Embedded Files
syllabus
Module 1
Module 1
Basic Algebra and functions
Basic Algebra and functions
(A) Reasoning and Logic
1. Simple statement (proposition), connectives (conjuction, disjunction, negation,
conditional, bi-conditional), compound statements.
2. Truth tables. truth tables video
3. Converse and contrapositive of statements.
4. Logical equivalence.
5. Identities involving propositions.
(B) The Real Number System – ℝ
1. Definition of binary operation.
2. Applications of the concepts of commutativity, associativity, distributivity, identity,
inverse and closure.video
3. Axioms of the system - including commutative, associative and distributive laws;
non-existence of the multiplicative inverse of zero.
4. Methods of proof - direct, counter-examples.
5. Simple applications of mathematical induction.proof by induction (example)
(C)Algebraic Operations
1. Factor Theorem. video
2. Remainder Theorem.
(D) Exponential and Logarithmic Functions
1. Graphs of the functions a^x and logx.
2. Properties of the exponential and logarithmic functions.
3. Exponential and natural logarithmic functions and their graphs.
4. Laws of logarithms applied to problems:
examples solving logarithmic equations
(E) Functions
1. Domain, range, many-to-one, composition.
2. Injective, surjective, bijective functions, inverse function. video
3. Transformation of the graph
(F) The Modulus Function
1. Definition of the modulus function.
2. Equations and inequalities involving simple rational and modulus functions.
(G) Cubic Functions and Equations
1. Sums and products, with applications, of the roots of cubic equations.
MORE VIDEOS
Module 2 Trigonomerty Geometry & Vectors
Module 2 Trigonomerty Geometry & Vectors
Trigonometry
interesting way to memorize unit circle
Trigonometry Equations : A sin x - B cos x = C Type : ExamSolutions
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