12th Mathematics Chapter Study Material English Medium 2021 By S Rajan M Sc M Phil M Ed Apr 2026

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.

Two months later, the results came. Arjun scored 95 in Mathematics—his highest mark ever.

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.

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.” In the exam hall, the paper was tricky, not hard

That night, he opened it.

The first page wasn't a formula. It was a letter.

Arjun turned to Chapter 1: Relations and Functions . Step 1: Write equations in symmetric form

“Dear Student, By now, you have crossed the bridge. Tomorrow, the examiner will not ask you to run faster than anyone else. They will simply ask you to walk steadily. Stay calm. Read the question twice. Show your steps. And remember: a mistake is just a data point, not a verdict. With respect, S. Rajan”

His friends asked, “Which coaching institute did you join?”

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…” Two months later, the results came

“Dear Student, Mathematics is not a race. It is a bridge. Every chapter is a plank. If you rush, you fall. My goal is not to give you 100 shortcuts, but to build you one strong, clear path. Turn the page when you are ready, not when you are anxious.”

He slumped over, defeated. "I don't need more problems," he whispered to himself. "I need a key ."

Chapter Study Material English Medium – 2021 S. Rajan, M.Sc., M.Phil., M.Ed.

Arjun slept at 10 PM.