| 1). Logarithm |
a) Logarithm Basic Definitions
b) Logarithm Properties
c) Logarithm Inequalities (Included in Functions Lecture) |
| 2). Trigonometry |
a) Measurement Systems, Length of Arc, Area of Sector, Trigonometric Ratios definition in circular system, Signs of Trigonometric ratios in different quadrants
b) Allied Angles and Reduction Formulae
c) Compound Angles
d) Trigonometric Ratios of Multiple, Sub-multiple Angles
e) Product to Sum Transformations, Sum to Product Transformations, Sine Series, Cosine Series |
| 3). Set Theory |
a) Basic Definitions, Representation of Sets, Types of Sets, Power of a Set, Venn Diagrams
b) Operations on Sets, Algebra of Sets |
| 4). Relations |
a) Definitions, Cartesian Product, Types of Relations |
| 5). Functions |
a) Definitions, Domain, Range, Co-Domain, Inequalities and Intervals, Wavy Curve Method
b) Finding Domain and Range, Polynomial Functions, Algebric Functions, Rational Functions, Indentity Functions, Constant Functions
c) Logarithmic Functions, Graphs and Inequalities, Exponential Functions, Graphs and Inequalities
d) Modulus Function, Graphs
e) Modulus Function Equation solving and Inequalities
f) Greatest Integer Function and Fractional Part Function
g) Identical Functions, One- One and Many One Functions, Onto- Into Functions, Odd- Even Functions
h) Composite of Uniformly and Non Uniformly defined Functions, Implicit & Explicit functions, Inverse of functions, Periodic functions |
| 6). Limits |
a) Basic Definitions, Basic Indeterminate Forms, Methods of Calculation of Limits, Binomial Approximation, L-Hopital Rule
b) Algebra of Limits, Sandwich Theorem, Standard Limits
c) Expansion Series
d) Advanced Indeterminate Forms |
| 7). Continuity |
a) Basic Definitions, Geometrical Meaning, Continuity in Open and Closed Intervals
b) Removable and Non Removable Discontinuities
c) Algebra of Continuity, Intermediate Value Theorem, Continuity of Composite Functions |
| 8). Differentiability |
a) Basic Definitions, First Principle of Derivative
b) Reasons for Non Differentiability, Algebra of Differentiability
c) Standard Derivatives, Functional Equations, Graph Based problems |
| 9). Methods of Differentiation |
a) Logarithmic Differentiation, Derivative of Implicit and Inverse functions
b) Parametric Differentiation, Differentiation wrt another function, Successive Differentiation |
| 10). Application of Derivatives |
a) Rate of Change, Tangents and Normals
b) Angle between two curves, Length of Tangents, Normals, Sub-Tangents and Sub Normals
c) Shortest distance between two curves, Monotonocity
d) Minima, Maxima, First order derivative test
e) Second Order derivative test, Rolles Theorem, LMVT |
| 11). Indefinite Integration |
a) Basic Definitions, Fundamental Integrals
b) Substitution, Standard Integrals
c) Advanced Substitutions
d) By parts and Partial Fractions Basics |
| 12). Definite Integration |
a) Basic Definitions, Geometrical meaning, Basic Properties
b) Advanced Properties
c) Lebiniz Rule, Limit of a Sum |
| 13). Area Under the Curve |
a) Area Under the curve, Area between two curves |
| 14). Quadratic Equations |
a) Basic Definitions, Identity, Formation of Quadratic Equation, Nature of Roots
b) Sign of Quadratic Expression
c) Location of Roots
d) Common Roots, Theory of Equations |
| 15). Progressions |
a) Basic Definitions of AP, General Term and Sum of AP
b) Properties of AP, Basics of GP, General Term and Sum of GP
c) Properties of GP, Basics of HP
d) Arithmetico Geometric Progression, Arithmetic Mean, Geometric Mean and Harmonic Mean
e) AM, GM, HM Inequalities, Different Summation methods, Method of Difference |
| 16). Binomial Theorem |
a) Binomial Expansion, General Term for positive integral Index, Term from the end
b) Middle Term, Numerically Greatest Term and Greatest Binomial Coefficient
c) Application Based concepts on remainders, Summation of Binomial Coefficients
d) Methods to find Series Summation, Variable upper Index
e) Binomial theorem for any index, Multinomial Theorem |
| 17). Permutations and Combinations |
a) Fundamental Principle of counting, Permutations and Combinations Basics and properties
b) Formation of Groups, Permutations of alike objects
c) Circular Permutations,
d) Total number of Combinations, Number of Divisors
e) Total Distributions |
| 18). Probability |
a) Basic definitions
b) Venn Diagrams, Laws of Probability
c) Conditional Probability, Multiplication theorem, Independent Events
d) Total Probability Theorem, Bayes' Theorem |
| 19). Matrices and Determinants |
a) Basic Definitions, Types of Matrices, Equality of Matrices, Algebra of Matrices
b) Multiplication of Matrices, Idempotent, Nilpotent, Periodic, Involuntary Matrix, Transpose of Matrix
c) Determinants, Minors, Cofactors, Row and Column Operations
d) Orthogonal, Adjoint, Inverse of a matrix
e) System of Equations (Cramer's Rule) |
| 20). Straight Lines |
a) Coordinates Systems, Distance and Section Formula, Area of Triangle
b) Coordinates of different centers of a Triangle, Locus
c) Condition of Collinearity, Slope and Inclination of a line
d) Intercepts, Forms of Equation of Straight Line
e) General Form of a line, Angle between two lines, Equation of lines parallel and perpendicular to a given line, Position of a point wrt a line
f) Length of perpendicular from a point on a line, Distance between two parallel lines, Reflection of a point wrt a line, Family of lines |
| 21). Pair of Straight Lines |
a) Homogenous equation of second degree, Combined equation of angle bisector, General equation of second degree |
| 22). Circles |
a) Basic Definitions, Standard Equation, General Equation, Intercepts, Equation in Diameter form
b) Circles under Special Conditions, S & S1 Notation, Position of a point wrt Circle
c) Position of a line wrt circle, Tangents and T Notation
d) Normals, Director circle, Power of a point, Length of Tangent
e) Chord of Contact, Chord with a given Mid Point, Pair of Tangents |
| 23). Parabola |
a) Basic Definitions, Terminologies, Types of Parabola
b) Position of a point, Chord Joining two points, Line and a parabola, Tangent to the Parabola
c) Normal to the Parabola, Pair of Tangents, Director Circle |
| 24). Ellipse |
a) Standard Equation and Definitions, Another form of ellipse
b) General Equation, Position of a point and line, Auxillary Circle, Tangent to the Ellipse
c) Normal to the Ellipse, Director Circle
|
| 25). Hyperbola |
a) Basic Definitions and terminologies
b) Conjugate and Rectangular Hyperbola, Position of a point and line, Auxillary Circle, Parametric Equation
c) Tangent to Hyperbola, Normal to the Hyperbola
|
Launch your Graphy