www.tntextbooks.in
GOVERNMENT OF TAMIL NADU
HIGHER SECONDARY SECOND YEAR
MATHEMATICS
VOLUME - I
A publication under Free Textbook Programme of Government of Tamil Nadu
Department of School Education
Untouchability is Inhuman and a Crime
, www.tntextbooks.in
Government of Tamil Nadu
First Edition - 2019
Revised Edition - 2020, 2022, 2023
Reprint - 2021, 2024
(Published under New Syllabus)
NOT FOR SALE
Content Creation
The wise
possess all
State Council of Educational Research
and Training
© SCERT 2019
Printing & Publishing
Tamil NaduTextbook and Educational
Services Corporation
www.textbooksonline.tn.nic.in
II
, www.tntextbooks.in
HOW TO USE THE BOOK ?
• Awareness on the scope of higher educational opportunities; courses,
Scope of Mathematics institutions and required competitive examinations.
• Possible financial assistance to help students climb academic ladder.
• Overview of the unit
Learning Objectives • Give clarity on the intended learning outcomes of the unit.
• Visual representation of concepts with illustrations
• Videos, animations, and tutorials.
• To increase the span of attention of concepts
• To visualize the concepts for strengthening and understanding
ICT • To link concepts related to one unit with other units.
• To utilize the digital skills in classroom learning and providing students
experimental learning.
• Recapitulation of the salient points of each chapter for recalling the
Summary concepts learnt.
• Assessing student’s understanding of concepts and get them acquainted
Evaluation with solving exercise problems.
Books for Reference • List of relevant books for further reading.
• To motivate students aspiring to take up competitive examinations such
Scope for as JEE, KVPY, Math olympiad, etc., the concepts and questions based on
Higher Order Thinking Higher Order Thinking are incorporated in the content of this book.
• Frequently used Mathematical terms have been given with their
Glossary Tamil equivalents.
Mathematics Learning
The correct way to learn is to understand the concepts throughly. Each chapter opens with an Introduction,
Learning Objectives, Various Definitions, Theorems, Results and Illustrations. These in turn are followed by
solved examples and exercise problems which have been classified in to various types for quick and effective
revision. One can develop the skill of solving mathematical problems only by doing them. So the teacher's
role is to teach the basic concepts and problems related to it and to scaffold students to try the other problems
on their own. Since the second year of Higher Secondary is considered to be the foundation for learning
higher mathematics, the students must be given more attention to each and every concept mentioned in this
book.
III
, www.tntextbooks.in
CONTENTS
MATHEMATICS
CHAPTER TITLE Page No. Month
1 Applications of Matrices and Determinants 1 Jun
1.1 Introduction 1
1.2 Inverse of a Non-Singular Square Matrix 2
1.3 Elementary Transformations of a Matrix 16
1.4 Applications of Matrices: Solving System of
Linear Equations 27
1.5 Applications of Matrices: Consistency of system of
linear equations by rank method 38
2 Complex Numbers 52 Jul
2.1 Introduction to Complex Numbers 52
2.2 Complex Numbers 54
2.3 Basic Algebraic Properties of Complex Numbers 58
2.4 Conjugate of a Complex Number 60
2.5 Modulus of a Complex Number 66
2.6 Geometry and Locus of Complex Numbers 73
2.7 Polar and Euler form of a Complex Number 75
2.8 de Moivre’s Theorem and its Applications 83
3 Theory of Equations 97 Jul
3.1 Introduction 97
3.2 Basics of Polynomial Equations 99
3.3 Vieta’s Formulae and Formation of Polynomial Equations 100
3.4 Nature of Roots and Nature of Coefficients of
Polynomial Equations 107
3.5 Applications of Polynomial Equation in Geometry 111
3.6 Roots of Higher Degree Polynomial Equations 112
3.7 Polynomials with Additional Information 113
3.8 Polynomial Equations with no additional information 118
3.9 Descartes Rule 124
4 Inverse Trigonometric Functions 129 Jul/Aug
4.1 Introduction 129
4.2 Some Fundamental Concepts 130
4.3 Sine Function and Inverse Sine Function 133
IV
GOVERNMENT OF TAMIL NADU
HIGHER SECONDARY SECOND YEAR
MATHEMATICS
VOLUME - I
A publication under Free Textbook Programme of Government of Tamil Nadu
Department of School Education
Untouchability is Inhuman and a Crime
, www.tntextbooks.in
Government of Tamil Nadu
First Edition - 2019
Revised Edition - 2020, 2022, 2023
Reprint - 2021, 2024
(Published under New Syllabus)
NOT FOR SALE
Content Creation
The wise
possess all
State Council of Educational Research
and Training
© SCERT 2019
Printing & Publishing
Tamil NaduTextbook and Educational
Services Corporation
www.textbooksonline.tn.nic.in
II
, www.tntextbooks.in
HOW TO USE THE BOOK ?
