Class 9 Mathematics Karnataka Board Syllabus

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: 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
  • 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.

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