UNIT I: SETS AND FUNCTIONS
- Cartesian product of sets
- Number of elements in the Cartesian product of two finite sets
- Cartesian product of the set of reals with itself (upto R x R x R)
- Definition of relation, pictorial diagrams, domain, co-domain and range of a relation
- Function as a special type of relation
- Pictorial representation of a function, domain, co-domain and range of a function
- Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs
- Sum, difference, product and quotients of functions
- 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 sin 2x + cos 2x = 1 , for all x
- Signs of trigonometric functions
- Domain and range of trigonometric functions and their graphs
- 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
- 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
- Mathematically acceptable statements
- 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
- Validating the statements involving the connecting words, difference between contradiction, converse and contrapositive
BETA
