# CBSE Grade 10 - MATHS

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• ##### Real Numbers
Euclid's Division Lemma
Euclid's Division Algorithm
Fundamental Theorem of Arithmetic - Prime FactorizationcHCF, LCM
Proofs of Irrationality
Decimal Representation of Rational Numbers- In terms of Terminating and Non-Terminating Recurring Decimals
• ##### Polynomials
Linear Polynomials
Zeros of a Polynomial- Geometric Meaning
Relationship between Zeros and Coefficients of Quadratic Polynomials
Division Algorithm for Polynomials with Real Coefficients
• ##### Pair of Linear Equations in Two Variables
Pair of Linear Equations in Two Variables
Graphical Method of Solution of a Pair of Linear Equations - Consistent, Inconsistent
Algebraic Methods of Solving a Pair of Linear Equations in Two Variables - By Substitution, By Elimination and By Cross Multiplication Method
Equations Reducible to a Pair of Linear Equations in Two Variables
Standard Form of a Quadratic Equation
Solutions of Quadratic Equations having Real Roots- By Factorization, By Completing Square, By using Quadratic Formula
Nature of Roots
Relationship between Discriminant and Nature of Roots
• ##### Arithmetic Progressions
Introduction to Arithmetic Progression
Derivation of the nth term of an Arithmetic Progression
Sum of the First n terms of A.P
• ##### Triangles
Similar Figures
Similarity of Triangles
Theorem - A line drawn parallel to one side of a triangle intersects the other two sides in distinct points
Theorem-A line divides two sides of a triangle in the same ratio is parallel to the third side
Criteria for Similarity of Triangles- SAS Similarity, AA Similarity, AAA Similarity, SSS Similarity
Areas of Similar Triangles
Pythagoras Theorem
• ##### Coordinate Geometry
Concepts of Coordinate Geometry
Distance Formula
Section Formula (Internal Division)
Area of a Triangle
• ##### Introduction to Trigonometry
Trigonometric Ratios of an Acute Angle of a Right-Angled Triangle- Sin, Cos, Tan
Values of the Trigonometric Ratios - 0, 30, 45, 60, 90 degree
Relationships between the Ratios
Trigonometric Identities and Applications
Trigonometric Ratios of Complementary Angles
• ##### Some Applications of Trigonometry
Heights and Distances
Properties-Horizontal Line, The Line of Sight, Angles of Elevation and Angle of Depression
• ##### Circles
Tangent to a Circle at a Point
Theorem-The tangent at any point of a circle is perpendicular to the radius through the point of contact
Theorem-The lengths of tangents drawn from an external point to circle are equal
• ##### Constructions
Division of a Line Segment in a given Ratio (Internally)
Tangent to a Circle from a Point Outside it
Construction- Triangle similar to a given Triangle as per given Scale Factor
• ##### Areas Related to Circles
Area of Circle
Perimeter of Circle
Area of Sectors and Segments of a Circle-Area of Sector of Angle $\theta$, Length of an Arc of Sector $\theta$
Areas of Combinations of Plane Figures
• ##### Surface Areas and Volumes
Surface Areas and Volumes of Combinations of Solids -Cubes, Cuboids, Spheres, Hemispheres and Right Circular Cylinders, Cones
Frustum of a Cone
Problems - Converting One Type of Metallic Solid into Another
• ##### Statistics
Grouped Data-Mean, Median and Mode
Cumulative Frequency Graph
• ##### Probability
Classical Definition of Probability
Event of an Experiment-Sure Event, Impossible Event