Tamil Nadu Board of Secondary Education Syllabus For Class 12th Mathematics: Knowing the Syllabus is very important for the students of Class 12th. Shaalaa has also provided a list of topics that every student needs to understand.

The Tamil Nadu Board of Secondary Education Class 12th Mathematics syllabus for the academic year 2022-2023 is based on the Board's guidelines. Students should read the Class 12th Mathematics Syllabus to learn about the subject's subjects and subtopics.

Students will discover the unit names, chapters under each unit, and subtopics under each chapter in the Tamil Nadu Board of Secondary Education Class 12th Mathematics Syllabus pdf 2022-2023. They will also receive a complete practical syllabus for Class 12th Mathematics in addition to this.

## Tamil Nadu Board of Secondary Education Class 12th Mathematics Revised Syllabus

Tamil Nadu Board of Secondary Education Class 12th Mathematics and their Unit wise marks distribution

### Tamil Nadu Board of Secondary Education Class 12th Mathematics Course Structure 2022-2023 With Marking Scheme

## Syllabus

- Introduction to Applications of Matrices and Determinants
- Inverse of a Non-singular Square Matrix
- Adjoint of a Square Matrix
- Definition of inverse matrix of a square matrix
- Properties of inverses of matrices
- Application of matrices to Geometry
- Application of matrices to Cryptography

- Elementary Transformations of a Matrix
- Elementary row and column operations
- Row-Echelon form
- Rank of a Matrix
- Gauss-Jordan Method

- Applications of Matrices: Solving System of Linear Equations
- Formation of a System of Linear Equations
- System of Linear Equations in Matrix Form
- Solution to a System of Linear equations

- Matrix Inversion Method
- Cramer’s Rule
- Gaussian Elimination Method

- Applications of Matrices: Consistency of System of Linear Equations by Rank Method
- Non-homogeneous Linear Equations
- Homogeneous system of linear equations

- Introduction to Complex Numbers
- Powers of imaginary unit i

- Complex Numbers
- Rectangular form
- Argand plane A complex number
- Algebraic operations on complex numbers

- Basic Algebraic Properties of Complex Numbers
- Properties of complex numbers

- Conjugate of a Complex Number
- Geometrical representation of conjugate of a complex number
- Properties of Complex Conjugates

- Modulus of a Complex Number
- Properties of Modulus of a complex number
- Square roots of a complex number

- Geometry and Locus of Complex Numbers
- Polar and Euler Form of a Complex Number
- Polar form of a complex number
- Euler’s Form of the complex number

- de Moivre’s Theorem and Its Applications
- de Moivre's Theorem
- Finding nth roots of a complex number
- The nth roots of unity

- Introduction to Theory of Equations
- Basics of Polynomial Equations
- Different types of Polynomial Equations
- Quadratic Equations

- Vieta’s Formulae and Formation of Polynomial Equations
- Vieta’s formula for Quadratic Equations
- Vieta’s formula for Polynomial Equations

- The Fundamental Theorem of Algebra
- Vieta’s Formula
- Formation of Polynomial Equations with given Roots

- Nature of Roots and Nature of Coefficients of Polynomial Equations
- Imaginary Roots
- Irrational Roots
- Rational Roots

- Roots of Higher Degree Polynomial Equations
- Polynomials with Additional Information
- Imaginary or Surds Roots
- Polynomial equations with Even Powers Only
- Zero Sum of all Coefficients
- Equal Sums of Coefficients of Odd and Even Powers
- Roots in Progressions
- Partly Factored Polynomials

- Polynomial Equations with No Additional Information
- Rational Root Theorem
- Reciprocal Equations
- Non-polynomial Equations

- Descartes Rule
- Statement of Descartes Rule
- Attainment of bounds

- Bounds for the number of real roots
- Bounds for the number of Imaginary (Nonreal Complex)roots

- Inverse Trigonometric Functions
- Inverse sine function
- Inverse cosine function
- Inverse tangent function
- Inverse cosecant function
- Inverse secant function
- Inverse cotangent function
- Principal Values of Inverse Trigonometric Functions
- Properties of inverse trigonometric functions

