# Class 9 Mathematics Karnataka Board Syllabus

### 1. Arithmetic

- Square-root
- Finding the square root of a perfect square number of at most 5 digits using the division method.
- Finding the square root of a decimal number by division method.
- Finding the square root of a number which are not perfect squares like 2,3,5 up to 3 decimal places.
- Learning the process of moving nearer to the square-root.
- Verbal problems on square-roots.

- Real Numbers
- Basic properties of real number: closure, commutativity, associativity, distributivity, existence of additive identity, existence of additive inverse, existence of multiplicative identity, and existence of multiplicative inverse for non-zero real numbers.
- Order property (comparing one real number with another).
- Non-negativity of the square of a real number.
- Identify rational numbers as those with recurring decimal expansion and irrationals as those with non-recurring decimal expansion.

- Surds
- Definition
- Order and Radicund
- Index form
- Pure and mixed surds, and their mutual conversion
- Like and unlike surds
- Representing √2, √3, √5 on the number line (assuming Pythagoras’ theorem)
- Knowing the position of √(n-1) on the number line, to represent √n.

- Sets
- Set operations like union, intersection.
- Difference of sets
- Complement of a set
- Symmetric difference
- Representing all these using the Venn Diagram

- Statistics
- Mean, Median, Mode of grouped and ungrouped data
- Range
- Quartile deviation and mean deviation for a given grouped and ungrouped data
- Graphical representation
- Construction and interpretation of histograms of varying width, ogives, and frequency polygons
- Review of random experiments leading to the concept of chance or probability

### 2. Commercial Mathematics

- Banking
- Savings bank account
- Passbook and Challan
- Cheques and drafts
- Calculation of interest on deposits in a savings bank account

- Compound Interest
- Definition of compound interest
- Difference between simple interest and compound interest
- Calculation of compound interest using ready reckoners
- Derivation of compound interest formula
- Problems using formula

- Hire purchase and Instalment
- Meaning of hire purchase and installment buying
- Difference between hire purchase and installment buying
- Calculation of interest in installment buying
- Some simple problems on how to calculate equated monthly installment (EMI)

- Proportion
- Meaning of proportion
- General form
- Types- direct, inverse, compound proportions
- Problems on time and work involving proportions

### 3. Algebra

- Multiplication
- Product of three binomials (x+a)(x+b)(x+c) and related identity
- Identities for (a+b)
^{3}, (a-b)^{3} - Product of two trinomials (a+b+c)
^{2} - Conditional Identities

- Factorization
- Standard identities: a
^{2}-b^{2 }= (a-b)(a+b), a^{3}+b^{3 }= (a+b)(a^{2}-ab+b^{2}), a^{3}-b^{3 }= (a-b)(a^{2}+ab+b^{2}) - Factorization using these identities
- Factorisation of a trinomial by splitting the middle term
- Involved problems on these identities

- Standard identities: a
- HCF and LCM
- Definition of HCF and LCM
- Finding HCF and LCM of binomials and trinomials using factorization

- Division
- Division of a monomial by a monomial
- Division of a polynomial by a binomial
- Division of a polynomial by a trinomial

- Simultaneous Linear Equations
- Elimination method
- Word problems involving simultaneous equations
- Graph of the equation ax+by=c
- The solution of two simultaneous linear equations by drawing their graphs

- Variation
- Definition
- Symbolic Representation
- Constant of variation
- Types of Variation- Direct, inverse, and compound
- Problems involving Variation.

### 4. Geometry

- Polygons
- Meaning of polygon
- Interior and exterior angles
- Convex and concave polygons
- Regular and irregular polygons
- The sum of interior angles of a polygon (both for convex and concave polygons)
- Sum of the exterior angles
- Inscribing a regular polygon of
*n*sides in a circle, for*n*= 3,4,5,6,8

- Quadrilaterals
- Revision of basics of quadrilaterad
- Definition
- Sides
- Angles and diagonals
- Properties of Quadrilaterals
- Construction of quadrilaterals given any 5 elements
- Area of a quadrilateral
- Types of quadrilateral
- Parallelogram
- Rhombus
- Trapezium
- Construction of a parallelogram (given adjacent sides and an angle; adjacent sides and a diagonal)
- Construction of a rhombus (given two diagonals; one side and one diagonal)
- Construction of a trapezium (given four sides; parallel sides and the altitude)
- Area of a parallelogram
- Area of a rhombus
- Area of a trapezium

- Theorems and problems on parallelogram
- Theorem: Each diagonal of a parallelogram divides the parallelogram in two congruent triangles. The diagonals of a parallelogram bisect each other. Corollaries this result
- Theorem: Two parallelograms standing on the same base and between the same parallels have same area
- Theorem: (Mid-point theorem) The line joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half the third side. Conversely, if a line joining two points on two sides of a triangle is parallel to the third side and has length equal to half the third side, then it must be passing through the mid-points

Some riders on each of these theorems

- Circles
- Revision of basic notions (definition; radius; diameter; chord arc; angle at the centre subtended by an arc; angle at a point on the circle subtended by an arc; chord)
- A chord divides the circle in to two arcs, minor and major arc
- Properties of chords (observation that perpendicular from the centre bisects a chord, using practical work)
- Equal chords are equidistant from the centre and its converse (again by practical work)

**Note:** This is the proposed syllabus as per the Karnataka Government.