyone who has done B.Tech / M.Tech / B.Sc / M.Sc and has interest in maths.

Myths around science subjects.

Coaching institutions have mastered the art of brainwashing students and creating an atmosphere of gloom and doom around science subjects. There are lots of myths circulating among students. Let’s bust these myths.

  1. Maths optional is only for students from IITs: Definitely not. Anyone willing to put in hard work can easily score very high marks. The best example being Nitish K (Rank 8) who is not from any IIT.
  2. There is heavy scaling: Let the data speak for itself. I attempted 240 marks in Paper 2 and got 170 marks. Now would you call it a scaling?
  3. It plays no role in GS: Yes it’s true that science optional subjects don’t overlap with GS but it’s equally true that GS has never been a rank decider in UPSC. There are 3 major things that decides your rank: Essay, Optional and Interview. Even if one puts in 2-3 years of efforts in GS the advantage in terms of marks would be around 30 marks or so but 1 year of dedicated effort in maths would give you 50+ marks advantage straightaway.

Do’s and Dont’s

  1. Practice, Practice and Practice. The key to success in maths is filling up as many notebooks as you can during the preparation stage. The more you sweat during preparation the less you will bleed in the battlefield !
  2. Don’t read maths book / notes like GS. It is a recipe for disaster. Rather always study with pen, paper and calculator.
  3. While solving examples don’t jump to see solution first. Try giving your best shot and after making sure that you are not able to solve it using your present knowledge then only look at the answer. This will ensure better retention.
  4. Generally we make lots of silly mistakes while solving a question. It is best to catch these errors early and not repeat them in exam hall. The best strategy for this is to maintain a notebook of errors that you usually commit and their mitigation measures. For example, I commit a lot of mistakes when doing Integration by parts and usually the error involves missing negative (-) sign etc. Therefore whenever I come across such type of question I try to devote extra 1 minute to re-check all my steps.
  5. is the best online resource for preparation. You can create an account and get your maths questions answered within minutes.

Why did I score only 262?

Among all the students in the final list who had maths as an optional, I have scored the least. My paper – 1 was a complete disaster and I only scored 92 marks in it. In fact I could only attempt 160 marks paper and had to leave 90 marks paper completely.

The reasons for the above situation in Paper – 1 are as follows:

  1. Lack of written practice: In many topics (especially statics and dynamics) I used to just look at a question and its solution without solving it first. As a result I forgot the exact method in the exam hall !
  2. Left many topics: I prepared only 25% 3-D, 80% Calculus and 25% Statics & Dynamics and had to pay a heavy price in the exam.

On the other hand my preparation for paper – 2 was excellent and therefore I scored an amazing 170 marks in it🙂

Topic Wise Detailed Plan of Action

Paper – 1

Linear Algebra

  • Difficulty: 2 / 5
  • If you have not studied it before then you will take sometime in getting used to Vector Space nomenclature. Rest all topics are straightforward.
  • The questions on Diagonalization are lengthy and therefore there are chances of committing errors.

3 Dimesional Geometry

  • Difficulty: 4 / 5
  • I found this topic difficult as the syllabus is vast and questions are very lengthy and difficult.
  • In many questions we simply have to mug up the method of doing questions.
  • The best way to prepare is to revise it as many times as possible. Simply doing it one or two times will not help.

Ordinary Differential Equation

  • Difficulty: 2.5 / 5
  • The number of methods to solve a question is overwhelming !
  • Differential equation with variable coefficient is the most difficult part from this section.
  • All questions from Raisinghania book must be done thoroughly.


  • Difficulty: 2 / 5
  • Single variable calculus is similar to what we prepare for JEE exam.
  • The questions on surface of revolution etc are lengthy.

Vector Analysis

  • Difficulty: 1.5 / 5
  • The most scoring portion in paper – 1
  • There are only 4 theorems and all the questions in the exam come directly from Krishna series book.

Statics & Dynamics

  • Difficulty: 2 – 4
  • If you are covering this topic from 10 marker point of view then it should not pose any problem.
  • However, covering it completely requires a lot of time as the questions are very lengthy.

Paper – 2

Modern Algebra

  • Difficulty : 4.5 / 5
  • The most difficult part of the exam.
  • If you are new to this topic then you will not understand even 10% of what is going on initially. It’s a completely different ball game altogether.
  • Mastering this topic is not at all easy.
  • However, the 10 markers are easy and can be prepared easily.

Real Analysis

  • Difficulty: 3 / 5
  • It has a huge syllabus but questions asked are relatively easy and repeated.
  • Sometimes questions from topology comes and we have left with no option but to leave it.

Partial Differential Equation

  • Difficulty: 3 / 5
  • Methods are quite similar to Ordinary Differential Equations.
  • Requires lots of practice especially in Charpit’s method (although officially it is not part of the syllabus).

Complex Analysis

  • Difficulty: 1.5 / 5
  • One of the easiest and highly scoring part.

Numerical Analysis

  • Difficulty: 1 / 5
  • Easiest portion of the syllabus.
  • No brainer🙂

Linear Programming

  • Difficulty: 1.5 / 5
  • Very easy topic. Only Simplex method questions tend to be lengthy.


  • Difficulty: 2 – 4 / 5
  • If one prepares from 10 marker point of view then it is not that difficult.
  • However, covering it completely is a difficult task.

Fluid Mechanics

  • Difficulty: 3.5 / 5
  • A difficult topic for those who have not studied Fluid Mechanics earlier
  • In case of time crunch it should be prepared with 10 markers point of view.

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