Aryan Shah: 120/120 in JEE Main Maths 2025

Aryan Shah from Ahmedabad achieved the rare distinction of a perfect 120/120 in JEE Main Mathematics in the January 2025 session, achieving an All India Rank of 34 with a total score of 341/360. A student of FIITJEE Ahmedabad, Aryan had consistently topped his classroom in mathematics but reached the perfect score through a specific revision and problem-solving system that he developed over 15 months of preparation. In this exclusive account, Aryan shares the exact techniques, books, practice routines, and mindset that led to a flawless mathematics performance.

Aryan's Mathematical Foundation: Theory Before Problems

Aryan is emphatic that understanding precedes problem-solving: "I spent the first 3 months of my preparation (May–July 2024) doing only theory — reading RD Sharma Class 11 and 12 for concept clarity, then SL Loney for Trigonometry and Coordinate Geometry, then G.N. Berman for Calculus problems. I did not solve any JEE-level problems in this phase. By August 2024, my conceptual foundation was so strong that JEE Main problems felt straightforward rather than hard." This theory-first approach is unusual among JEE aspirants who typically jump into problem practice immediately, but Aryan credits it as the foundation of his perfect score. His chapter sequence in the theory phase: Sets and Relations, Functions, Trigonometry, Algebra (progressions, binomial, complex numbers), Coordinate Geometry (all conics), Calculus (limits, differentiation, integration, ODEs), Vectors and 3D, Probability and Statistics. For the strategic framework for maths that Aryan's approach embodies, see our JEE Main Math Score 100 Strategy Guide.

His most distinctive preparation habit: "Proof by derivation." Before every problem session in a chapter, Aryan would re-derive all major formulas from first principles — the quadratic formula, the tangent to a conic, the integration by parts formula. "If you can derive a formula, you will never misapply it. If you just memorise it, you'll make sign errors and forget conditions. I derived formulas in the margin of my notebook every day." This derivation habit took 20–30 minutes per session but eliminated formula errors from his practice and exam work.

Problem-Solving Methodology

After the theory phase, Aryan moved to a systematic problem-solving routine. He used 3 sources per chapter: ML Aggarwal for base-level practice (50–100 problems per chapter), Cengage Mathematics for JEE Main-level problems (100–150 problems per chapter), and Arihant JEE Advanced problem bank for the top 20% hardest problems in each chapter. "I never solved more problems than I needed to reach 90%+ accuracy in that chapter. Some chapters needed 50 problems to reach 90%; complex chapters like Calculus and Coordinate Geometry needed 200+." His practice philosophy: stop when 9 out of 10 randomly selected problems are solved correctly in under 4 minutes each. This accuracy-based stopping rule prevents over-investing time in already-mastered chapters. Experience JEE Main math at the difficulty level Aryan prepared for with our full-length mock tests — he recommends regular timed practice to build exam conditions familiarity.

Aryan's approach to hard problems: "When I encountered a problem I couldn't solve in 10 minutes, I did not look at the solution. I added it to a 'problem journal' and came back 24 hours later. Often, I could solve it the next day — the unconscious mind continues processing. If I still couldn't solve it after 3 attempts (on consecutive days), only then would I look at the solution." This deliberate struggle method developed genuine problem-solving insight rather than solution-memorisation. His problem journal had 340 entries by exam day — every one of them solved eventually.

The Final 3 Months: Mock Tests and Formula Mastery

From October 2024 to January 2025, Aryan gave one full 3-hour mock test every 3 days — approximately 30 total mocks in this period. His unique mock analysis system: he did not mark questions wrong in his mock test. Instead, after each mock, he re-solved every mathematics question independently (even those he got right) and timed himself. Questions he could solve in under 3 minutes he classified as "fast." Questions taking 3–5 minutes: "normal." Questions taking more than 5 minutes or requiring a second attempt: "slow." He then specifically drilled "slow" questions in the following day's practice session. This process took 2–3 hours post-mock, but Aryan considers it the most important preparation activity of his final 3 months: "The mock analysis is more valuable than the mock itself. Most students analyse their wrong answers. I analysed my slow answers — that's the key difference."

Formula mastery programme for the final month: every day, Aryan wrote all formulas for 2 chapters from memory, without reference, in the first 30 minutes of his study session. Chapter pairs: Limits + Continuity, Differentiation + AOD, Integration + Definite Integrals, Vectors + 3D, Conic Sections pairs (parabola+ellipse, hyperbola+circle), Probability + Statistics, Complex Numbers + Matrices. This daily exercise across 14 pairs (28 days) ensured every formula was fresh and instantly accessible on exam day. "I never had to 'think' about a formula on exam day. My hand wrote them automatically."

Exam Day: The Perfect 120

On exam day, Aryan's sequence: started with algebra and probability (his strongest areas, solved in 25 minutes, securing 8 questions). Then coordinate geometry (20 minutes, 6 questions). Then calculus (15 minutes, 8 questions — he was surprised at how quickly they fell). Final 10 minutes: he solved the 3 remaining questions he had skipped (all integration and limits) and then reviewed his paper twice. "I caught one algebraic error in my second review — the answer was 36 but I had written 34 in the answer box. That correction changed a -1 to +4 and was worth 5 marks." His final time: paper completed with 8 minutes spare. Register on our platform to access Aryan's recommended mock test programme and formula revision system. Our premium subscription includes all full-length JEE Main mocks with detailed error analytics. For the calculus sections where Aryan feels his derivation habit paid the highest dividend, see our JEE Main Calculus Complete Guide.

Aryan is currently at IIT Bombay (Electrical Engineering), consistently ranked in the top 3 of his batch. His message: "Mathematics is a language, not a collection of formulas. Learn to speak it fluently — understand every symbol, every operation — and perfect scores become possible. Shortcuts and tricks are crutches that fail at the hardest problems. Foundations never fail."