Traditionally, Mathematical Olympiads reward out-of-the-box thinking and the ability to reason logically rather than extensive mathematical knowledge. Familiarity with basic concepts from Number Theory, Geometry, Algebra, and Combinatorics is helpful (Calculus and Statistics are excluded), but success typically depends more on clarity of thought and problem-solving ability. HBCSE provides an indicative syllabus at
https://olympiads.hbcse.tifr.res.in/how-to-prepare/syllabus/.
The syllabus is based primarily on foundational concepts in the school curriculum. However, the problems are designed to test logical reasoning, creativity, and mathematical thinking rather than routine application of formulas.