10 - Mensuration

10.1. Introduction

10.2. Surface Area of the Combination of Solids

10.3. Volume of the Combination of Solids

10.4. Conversion of Solid from one shape to another

10.4.1.Cuboid

10.4.2.Cube

10.4.3.Right Prism

1. Real Numbers

1.1. Introduction

1.2. Exploring Real Numbers

1.2.1. The Fundamental Theorem of Arithmetic

1.2.2. Rational Numbers and their Decimal Expansions

1.2.3. Non-terminating, Recurring Rational Numbers

1.3. More about Irrational Numbers

1.4.Properties of Real Numbers

1.5. Understanding Logarithms

1.5.1. Exponential Forms

1.5.2. Writing Exponents as Logarithms

1.5.3. Laws of Logarithms

1.5.3.a. The First Law of Logarithms

1.5.3.b. The Second Law of Logarithms

1.5.3.c. The Third Law of Logarithms

1.5.4. Standard Bases of a Logarithm

1.5.5. Application of Logarithms

1.5.5. Application of Logarithms

2 - Sets

2.1. Introduction

2.2. Well Defined Sets

2.3. Naming of Sets and Elements of a Set

2.4. Types of Sets

2.5. Using Diagrams to Represent Sets

2.6. Universal Set and Subsets

2.6.1. Equal Sets

2.7. Venn Diagrams

2.8. Basic Operations on Sets

2.8.1. Union of Sets

2.8.2. Intersection of Sets

2.8.3. Disjoint Set

2.8.4. Difference of Sets

2.8.5.Roaster Form

2.8.6.Builder Form

2.8.7.Empty Set

2.8.8.Finite Set

2.8.9.Finite & Infinite Sets

2.8.10.Cardinal Numbers

2.8.6.Builder Form

3 - Polynomials

3.1. Introduction

3.2. What are Polynomials?

3.2.1. Degree of a Polynomial

3.2.2. Value of a Polynomial

3.2.3. Zeros of a Polynomial

3.3. Working With Polynomials

3.4. Geometrical Meaning of the Zeroes of a Polynomial

3.4.1. Graphical Representation of a Linear Polynomial

3.4.2. Graphical Representation of a Quadratic Polynomial

3.4.3. Geometrical Meaning of Zeroes of a Cubic Polynomial

3.5. Relationship between Zeroes and Coefficients of a Polynomial

3.6. Cubic Polynomials

3.6. Cubic Polynomials

3.7. Division Algorithm for Polynomials

4 - Pair of Linear Equations in Two Variables

4.1. Introduction

4.1.1. How do we find Unknown Quantities?

4.1.2. Using Both Equations toget

4.2. Solutions of Pairs of Linear Equations in Two Variables

4.2.1. Graphical Method of finding Solution of a Pair of Linear Equations

4.2.2. Relation between Coefficients and Nature of System of Equations

4.2.2. Relation between Coefficients and Nature of System of Equations

4.3. Algebraic Methods of finding the Solutions for a Pair of Linear Equations

4.3.1. Substitution Method

4.3.2. Elimination Method

4.4. Equations Reducible to a Pair of Linear Equations in Two Variables

5 - Quadratic Equations

5.1. Introduction

5.2. Quadratic Equations

5.3. Solution of a Quadratic Equation by Factorization

5.4. Solution of a Quadratic Equation by Completing a Square

5.5. Nature of Roots

6 - Progressions

6.1. Introduction

6.2. Arithmetic Progressions

6.2.1. What is an Arithmetic Progression?

6.2.2. Parameters of an Arithmetic Progression

6.3. nth term of Arithmetic Progression

6.4. Sum of first n terms of an Arithmetic Progression

6.4.1. What Gauss Did?

6.4.2. Sum of n terms of an AP.

6.5. Geometric Progressions

6.6. nth term of a GP

6.6. nth term of a GP

7 - Coordinate Geometry

7.1. Introduction

7.2. Distance between Two Points

7.3. Distance between Two Points on a Line Parallel to Coordinate Axis

7.4. Distance between Any Two Points (on a Line) in a Plane

7.5. Section Formula

7.6. Centroid of a Triangle

7.7. Trisectional Points of a Line

7.8. Area of the Triangle

7.8.1. Collinearity

7.8.2. Area of a Triangle – 'Heron's Formula'

7.9. Straight Lines

7.9.1. Slope between Two Points on a Line

8 - Similar Triangles

8.1. Introduction

8.2. Similar Figures

8.3. Similarity of Triangles

8.3.1. Basic Proportionality Theorem (Thales Theorem)

8.4. Criteria for Similarity of Triangles

8.4.1. AAA Criterion for Similarity of Triangles

8.4.2. SSS Criterion for Similarity of Triangles

8.4.3. SAS Criterion for Similarity of Triangles

8.5. Areas of Similarity of Triangles

8.6. Pythagoras Theorem

8.6.1. Baudhayan Theorem (Pythagoras Theorem)

8.6.2.Negation of Statement

8.6.3.Converse of a Statement

8.6.4.Proof by Contradiction

9 - Tangents & Secants to a Circle

9.1. Introduction

9.1.1. A line and A Circle

9.2. Tangents of a Circle

9.2.1. Construction of Tangent to a Circle

9.2.2. Finding Length of the Tangent

9.3. Number of Tangent on a Circle from Any Point

9.3.1. Construction of Tangents to a Circle

9.4. Segment of a Circle formed by a Secant

9.4.1. Finding the Area of Segment of a Circle

11 - Trigonometry

11.1. Introduction

11.1.1. Naming the Sides in a Right Triangle

11.2. Trigonometric Ratios

11.2.1. Defining Trigonometric Ratios

11.3. Trigonometric Ratios of Some Specific Angles

11.3.1. Trigonometric Ratios of 45 degrees

11.3.2. Trigonometric Ratios of 30 and 60 degrees

11.3.3. Trigonometric Ratios of Zero and 90 degrees

11.4. Trigonometric Ratios of Complimentary Angles

11.5. Trigonometric Identities

12 - Applications of Trigonometric

12.1. Introduction

12.2. Drawing Figures to Solve Problems

12.3. Solution for Two Right Angle Triangles

13 - Probability

13.1. Introduction

13.1.1. What is Probability?

13.2. Probability – A Theoretical Approach

13.3. Mutually Exclusive Events

13.4.1. Finding Probability

13.4.2. Events and Probability

13.4.3. Impossible and Certain Events

13.5. Deck of Cards and Probability

13.6. Use of Probability

13.7. Probability concepts and applications

14 - Statistics

14.1. Introduction

14.2. Mean of Ungrouped Data

14.3. Mode

14.4. Median of Grouped Data