Mathematics SSLC (English Medium) Class 10 Tamil Nadu Board of Secondary Education Syllabus 2024-25

• Cartesian Product of three Sets

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

• Function, Domain, Co-domain, Range
• Types of function
  1. One-one or One to one or Injective function
  2. Onto or Surjective function
• Representation of Function
• Graph of a function
• Value of funcation
• Some Basic Functions - Constant Function, Identity function, Power Functions, Polynomial Function, Radical Function, Rational Function, Exponential Function, Logarithmic Function, Trigonometric function

• Vertical line test

• One – one function
• Many – one function
• Onto function
• Into function
• Bijection
• Horizontal Line Test

1. Constant function
2. Identity function
3. Real valued function

• Composition of three functions

• Linear Function
• Modulus or Absolute valued Function
• Quadratic Function
• Cubic Function
• Reciprocal Function
• Constant Function

• Significance of the Fundamental Theorem of Arithmetic

• Congruence Modulo
• Connecting Euclid’s Division lemma and Modular Arithmetic
• Modulo operations

• Terms and Common Difference of an A.P.

• Sum to n terms of an A.P.

• General form of Geometric Progression
• General term of Geometric Progression
• The General term or the n^th term of a G.P.
• Sum of the first n terms of a G.P. (S_n)

• Sum to infinite terms of a G.P.

• Sum of first n natural numbers
• Sum of first n odd natural numbers
• Sum of squares of first n natural numbers
• Sum of cubes of first n natural numbers

• System of Linear Equations in Three Variables

• Greatest Common Divisor (GCD) or Highest Common Factor (HCF) of Polynomials
• Least Common Multiple (LCM) of Polynomials
• Relationship between LCM and GCD

• Reduction of Rational Expression
• Excluded Value
• Operations of Rational Expressions
  - Multiplication of Rational Expressions
  - Division of Rational Expressions
  - Addition and Subtraction of Rational Expressions
  Addition and Subtraction of Rational Expressions with Like Denominators
  - Addition and Subtraction of Rational Expressions with unlike Denominators

• Find the Square Root by Factorization Method
• Finding the Square Root of a Polynomial by Division Method

• Zeroes of a Quadratic Polynomial
• Roots of Quadratic Equations
• Formation of a Quadratic Equation
• Solving Quadratic Equations
  - Solving a quadratic equation by factorization method
  - Solving a Quadratic Equation by Completing the Square Method
  - Solving a Quadratic Equation by Formula Method
• Solving Problems Involving Quadratic Equations
• Nature of Roots of a Quadratic Equation 
• The Relation between Roots and Coefficients of a Quadratic Equation

• Variables
• Constants
• Two types of variation: Direct variation, Indirect variation

• Finding the Nature of Solution of Quadratic Equations Graphically
• Solving quadratic equations through the intersection of 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

• Basic Proportionality Theorem (BPT) or Thales theorem Statement
• Converse of Basic Proportionality Theorem
• Angle Bisector Theorem
• Converse of Angle Bisector Theorem
• Construction of triangle
  - Construction of a segment of a circle on a given line segment containing an angle θ.
  - Construction of a triangle when its base, the vertical angle, and the median from the vertex of the base are given.
  - Construct a triangle when its base, the vertical angle, and the altitude from the vertex to the base are given.
  - Construct a triangle when its base, the vertical angle, and the point on the base where the bisector of the vertical angle meets the base.

In a triangle if the square of one side is equal to the sum of the squares of the remaining two sides, then the triangle is a right angled triangle. 

• Real-life examples of tangents to circles
• Some results on circles and tangents
• Alternate Segment theorem
• Construction
  - Construction of a tangent to a circle (Using the center)
  - Construct of a tangent to a circle (Using alternate segment theorem)
  - Construction of pair of tangents to a circle from an external point P.

• Special cevians 
• Ceva’s Theorem
• Menelaus Theorem

• To find distance between any two points on an axis. 
• To find the distance between two points if the segment joining these points is parallel to any axis in the XY plane.

• Collinearity of three points

• Slope of a Straight line
• Slopes of parallel lines
• Slopes of perpendicular lines

• Equation of coordinate axes
• Equation of a straight line parallel to X-axis
• Equation of a Straight line parallel to the Y-axis
• Slope-Intercept Form
• Point-Slope form
• Two Point form
• Intercept Form

• Equation of a line parallel to the line ax + by + c = 0
• Equation of a line perpendicular to the line ax + by + c = 0
• Slope of a straight line

• Problems involving Angle of Elevation
• Problems involving Angle of Depression
• Problems involving Angle of Elevation and Depression

• Right Circular Cylinder
• Hollow Cylinder

• Surface area of a sphere
• Hemisphere
• Hollow Hemisphere

• Consideration of the time volume/surface area for solid formed using two or more shapes

• Range
• Deviations from the mean
• Squares of deviations from the mean
• Variance 
• Standard Deviation
  - Calculation of Standard Deviation for ungrouped data: Direct Method, Mean method, Assumed Mean method, Step deviation method
  - Calculation of Standard deviation for grouped data: Mean method, Assumed Mean method
  - Calculation of Standard deviation for continuous frequency distribution: Mean method, Shortcut method (or) Step deviation method

• Tree diagram
• Probability of an Event