1. Introduction to Bharatiya Ganit Shastra
- Ancient Bharatiya mathematicians and their contribution to modern world
- Number Formation in Decimal
- Fundamentals of Number Theory in Decimal system
- Properties of natural numbers from 1 to 100
2. Definition of Bharatiya Ganit Shastra Terminology
- Concepts of Complements with respect to the sum as 10, 100, 9 & 90
- Sum of Complements
- Vinculum using standard not more than 5 rule
- Beejank (Digital Root) using casting out 9s
- Use of Beejank for checking addition, subtraction, multiplication, division etc.
3. Addition
- General method_Carry over method
- Dot method
4. Subtraction
- General method_Borrowing method
- Using Complements
- Using Vinculum
5. Multiplication
- Multiplication using standard base (10, 100, 1000, …….)
- Multiplication using subsidiary bases (20, 30, …….)
- Multiplication by 11, 111, 101 etc.
- Vertical & crosswise rule starting from 1 x 1, 2 x 2, 3 x 3 multiplication
- Vertical & crosswise rule starting from 3 x 2, 4 x 4 multiplication
- Multiplication 1 x 1 to 20 x 20 patterns
6. Magic Square 3 x 3, 5 x 5, 7 x 7
7. Properties of Divisors
- Division & Divisibility Rules
- Osculator and Osculation
8. Division
- Division using horiontal method
- Division by 2 & 3 flag digits
- Division using Vinculum Divisibility by numbers from 1 to 20
9. Squares & Cubes
- Squares using base method & Duplex method Cubes using triplex
- Squares using duplex method (Perect suare numbers ONLY)
- Cubes using triplex method (Perect cube numbers ONLY)
10. Square Roots & Cube Roots
- Recapitulation of Elementary sessions & Assessment
11. Inverse/Reciprocals of primes and Recurring Decimals
12. Bauadhayan Numbers
- Right Angled Triangle Theory
- Addition & Subtraction of angles
13. Combinatorics
- Meru Prastaar : 5th order expansion, 3rd order application
14. LCM & its Applications
- Prime base pattern and aptitude based problems
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15. HCF & its Applications
- Prime base pattern and aptitude based problems
16. Proportionality
- Ratio & Proportion
- Variation
- Time & work
- Time, Speed & Distance
17. Geometry
- Straight Lines
- Triangles
- Quadrilaterals
- Polygons
- Circle
18. Trigonometry
- Angular Measure
- Unit Circle & Trigonometrical Functions
- Application of Baudhaayan Triplets
- Ratios of Angles, Sum & Difference of Angles
- Trigonometric Equations
- Heights & Distances
19. Algebra
- Linear Equations Linear equations in one Variable
- Linear Equations Linear equations in two Variables
- Linear Equations Linear equations in three Variables
- Quadratic equations in single variable
- Determinants
- Matrices
- Sequences & Series
- Binomial Theorem
20. Coordinate Geometry
- Points, Images of points & Ratios
- Straight Lines
21. Graph Theory : Linear & quadratic functions
23. Probability : Fundamentals of probability
25. Calculus : Differention & Integration
