UNIT I: SETS AND FUNCTIONS
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Cartesian product of sets
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Number of elements in the Cartesian product of two finite sets
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Cartesian product of the set of reals with itself (upto R x R x R)
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Definition of relation, pictorial diagrams, domain, co-domain and range of a relation
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Function as a special type of relation
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Pictorial representation of a function, domain, co-domain and range of a function
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Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs
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Sum, difference, product and quotients of functions
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Positive and negative angles
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Measuring angles in radians and in degrees and conversion from one measure to another
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Definition of trigonometric functions with the help of unit circle
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Truth of the identity sin 2x + cos 2x = 1 , for all x
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Signs of trigonometric functions
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Domain and range of trigonometric functions and their graphs
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Expressing sin (x±y) and cos (x±y) in terms of sin x , sin y ,cos x & cos y and their simple applications. Deducing identities like the following: tan(x ± y) = tan x ± tan y / 1 ± tan x tan y , cot(x ± y) = cot x cot y ± 1 / cot y ± cot x sin α ± sin β = 2sin(½(α ± β))cos(½(α ∓ β)) cos α + cos β = 2cos(½(α + β))cos(½(α − β)) cos α − cos β = −2sin(½(α + β))sin(½(α − β)) Identities related to sin 2x , cos 2x ,tan 2x ,sin 3x ,cos 3x and tan 3x
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General solution of trigonometric equations of the type sin y = sin a , cos y = cos a and tan y = tan a
UNIT-V: MATHEMATICAL REASONING
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Mathematically acceptable statements
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Connecting words/phrases-consolidating the understanding of “if and only if (necessary and sufficient) condition,” “implies”, “and/ or”, “implied by”, “and”, “or”, “there exists” and their use through variety of examples related to real life and Mathematics
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Validating the statements involving the connecting words, difference between contradiction, converse and contrapositive
BETA