• Awareness on the scope of higher educational opportunities; courses,
Scope of Mathematics institutions and required competitive examinations.
• Possible financial assistance to help students climb academic ladder.
• Overview of the unit
Learning Objectives • Give clarity on the intended learning outcomes of the unit.
• Visual representation of concepts with illustrations
• Videos, animations, and tutorials.
• To increase the span of attention of concepts
• To visualize the concepts for strengthening and understanding
ICT • To link concepts related to one unit with other units.
• To utilize the digital skills in classroom learning and providing students
experimental learning.
• Recapitulation of the salient points of each chapter for recalling the
Summary concepts learnt.
• Assessing student’s understanding of concepts and get them acquainted
Evaluation with solving exercise problems.
Books for Reference • List of relevant books for further reading.
• To motivate students aspiring to take up competitive examinations such
Scope for as JEE, KVPY, Math olympiad, etc., the concepts and questions based on
Higher Order Thinking Higher Order Thinking are incorporated in the content of this book.
• Frequently used Mathematical terms have been given with their
Glossary Tamil equivalents.
Mathematics Learning
The correct way to learn is to understand the concepts throughly. Each chapter opens with an Introduction,
Learning Objectives, Various Definitions, Theorems, Results and Illustrations. These in turn are followed by
solved examples and exercise problems which have been classified in to various types for quick and effective
revision. One can develop the skill of solving mathematical problems only by doing them. So the teacher's
role is to teach the basic concepts and problems related to it and to scaffold students to try the other problems
on their own. Since the second year of Higher Secondary is considered to be the foundation for learning
higher mathematics, the students must be given more attention to each and every concept mentioned in this
book.
III
, www.tntextbooks.in
CONTENTS
MATHEMATICS
CHAPTER TITLE Page No. Month
1 Applications of Matrices and Determinants 1 Jun
1.1 Introduction 1
1.2 Inverse of a Non-Singular Square Matrix 2
1.3 Elementary Transformations of a Matrix 16
1.4 Applications of Matrices: Solving System of
Linear Equations 27
1.5 Applications of Matrices: Consistency of system of
linear equations by rank method 38
2 Complex Numbers 52 Jul
2.1 Introduction to Complex Numbers 52
2.2 Complex Numbers 54
2.3 Basic Algebraic Properties of Complex Numbers 58
2.4 Conjugate of a Complex Number 60
2.5 Modulus of a Complex Number 66
2.6 Geometry and Locus of Complex Numbers 73
2.7 Polar and Euler form of a Complex Number 75
2.8 de Moivre’s Theorem and its Applications 83
3 Theory of Equations 97 Jul
3.1 Introduction 97
3.2 Basics of Polynomial Equations 99
3.3 Vieta’s Formulae and Formation of Polynomial Equations 100
3.4 Nature of Roots and Nature of Coefficients of
Polynomial Equations 107
3.5 Applications of Polynomial Equation in Geometry 111
3.6 Roots of Higher Degree Polynomial Equations 112
3.7 Polynomials with Additional Information 113
3.8 Polynomial Equations with no additional information 118
3.9 Descartes Rule 124
4 Inverse Trigonometric Functions 129 Jul/Aug
4.1 Introduction 129
4.2 Some Fundamental Concepts 130
4.3 Sine Function and Inverse Sine Function 133
IV
