Related Unit Name
- 1.Sets and their Representations,Types of Sets
- 1. Cartesian Products of Sets
- 1. Angles,Measurement of Angles(Degree,Radian,Gradian) and Notational Convention
- 2. Venn Diagrams and Operations on Sets
- 3. Practical Problems on Union and Intersection(Applications of Sets)
- Equal sets.
- Subsets.
- Subsets of a set of real numbers especially intervals (with notations).
- Power set.
- Universal set.
- Venn diagrams.
- Union and Intersection of sets.
- Difference of sets.
- Complement of a set.
- Properties of Complement Sets.
- Practical Problems based on sets.
- 2. Relations and Types of Relations
- 3. Functions and Types of Functions
- 4. Some Special functions,Domain,Range and their graphs
- 5. Algebra of real functions
- 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.
- 2. Trigonometric Functions ,Sign,Domain ,Range and their graphs
- 3. Trigonometric Functions of Sum and Difference of Two Angles
- 4. Trigonometric Equations
- Domain and range of trignometric functions and their graphs.
- Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application.
- 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.
- 1. Motivation and Process of proof by induction
- 1. Imaginary Numbers and Powers
- 1. Inequalities and Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
- 1. Fundamental Principle of Counting
- 1. Binomial Theorem for Positive Integral Indices
- 1. Sequences and Series
- 2. Principles of Mathematical induction and simple applications
- 2. Complex Numbers and Algebra of Complex Numbers
- 3. The Modulus and the Conjugate of a Complex Numbers
- 4. Solving Quadratic equations in complex numbers
- 5. Square Root and Cube Root Of Complex Numbers
- 2. Graphical methods and Solution of Linear Inequalities in Two Variables
- Graphical solution of linear inequalities in two variables.
- Graphical solution of system of linear inequalities in two variables.
- 2. Permutations and Factorial notation
- 3. Combinations and Simple applications
- 2. Pascal’s triangle
- 2. Arithmetic Progression (AP) and Arithmetic Mean (AM)
- 3. Geometric Progression (GP) and Geometric Mean (GM)
- 4. Sum to n Terms of Special Series
- 5. Infinite GM and its sum
- geometric mean (G.M.),
- relation between A.M. and G.M
- 3. General and Middle Terms
- 1. The slope of line and angles between two lines
- 1. Sections of a cone: parabola, hyperbola, ellipse
- 1. Coordinate axes and planes in 3D
- 2. Conditions for parallelism and perpendicularity of lines and Collinearity of three points
- 3. Various Forms of the Equation of a Line
- 4. General Equation of a Line
- 5. Distance of a Point From a Line and Distance between two parallel lines
- Equation of family of lines passing through the point of intersection of two lines.
- Distance of a point from a line.
- 2. Standard equations, Properties and Application of a circle
- 3. Standard equations, Properties and Application of a parabola
- 2. Distance between 2 points, section formula
- 3. Coordinates of a points
- 4. Standard equations, Properties and Application of a ellipse
- 5. Standard equations, Properties and Application of a hyperbola
- 1. Intuitive idea of limits and Derivatives
- 2. Limits ,Types Of limits ,Existence of limits and Algebra of limits
- 3. Limits of polynomial, rational, trigonometric, exponential and logarithmic functions
- 4. Derivatives ,Existence of Derivative and Algebra of Derivatives
- 5. The derivative of the sum, difference, quotient, and product of functions
- 6. Derivatives of polynomial and trigonometric functions
- 1. Statements and Connecting words
- 2. Understanding of conditions such as “if-then”, “only if” and “if and only if ”, “and/or”, “implies” , “implies by” and Quantifiers and their uses
- 3. Validating the statements involving the connecting words and statements
- 4. Difference between contradiction, contrapositive, and converse