Learning and completing the course - It takes 6 months or 12 months or 6 years depends on you how fast you finish. Many students feel that completing the syllabus is the last step of the preparation. But this is absolutely wrong, it is just the beginning.
Make a list of books from where you will prepare each topic in the syllabus. You can also take guidance from your seniors and mentors for this.
Always prepare and keep a formula sheet ready. This will help you memories certain formulae that would be needed to solve the problems.
Practice and more practice - This is the crucial step where almost everyone skips. Most of the students do not understand its importance. They go straight to the exam after finishing the syllabus and do not get good marks. You should give the next 50% time for practice.
You should explore new questions - UPSC picks up questions from Standard Indian Books. Checkout Success Clap Question Bank which has a ready made collection of problems and solutions at one place. You should solve the same question again and again, because same question is repeated in the exam.
Solve Previous Year Questions - Solve all questions from UPSC paper. Questions are repeated directly or indirectly in the optional paper of Mathematics. So it is mandatory to solve previous year's questions.
Taking Mock Tests - Evaluate yourself before UPSC evaluates you. In the actual exam, you have to solve around 25 questions in 3 hours. It requires speed, accuracy and more importantly.
Selecting the correct question. It comes from practice and learning from your mistakes. It gains confidence before the exam.