**ISBN:**9789350944011**Authors:**Agarwal A M

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**Author:** Agarwal A M

**Language:** English

**Length (Pages):**

**Publisher: **Arihant Publications(I) Pvt.Ltd - Meerut

**Publication Year** 2013

**Edition:**

**Exam:**

**ISBN:** 9789350944011

Table of Contents

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 Units Digit of any Number

Peanos 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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