Tamil Nadu Board of Secondary Education Syllabus For Class 10th Mathematics: Knowing the Syllabus is very important for the students of Class 10th. Shaalaa has also provided a list of topics that every student needs to understand.

The Tamil Nadu Board of Secondary Education Class 10th Mathematics syllabus for the academic year 2022-2023 is based on the Board's guidelines. Students should read the Class 10th 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 10th Mathematics Syllabus pdf 2022-2023. They will also receive a complete practical syllabus for Class 10th Mathematics in addition to this.

## Tamil Nadu Board of Secondary Education Class 10th Mathematics Revised Syllabus

Tamil Nadu Board of Secondary Education Class 10th Mathematics and their Unit wise marks distribution

### Tamil Nadu Board of Secondary Education Class 10th Mathematics Course Structure 2022-2023 With Marking Scheme

# | Unit/Topic | Weightage |
---|---|---|

1 | Relations and Functions | |

2 | Numbers and Sequences | |

3 | Algebra | |

4 | Geometry | |

5 | Coordinate Geometry | |

6 | Trigonometry | |

7 | Mensuration | |

8 | Statistics and Probability | |

Total | - |

## Syllabus

- Introduction of Relations and Functions
- Ordered Pair
- Cartesian Product
- Cartesian Product of three Sets

- Relations
- Functions
- Representation of Functions
- Vertical line test

- Types of Functions
- One – one function
- Many – one function
- Onto function
- Into function
- Bijection
- Horizontal Line Test

- Special Cases of Functions
- Constant function
- Identity function
- Real valued function

- Composition of Functions
- Composition of three functions

- Identifying the Graphs of Linear, Quadratic, Cubic and Reciprocal Functions
- Linear Function
- Modulus or Absolute valued Function
- Quadratic Function
- Cubic Function
- Reciprocal Function
- Constant Function

- Introduction of Numbers and Sequences
- Euclid’s Division Lemma
- Euclid’s Division Algorithm
- Fundamental Theorem of Arithmetic
- Significance of the Fundamental Theorem of Arithmetic

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

- Sequence
- Arithmetic Progression
- Terms and Common Difference of an A.P.

- Series
- Sum to n terms of an A.P.

- Geometric Progression
- 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 n Terms of a Geometric Progression
- Sum to infinite terms of a G.P.

- Special Series
- 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

- Introduction to Algebra
- Simultaneous Linear Equations in Three Variables
- System of Linear Equations in Three Variables

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

- Rational Expressions
- 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

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

- Quadratic Equations
- 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

- Graph of Variations
- Variables
- Constants
- Two types of variation: Direct variation, Indirect variation

- Quadratic Graphs
- Finding the Nature of Solution of Quadratic Equations Graphically
- Solving quadratic equations through the intersection of lines

- Matrices
- Order of a Matrix
- Types of Matrices - Row Matrix, Column Matrix, Square Matrix, Diagonal Matrix, Scalar Matrix, Identity (or) Unit Matrix, Zero matrix (or) null matrix, Transpose of a matrix, Triangular Matrix, Equal Matrices, The negative of a matrix
- Operations on Matrices

- Addition and subtraction of matrices

- Multiplication of Matrix by a Scalar

- Properties of Matrix Addition and Scalar Multiplication

- Additive Identity

- Additive Inverse

- Multiplication of Matrices

- Properties of Multiplication of Matrix

(a) Matrix multiplication is not commutative in general

(b) Matrix multiplication is distributive over matrix addition

(c) Matrix multiplication is always associative

(d) Multiplication of a matrix by a unit matrix

- Introduction of Geometry
- Similarity of Triangles
- Thales Theorem and Angle Bisector Theorem
- 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.

- Right-angled Triangles and Pythagoras Property
- In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of remaining two sides.

- Converse of Pythagoras Theorem
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.

- Circles and Tangents
- 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.

- Concurrency Theorems
- Special cevians
- Ceva’s Theorem
- Menelaus Theorem

- Coordinate Geometry
- 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.

- Area of a Triangle by Heron's Formula
- Collinearity of three points

- Area of a General Quadrilateral
- Inclination of a Line
- Slope of a Straight line
- Slopes of parallel lines
- Slopes of perpendicular lines

- Straight Line
- 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

- General Form of a Straight Line
- 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

- Trigonometry
- Trigonometric Identities
- Heights and Distances
- Problems involving Angle of Elevation
- Problems involving Angle of Depression
- Problems involving Angle of Elevation and Depression

- Mensuration
- Surface Area of Cylinder
- Right Circular Cylinder
- Hollow Cylinder

- Surface Area of a Right Circular Cone
- Surface Area of a Sphere
- Surface area of a sphere
- Hemisphere
- Hollow Hemisphere

- Frustum of a Cone
- Volume of a Cylinder
- Volume of a Right Circular Cone
- Volume of a Sphere
- Volume of Frustum of a Cone
- Surface Area and Volume of Different Combination of Solid Figures
- Consideration of the time volume/surface area for solid formed using two or more shapes

- Conversion of Solids from One Shape to Another with No Change in Volume

- Introduction of Statistics and Probability
- Measures of Dispersion
- 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

- Coefficient of Variation
- Probability
- Tree diagram
- Probability of an Event

- Algebra of Events
- Addition Theorem of Probability