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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

4. QUADRATIC EQUATIONS

Introduction

Quadratic Equations

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

Proof by Contradiction

Summary

APPENDIX A2: MATHEMATICAL MODELLING

Introduction

Stages in Mathematical Modelling

Some Illustrations

Why is Mathematical Modelling Important?

Summary

Answers/Hints