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The following is the list of topics covered under Grade 10. However it can be customized according to each student’s requirements.
Number Theory
- Sequences
- Series
- Modular Arithmetic
- Number Patterns
- Euclid’s Division Lemma
- The Fundamental Theorem of Arithmetic
- Irrational Numbers
- Rational Numbers and Their Decimal Expansions
Algebra/Linear Algebra
- Sets
- Relations and Functions
- Square root
- Linear equations with two variables
- Simultaneous Equations
- Polynomials
- Greatest common divisor and Least Common Multiple of polynomials
- Rational expressions
- Zeroes of a Polynomial
- Relationship between Zeroes and Coefficients of a Polynomial
- Division Algorithm for Polynomials
- System of Linear Equations in Two Variables
- Solving systems of Linear Equations graphically
- Solving systems of Linear Equations algebraically
- Substitution Method, Elimination Method, Cross-Multiplication Method
- Quadratic Equations
- Solution of a Quadratic Equation by Factorization
- Solution of a Quadratic Equation by Completing the Square
- Nature of Roots
- Arithmetic progression
Geometry and Measurement
- Locus
- Circles
- Angles in a Circle
- Tangents to a circle
- Number of Tangents from a Point on a Circle
- Similar Figures
- Similarity of Triangles
- Areas of Similar Triangles
- Pythagoras Theorem
- Coordinate geometry
- Volumes and Surface Areas
- Cuboid and cube
- Right circular cylinder, Right circular cone, Sphere
- Surface areas and volumes of combinations of solids
- Frustum of a right circular cone
- Ratio Formula
- Area of a Triangle
- Straight Lines
- Some Properties of Straight Lines
- Distance Formula
- Section Formula
- Perimeter and Area of a Circle
- Areas of Combinations of Plane Figures
- Conversion of Solid from One Shape to Another
Trigonometry
- Degree/radian measures
- Trigonometric ratios
- Trigonometric Ratios of Some Specific Angles
- Trigonometric Ratios of Complementary Angles
- Trigonometric Identities
- Special right triangles
- Use of Trigonometric Tables
- Heights and Distances
Probability and Statistics
- Probability
- Counting procedures
- Conditional probability
- Pictorial representation of data
- Mean, median, mode and range
- Dispersion
- Graphical Representation of Cumulative Frequency Distribution
- Permutations and combinations
Mathematical Models with Applications
- Stages in Mathematical Modeling
- Some Examples
- Importance of Mathematical Modeling
- Techniques to study patterns and analyze data
- Problems related to personal income and credit
- Problems related to financial planning
- Transformations, symmetry
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