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How to Score Well in UPSC 2021 Mathematics Optional?

Updated on 26 February 2021
UPSC & State PSC
6 min read 14 views
Updated on 26 February 2021

The UPSC 2021 Exam is just a few months away and so aspirants are already on the edge to prepare for this exam. As this is a national-level exam, there is a lot of competition and not many candidates are able to clear this exam on their first attempt. Many of them enroll for UPSC courses or take up self-study as their mode of preparation strategies. Well, talking about Mathematics, it is an optional subject that candidates opt for this exam. 

Unlike other subjects like humanities, mathematics focuses more on the practical part rather than the theoretical part. Many candidates also take up mathematics in their optional only to realize that they cannot crack this subject easily. However, candidates must note that mathematics is one such optional subject that can either make your or break your chances as not everyone has the ability to clear this subject in the first go. Therefore, candidates who opt for maths should pay special attention to certain things which we shall discuss below. 

Before proceeding further, let’s first understand who should opt for mathematics as their Optional subject.

Candidates who are proficient in maths and are B.Tech, B.A/ in Mathematics and IITs should preferably go for this subject. This is because only those candidates who have a genuine interest and past experience in math will be able to solve the concepts easily, adding to their chances of clearing the UPSC exam in the first attempt. 

How to Prepare for Maths Optional in UPSC 2021?

Know the Maths Syllabus 

Candidates should be thorough with the complete maths syllabus for both Mains as well as prelims exam. Even if candidates have enrolled for UPSC courses still they need to carefully study the syllabus first on their own and only then proceed with the exam preparation. This will help them to know each topic and understand their approach for preparation. 

Refer to the maths syllabus for Paper 1 & Paper 2:


  1. Linear Algebra 
  2. Analytic Geometry
  3. Calculus
  4. Ordinary Differential Equations 
  5. Vector Analysis
  6. Dynamics & Statistics


  1. Algebra 
  2. Real Analysis
  3. Linear Programming 
  4. Complex Analysis
  5. Partial Differential Equations
  6. Mechanics and Fluid Dynamics 
  7. Numerical Analysis and Computer Programming 

Work On Paper Presentation Skills 

Now candidates must realize that apart from solving the problems given in math, they need to also focus on their paper presentation skills. You sure don’t want to create a mess and make a bad impression on the examiner. So to ensure good marks in this paper, you should practice the problems in a rough notebook daily and pay attention to your presentation skills. 

How to Prepare for Essay Paper in UPSC 2021?

Candidates must also make sure that they avoid silly mistakes like writing the wrong numbers in the paper, canceling the whole answer or simply doing rough work in the main answer sheet. Presenting the paper in a neat manner will surely reward them with good marks. 

Make a Study Plan 

A study plan is very effective to keep candidates on track. So, candidates must make one and dedicate an equal amount of time to each subject as per their flexibility. If candidates have enrolled for UPSC online coaching or offline classes then make sure to adjust the time accordingly. We suggest you spare some time for self-study as well since you need to evaluate yourself and identify where you stand in your preparation. Remember to follow the study plan religiously as that will help to stay organized till the end of your examination.

Enroll in UPSC Online Coaching 

Candidates must have a hectic schedule as they juggle between their college, completing assignments, getting ready for their examinations, etc. In this process, they are left with a little time and so online coaching will be very helpful for them as they can save a lot of time and money.

Online coaching will make candidates ready for their examination with updated notes, personalized learning experience, immediate guidance from mentors and so on. However, make sure to choose the best online coaching for UPSC 2021 to ace this paper in the first attempt itself. 

Pay Attention to Important Topics 

A smart way to prepare for mathematics is to pay special attention to important topics. Study the previous year’s papers and identify the trends and repeated questions that are asked in the exam. Do not leave Linear Algebra, Calculus and geometry as the maximum number of questions are asked from these topics which are highly important from the exam point of view.  

Study From Relevant Reference Books 

Candidates must first brush up their past concepts of maths from NCERT and then proceed with standard textbooks. If candidates have joined a UPSC online coaching or offline classes then the coaching will provide relevant study materials to candidates. However, make sure that the study materials are in line with the latest syllabus of UPSC. 

Refer to some of the Reliable Reference Books for Mathematics below:



Author Name 

Linear Algebra 

K.C Prasad, Hoffman and Kunze, K B Datta

Differential Calculus 

Shanti Narayan, PK Mittal 

Analytic Geometry 

Shanti Narayan, PK Mittal, HC Sinha and Sharma 

Differential Equations 

Golden Series by NP Bali, Ordinary and Partial Differential Equations by MD Raisinghania

Vector Analysis

Shanti Narayan, PK Mittal

Dynamics, Statistics and Hydrostatics 

M. Ray



Author Name 


K.C Prasad, K B Datta

Complex Analysis 

GK Ranganath, IAS Maths series by Krishna Prakashan 

Real Analysis

H.L Royden

Linear Programming & Theory of Games

SD Sharma, Lakshishree Bandopadhyay

Ordinary and Partial Differential Equation 

M.D Raisinghania 

Introductory Methods of Numerical Analysis

SS Sastry

Solve Previous Years Question Papers 

Solving previous year question papers will help in understanding the exam pattern, structure and the type of questions expected from UPSC. So candidates must solve these papers after they have completed their exam preparation.

Solve Mock Tests Daily

Mock tests are an excellent way to practice and know your progress in the preparation. Apart from that, it also helps to manage the time spent to solve each problem effectively. So, candidates must solve mock tests daily without fail. 

Keep Formula Sheet Handy! 

Candidates must be well-aware of the fact that there are tons of formulas in maths and remembering each formula becomes a difficult task. In addition to this, the maths syllabus is quite vast and so remembering each formula till the day of the exam is not possible. So, before proceeding with the preparation, candidates must keep a formula sheet handy. Note down each formula that you have come across according to each chapter. 

Practice, Practice and Practice

Practice is the key when it comes to clearing this paper. Candidates must practice the concepts daily as they just simply cannot mug up the concepts of maths. Understand the concepts first, clear your basics and then solve the problems. 

Common Mistakes to avoid while appearing for UPSC 2021 Exam

As the quote by William Paul Thurston goes, “Mathematics is not about numbers, equations, computations or algorithms: it is about understanding”

To conclude, clearing mathematics can be tricky and candidates need to perform exceptionally well in this paper because they might have to compete with mathematics toppers. So, first, make sure that you possess an interest in that subject and are able to solve the concepts easily, only then you must select maths in your UPSC optional. Take up the above-mentioned tips and choose the best online coaching for IAS to boost your preparation. Good luck!

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