 # 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
• 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: a2-b2 = (a-b)(a+b), a3+b3 = (a+b)(a2-ab+b2), a3-b3 = (a-b)(a2+ab+b2)
• Factorization using these identities
• Factorisation of a trinomial by splitting the middle term
• Involved problems on these identities
• 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
• Definition
• Sides
• Angles and diagonals
• Construction of quadrilaterals given any 5 elements
• 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.  Study Materials for Class 9   