# Mathematics - Textbook for Class X

Product ID: 24909

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Author: Shveta Uppal
Foreword/Introduction: Director,National Council of Educational Research
Publisher: NCERT
Year: 2006
Language: English
Pages: 364
ISBN/UPC (if available): 8174506349

Description

From Foreword:

Based on the understanding developed over the years, a National Curriculum Framework (NCF) was finalized in 2005. As part of this exercise, a National Focus Group on Teaching of Mathematics was formed. Its report, which came in 2005. As part of this exercise, a National Focus Group on Teaching of Mathematics was formed. Its report, which came in 2005, highlighted a constructivist approach to the teaching and learning of mathematics.

The essence of this approach is that children already know, and do some mathematics very naturally in their surrounding, before they even join school. The syllabus, teaching approach, textbooks etc, should build on this knowledge in a way that allows children to enjoy mathematics, and to realize that mathematics is more about a way of reasoning than about mechanically applying formulae and algorithms.

The book has particularly been created with the view to giving children space to explore mathematics and develop the abilities to reason mathematically. Further, two special appendices have been given - Proofs in Mathematics, and Mathematical Modeling. These are placed in the book for interested students to study, and are only optional reading at present. These topics may be considered for inclusion in the main syllabi in due course of time.

Contents

Foreword
Preface

1. REAL NUMBERS
Introduction
Euclid’s Division Lemma
The Fundamental Theorem of Arithmetic
Revisiting Irrational Numbers
Revisiting Rational Numbers and Their Decimal Expansions
Summary

2. POLYNOMIALS
Introduction
Geometrical Meaning of the Zeroes of a Polynomial
Relationship between Zeroes and Coefficients of a Polynomial
Division Alogorithm for Polynomials
Summary

3. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Introduction
Pair of Linear Equations in Two Variables
Graphical Method of Solution of a Pair of Linear Equations
Algebraic Methods of Solving a Pair of Linear Equations
Substitution Method
Elimination Method
Cross-Multiplication Method
Equations Reducible to a Pair of Linear Equations in Two Variables
Summary

Introduction
Solution of Quadratic Equation by Factorisation
Solution of a Quadratic Equation by Completing the Square
Nature of Roots
Summary

5. ARITHMETIC PROGRESSIONS
Introduction
Arithmetic Progressions
Nth Term of an AP
Sum of First n Terms of an AP
Summary

6. TRIANGLES
Introduction
Similar Figures
Similarity of Triangles
Criteria for Similarity of Triangles
Areas of Similar Triangles
Pythagoras Theorem
Summary

7. COORDINATE GEOMETRY
Introduction
Distance Formula
Section Formula
Area of a Triangle
Summary

8. INTRODUCTION TO TRIGONOMETRY
Introduction
Trigonometric Ratios
Trigonometric Ratios of Some Specific Angles
Trigonometric Ratios of Complementary Angles
Trigonometric Identities
Summary

9. SOME APPLICATIONS OF TRIGONOMETRY
Introduction
Heights and Distances
Summary

10. CIRCLES
Introduction
Tangent to a Circle
Number of Tangents from a Point on a Circle
Summary

11. CONSTRUCTIONS
Introduction
Division of a Line Segment
Construction of Tangents to a Circle
Summary

12. AREAS RELATED TO CIRCLES
Introduction
Perimeter and Area of a Circle – A Review
Areas of Sector and Segment of a Circle
Areas of Combinations of Plane Figures
Summary

13. SURFACE AREAS AND VOLUMES
Introduction
Surface Area of a Combination of Solids
Volume of a Combination of Solids
Conversion of Solid from One Shape to Another
Frustum of a Cone
Summary

14. STATISTICS
Introduction
Mean of Grouped Data
Mode of Grouped Data
Median of Grouped Data
Graphical Representation of Cumulative Frequency Distribution
Summary

15. PROBABILITY
Introduction
Probability – A Theoretical Approach
Summary

APPENDIX AI: PROOFS IN MATHEMATICS
Introduction
Mathematical Statements Revisited
Deductive Reasoning
Conjectures, Theorems, Proofs and Mathematical Reasoning
Negation of a Statement
Converse of a Statement