- Some Fundamental Concepts
- Domain and Range of trigonometric functions
- Graphs of functions
- Amplitude and Period of a graph
- Inverse functions
- Graphs of inverse functions

- Sine Function and Inverse Sine Function
- The graph of sine function
- Properties of the sine function
- The inverse sine function and its properties
- Graph of the inverse sine function

- The Cosine Function and Inverse Cosine Function
- Graph of cosine function
- Properties of the cosine function
- The inverse cosine function and its properties
- Graph of the inverse cosine function

- The Tangent Function and the Inverse Tangent Function
- The graph of tangent function
- Properties of the tangent function
- The inverse tangent function and its properties
- Graph of the inverse tangent function

- The Cosecant Function and the Inverse Cosecant Function
- Graph of the cosecant function
- The inverse cosecant function
- Graph of the inverse cosecant function

- The Secant Function and Inverse Secant Function
- The graph of the secant function
- Inverse secant function
- Graph of the inverse secant function

- The Cotangent Function and the Inverse Cotangent Function
- The graph of the cotangent function
- Inverse cotangent function
- Graph of the inverse cotangent function

- Principal Value of Inverse Trigonometric Functions
- Properties of Inverse Trigonometric Functions
Inverse of Sin, Inverse of cosin, Inverse of tan, Inverse of cot, Inverse of Sec, Inverse of Cosec

- Two Dimensional Analytical Geometry-II
- Circles
3.4.1 The equation of a circle when the centre and radius are given

3.4.2 Equation of a circle when the end points of a diameter are given

3.4.3 General equation of a circle

3.4.4 Parametric form of a circle

3.4.5 Tangents

- Length of the tangent to the circle

- Conics
3.5.1 Parabola

3.5.2 Definitions regarding a parabola: y

^{2}= 4ax3.5.3 Other standard parabolas

3.5.4 General form of the standard equation of a parabola, which is open rightward

- Conic Sections
- Geometric description of conic section
- Degenerate Forms
- Identifying the conics from the general equation of the conic

- Parametric Form of Conics
- Parametric equations

- Tangents and Normals to Conics
- Equation of tangent and normal to the parabola y
^{2}=4ax - Equations of tangent and normal to Ellipse and Hyperbola
- Condition for the line y=mx+c to be a tangent to the conic sections

- Equation of tangent and normal to the parabola y
- Real Life Applications of Conics
- Parabola
- Ellipse
- Hyperbola
- Reflective property of parabola
- Reflective Property of an Ellipse
- Reflective Property of a Hyperbola

- Introduction to Applications of Vector Algebra
- Geometric Introduction to Vectors
- Scalar Product and Vector Product
- Geometrical interpretation
- Application of dot and cross products in plane Trigonometry
- Application of dot and cross products in Geometry
- Application of dot and cross product in Physics

- Scalar Triple Product of Vectors
- Vector Triple Product
- Jacobi’S Identity and Lagrange’S Identity
- Application of Vectors to 3-dimensional Geometry
- Different forms of equation of a straight line
- A point on the straight line and the direction of the straight line are given
- Straight Line passing through two given points
- Angle between two straight lines
- Point of intersection of two straight lines
- Shortest distance between two straight lines

- Different Forms of Equation of a Plane
- Equation of a plane when a normal to the plane and the distance of the plane from the origin are given
- Equation of a plane perpendicular to a vector and passing through a given point
- Intercept form of the equation of a plane
- Equation of a plane passing through three given non-collinear points
- Equation of a plane passing through a given point and parallel to two given non-parallel vectors
- Equation of a plane passing through two given distinct points and is parallel to a non-zero vector
- Condition for a line to lie in a plane
- Condition for coplanarity of two lines
- Equation of plane containing two non-parallel coplanar lines
- Angle between two planes
- Angle between a line and a plane
- Distance of a point from a plane
- Distance between two parallel planes
- Equation of line of intersection of two planes
- Equation of a plane passing through the line of intersection of two given planes

- Image of a Point in a Plane
- The coordinates of the image of a point in a plane

