 ## Class 9 Mathematics Maharashtra Board

Maharashtra Board Mathematics Syllabus

# Class 9 Mathematics Maharashtra Board

### Part 1: Algebra

• Sets:
• Introduction
• Methods of writing sets
• Types of sets
• Subset - Proper, Improper subset
• Super set
• Universal set
• Venn diagrams
• Operations on sets
• Relations between various operations
• Number of elements in the set and related results
• Real Numbers:
• Revision of natural numbers, integers, rational numbers and irrational numbers
• Existence of irrational numbers and their representations on the number line
• Every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number
• Properties of real numbers
• Definition of nth root of a real number
• Surds - Definition
• Forms of surds
• Operations and Laws of surds
• Rationalization of Surds
• Absolute value of real numbers
• Euclid's division Lemma
• Fundamental theorem of Arithmetic
• Algebraic Expressions:
• Introduction to algebraic expression
• Operations on algebraic expressions
• Methods of factorization of algebraic expression
• Introduction to polynomials
• Operations on polynomials
• Value of polynomials
• Zeros/roots of polynomial
• Relation between zeros and coefficient of polynomials
• Remainder theorem
• Factor theorem
• Graphs:
• Cartesian coordinate system
• Understanding of graphs of lines parallel to axes
• Graph of line ax + by + c = o
• Linear equations in two variables
• System of linear equations
• Solution of system of linear equations in two variables (Algebraic methods)
• Ratio, proportion and variation
• Introduction to ratio
• Properties of ratio
• Properties of equal ratios
• Theorem on equal ratios
• Percentage as a ratio
• Introduction to proportion
• Introduction to variation
• Revision of concepts based on Direct
• Variation, Inverse variation
• Mixed variation
• Real life problems based on ratio, proportion and variation
• Statistics:
• Collection of data
• Classification and tabulation of data
• Diagrammatic representation of data
• Graphical representation of data
• Mean, median, mode of ungrouped data

### Part 2: Geometry

• Lines and Angles:
• Introductions to line
• Basic terms and definitions related to line
• Introduction to Euclid's Geometry
• Plane separation axiom
• Introduction to angles in terms of rotation
• Directed angles, Sexagesimal system
• Types of angles
• Zero angle, straight angle, co terminal angle
• Relation between angles
• Introduction to mathematical proofs
• Parallel lines
• Results on parallel lines and transversal
• Tests of parallel lines
• Results on perpendicular lines
• Distance of a point from a line
• Triangles:
• Types of triangles
• Terms related to triangle
• Properties of triangle
• Exterior angles and corresponding interior opposite angles
• Results involving exterior angle and corresponding interior opposite angles
• Similar triangles
• Congruence of triangles:
• Criteria of congruent triangles
• Theorem of an isosceles triangle and its converse
• Perpendicular bisector theorem
• Angle bisector theorem
• Properties of triangles based on inequalities
• Property of perpendicular drawn from a point outside the line.
• Circle:
• Introduction to circle and related terms
• Circle passing through the given points
• One and only one circle passes through the three non collinear points.
• Congruence of circles
• Properties of chords of the circle
• Properties of parallelogram
• Properties of rectangle
• Properties of a trapezium
• Properties of a rhombus
• Properties of a square
• Kite
• Theorem on midpoints of two sides of a triangle and its converse
• Geometry
• Coordinate Geometry:
• Distance formula
• Section formula
• Area of a triangle
• Geometric constructions:
• Basic construction – perpendicular bisector of given segment.
• Construction of a triangle( Sum/difference of two sides and base angles is given Perimeter and base angles are given
• Trigonometry:
• Introduction to trigonometric ratios
• Trigonometric Ratios of angles 0o, 30 o, 45 o, 60 o, 90 o
• Trigonometric identities for complementary angles
• Mensuration:
• Area of triangle
• Area of regular hexagon, polygon
• If two parallelograms lie between two parallel lines and have the same base then they have the same area. If a triangle and a parallelogram have the same base and lie between the same parallel lines, then the area of the triangle is half the area of the parallelogram.
• Perimeter of triangle and quadrilateral
• Area of circle  Study Materials for Class 9   