Chapter 1. Real Numbers

 

1.1 Euclid’s Division Lemma

  • Euclid’s Division Lemma
  • Euclid’s Division Algorithm
  • Applications of Euclid’s Division Lemma

1.2 The Fundamental Theorem of Arithmetic

  • Fundamental Theorem of Arithmetic
  • Prime Factorisation
  • HCF and LCM using Prime Factorisation
  • Relationship between HCF and LCM

1.3 Revisiting Irrational Numbers

  • Irrational Numbers
  • Proof of Irrationality

1.4 Revisiting Rational Numbers and Their Decimal Expansions

  • Rational Numbers
  • Decimal Expansion of Rational Numbers
  • Terminating Decimal Expansion
  • Non-terminating Recurring Decimal Expansion

Chapter 2. Polynomials

 

2.1 Geometrical Meaning of the Zeroes of a Polynomial

  • Zeroes of a Polynomial
  • Geometrical Interpretation of Zeroes
  • Number of Zeroes of a Polynomial

2.2 Relationship between Zeroes and Coefficients of a Polynomial

  • Zeroes and Coefficients of a Quadratic Polynomial
  • Sum of Zeroes
  • Product of Zeroes
  • Finding Zeroes using the Relationship

2.3 Division Algorithm for Polynomials

  • Division Algorithm
  • Division of Polynomials
  • Verification of the Division Algorithm

Chapter 3. Pair of Linear Equations in Two Variables

 

3.1 Pair of Linear Equations in Two Variables

  • Linear Equations in Two Variables
  • Graphical Representation
  • Solution of a Pair of Linear Equations

3.2 Graphical Method of Solution of a Pair of Linear Equations

  • Graphical Method
  • Intersecting Lines
  • Parallel Lines
  • Coincident Lines
  • Consistency of a Pair of Linear Equations

3.3 Algebraic Methods of Solving a Pair of Linear Equations

  • Substitution Method
  • Elimination Method
  • Cross-Multiplication Method
  • Comparison Method
  • Applications and Word Problems

3.4 Equations Reducible to a Pair of Linear Equations in Two Variables

  • Equations Reducible to Linear Equations
  • Solving Reducible Equations
  • Word Problems

Chapter 4. Quadratic Equations

 

4.1 Quadratic Equations

  • Introduction to Quadratic Equations
  • Standard Form of a Quadratic Equation
  • Roots of a Quadratic Equation

4.2 Solution of a Quadratic Equation by Factorisation

  • Factorisation Method
  • Finding Roots by Factorisation

4.3 Solution of a Quadratic Equation by Completing the Square

  • Completing the Square
  • Solving Quadratic Equations by Completing the Square

4.4 Nature of Roots

  • Discriminant
  • Nature of Roots
  • Real and Distinct Roots
  • Real and Equal Roots
  • No Real Roots

Chapter 5. Arithmetic Progressions

 

5.1 Introduction

  • Sequences
  • Arithmetic Progression
  • Common Difference

5.2 Arithmetic Progressions

  • Terms of an AP
  • Identification of an AP
  • Finding the Common Difference

5.3 nth Term of an AP

  • nth Term
  • Finding a Particular Term
  • Finding the Number of Terms

5.4 Sum of the First n Terms of an AP

  • Sum of Terms
  • Finding the Sum of an AP
  • Applications of Arithmetic Progressions

Chapter 6. Triangles

 

6.1 Similar Figures

  • Similar Figures
  • Similarity and Congruence
  • Properties of Similar Figures

6.2 Similarity of Triangles

  • Similar Triangles
  • Basic Proportionality Theorem
  • Converse of Basic Proportionality Theorem

6.3 Criteria for Similarity of Triangles

  • AA Similarity Criterion
  • SSS Similarity Criterion
  • SAS Similarity Criterion

6.4 Areas of Similar Triangles

  • Ratio of Areas of Similar Triangles
  • Relationship between Areas and Corresponding Sides

6.5 Pythagoras Theorem

  • Pythagoras Theorem
  • Converse of Pythagoras Theorem
  • Applications of Pythagoras Theorem

Chapter 7. Coordinate Geometry

 

