I am Kanishak Kataria. I secured Rank 1 in UPSC CSE 2018 with Mathematics optional (361 marks / 500). I have written this post to throw some light on Maths an an optional subject and how it should be covered.
This strategy post will be split into 2 parts
- Overview of Mathematics as an optional (in this post)
- Specific topic wise strategy on covering the syllabus (in next post)
Please evaluate your own strengths and weaknesses before reading my strategy.
- If you are undecided about Mathematics:
- Optional selection is a very important process and shouldn’t be done because some person X has done well in it.
- If you have interest and are comfortable in a subject, then only select it as an optional.
- If you have already made up your mind on Mathematics:
- Follow my strategy only if it matches your preparation level and comfort in other GS topics.
- Try to pick up pointers which make sense and adapt those in your own strategy.
I will give you some insights into Mathematics which might be helpful in your evaluation.
- High Reward / scoring
- Static -> marks tend to increase with attemps
- Reference material readily available (IMS notes)
- Break from monotonicity from GS topics
- Good performance over past few years (toppers getting 330+)
- With good preparation, 50-55% marks are easily achievable
- Very lengthy – can take upwards of 6 months to finish it
- High risk – scoring can be 0/1 which means extreme marks are observed
- Zero overlap with other GS topics
- Fear of scaling / marks moderation
- Extra effort needed for Personality Test preparation
- There is heavy scaling in Mathematics: It is an uncontrollable factor. So don’t worry about it too much. If you do well, there is not much need to worry. Scaling hurts low scorers more as compared to high scorers. So aim for the higher end of the spectrum. Past 3 years toppers have scored 356, 374 and 361 in Maths despite scaling.
- It takes 9 months to finish syllabus: Again very subjective. On average it will take 6-7 months. Then as per your understanding, comfort level and efforts, you can take less or more time. People who do not have prior exposure to Maths are going to take 7-8 months at least.
- There is need for external guidance: Not at all! Good quality notes and reference books are available. If you are confident, it is fully manageable through self-study.
- The difficulty level is just like IITJEE: No, it has theoretical and subjective elements as well. Your JEE approach won’t work here directly. You might have to cram some concepts and deal with abstract topics like Rings, Fields etc.
Before selecting Maths as an optional:
- Go through the syllabus and Previous Year Questions and see if you are able to make any sense and would be comfortable in studying them for 2 years atleast.
- If you are not familiar with the topics, then try to talk to few people who have similar background as you and opted/didn’t opt for Maths. They will be able to relate to your concerns in a better way.
- If you are unsure, pick up one or two easier topics at the start such as ODE or LPP and study them for 2-3 weeks. If you are uncomfortable in them, Maths is not the right optional for you.
- Remember that there are few topics such as Modern Algebra, Real Analysis, Fluid and Mechanis, Dynamics and Statics. They are a struggle in themselves (specially for those without prior exposure), so you have to labour through them and not give up as and when you encounter them.
My decision to select Mathematics:
I wasted very little time while opting Mathematics. The decision was very easy for me:
- No optional from by graduation stream (Computer Science)
- My aptitude and prior performance in Maths gave me confidence.
- On a precursory look at the syllabus, I saw some topics which I had encountered during my graduation like Linear Algebra, ODE, Numerical Analysis, Calculus, Linear Programming etc.
- I loved doing Maths problems and looked at it as a source of refreshment and break away from GS syllabus.
In my opinion, performance in Optional is THE DIFFERENCE MAKER in overall rank. General Studies gets averaged across the 4 papers. I always envisioned Maths as an X-factor in my preparation. Having seen scores of 350+ in Maths in CSE2016 when other optionals were just touching 300, I saw it as an golden opportunity. My intention right from beginning was 350+ in Maths. I formulated my whole strategy and allocated time to GS and optional based on this sole objective. One thing was clear in my mind: If I do not score 350 in Mathematics, I should give up on any hope for IAS. With this thought process, even the bulky Maths syllabus didn’t feel burdensome to me. 370+ in CSE2017 further boosted my confidence for Mains.
