Strategy for UPSC Mathematics

Complete guide to Upsc Mathematics Optional Paper. 

Why  Mathematics is a very good Optional for UPSC ?

1) Take you directly to TOP SLOT RANK.     It may take you to RANK 1 .

2) FIXED, WELL DEFINED Syllabus. 

3) High Scope of Improvement. Easy to Test yourself.

4) Mathematics can be a Savior, if GS Exam goes BAD.

5) Best Suited for B.Sc and Engineering Students.

6) All Optional Paper takes roughly same amount of time, to finish syllabus. But Mathematics will have edge in Scoring.

7) You Don't NEED FLOWERY language to express your views.

8) Not connected to Current Affairs .

I want to take Humanities Optional, because it will help in GS ?

It is a misconception that taking Humanities optional will help in GS.

It will help you in 10% (May be 50 Marks ) for GS. But you have to PAY HIGH PENALTY.  You are risking 500- Marks Optional Paper. 

Sometimes Optional Paper becomes the Savior to get into Civil Services.

 Choose Optional Paper wisely.

Don't choose Optional based on trend and what others are taking. 


How to Start Preparation-- for Freshers ?

Step 1:  Take Printout of the Syllabus. Read each topic carefully and underline the topics which you know.

Step 2: Take Each Unit ( Example Linear Algebra ) and go through all 20 years Previous Paper . You will understand the pattern.

Step 3: Take a Note book and make a Schedule to finish the Syllabus. Always try to finish syllabus 6 months prior to the Prelims.

How to Study ?

List out Easy , Medium and Hard Units.

Do Easy Units First. Finish it as fast as possible. Just Finish it. 

Do Hard Units at last . Don't waste time in doing these Topics. 

Easy Topics are Linear Algebra, Numerical Analysis, Vector Analysis, ODE, PDE, LPP , 

Medium Units are Calculus, Real Analysis, Complex Analysis, Mechanics, Fluid Dynamics, Analytic Geometry

Hard Units are Modern Algebra, Statics and Dynamics


Strategy for Exam ?

Stage 1 : 25% Time : Learning and Finishing the Syllabus . It takes 6 months or 12 months or 6 years depends on you , how fast you finish.

Many students feel that finishing the syllabus is final stage of preparation. But it is totally wrong, It is just beginning.


Stage 2 : 50% Time : Practice and More Practice. Getting clarity of concepts. This is Important Stage . Most of the students don't understand its importance. They finish syllabus and directly go to exam and could not get good marks. You must spend the next 50% time   for Practice.

You must explore new questions, solve previous year questions.

You must solve the same question again and again


Stage 3: 25% Time : Taking Test Series in Exam Mode. It increases your Speed and Accuracy.Gets Confidence for the exam.


How many Rounds of Readings should I do ?

Minimum 3 Rounds. 

Round 1: It should be Fast and Try to Complete Syllabus Fast

Round 2: Practice Round. In this round you will learn much better.

Round 3 : More Practice. It will make your preparation PERFECT


Should I learn Proofs of Theorem ?

During initial preparation  - Just note down theorems . But don't waste time in understanding proofs

Once your Syllabus is Complete , then go through previous paper and do theorems as per exam pattern


What should be the Preparation Approach and Strategy  ?

It should always be Problem oriented approach . Always concentrate on problem Solving .

Example: Students waste days/Months on Theorems related to Linear Algebra. But Cannot do SImple finding Basis and dimensions of a Linear Transformation or a Matrix. There are only limited proofs  in Linear Algebra, which you can do it before exam.

Once your Syllabus is Complete , then go through previous paper and do theorems as per pattern


Books for Exam - Readymade Notes?

I always suggest : learn from Standard Text Books only . You get First Hand information, directly from the author . Author is directly telling  you the concept .

Read from Standard Book PDFs or from Standard Books.

No Study material or Book is Complete. You must Refer to different books for different topics.


 Is ONE Study material / Book is ENOUGH for the Exam

Answer: No book is Complete. You must study and practice from different books. 

If you want more marks, you must read more books and practice more books


Internet Resources , NPTEL videos, YouTube Channels ---- TIME  etc?

Internet is full of Study Material and it is a OCEAN. The more you search, the more information you get and FINALLY the more TIME you WASTE. RESULT Is ZERO.

Everything for the exam is available in Text Book.

NPTEL , College Videos are meant for THEM.... Not for your Exam.  


DON'T WASTE YOUR TIME on INTERNET . TAKE YOUR STANDARD TEXT BOOK and START PREPARING.


Study Groups - Whatsapp Groups, Facebook Groups, Telegram Groups ?

Form Study Group of 2-3  serious students ONLY .  Always Form a group who are better than you.

If you don't have serious friends , then It is better to Study Alone . Otherwise they will SINK you down. 

Don't form a group with Unknown people. You will waste your Time.

ASK and Share your difficulties only with Experts. Only they can guide you.

Don't waste your time in Telegram, What's-App DISCUSSION.  Its TIME WASTE. 

You have to Solve 1000+ problems . Don't waste your time in discussing one problem with MANY PEOPLE. 


Making Notes  Strategy for Upsc mathematics ?

Everyone should maintain their Own Handwritten Notes.

Maintain 2 types of Books. One book should have Formulae Only, and the other book should have definition, Important Solved Problems.

Don't read someone else handwritten notes.

This notes will help you in Quick Revision.


I DONOT have TIME. I want to Prepare in Less Time?

Never Say: You don't have TIME. You have to manage TIME. Everone has same time. 

