Maths Optional Preparation strategy for USPC Mains

UPSC Mains and Optional Papers-Mathematics:

UPSC is an official examination conducted under the supervision and direction of Govt. of India.

The exam consists of a total of ‘7’ papers out of which ‘2’ are optional depending on the choice of the aspirant. Looking furtherly into subjects offered in optional section we have section ‘Mathematics’.

Depending upon the scope & nature of the subject mathematics, aspirants having an aptitude & having an interest in the given subject are highly recommended to select the subject as optional when appearing for their UPSC preliminary examination. Even for aspirants looking for achieving a big score in the examination, choosing mathematics as optional is recommended. As, compared to other subjects, this one involves more accuracy, direct approach, no theory and also greater no. of chances to succeed depending upon the nature of aspirants’ preparation.

Maths Optional Preparation Strategy

Preparation Stage:

After Selection of the optional stage i.e. Mathematics, next stage is attaining complete knowledge of the syllabus given, devising a strategic plan & memorizing in the head, the Important Do’s & Don’ts.

Syllabus Offered: Optional Mathematics – UPSC Mains

The 1st goal for any aspirant to achieve in the IAS preparation stage is to get deep and thorough knowledge of the Syllabus. The pattern and detail of which is:

  • The paper pattern for Optional Mathematics-UPSC Mains consists of a total of two (2) papers: Paper-I and Paper-II. Each paper is 250 marks, making a total of 500 marks for the optional.

Optional Mathematics – UPSC Mains 

Paper – I

1-Linear Algebra: 

This section mostly includes the topics the aspirants are more likely to have knowledge of from Grade 11 & 12


Calculus- as the name states, the study of continuous change. A straight topic, mainly involving integration and family.

3-Analytic Geometry:

Concerned with theorems at most, this section requires practice like every other topic.

4- Ordinary Differential Equations:

Maximum scoring section. The scoring element of the section is repeated no. of questions that appear in the exams every year from this section. 

5-Dynamics & Statistics:

Section/part of the syllabus relates to Physics and also partly Stats. Can become a factor playing high scorer.

6-Vector Analysis:

This part involves theorems. Excellent performance is assured after having learned well, theorems and their various applications.

Paper – I

1-Modren Algebra:

 Section worrying students the most. However, repeated study and attention can vanish all those worries.

2-Real Analysis:

Number theory plays most of the part in this section. And Practice.

3-Complex Analysis:

Having the Cauchy theorem as the major part .This Analysis is also among one of the easy learned high scorer too, provided learned thoroughly. 

4-Linear Programming:

Linear Programming- an easy one having selected no. of questions being asked.

5-Partial Differential equations:

Laplace is specifically of importance from this sec.

6-Mechanics & Fluid Dynamics:

Relating to Physics – a time-consuming section this is. Past papers are a good aid of consultancy in learning this section.

Important Strategies:

The second stage in the series is devising important strategies to follow up when preparing for this optional:

1-PPP (Practice, Practice &Practice) strategy:

Hear of mathematics, the next cue is Practice. Math is all about problem-solving so, is practice. Both are interlinked. 

2-Consult past papers:

Past papers are an essential aid when comes to preparing for any official exam. Talking of optional math, past papers are what is going to make most of the paper awaiting you in the final examination.

3-Keeping of Formulae sheet:

Always, keeping the formulae sheet with you so, that by the time you sit around to solve the problems you don’t have to waste extra time memorizing the formulas first. 

Important Do’s & Don’ts:

The third stage – important Do’s & Don’ts to be memorized well in the head


  • Study the question statement before solving the question.
  • Your solutions in alignment & in the right order.
  • A recheck after having done each question, for any unnoticed mistake.


  • Make silly mistakes especially that of signs as ‘+’, ‘-‘etc.
  • Learn any solution by heart.
  • Panic & get confused.

“Mathematics is the mother of all sciences”, a wonderful subject, and mastering it is none of an undoable thing. Stay high-spirited, stay focused and you’ll get what you want. Maths Optional Preparation Strategy

Read More:- 10 Myths About UPSC Exam