The First Step to IIT JEE Mathematics

Rs265

Publisher

Arihant Publication

Publication Year 2013
ISBN-13

ISBN 9789350944011

ISBN-10 9350944014
Binding

Paperback

Number of Pages 400 Pages
Language (English)
Subject

Engineering: general

Salient 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.

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

• 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 Calculus

• 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)

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