The First Steps IIT JEE Mathematics (Paperback) by Amit M Agarwal

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Book Summary of The First Steps IIT JEE Mathematics

Key Features

• Concepts, Terms, & Formulas are provided to understand the chapter well.
• In the end of the chapter “Proficiency in Concept” subjective and objective problems are given with full detailed solutions to help the students.
• 3 different leveled exercises are provided in the end of the chapter.
• Level 1 & 2 are of objective nature and level 3 consist subjective type questions.
• Chapter-wise hints & solutions are provided in the end of chapter.
• Workouts (20 Mock Papers) are given at the end of the book with their answers.

Table Of Contents 
Introduction: First Step IIT JEE Mathematics
1. Plane Geometry

• Similar Triangle
• Definitions and Important Results
• Some More Theorem Statements on Triangle
• Circle
• Terms Related to Circle
• Properties of Circle
• Properties Related to Tangent to a Circle
• Area, Volume and Surface Area
• Concept Building Illustrations
• Proficiency in Concepts (PIC) Problems with Multi-leveled Exercise

2. Cartesian Coordinate System and Straight Line

• Comprehension of Concepts
• Straight Line
• Concept Building Illustrations
• Proficiency in Concepts (PIC) Problems with Multi-leveled Exercise

3. Trigonometry

• Definition
• Measurement of Angles
• Trigonometrical Ratios
• Signs Conventions for Quadrants
• Relation between Trigonometric Ratios
• Trigonometrical Functions of Angles of any Size and Sign
• Functions of Compound Angles
• A List of Trigonometric Formulae
• Concept Building Illustrations
• Proficiency in Concepts (PIC) Problems with Multi-leveled Exercise

4. Number Theory

• The Set of Real Numbers
• Real Numbers and Important Subsets
• Divisibility
• To Find Unit’s Digit of any Number
• Peano’s Postulates
• Some Basic Definitions
• Concept Building Illustrations
• Proficiency in Concepts (PIC) Problems with Multi-leveled Exercise

5. Theory of Equations, Inequations, Polynomials and Logarithms

• Polynomials
• Division Algorithm
• Remainder Theorem
• Factor Theorem
• Multinational Theorem
• Equation v/s Identity
• Relation between Roots and Coefficients
• Nature of Roots
• Symmetric Function of the Roots
• Transformation of an Equation
• Inequalities
• Cauchy-Schwarz Inequality
• The Method of Intervals (Wavy Curve Method)
• Logarithms
• Properties of Logarithms
• Concept Building Illustrations
• Proficiency in Concepts (PIC) Problems with Multi-leveled Exercise

6. Permutations and Combinations

• Factorial
• Exponent of Prime p in n!
• Relation between nCr and nPr
• Fundamental Principle of Counting
• Permutations (Arrangements of Objects)
• Circular Permutations
• Combinations
• Concept Building Illustrations
• Proficiency in Concepts (PIC) Problems with Multi-leveled Exercise

7. Sequences and Series

• Sequence
• Arithmetic Progression and Its General Term
• Sum of Some Powers of Natural Numbers
• Arithmetic Mean
• Geometric Progression and Its General Term
• Harmonic Progression
• Harmonic Means
• Relation Amongst AM, GM, HM
• Concept Building Illustrations
• Proficiency in Concepts (PIC) Problems with Multi-leveled Exercise

8. Functions

• Function
• Function as a Set of Ordered Pairs
• Domain, Codomain and Range of a Function
• Identity Function
• Equal Function
• Domain of Real Valued Function
• Number of Functions (or Mapping) from X to Y
• Representation and Testing for a Function
• Classification of Functions
• Explicit and Implicit Function
• Continuous and Discontinuous Function
• Increasing Function
• Decreasing Function
• Periodic Function
• Value of the Function
• Type of Function
• Composite of Functions
• Inverse Functions
• Concept Building Illustrations
• Proficiency in Concepts (PIC) Problems with Multi-leveled Exercise

9. Introductory Differentiation and Integral Calculu

• Graphs of Some Elementary Functions
• Trigonometric or Circular Functions
• The Inverse Circular (Trigonometric) Functions
• List of Derivatives of Important Functions
• Rule of Differentiation
• Different types of Differential Function
• Indefinite Integral
• Definition: Basic Concept
• Important Formulae
• Properties of Indefinite Integration
• Methods of Increasing Polynomial Division
• Concept Building Illustrations
• Proficiency in Concepts (PIC) Problems with Multi-leveled Exercise

Workouts

• (20 Mock Papers, Mathematics)

Details of Book: The First Steps IIT JEE Mathematics

Book:	The First Steps IIT JEE Mathematics
Author:	Amit M Agarwal
ISBN:	9380068633
ISBN-13:	9789380068633 ,  978-9380068633
Binding:	Paperback
Publishing Date:	2012
Publisher:	Arihant
Edition:	2012
Number of Pages:	400
Language:	English