12th Mathematics Chapter Study Material English Medium 2021 By S Rajan M Sc M Phil M Ed Online
Arjun stared at the mountain of textbooks on his desk. The clock on his wall read 11:47 PM. Outside his window in Patna, the December fog was rolling in, but inside his room, the air was thick with a different kind of pressure. It was 2021, and the CBSE Class 12 Mathematics exam was exactly nine weeks away.
His problem wasn't hard work. It was chaos . His notes were a scrambled mix of his school teacher's rushed scribbles, YouTube screenshots, and three different reference books. Calculus was a warzone of conflicting methods. Vectors and 3D Geometry felt like a foreign language. Probability was a cruel joke.
The difference was immediate. Where his school textbook used dense paragraphs, Rajan sir used a single, hand-drawn flowchart. For every definition—Reflexive, Symmetric, Transitive—there was a tiny, real-life example. “Reflexive? You are related to yourself. Symmetric? If Arjun is Shreya’s friend, then Shreya is Arjun’s friend (hopefully!). Transitive? If Arjun is taller than Rohan, and Rohan is taller than Priya, then…”
Chapter Study Material English Medium – 2021 S. Rajan, M.Sc., M.Phil., M.Ed. Arjun stared at the mountain of textbooks on his desk
Arjun smiled and held up the thin, worn-out, white-covered book. “No institute. Just a bridge builder named S. Rajan, M.Sc., M.Phil., M.Ed.”
His friends asked, “Which coaching institute did you join?”
He slumped over, defeated. "I don't need more problems," he whispered to himself. "I need a key ." It was 2021, and the CBSE Class 12
Arjun slept at 10 PM.
That Saturday, his father took him to the old book market near the Gandhi Maidan. Among the piles of dusty, second-hand guides, a thin, unassuming book caught his eye. Its cover was clean, white, and printed in a simple, bold font:
Week 3: Integrals. The material had a two-page table titled “The Hunter’s Guide to Integration.” It taught him to recognize “disguised forms”—how a terrifying fraction was actually a simple log in a mask, or a trigonometric mess was just a sin² waiting to be simplified. His notes were a scrambled mix of his
In the exam hall, the paper was tricky, not hard. One question—a 3D Geometry line-of-shortest-distance problem—froze him for a minute. Then he remembered Rajan sir’s flowchart from the “Three-Dimensional Geometry” Milestone. Step 1: Write equations in symmetric form. Step 2: Identify direction ratios. Step 3: Apply the determinant formula for shortest distance.
That summer, he wrote a thank-you letter to the address printed inside the cover. He never got a reply. But he knew, somewhere, a quiet teacher was still designing bridges for anxious students lost in the fog of numbers.
— S. Rajan
Week 6: Differential Equations. The study material introduced a simple “Order, Degree, and Method” checklist. It was like a doctor’s diagnostic chart: “Is it variable separable? If yes, do this. Is it linear? If yes, find the Integrating Factor.” No confusion. No panic.