If you want to Prepare in Less Time, then Double your Hardwork and Plan Properly.


What is the difference between Toppers and Losers ?

Topper Practice and Revise Topics several times. They do Same thing again and again. They work hard and very very hard.

Losers study only once. They donot Revise  and they donot Practice .


UPSC Mathematics- Phd in Mathematics ?

Always remember that you are appearing for UPSC Exam. You don't have to do PhD in Mathematics. 

Your aim should be CLEAR , ie ... In Exam you have to Solve  problems and get Maximum Marks. 

There are many topics where it becomes difficult to understand the CONCEPT and LOGIC.    Then ---You try to find out the Formula used, Substitution made and the Process used  to arrive at the Answer.

Don't waste time in learning in Depth.

Just know: How to Solve Problems.

Don't ask for LOGIC.  Show it as MAGIC, by producing the Answer.


Are the Toppers Extra Ordinary People ?

My view is that 5% Toppers  are extraordinary. They have High IQ. They are Super and their thinking level is Very High. They can understand the concept in just one reading .They developed these qualities through practice . What ever they do, they excel. 

What about rest 95 %. They are ordinary people, who became toppers by learning and hard working.

So whoever works hard in right direction will become Topper


Toppers Interview Vs Losers Interview  ?

Watch Genuine Toppers Interview, it will Motivate you .They will tell you the Right Strategy and Right Direction.

Watch Genuine Losers Interview: They will tell you, why they Failed. So you can avoid their mistakes.

Always use your own commonsense and wisdom to identify the Genuine interview. Don't follow blindly.


How to Study Modern Algebra ?

Modern Algebra is very vast and it has surprising questions.

50% Questions are Easy , because you can see those questions in any Textbooks. They are easily solvable with basic concept.

50% questions are Tough and they are really Tough to crack.

Read 1) Any B.Sc Text Book of your state university 2) R.Kumar Book on Group and Ring theory 3) Algebra by Gopalkrishnan ( Small and Excellent Book ) .

Donot try to master this Unit. It is a ocean, the more you dive, the more depth you see.

Do this topic in Last


How to Study Statics and Dynamics ?

Read Krishna Series Books on Statics and Dynamics.

Practice the starting 15 Questions from each Topic. Afterwards the steps become difficult to remember, so practice well only few questions.

Do this topics in Last


Role of Solving Previous Year Paper ?

Practice 20 Years Previous Year Paper.

Ever year some Questions are Repeated. It will feel you happy and confident in exam hall, when you see such questions and when you know the solutions.

Many Solutions are available in the market. Don't follow them blindly. Try to solve the problems using your knowledge. Most of the Solutions are available in the Standard Text Books. 

SuccessClap provides previous year solutions from 1992-2019


How to Solve  Problems in Actual Exam?

In Exam, you have to solve 20-25 Questions in 3 hours. 

Your aim should be : Solve Maximum questions  in Less Time .

Your aim should be : Get Correct Answer.

Your aim should be : Attempt as many questions as you can.

Donot Explain each and every step : You are not writing Class 6 Mathematics Exam, where your teacher checks all the steps.

You have to carefully Skips the explanation part

Example 1: ODE- Homogeneous eqns : Don't derive the equations with substitution X=log x ... Directly write down it is D(D-1)(D-2) and solve it

Example 2: PDE- Boundary Problems; Don't explain in details when  c= 0 or c > 0 or c< 0. It kills Time.  Write in one step and Start Integrating the terms. JUST SAY ITS PERIODIC FUNCTION and MOVE ON.

Just write down formula and Start getting Answer.

in Exam , you have no time to explain in flowery language.

Imagine, you are a Examiner: How will you check papers :  Examiner easily catch your knowledge by seeing the solution . 

When you take Mock tests, try to follow these things . Also don't waste time in Making Margins, Space Restriction Ideas, taking printouts etc.  Take a piece of paper and start taking Mock Tests.

DONOT waste time on THIS TOPIC  during your preparation. It comes automatically on Exam Day. 

Put a GUN on your head, and you start running . This is what happens during exam hour. If your preparation is GOOD, then you run in right direction.


 IIT and Mathematics Optional  ?

Facts: You must KNOW and ACCEPT.

1) Not All IITians take Mathematics as Optional.

2) Many IITians take  Humanities Optional and Literature Optional

3) There are MANY Non-IITians  and B.Sc graduates , who cracked UPSC with Mathematics.

4) Very Few IITians take Mathematics. But they study sooo hard that they get top rank.

5) Exam Pattern of IIT-JEE is different from UPSC Mathematics . IIT-JEE needs In-Depth Application of knowledge, where as UPSC expects you to have Over-All understanding of the Subject. 

ANYONE who prepares seriously with Mathematics optional CAN CRACK the exam


Blame Game - Hard work- Luck ?

You decide your Future. Your Future depends on what you do Today.

What ever happened yesterday , nothing can be changed, but you can change your Future

Give you maximum effort for the preparation.  Hard work is 80% and Luck is 20% . Luck comes only to those who have worked hard.

There are few things which are beyond our control. So one must give our BEST.


How SuccessClap helps you for your Upsc Maths preparation ?

SuccessClap provides FREE Exam Oriented Study Material . 

SuccessClap provides Videos covering entire Syllabus, which saves time in understanding the concept.

SuccessClap provides Question Bank and its solutions. Question Bank is a collection of problems from various sources.

SuccessClap provides Very Important questions to practice before MAINS Exam

Successclap provides Exam oriented FULL LENGTH TESTS

SuccessClap provides True Guidance .

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