1. Real Numbers
- Introduction
- The Fundamental Theorem of Arithmetic
- Revisiting Irrational Numbers
- Summary
- EXERCISE 1.1 - Solutions
- EXERCISE 1.2 - Solutions
- Practice Questions with Solutions
2. Polynomials
- Introduction
- Terms used in Algebraic expression
- Some Key components of an algebraic expression
- BODMAS /PEMDAS Rules
- Linear polynomial
- Quadratic Polynomial
- Cubic Polynomial
- Geometrical Meaning of the Zeroes of a Polynomial
- Zeros of a Polynomial
- The value of a polynomial
- Equations representation on a Graph
- Geometrical Representation of a Linear Polynomial
- Geometrical Representation of a Quadratic Polynomial
- Find the vertex
- Three possible zeroes
- Relationship between Zeroes and Coefficientsof a Polynomial
- Relationship between Zeroes and Coefficients of a Linear Polynomial
- The sum of the reciprocals of the zeros
- Relationship between Zeroes and Coefficients of a Quadratic Polynomial
- By using Viète's Formulas
- By using the Quadratic Formula
- Discriminant
- Difference between both methods
- Relationship between Zeroes and Coefficients of a Cubic Polynomial
- The sum of the reciprocals of the zeros
- Summary
- Exercise 2.1
- Exercise 2.2
- Practice Questions with Solutions
3. Pair of Linear Equations in Two Variables
- Graphical Method of Solution of a Pair of LinearEquations
- Exercise 3.1
- Algebraic Methods of Solving a Pair of LinearEquations
- Substitution Method
- Exercise 3.2
- Elimination Method
- Exercise 3.3
- Summary
- Practice Questions with Solutions
4. Quadratic Equations
- Introduction
- Quadratic Formula
- Solution of a Quadratic Equation by Factorisation
- Nature of Roots
- Examples
- Exercise 4.1
- Exercise 4.2
- Exercise 4.3
- Summary
- Practice Questions with Solutions
5. Arithmetic Progressions
- Introduction
- Rationalised 2023-24
- Arithmetic Progressions
- nth Term of an AP
- Sum of First n Terms of an AP
- Summary
- Exercise 5.1
- Exercise 5.2
- Exercise 5.3
- Exercise 5.4 * Optional
- Practice Questions with Solutions
6. Triangles
- Introduction
- Similar Figures
- Similarity of Triangles
- Criteria for Similarity of Triangles
- Summary
- Exercise 6.1
- Exercise 6.2
- Exercise 6.3
- Practice Questions with Solutions
7. Coordinate Geometry
- Introduction
- Distance Formula
- Section Formula
- Summary
- Exercise 7.1
- Exercise 7.2
- Practice Questions with Solutions
8. Introduction to Trigonometry
- Introduction
- Trigonometric Ratios
- Trigonometric Ratios of Some Specific Angles
- Trigonometric Identities
- Summary
- Examples
- Exercise 8.1
- Exercise 8.2
- Exercise 8.3
- Practice Questions with Solutions
9. Some Applications of Trigonometry
- Heights and Distances
- Summary
- Exercise 9.1
- Practice Questions with Solutions
- Introduction
- Tangent to a Circle
- Number of Tangents from a Point on a Circle
- Summary
- Practice Questions with Solutions
11. Areas Related to Circles
- Areas of Sector and Segmentk of a Circle
- Summary
- Rationalised 2023-24
- Exercise 11.1
- Practice Questions with Solutions
12. Surface Areas and Volumes
- Introduction
- Surface Area of a Combination of Solids
- Volume of a Combination of Solids
- Summary
- Examples
- Exercise 12.1
- Exercise 12.2
- Practice Questions with Solutions
13. Statistics
- Introduction
- Mean of Grouped Data
- Mode of Grouped Data
- Median of Grouped Data
- Summary
- Practice Questions with Solutions
14. Probability
- Probability — A Theoretical Approach
- Summary
- Practice Questions with Solutions
Appendix A1: Proofs in Mathematics
- Introduction
- Mathematical Statements Revisited
- Deductive Reasoning
- Conjectures, Theorems, Proofs and Mathematical Reasoning
- Negation of a Statement
- Converse of a Statement
- Proof by Contradiction
- Summary
- Practice Questions with Solutions
Appendix A2: Mathematical Modelling
- Introduction
- Stages in Mathematical Modelling
- Some Illustrations
- Why is Mathematical Modelling Important?
- Summary