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.
  • 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.


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