# Basic Debating Skills Essay

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MATHEMATICS (CLASSES XI –XII) General Guidelines (i) All concepts/identities must be illustrated by situational examples. (ii) The language of ‘word problems’ must be clear, simple and unambiguous. (iii) Problems given should be testing the understanding of the subject. (iv) All proofs to be produced in a manner that allow the learner to see flow of reasons. Wherever possible, give more than one proof. (v) Motivate results, wherever possible. Prove explicitly those results where a short and clear argument reinforces mathematical thinking and reasoning. There must be emphasis on correct way of expressing the arguments. 1 CLASS XI (Total Periods 180) UNIT I: SETS AND FUNCTIONS 1. Sets (Periods 12) Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of the set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and intersection of sets. Difference of sets. Complement of a set, Properties of Complement sets. 2. Relations and Functions (Periods 14) 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). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. 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 these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions. 3. Trigonometric Functions (Periods 18) Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric