Mathematics · Class 12

A Class 11 or 12 student with no coaching class can learn every syllabus topic from this book alone, well enough for the board exam and for the JEE or NEET questions built on it.

That means the explaining is done here, on the page. Each chapter opens where you are, builds the idea step by step, and shows worked examples before it sets you a problem. Every printed problem is solved in the back, step by step, with the reason beside each step. No teacher, no tuition class and no second book is assumed anywhere in it.

Mathematics, Class 12, on the 2026–27 CBSE syllabus.

1. Relations & Functions

   • "Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions."
2. Inverse Trig Functions

   • "Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions."
3. Matrices

   • concept/notation/order/types
   • transpose
   • symmetric & skew-symmetric
   • addition
   • multiplication
   • scalar multiplication + simple properties
   • non-commutativity
   • non-zero matrices with zero product (order 2)
   • invertible matrices + uniqueness of inverse
4. Determinants

   • determinant up to 3×3
   • minors
   • cofactors
   • area of triangle
   • adjoint
   • inverse
   • consistency/inconsistency
   • solving 2–3 variable systems (unique solution) by matrix inverse
5. Continuity & Differentiability

   • continuity
   • differentiability
   • chain rule
   • composite functions
   • derivatives of inverse trig
   • implicit functions
   • exponential/log
   • logarithmic differentiation
   • parametric forms
   • second-order derivatives
6. Applications of Derivatives

   • rate of change
   • increasing/decreasing
   • maxima and minima (first derivative test geometric, second derivative test as provable tool)
   • simple problems
7. Integrals

   • integration as inverse of differentiation
   • substitution
   • partial fractions
   • by parts
   • the ten listed special forms
   • Fundamental Theorem of Calculus (without proof)
   • basic properties of definite integrals and their evaluation
8. Applications of Integrals

   • area under simple curves — lines
   • circles/parabolas/ellipses (standard form only)
9. Differential Equations

   • definition
   • order and degree
   • general/particular solutions
   • separation of variables
   • homogeneous first-order first-degree
   • linear DE of dy/dx + py = q and dx/dy + px = q
10. Vector Algebra

    • vectors/scalars
    • magnitude/direction
    • direction cosines and ratios
    • types
    • position vector
    • negative
    • components
    • addition
    • scalar multiplication
    • position vector of a point dividing a segment in a given ratio (section formula)
    • scalar (dot) product
    • vector (cross) product — definition
    • geometrical interpretation
    • properties
    • application
11. Three-Dimensional Geometry

    • direction cosines/ratios of a line joining two points
    • Cartesian and vector equation of a line
    • skew lines
    • shortest distance between two lines
    • angle between two lines. Lines only — no planes.
12. Linear Programming

    • terminology
    • graphical method for two variables
    • feasible/infeasible regions (bounded/unbounded)
    • feasible/infeasible solutions
    • optimal feasible solutions (up to three non-trivial constraints)
13. Probability

    • conditional probability
    • multiplication theorem
    • independent events
    • total probability
    • Bayes' theorem. No random variable /distribution /mean /variance /binomial.

It follows the CBSE Mathematics syllabus for 2026–27 chapter by chapter, in NCERT's order. Each chapter teaches its idea from the beginning, shows worked examples before it sets a problem, names the mistakes students actually make. Every printed problem is solved in the back, step by step with the reason beside each step, next to a glossary and the reference pages the subject needs.

What it is not: an NCERT solutions book — it solves its own problems only; a sample-paper or previous-year-paper bank; a coaching module or test series; a CBSE or NCERT publication; the school — no lab work, projects or internal-assessment help. Nor is it a JEE Advanced or NEET-level problem book — the ceiling is NCERT plus the entrance-exam application tier — a formula-sheet crammer, or a bridge course from the previous class beyond its assumed-skills page.

Free to read: these chapters open in any browser, with no account.

• Chapter 1: Relations and Functions
• Chapter 2: Inverse Trigonometric Functions