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# Class 10 Mathematics Maharashtra Board

### Part 1: Algebra

- Arithmetic Progression:
- Introduction to Sequence
- Arithmetic Progression (A.P.) and Geometric Progression (G.P.)
- General term of an A.P. and G.P.
- Sum of the first 'n' terms of an A.P. and G.P.
- Arithmetic Mean and Geometric Mean.

- Quadratic Equations
- Introduction to quadratic equations
- Solutions of quadratic equations
- Nature of roots based on discriminate
- Relation between roots of the equation and coefficient of the terms in the equation Equations reducible to quadratic form

- Linear equations in two variables
- System of linear equations in two variables
- Algebraic methods of solving linear equations in two variables
- Graphical representation of different possibilities of solutions/Inconsistency
- Graphical method of solving a system of linear equations
- Determinant of order two
- Cramer's rule
- Consistency of pair of linear equations

- Probability:
- Introduction to probability and related terms
- Classical definition of probability
- Types of events
- Equally likely outcomes
- Probability of an event
- Properties of Probability
- Addition theorem (without proof)

- Statistics:
- Brief revision of Tabulation of data, inclusive and exclusive type of tables
- Mean, median and mode of grouped data
- Histograms, frequency polygon, frequency curve, pie diagram
- Ogives (Cumulative frequency graphs)
- Applications of ogives in determination of median
- Relation between measures of central tendency
- Introduction to normal distribution
- Properties of normal distribution

### Part 2: Geometry

- Similarity:
- Properties of ratios of areas of two triangles
- Basic proportionality theorem
- Introduction to similarity
- Similar triangles
- Areas of two similar triangles
- Similarity in right angled triangles
- Pythagoras theorem and its converse
- 30o-60o-90o theorem and 45 o-45 o-90 o theorem
- Application of Pythagoras theorem in acute and obtuse angle.

- Circle:
- Tangents and its properties
- Theorem - Tangent at any point to the circle is perpendicular to the radius and its converse
- Number of tangents from a point to a circle
- Theorem- The length of two tangent segments drawn from a point outside the circle are equal
- Touching circles
- Introduction to an arc
- Angle subtended by the arc to the centre and to the point on the circle
- Cyclic quadrilateral
- Tangent - Secant theorem

- Co-ordinate Geometry:
- Slope of a line
- Intercepts made by a line
- Standard forms of equation of a line
- General equation of a line.

- Geometric Constructions:
- Division of line segment in a given ratio
- Basic geometric constructions
- Construction of tangent to the circle from the point on the circle and out side the circle.
- Construction of tangent without using centre
- Construction of triangle If the base, angle apposite to it and either median altitude is given
- Construction of a triangle similar to a given triangle

- Trigonometry:
- Angles in standard position.
- Trigonometric ratios in terms of coordinates of point
- Trigonometric Identities (with proof)
- Use of basic identities and their applications
- Problems on height and distance

- Menstruation:
- Length of an arc
- Area of the sector
- Area of a Circular Segment
- Euler's formula
- Surface area and volume of cuboids Spheres, hemispheres, right circular cylinders cones, frustum of a cone.
- Problems based on areas and perimeter/circumference of circle, sector and segment of a circle.
- Problems on finding surface areas and volumes of combinations of any two of the following : cuboids, spheres, hemispheres and right circular cylinders/ cones
- Problems involving converting one type of metallic solid into another.