Introduction:
The UPSC Mathematics Optional subject exam requires strong problem-solving skills. Here are some effective strategies to improve your problem-solving abilities for this exam:

1. Understand the Syllabus:
- Familiarize yourself with the complete syllabus for the UPSC Mathematics Optional subject exam.
- Analyze the weightage given to different topics and prioritize your preparation accordingly.

2. Build a Strong Foundation:
- Review the fundamentals of mathematics, including algebra, calculus, and geometry.
- Strengthen your understanding of concepts and formulas by practicing a variety of problems.

3. Solve Previous Year Question Papers:
- Solve previous year question papers to get a clear idea of the exam pattern and the type of questions asked.
- Analyze your performance, identify weak areas, and work on improving them.

4. Practice Regularly:
- Regular practice is key to improving problem-solving skills. Set aside dedicated time each day for practicing mathematical problems.
- Solve a wide range of problems, including those from different sources like textbooks, reference books, and online platforms.

5. Seek Guidance:
- If you face difficulties in understanding certain concepts or solving specific problems, seek guidance from teachers, classmates, or online forums.
- Join coaching classes or online courses specifically designed for the UPSC Mathematics Optional subject exam.

6. Develop a Problem-Solving Approach:
- Develop a systematic approach for solving problems. Break down complex problems into simpler steps and solve them one by one.
- Learn different problem-solving techniques and apply them appropriately.

7. Time Management:
- Time management is crucial during the exam. Practice solving problems within a limited time frame to improve your speed and accuracy.
- Use mock tests and practice papers to simulate exam-like conditions and assess your performance.

8. Analyze Mistakes:
- After solving problems, analyze your mistakes and understand the reasons behind them.
- Keep a record of common mistakes and revise those topics regularly to avoid repeating them.

9. Stay Updated:
- Stay updated with the latest developments in mathematics. Read books, journals, and articles to enhance your knowledge.
- Follow reputable online platforms like EduRev for additional study material and resources.

10. Stay Motivated:
- Stay motivated throughout your preparation journey. Set achievable goals, reward yourself for milestones achieved, and maintain a positive mindset.

Conclusion:
Improving problem-solving skills for the UPSC Mathematics Optional subject exam requires consistent practice, a strong foundation, and a systematic approach. By following the strategies mentioned above and staying dedicated, you can enhance your problem-solving abilities and perform well in the exam.