# 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

- Quadrilateral:
- Properties of quadrilateral
- Properties of parallelogram
- Properties of rectangle
- Properties of a trapezium
- Properties of a rhombus
- Properties of a square
- Kite
- Tests for particular quadrilateral
- 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
- Area of quadrilaterals
- 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