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.