Mathematics HSC Science Class 11 Tamil Nadu Board of Secondary Education Syllabus 2024-25

• Properties of Set Operations

• Constants and Variables
• Intervals and Neighbourhoods

1. Type of Intervals
2. Neighbourhood

• Definition of Relation
• Domain
• Co-domain and Range of a Relation

• Ways of Representing Functions

1. Tabular Representation of a Function
2. Graphical Representation of a Function
3. Analytical Representation of a Function

• Some Elementary Functions
• Types of Functions
• Operations on Functions
• Inverse of a Function
• Algebra of Functions
• Some Special Functions

• Type of Transformations

1. Reflection
2. Translation
3. Dilations

• Rational Numbers
• The Number Line
• Irrational Numbers
• Properties of Real Numbers

• Definition and Properties
• Equations Involving Absolute Value
• Some Results For Absolute Value
• Inequalities Involving Absolute Value

Given `alpha`,`beta` as roots then find the equation whose roots are of the form `alpha^3`, `beta^3` , etc

Case I:a>0 -> 1)Real roots, 2)Complex roots,3)Equal roots

Case II:a<0 -> 1)Real roots, 2)Complex roots,3)Equal roots

Where ‘a’ is the coefficient of x² in the equations of the form ax² + bx + c = 0.

Understanding the fact that a quadratic expression (when plotted on a graph) is a parabola.

• Quadratic Formula
• Quadratic Inequalities

• Steps to Solve Quadratic Inequalities

•  Division Algorithm
•  Important Identities

• Rational Inequalities
• Partial Fractions
• Graphical Representation of Linear Inequalities

•  Exponents

• Properties of Exponents

• Radicals
• Exponential Function

• Properties of Exponential Function
• A Special Exponential Function

• Properties of Logarithm

• Angles
• Different Systems of measurement of angle
• Degree Measure
• Angles in Standard Position
• Coterminal angles
• Basic Trigonometric ratios using a right triangle
• Exact values of trigonometric functions of widely used angles
• Basic Trigonometric Identities

• Relationship between Degree and Radian Measures

• Trigonometric Functions of any angle in terms of Cartesian coordinates

• Trigonometric ratios of Quadrantal angles

•  Trigonometric Functions of real numbers

• Signs of Trigonometric functions

•  Allied Angles
•  Some Characteristics of Trigonometric Functions

• Periodicity of Trigonometric Functions
• Odd and Even trigonometric functions

• Trigonometric Identities

1.  Sum and difference identities or compound angles formulas
2.  Multiple angle identities and submultiple angle identities
3.  Conditional Trigonometric Identities

• The Law of Sines or Sine Formula

• Law of Sines
• Law of Cosines
• Projection Formula
• Projection Formula
• Half-Angle formula

• Area of a triangle (Heron’s Formula )

• Introduction of Inverse Trigonometric Functions

• Tree Diagram 
• Addition Principle 
• Multiplication principle

• Permutation
• Permutation of repeated things
• Permutations when all the objects are not distinct
• Number of Permutations Under Certain Restricted Conditions
• Circular Permutations

• Properties of Combinations

• Binomial Coefficients
• Binomial theorem for positive integral inde

• Arithmetic and Geometric Progressions
• Arithmetico-Geometric Progression (AGP)
• Harmonic Progression (HP)

• Sum of Arithmetic, Geometric and Arithmetico-Geometric Progressions
• Telescopic Summation for Finite Series
• Some Special Finite Series

• Fibonacci Sequence
• Infinite Geometric Series
• Infinite Arithmetico-Geometric Series
• Telescopic Summation for Infinite Series
• Binomial Series
• Exponential Series
• Logarithmic Series

• Procedure for finding the equation of the locus of a point

• Inclination of a line
• Slope of a line
• Perpendicular Lines
• Angle between intersecting lines
• Different Forms of an equation of a straight line
• General form to other forms

• Condition for Parallel Lines
• Condition for perpendicular Lines
• Position of a point with respect to a straight line
• Distance Formulas
• Family of lines
• One parameter families
• Two parameters families
• The family of equation of straight lines through the point of intersection of the two givenlines

3.3.1 Combined equation of the pair of straight lines

3.3.2 Pair of straight lines passing through the origin

3.3.3 Angle between pair of straight lines passing through the origin

3.3.4 The condition for general second degree equation to represent the pair of straight

lines

•  Equation of the bisectors of the angle between the lines
•  General form of Pair of Straight Lines

• General form of a matrix
• Types of Matrices
• Equality of Matrices
• Algebraic Operations on Matrices
• Properties of Matrix Addition, Scalar Multiplication and Product of Matrices
• Operation of Transpose of a Matrix and its Properties
• Symmetric and Skew-symmetric Matrices

• Determinants of Matrices of different order
• Properties of Determinants
• Application of Factor Theorem to Determinants
• Product of Determinants
• Relation between a Determinant and its Cofactor Determinant
• Area of a Triangle
• Singular and non-singular Matrices

• Scalars 
• Vectors
• Position vector
• Displacement vector
• Resultant vector

• Addition of Two Vectors
  - Parallelogram Law
  - Triangle Law of addition of two vectors
• Subtraction of two vectors
• Scalar multiplication of a vector

• Resolution of a vector in two dimension
• Resolution of a vector in three dimension
• Matrix representation of a vector

• Direction cosines of a line passing through two points.

•  Angle between two vectors
• Scalar product 
• Properties of Scalar Product
• Vector Product
• Properties

• Definition of Limit
• One-Sided Limit
• Left-hand Limit
• Right-hand Limit
• Existence of a limit of a function at a point x = a
• Algebra of limits:
  Let f(x) and g(x) be two functions such that
  `lim_(x→a) f(x) = l and lim_(x → a) g(x) = m, then`
  1. `lim_(x → a) [f(x) ± g(x)] = lim_(x → a) f(x) ± lim_(x → a) g(x) = l ± m`
  2. `lim_(x → a) [f(x) xx g(x)] = lim_(x→ a) f(x) xx lim_(x→ a) g(x) = l xx m`
  3. `lim_(x → a) [kf(x)] = k xx lim_(x→ a) f(x) = kl, "where" ‘k’ "is a constant"`
  4. `lim_(x → a) f(x)/g(x) = (lim_(x → a) f(x))/(lim_(x → a) g(x)) = l/m "where" m≠ 0`.

• Examples of functions Continuous at a point 
• Algebra of continuous functions 
• Removable and Jump Discontinuities 

• The tangent line problem 
• Velocity of Rectilinear motion
• The derivative of a Function
• One sided derivatives (left hand and right hand derivatives) 

• Derivatives of basic elementary functions 

1. The derivative of a constant function is zero
2. The power function y = xn, n > 0 is an integer
3. Derivative of the logarithmic function
4. Derivative of the exponential function
5. The derivatives of the Trigonometric functions 

• Examples on Chain Rule
• Implicit Differentiation
• Logarithmic Differentiation
• Substitution method 
• Derivatives of variables defined by parametric equations
• Differentiation of one function with respect to another function
• Higher order Derivatives

• Integration
• Meaning
• Basic Rule of Integration
• Application of Integration
• Consumer’s Surplus 

• Types of events 
• Methods to find sample space
• Notations

• Basic concepts of Probability
• Independent and Dependent events
• Conditional Probability
• Baye’s Theorem
• Axiomatic approach to Probability
• ODDS

• Independent Events

• Partition of a sample space
• Theorem of total probability