Published | 2022-07-07 |
Platform | Udemy |
Price | $19.99 |
Instructors |
Kuldeep Yadav
|
Subjects |
examination for all forms of entrance examinations and secondary school
I've covered the majority of the math topics for practice.
SETS
RELATION AND FUNCTION
TRIGONOMETRY
COMPLEX NUMBER
QUADRATIC EQUATION
PERMUTATION AND COMBINATION
SEQUENCE AND SERIES
STRAIGHT LINE
CONIC SECTION
LIMIT AND DERIVTIVES
PROBABILITY
s
Chapter 1: Sets
Sets and their representations
Empty set
Finite and infinite sets
Equal sets. Subsets
Subsets of a set of real numbers, especially intervals (with notations)
Power set
Universal Set
Venn diagrams
Sets: Union and Intersection of Sets
Difference of sets
Complement of a set
Properties of Compound Sets
Practical Problems based on Sets
Chapter 2: Relations and Functions
Ordered pairs
The Cartesian product of sets
The number of elements in the cartesian product of two finite sets
The Cartesian product of the sets of real (up to R R)
The definition of
Relation
Pictorial diagrams
Domain
co-domain
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 functions, the domain and range of these functions
Constant
Identity
polynomial
Rational
Modulus
Signum
Exponential
Logarithmic
The greatest integer functions (with their graphs)
sum, difference, product, quotients of functions.
Chapter 3: Trigonometric Functions
Positive and negative angles
Measuring angles in radians and in degrees and conversion of one into the other
Definition of trigonometric functions with the help of the unit circle
Truth of the sin2x + cos2x = 1, for all x
Signs of trigonometric functions
The domain and range of trigonometric functions and their graphs
Expressing sin (xy) and cos (xy) in terms of sinx, siny, cosx, and cosy and their simple application
Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x, tan3x,
general solution of trigonometric equations of the type sin y = sin a, cos y = cos a, and tan y = tan a.
Unit-II: Algebra
Chapter 1: The Principle of Mathematical Induction
Process of the proof by induction
Motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers
The principle of mathematical induction and its simple applications
Chapter 2: Complex Numbers and Quadratic Equations
The need for complex numbers, especially 1, to be motivated by the inability to solve some of the quadratic equations
Algebraic properties of complex numbers
The Argand plane and polar representation of complex numbers
Statement of the Fundamental Theorem of Algebra
Solution of quadratic equations in the complex number system
The square root of a complex number
Chapter 3: Linear Inequalities
Linear inequalities
Algebraic solutions of linear inequalities in one variable and their representation on the number line
Graphical solution of linear inequalities in two variables
Graphical solution of a system of linear inequalities in two variables
Chapter 4: Permutations and Combinations
The fundamental principle of counting
Factorial
Permutations and combinations
The derivation of formulae and their connections
Simple applications
Chapter 5: Binomial Theorem
History
Statement and proof of the binomial theorem for positive integral indices
Pascal's triangle
General and middle terms in binomial expansion
Simple applications
Chapter 6: Sequence and Series
A Sequence and Series
Arithmetic Progression (A.P.)
Arithmetic Mean (A.M.)
Geometric Progression (G.P.)
general term of a G.P.
sum of n terms of a G.P.
The arithmetic and geometric series G.P. and its sum
Geometric mean (G.M.)
Relationship between A.M. and G.M.
Unit-III: Coordinate Geometry
Chapter 1: "Straight Lines"
Brief recall of two-dimensional geometries from earlier classes
Shifting of origin
The slope of a line and the angle between two lines
Various forms of equations for a line
Parallel to the axis
Point-slope form
Slope-intercept form
Two-point form
Intercept form
Normal form
A general equation of a line
equation of a family of lines passing through the point of intersection of two lines
The distance of a point from a line
Chapter 2: Conic Sections
Sections of a cone
Circles
Ellipse
Parabola
a point, a straight line, and a pair of intersecting lines as a degenerated case of a conic section.
Standard equations and simple properties of −
Parabola
Ellipse
Hyperbola
The standard equation of a circle
Chapter 3. Introduction to Three-dimensional Geometry
Coordinate axes and coordinate planes in three dimensions.
The coordinates of a point
Distance between two points and section formula
Unit-IV: Calculus
Chapter 1: Limits and Derivatives
Derivative introduced as rate of change both as that of distance function and geometrically
Intuitive idea of limit
Limits of −
Polynomials and rational functions
Trigonometric, exponential and logarithmic functions
Definition of derivative, relate it to slope of tangent of a curve, derivative of sum, difference, product and quotient of functions
The derivative of polynomial and trigonometric functions