Class 12 Maths NCERT Pdf Books

Class 12 NCERT Maths Chapter Names

Chapter 1: Relations and Functions
Chapter 2: Inverse Trigonometric Functions
Chapter 3: Matrices
Chapter 4: Determinants
Chapter 5: Continuity and Differentiability
Chapter 6: Application of Derivatives
Chapter 7: Integrals
Chapter 8: Application of Integrals
Chapter 9: Differential Equations
Chapter 10: Vector Algebra
Chapter 11: Three Dimensional Geometry
Chapter 12: Linear Programming
Chapter 13: Probability

Class 12 Maths Chapter 1: Relations and Functions

What We will Learn

1. Relations – Revision of reflexive, symmetric, transitive, and equivalence relations from Class 11.
2. Functions – One-one (injective), onto (surjective), and bijective functions.
3. Composition of Functions – How to combine two functions (gof)(x)(g \circ f)(x)(gof)(x) and find its domain.
4. Invertible Functions – Definition, condition for a function to be invertible (must be bijective), and method to find the inverse.
5. Graphical and Algebraic Understanding – How to represent and analyze functions.

Class 12 Maths – Chapter 2: Inverse Trigonometric Functions:

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What We Will Learn

1. Meaning and notation of inverse trigonometric functions.
2. Need for restricting domains to make trig functions bijective.
3. Principal value ranges for all six inverse trig functions.
4. Domains and ranges for each function.
5. Important identities and relationships.
6. Simplification of inverse trig expressions.
7. Solving equations involving inverse trig functions.
8. Graphs of inverse trig functions.

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Class 12 Maths – Chapter 3: Matrices

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What We Will Learn

1. Concept of a Matrix – Definition, notation, and order of a matrix.
2. Types of Matrices – Row, column, square, zero, diagonal, scalar, identity, symmetric, skew-symmetric, etc.
3. Equality of Matrices – Conditions for two matrices to be equal.
4. Operations on Matrices – Addition, subtraction, scalar multiplication.
5. Multiplication of Matrices – Definition, rules, and properties.
6. Transpose of a Matrix – Definition and properties.
7. Symmetric & Skew-Symmetric Matrices – Concept and examples.
8. Properties of Matrix Operations – Associative, distributive, commutative (for addition).
9. Special Types of Matrices in Multiplication – Identity matrix, zero matrix.
10. Elementary Transformations – Row and column operations (introduction).
11. Invertible Matrices – Concept, conditions, and finding the inverse using the adjoint method.

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Class 12 Maths – Chapter 4: Determinants

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What We Will Learn – Chapter 4

1. Determinant of a Square Matrix – Definition for 2×2 and 3×3 matrices.
2. Properties of Determinants – Effect of row/column operations, interchange, multiplication, etc.
3. Elementary Transformations – Using properties to simplify determinants.
4. Applications of Determinants – Solving systems of linear equations using Cramer’s Rule.
5. Adjoint and Inverse of a Matrix – Finding inverse via adjoint and determinant.
6. Area of Triangle – Using determinant formula for coordinates of vertices.
7. Conditions for Collinearity – Using determinant value zero.
8. Miscellaneous Applications – Checking consistency of equations, transformations.

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Class 12 Maths – Chapter 5: Continuity and Differentiability:

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What We Will Learn

1. Continuity of a Function – Definition, checking continuity at a point, and over an interval.
2. Differentiability of a Function – Definition and relationship with continuity.
3. Algebra of Continuous and Differentiable Functions – Sum, difference, product, quotient rules.
4. Continuity and Differentiability of Composite Functions – Chain rule application.
5. Derivatives of Inverse Trigonometric Functions.
6. Exponential and Logarithmic Functions – Differentiation formulas.
7. Logarithmic Differentiation – Method and applications.
8. Derivatives of Functions in Parametric Form.
9. Second-Order Derivatives – Concept and calculation.
10. Implicit Differentiation – Finding derivatives without explicitly solving for yy.

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Class 12 Maths – Chapter 6: Application of Derivatives

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What We Will Learn – Chapter 6: Application of Derivatives

1. Rate of Change – Finding the rate of change of one quantity with respect to another.
2. Increasing and Decreasing Functions – Using first derivative to determine intervals of increase/decrease.
3. Tangents and Normals – Equations of tangent and normal lines to curves.
4. Approximations – Using differentials for small changes.
5. Maxima and Minima – Finding local maxima, minima, and turning points using the first and second derivative tests.
6. Optimization Problems – Solving real-life problems for maximum or minimum values.

