Organisation : Department of Pre University Education
Subject : Maths
Announcement : Syllabus
Website : https://pue.karnataka.gov.in/
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Maths Syllabus :
Unit I : Sets And Functions
1. Sets
Sets and their representations : Definitions, examples, Methods of Representation in roster and rule form, examples
Related : Computer Science Syllabus Pre University Education : www.syllabus.gen.in/1164.html
Types of sets : Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of the set of real numbers especially intervals (with notations). Power set. Universal set.
examples Operation on sets: Union and intersection of sets. Difference of sets. Complement of a set, Properties of Complement sets. Simple practical problems on union and intersection of two sets.
Venn diagrams: simple problems on Venn diagram representation of operation on sets
2. Relations and Functions Cartesian product of sets : Ordered pairs, Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the reals with itself (upto R × R × R).
Relation: Definition of relation, pictorial diagrams, domain, co-domain and range of a relation and examples Function : Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain and range of a function.
Real valued function of the real variable, domain and range of constant, identity, polynomial rational, modulus, signum and greatest integer functions with their graphs. Algebra of real valued functions : Sum, difference, product and quotients of functions with examples.
3. Trigonometric Functions Angle : Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle.
Truth of the identity sin2x + cos2 x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Trigonometric functions of sum and difference of two angles: Deducing the formula for cos(x+y) using unit circle
Unit II : Algebra
1. Principle of Mathematical Induction :
Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple problems based on summation only.
2. Complex Numbers and Quadratic Equations :
Need for complex numbers, to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers.
Argand plane and polar representation of complex numbers and problems Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system, Square-root of a Complex number given in supplement and problems.
3. Linear Inequalities :
Linear inequalities,Algebraic solutions of linear inequalities in one variable and their representation on the number line and examples.
Graphical solution of linear inequalities in two variables and examples Solution of system of linear inequalities in two variables graphically and examples