7.1 Introduction

  • Coordinate Plane
  • Coordinates of a Point
  • Distance between Points

7.2 Distance Formula

  • Distance Formula
  • Distance between Two Points
  • Applications of Distance Formula

7.3 Section Formula

  • Section Formula
  • Internal Division
  • Coordinates of a Point Dividing a Line Segment

7.4 Area of a Triangle

  • Area of a Triangle using Coordinates
  • Collinearity of Points
  • Applications of Coordinate Geometry

Chapter 8. Introduction to Trigonometry

 

8.1 Trigonometric Ratios

  • Trigonometric Ratios
  • Sine
  • Cosine
  • Tangent
  • Cosecant
  • Secant
  • Cotangent

8.2 Trigonometric Ratios of Some Specific Angles

  • Trigonometric Ratios of 0°
  • Trigonometric Ratios of 30°
  • Trigonometric Ratios of 45°
  • Trigonometric Ratios of 60°
  • Trigonometric Ratios of 90°

8.3 Trigonometric Ratios of Complementary Angles

  • Complementary Angles
  • Trigonometric Ratios of Complementary Angles

8.4 Trigonometric Identities

  • Trigonometric Identities
  • Fundamental Trigonometric Identity
  • Simplification using Trigonometric Identities
  • Verification of Trigonometric Identities

Chapter 9. Some Applications of Trigonometry

 

9.1 Heights and Distances

  • Line of Sight
  • Angle of Elevation
  • Angle of Depression
  • Heights and Distances

9.2 Angle of Elevation

  • Finding Heights
  • Finding Distances
  • Applications of Angle of Elevation

9.3 Angle of Depression

  • Finding Heights
  • Finding Distances
  • Applications of Angle of Depression

Chapter 10. Circles

 

10.1 Tangent to a Circle

  • Tangent to a Circle
  • Tangent and Radius
  • Theorem Related to Tangents

10.2 Number of Tangents from a Point on a Circle

  • Tangent at a Point on the Circle
  • Number of Tangents

10.3 Number of Tangents from a Point Outside a Circle

  • Tangents from an External Point
  • Two Tangents from an External Point

10.4 Properties of Tangents to a Circle

  • Equal Tangents
  • Length of Tangents
  • Tangent-related Problems

Chapter 11. Areas Related to Circles

 

11.1 Areas of Sectors and Segments of a Circle

  • Sector of a Circle
  • Segment of a Circle
  • Area of a Sector
  • Area of a Segment

11.2 Area of a Sector of a Circle

  • Area of a Sector
  • Major Sector
  • Minor Sector
  • Applications

11.3 Area of a Segment of a Circle

  • Minor Segment
  • Major Segment
  • Area of a Segment
  • Areas of Combined Figures

Chapter 12. Surface Areas and Volumes

 

12.1 Surface Area of a Combination of Solids

  • Combination of Solids
  • Surface Area of Combined Solids
  • Cylinder and Hemisphere
  • Cone and Hemisphere
  • Other Combinations of Solids

12.2 Volume of a Combination of Solids

  • Volume of Combined Solids
  • Cylinder and Hemisphere
  • Cone and Hemisphere
  • Applications

12.3 Conversion of Solid from One Shape to Another

  • Conversion of Solids
  • Volume Conservation
  • Recasting of Solids
  • Applications

Chapter 13. Statistics

 

13.1 Mean of Grouped Data

  • Mean of Grouped Data
  • Direct Method
  • Assumed Mean Method
  • Step-Deviation Method

13.2 Mode of Grouped Data

  • Mode
  • Modal Class
  • Mode Formula
  • Finding Mode from Grouped Data

13.3 Median of Grouped Data

  • Median
  • Median Class
  • Cumulative Frequency
  • Median Formula

13.4 Empirical Relationship between Mean, Median and Mode

  • Empirical Relationship
  • Relationship between Mean, Median and Mode
  • Finding One Measure from the Other Two

Chapter 14. Probability

 

14.1 Introduction to Probability

  • Random Experiments
  • Outcomes
  • Events
  • Probability of an Event

14.2 Probability – A Theoretical Approach

  • Equally Likely Outcomes
  • Probability Formula
  • Probability of an Event
  • Probability of the Complement of an Event
  • Impossible Event
  • Certain Event
  • Applications of Probability