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Class 12 Maths – Chapter 7: Integrals

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What We Will Learn – Chapter 7: Integrals

1. Integration as the Inverse Process of Differentiation.
2. Basic Integration Formulas – Standard results for polynomials, trigonometric, exponential, and logarithmic functions.
3. Methods of Integration
   • By substitution
   • By partial fractions
   • By parts
4. Integration of Some Special Types of Functions.
5. Definite Integrals – Definition and properties.
6. Definite Integral as a Limit of a Sum – Link with area under a curve.
7. Fundamental Theorem of Calculus – Relationship between differentiation and integration.
8. Evaluation of Definite Integrals – Using properties and standard results.

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Class 12 Maths – Chapter 8: Application of Integrals:

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What We Will Learn – Chapter 8: Application of Integrals

1. Area Under a Curve – Concept and formula using definite integrals.
2. Area Bounded by a Curve and Coordinate Axes.
3. Area Between Two Curves – Using definite integrals to find the enclosed area.
4. Areas in Standard Geometric Shapes – Circles, parabolas, ellipses, and other curves.
5. Application in Real-Life Problems – Calculating physical areas from given functions.

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Class 12 Maths – Chapter 9: Differential Equations

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What We Will Learn – Chapter 9: Differential Equations

1. Basic Concepts – Definition of a differential equation, order, and degree.
2. General and Particular Solutions – Difference and meaning.
3. Formation of Differential Equations – From given functions or conditions.
4. Methods of Solving:
   • Variables separable form.
   • Homogeneous differential equations.
   • Linear differential equations.
5. Applications – Solving real-life problems using differential equations.
6. Verification of Solutions – Checking if a function satisfies a given differential equation.

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Class 12 Maths – Chapter 10: Vector Algebra

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What We Will Learn – Chapter 10: Vector Algebra

1. Basics of Vectors – Definition, types (zero, unit, equal, collinear), and notation.
2. Direction Cosines and Direction Ratios of a vector.
3. Operations on Vectors – Addition, subtraction, and multiplication by a scalar.
4. Scalar (Dot) Product – Definition, properties, and applications (finding angle between vectors, projections).
5. Vector (Cross) Product – Definition, properties, and applications (area of parallelogram/triangle).
6. Position Vector and Displacement Vector – Concept and uses.
7. Geometrical Applications – Collinearity, coplanarity, and solving geometric problems using vectors.

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Class 12 Maths – Chapter 11: Three Dimensional Geometry

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What We Will Learn – Chapter 11: Three Dimensional Geometry

1. Direction Cosines (DCs) and Direction Ratios (DRs) of a line in space.
2. Equation of a Line in 3D:
   • Passing through a point and parallel to a given vector.
   • Passing through two given points.
3. Angle Between Two Lines – Using direction cosines and vector approach.
4. Shortest Distance Between Two Skew Lines – Formula and method.
5. Equation of a Plane:
   • In normal form.
   • Passing through a point and perpendicular to a vector.
   • Passing through three non-collinear points.
6. Angle Between Two Planes – Using normal vectors.
7. Angle Between a Line and a Plane – Formula and applications.
8. Distance of a Point from a Plane – Perpendicular distance formula.

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Class 12 Maths – Chapter 12: Linear Programming

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What We Will Learn – Chapter 12: Linear Programming

1. Introduction to Linear Programming Problems (LPP) – Meaning and applications in real life.
2. Mathematical Formulation – Converting a word problem into linear inequalities and objective function.
3. Graphical Method of Solution – For problems involving two variables.
4. Feasible Region & Feasible Solutions – Definition and graphical representation.
5. Optimal Solutions – Finding maximum or minimum value of objective function.
6. Corner Point Method – Using vertices of the feasible region to find the optimal solution.
7. Applications of LPP – In business, manufacturing, and daily-life optimization problems.

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Class 12 Maths – Chapter 13: Probability

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What We Will Learn – Chapter 13: Probability

1. Conditional Probability – Definition, formula, and applications.
2. Multiplication Theorem of Probability – For independent and dependent events.
3. Independent Events – Concept and identification.
4. Bayes’ Theorem – Statement, formula, and use in solving problems.
5. Random Variables – Definition and examples.
6. Probability Distribution – Discrete probability distributions and their properties.
7. Mean (Expected Value) and Variance of a probability distribution.

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