 ## Class 10 Mathematics Maharashtra Board

Maharashtra Board Mathematics Syllabus

# 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.
• 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
• 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
• 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.  Study Materials for Class 10   