Having said that, I am aware that not everyone can afford to put so much emphasis on one subject. I opted for a High Risk, High Reward approach which paid off, fortunately!
I will just give an insight into how I calculated things in my mind:
- My friend Rahul Shinde had scored Rank 95 in CSE 2017 with around 1050 marks.
- To get into IAS in CSE 2018, I had to match his performance at least, that is, score 1050 marks.
- I targeted 550 marks in Optional + Personality Test. It could be (400+150) or (350+200) or (375+175).
- That left me with 500 marks across 4 GS papers + 1 Essay paper.
- If I was able to score an average 120-130 marks in Essay, I would only need 370 marks in GS.
- 370 in GS implies ~90-95 marks on an average in each of the 4 papers, which is quite manageable.
As you can see, I never went for glory in GS. To my surprise, I exceeded my own expectations in GS + Essay but my calculation in Maths + Optional was almost upto the mark (361 + 179 = 540).
I request all the aspirants who are reading this post to self-evaluate their expectation first before adopting my strategy. Self awareness and understanding of strengths and weaknesses is very important. It will help in bringing some level of focus in this “uncertain” examination!
Is Mathematics coaching necessary?
Classroom coaching is neither necessary nor sufficient, be it GS or any optional. You need sincerity, self-belief, hardwork and if possible, a group of 1/2 friends to discuss doubts. Earlier also people have cleared with Maths optional by relying on self study.
Coaching only acts as a facilitator in your studies. You can’t rely on them fully. I had joined IMS coaching in order to be sincere and finish my syllabus on time. They have good quality notes and a good ecosystem for Mathematics optional students. I hoped to get in touch with few students with whom I could discuss problems and match answers. After I realised that only following classroom lectures would take nearly 9 months to finish the syllabus, I doubled up and started studying multiple topics simultaneously on my own. My target was to finish 80% of syllabus in 4 months.
If you can put in 4-5 hours daily without any break, then you can also finish Maths in less amount of time. The key lies in not giving up. Those who want to join coaching, be aware that you have to self-study at home for as much amount of time as spent in the coaching. Otherwise, you will end up wasting time and going nowhere with both optional and GS.
Sources to study:
I relied fully on IMS (Venkanna Sir) notes and test series. They are quite comprehensive and can be studied stand-alone also. In few topics you can refer to standard books, if you need. Personally, I didn’t refer to many books though. You can get these notes from ORN market or take from the coaching as well by enrolling.
Notes provide the benefit of theory and problems at one place. Additionally there is no wastage of time scanning multiple books.
If you do not have access to those notes, please refer to a booklist given by Prakash Rajpurohit Sir.
My strategy of covering the syllabus will be specific to IMS notes. You can modify it from standard book point of view.
My preparation timeline:
- Started Maths preparation on 20th June 2017 with ODE
- Finished all the topics (except Fluid Dynamics and Mechanics) once by 31st October 2017
- January 2018 till February 2018: 1st round of fast track revision + covered the Fluid and Mechanics topics.
- Post prelims till 21st July 2018: 2nd round of revision from IMS notes + self made short notes for Test series and quick revision during Mains
- IMS Test series (2018 and 2017) for during Prelims and Mains.
Covering IMS Notes:
Don’t do the mistake of treating Maths as any other subject and only “reading” the notes. You have to use Pen and Paper and solve the problems to understand it.
In olden days, people would cover only 75-80% of the topics and strategically leave out few portions and hedge their overall risk. With UPSC reducing the number of optionals to only 1 and also mixing topics in subparts in different questions, you can’t afford to leave out any topic.
I followed the strategy which my friend Akshay Godara had shared with me.
- In 1st iteration of the topics, solve ALL the problems till the last step, even if they are simple and follow repetitive models.