- Meeting Point of a Line and a Plane

- Applications of Differential Calculus
- Early Developments

- Meaning of Derivatives
- Derivative as slope
- Derivative as rate of change
- Related rates
- Equations of Tangent and Normal
- Angle between two curves

- Mean Value Theorem
- Rolle’s Theorem
- Lagrange’s Mean Value Theorem
- Applications

- Series Expansions
- Indeterminate Forms
- A Limit Process
- The l’Hôpital’s Rule
- Indeterminate forms
- Indeterminate forms 0
^{0},1∞ and ∞^{0}

- Applications of First Derivative
- Monotonicity of functions
- Absolute maxima and minima
- Relative Extrema on an Interval
- Extrema using First Derivative Test

- Applications of Second Derivative
- Concavity, Convexity, and Points of Inflection
- Extrema using Second Derivative Test

- Applications in Optimization
- Symmetry and Asymptotes
- Symmetry
- Asymptotes

- Sketching of Curves

- Introduction to Differentials and Partial Derivatives
- Linear Approximation and Differentials
- Linear Approximation
- Errors: Absolute Error, Relative Error, and Percentage Error

- Functions of Several Variables
- Recall of Limit and Continuity of Functions of One Variable

- Limit and Continuity of Functions of Two Variables
- Partial Derivatives
- Successive partial derivatives
- Euler’s theorem and its applications

- Linear Approximation and Differential of a Function of Several Variables
- Function of Function Rule
- Homogeneous Functions and Euler’s Theorem

- Applications of Integrations
- Definite Integral as the Limit of a Sum
- Riemann Integral
- Limit Formula to Evaluate

- Fundamental Theorems of Integral Calculus and Their Applications
- Bernoulli’s Formula
- Improper Integrals
- Reduction Formulae
- Gamma Integral
- Evaluation of a Bounded Plane Area by Integration
- Area of the region bounded by a curve, x – axis and the lines x = a and x = b
- Area of the region bounded by a curve, y–axis and the lines y = cand y = d
- Area of the region bounded between two curves

- Volume of a Solid Obtained by Revolving Area About an Axis

- Introduction to Ordinary Differential Equations
- Differential Equation, Order, and Degree
- Classification of Differential Equations
- Formation of Differential Equations
- Formation of Differential equations from Physical Situations
- Formation of Differential Equations from Geometrical Problems

- Solution of Ordinary Differential Equations
- Solution of First Order and First Degree Differential Equations
- Variables Separable Method
- Substitution Method
- Homogeneous Form or Homogeneous Differential Equation
- General solution and particular solution
- Differential Equation in which variables are separable
- Linear differential equations of first order

- First Order Linear Differential Equations
- Applications of First Order Ordinary Differential Equations
- Population growth
- Radioactive decay
- Newton’s Law of cooling/warming
- Mixture problems

- Introduction to Probability Distributions
- Random Variable
- Definition of a random variable
- Types of Random Variable
- Discrete random variable
- Continuous random variable

- Types of Random Variables
- Discrete random variable
- Continuous random variable
- Probability Mass Function
- Cumulative Distribution Function or Distribution Function
- Cumulative Distribution Function from Probability Mass function
- Probability Mass Function from Cumulative Distribution Function

- Continuous Distributions
- The definition of continuous random variables
- Probability density function
- Distribution function (Cumulative distribution function)
- Distribution function from Probability density function
- Probability density function from Probability distribution function

- Mathematical Expectation
- Mean
- Variance
- Expected value and Variance
- Properties of Mathematical expectation

- Theoretical Distributions: Some Special Discrete Distributions
- The One point distribution
- The Two point distribution
- The Bernoulli distribution
- The Binomial Distribution

- Introduction to Discrete Mathematics
- Concept of Binary Operations
- Commutative Binary Operations
- Associative Binary Operations
- Identity Binary Operation,
- Invertible Binary Operation

- Mathematical Logic
- Statement and its truth value
- Compound Statements, Logical Connectives, and Truth Tables
- Tautology, Contradiction, and Contingency
- Duality
- Logical Equivalence