Grade 10

1. Real Numbers

  • 1.1 Introduction
  • 1.2 Euclid’s Division Lemma
  • 1.3 The Fundamental Theorem of Arithmetic
  • 1.4 Revisiting Irrational Numbers
  • 1.5 Revisiting Rational Numbers and Their Decimal Expansions
  • 1.6 Summary

2. Polynomials

  • 2.1 Introduction
  • 2.2 Geometrical Meaning of the Zeroes of a Polynomial
  • 2.3 Relationship between Zeroes and Coefficients of a Polynomial
  • 2.4 Division Algorithm for Polynomials
  • 2.5 Summary

3. Pair of Linear Equations in Two Variables

  • 3.1 Introduction
  • 3.2 Pair of Linear Equations in Two Variables
  • 3.3 Graphical Method of Solution of a Pair of Linear Equations
  • 3.4 Algebraic Methods of Solving a Pair of Linear Equations
    • 3.4.1 Substitution Method
    • 3.4.2 Elimination Method
    • 3.4.3 Cross-Multiplication Method
  • 3.5 Equations Reducible to a Pair of Linear Equations in Two Variables
  • 3.6 Summary

4. Quadratic Equations

  • 4.1 Introduction
  • 4.2 Quadratic Equations
  • 4.3 Solution of a Quadratic Equation by Factorisation
  • 4.4 Solution of a Quadratic Equation by Completing the Square
  • 4.5 Nature of Roots
  • 4.6 Summary

5. Arithmetic Progressions

  • 5.1 Introduction
  • 5.2 Arithmetic Progressions
  • 5.3 nth Term of an AP
  • 5.4 Sum of First n Terms of an AP
  • 5.5 Summary

6. Triangles

  • 6.1 Introduction
  • 6.2 Similar Figures
  • 6.3 Similarity of Triangles
  • 6.4 Criteria for Similarity of Triangles
  • 6.5 Areas of Similar Triangles
  • 6.6 Pythagoras Theorem
  • 6.7 Summary

7. Coordinate Geometry

  • 7.1 Introduction
  • 7.2 Distance Formula
  • 7.3 Section Formula
  • 7.4 Area of a Triangle
  • 7.5 Summary

8. Introduction to Trigonometry

  • 8.1 Introduction
  • 8.2 Trigonometric Ratios
  • 8.3 Trigonometric Ratios of Some Specific Angles
  • 8.4 Trigonometric Ratios of Complementary Angles
  • 8.5 Trigonometric Identities
  • 8.6 Summary

9. Some Applications of Trigonometry

  • 9.1 Introduction
  • 9.2 Heights and Distances
  • 9.3 Summary

10. Circles

  • 10.1 Introduction
  • 10.2 Tangent to a Circle
  • 10.3 Number of Tangents from a Point on a Circle
  • 10.4 Summary

11. Constructions

  • 11.1 Introduction
  • 11.2 Division of a Line Segment
  • 11.3 Construction of Tangents to a Circle
  • 11.4 Summary

12. Areas Related to Circles

  • 12.1 Introduction
  • 12.2 Perimeter and Area of a Circle — A Review
  • 12.3 Areas of Sector and Segment of a Circle
  • 12.4 Areas of Combinations of Plane Figures
  • 12.5 Summary

13. Surface Areas and Volumes

  • 13.1 Introduction
  • 13.2 Surface Area of a Combination of Solids
  • 13.3 Volume of a Combination of Solids
  • 13.4 Conversion of Solid from One Shape to Another
  • 13.5 Frustum of a Cone
  • 13.6 Summary

14. Statistics

  • 14.1 Introduction
  • 14.2 Mean of Grouped Data
  • 14.3 Mode of Grouped Data
  • 14.4 Median of Grouped Data
  • 14.5 Graphical Representation of Cumulative Frequency Distribution
  • 14.6 Summary

15. Probability

  • 15.1 Introduction
  • 15.2 Probability — A Theoretical Approach
  • 15.3 Summary

Appendix A1. Proofs in Mathematics

  • A1.1 Introduction
  • A1.2 Mathematical Statements Revisited
  • A1.3 Deductive Reasoning
  • A1.4 Conjectures, Theorems, Proofs and Mathematical Reasoning
  • A1.5 Negation of a Statement
  • A1.6 Converse of a Statement
  • A1.7 Proof by Contradiction
  • A1.8 Summary

Appendix A2. Mathematical Modelling

  • A2.1 Introduction
  • A2.2 Stages in Mathematical Modelling
  • A2.3 Some Illustrations
  • A2.4 Why is Mathematical Modelling Important?
  • A2.5 Summary
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