- Chances of silly mistakes in last steps is high. Examiner might see your last step and final answer first. If that is wrong your marks might reduce drastically, even though you did 95% of the problem correctly.
- After solving, write down answers at the side in the notes themselves. You can use them to cross check with others.
- 1st revision: Again go through entire notes, do 1 question atleast from each model/pattern and mark the important ones. Your older answer will act as an error check (just like checksum).
- 2nd revision: Only do the problems marked in 1st revision. This is the time to make short handy notes for quick revision for test series and examination perspective.
- I have shared my revision notes here. Unless there is paucity of time, do not read from my notes directly. If you make your own notes, they will serve you much better.
Attempting test series + Mains:
- Revise from the short notes which you made after 2nd revision .
- Don’t put too much time in revising again and again from short notes before attempting a test. If you have done one iteration, start giving the tests.
- You will feel as if you don’t remember the formulas. But as you give more tests this problem will go away automatically.
- Initially, I used to revise before attempting a test. But I realised that a lot of time was consumed revision and not actual problem solving and analysis of the test. You should avoid this habit. Revision without practice is waste.
- Don’t wait for evaluation from the coaching. Get the initial tests evaluated. After getting a fair idea of how to write and evaluate, refer the solutions directly and see your mistakes. You should apply your own mind in finding your mistakes and room for improvement.
- All tests should be given with full sincerity as if you are writing Mains. If you do not do this, test series is a waste of time and money.
- Try to finish full paper. Don’t leave any question blank.
- You can either give tests every weekend or give tests in a single batch by allotting 1 whole week for mathematics. I tried the former but failed, so opted for the latter. Few of my friends have succeeded with the former approach as well.
- Full Analysis of the test is very important. After completion try to solve other problems and see why you didn’t opt for that problem. Try to fill the gaps in your study.
- Compulsory questions: try to get them done with in 60-75 minutes. If you have left some of them initially, time should be less than 60 minuets .
- In short don’t waste time by getting stuck on some problems. In Maths you would feel there is more time, but it flys by very quickly.
- Test series is just a simulation for Mains. So your actual strategy would not deviate too much from what you do in test series. While writing Mains, just treat the question paper as any other test series paper and you will not feel any extra pressure.
Before Mains, revise your weak topics from the short notes and look into some specific test series problems which you weren’t able to do. I actually benefited from this exercise. I had marked one question on generator lines in Paper 1 which came in the Mains exam the next day!
How to write Maths answers?
- No need to be verbose, there is lack of space in some questions. You have to adjust as per the space given. Steps can be combined to save space.
- Few steps you can do on the rough pages and then make it fair in the actual problem. But be wary of mistake while copying values from rough page to actual page. Also, if you do not have time, no point doing in rough.
- Make sure you do write the most important steps, formulas and theorems.
- Many results can be directly quoted. Here remembering all the formulas correctly is key.
- Use calculator extensively in topics like Numerical Analysis. Solve the question on calci and then copy values on the answer sheet.
- If you do not know any question, write as many steps as you can remember. It will help you fetch partial marks at least.
My performance in test series vs Mains:
I couldn’t do well in the test series as I wasn’t able to finish all the papers. But I was confident that come Mains, I will rectify my problems. I just tried to learn from the mistakes and make sure I do not repeat them later. In fact, I used to become happy when I committed mistakes while practicing at home as it gave me an opportunity to rectify it in the exam.
In Mains, I was able to attempt all 500 marks. Paper 1 was easier which I could finish 30 minutes in advance. But paper 2 was little challenging. My final score was
Paper 1: 170 / 250
Paper 2: 191 / 250
Total: 361 / 500
I might have committed few silly mistakes in Paper 1. Also, there might have been little more scaling as the paper was easy. Paper 2 marks shows that it has huge reward. If you are able to master it, it can be a difference maker.
After giving you an overview into Maths optional, I will share the recommended way of finishing syllabus and topic wise tips in the next post.
Best of luck!