Strategy to Score Well in Mathematics Optional Paper

“Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers.” – Shakuntala Devi

Choosing an optional subject can be a dicey affair. There are many rules regarding what optional subject to choose for the UPSC civil services exam. A general rule of thumb is that you should take the subject in which you have some background and genuine interest. In case you are a mathematics graduate and enjoy learning this subject, choosing maths as your UPSC optional might be a good idea. This article discusses all you need to know about mathematics optional for your UPSC civil services.

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There are two papers called Paper I and Paper II in the UPSC mains for the optional subject. Each paper is out of 250 marks with a total of 500 marks. Get detailed syllabus by downloading the IAS Notification 2022, PDF of which is available in the linked article.

UPSC mathematics optional syllabus:


  • Linear Algebra
  • Calculus
  • Analytic Geometry
  • Ordinary Differential Equations
  • Dynamics & Statics
  • Vector Analysis


  • Algebra
  • Real Analysis
  • Complex Analysis
  • Linear Programming
  • Partial differential equations
  • Numerical Analysis and Computer programming
  • Mechanics and Fluid Dynamics

UPSC mathematics optional syllabus can be checked at the linked article.

Advantages of taking maths an optional


Maths is and has always been a scoring subject, be it in the UPSC exams or any other exam. If you have prepared well and have written the answers correctly, you will most definitely score high marks.

Generally easy

The questions in this paper are generally taken directly from the text books. Any good maths graduate should find the questions of an easy to medium difficulty level.

Not much competition

Not many UPSC candidates take up this optional, so your competition is limited when compared to subjects like history or sociology.

You know how well you’ve done

In other subjects like humanities, there is always an element of subjectivity involved, with the examiner’s personal prejudices coming into play. For the same answer, two examiners might grade differently. But not so with mathematics which is considered an exact science. The answer is either right or wrong. So, after taking the exam, you can have a pretty clear picture of how you have fared.

Static subject

The syllabus for this subject is static. It is not linked to current affairs. So, once you are done with the syllabus you don’t have to constantly update your knowledge, you just need to revise.

Disadvantages of taking maths as optional

Preparation might take more time

You cannot just read through all the study material in mathematics. You must always study with a pen and paper. You can prepare maths only by working out the solutions. As mathematician Paul Halmos put it, “The only way to learn mathematics is to do mathematics.”

Not helpful for general studies paper

Unlike in history, geography, polity, etc., preparation in maths will not aid your general studies preparation as the syllabus does not overlap.

No marks for attempting

As explained earlier, mathematics involves either right or wrong answers. You will generally not be given marks for wild attempts. Only if the solution provided by you is in the right direction, you can expect some marks for attempting.

Book list for UPSC mathematics optional/UPSC Maths optional study material:

  1. Linear Algebra: A.R.Vasista, Schaum Series
  2. Calculus and Real Analysis: S.C  Malik and Savita Arora, Shanti Narayana
  3. 3-D Geometry: P.N. Chatterjee
  4. Ordinary Differential Equations: M.D. Raisinghania, Ian Sneddon
  5. Vector Analysis: A.R.Vasista, Schaum Series
  6. Algebra: Joseph A. Gallian, Shramik Sen Upadhayay
  7. Complex Analysis: Schaum Series, J.N. Sharma, Ponnu Swami, G K Ranganath
  8. Linear Programming: Shanti Swarup, Kanti Swarup, S D Sharma
  9. Numerical Analysis: Jain and Iyengar, K. Shankar Rao, S. S. Sastry
  10. Computer Programming: Raja Raman
  11. Dynamics & Statics: A.R.Vasista, M. Ray
  12. Mechanics and Fluid Dynamics: M.D. Raisinghania, R.K. Gupta, J.K. Goyal and K.P. Gupta, Azaroff Leonid

Get previous year mathematics optional question papers in the linked article.

Tips to score high in maths optional papers

  1. Practice

Your high school maths teacher was right when she reiterated the importance of practice to score well in your maths paper. Although answer writing is essential for any UPSC civil services paper, it gets double the import in the maths paper. Practising makes you faster in your problem-solving.

  1. Avoid silly mistakes

Avoid silly mistakes like ignoring a ‘+’ or ‘-’ sign, copying numbers wrong, or making simple addition/subtraction mistakes. These can be very costly. Practice till you are perfect.

  1. Go through a problem carefully. Write down what is given in the question. Then work out the answer step-by-step.
  2. Present your solutions clearly in steps, line-by-line.

Always write the solutions neatly. Don’t make the examiner’s work harder by providing haphazardly written answers.

  1. Always understand the topic. Never try and learn the process by heart. It doesn’t work in mathematics.
  2. Always understand the question correctly before venturing to work out the solution. Once you start writing the answer and it is incorrect, you lose precious space in the question-answer booklet. And later, even if you figure out you have to rework your answer; you might not be able to because of a space crunch.
  3. Always prepare and keep a formula sheet handy with you. This will help you memorise certain formulae that would be required to solve the problems.
  4. Always solve mathematical problems with a relaxed mind. Panic can cause confusion and you will end up faring badly in your UPSC optional paper.

Mathematics is a beautiful subject and if you think about it, it concerns everything around us. In the words of the great German mathematician, Johann Carl Friedrich Gauss, “Mathematics is the queen of the sciences.”

Treat this queen with the respect she deserves and you will be rewarded in your IAS exam!

Also read:

How to Conquer the Civil Services Aptitude Test Paper (GS CSAT Paper II)?

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