Unit | Area Covered | Marks | |
---|---|---|---|
Unit 1 | SETS | 05 | read more |
Unit 2 | Relations and Functions | 10 | read more |
Unit 3 | Trigonometric Functions | 05 | read more |
Unit 4 | Complex Numbers and Quadratic Equations | 15 | read more |
Unit 5 | Linear and Quadratic Inequalities | 05 | read more |
Unit 6 | Permutation and Combination | 10 | read more |
Unit 7 | Binomial Theorem | 10 | read more |
Unit 8 | Sequences and Series | 10 | read more |
Unit 9 | Straight Lines | 10 | read more |
Unit 10 | Conic Section | 05 | read more |
Unit 11 | Introduction to Three dimensional Geometry | 05 | read more |
Unit 12 | Limits and Continuity | 05 | read more |
Unit 13 | Probability | 05 | read more |
Total Marks | 100 | Time: 3 Hours |
Sets and their representations
Empty Set
Singleton Set
Finite and infinite Sets
Equivalent and Equal Sets
Subsets
Power Set
Universal Set
Complement of a Set
Intervals as Subsets of R
Venn Diagrams
Union and Intersection of Sets
Difference of Sets
Laws of Operations on Sets
Properties of Complement Sets
Practical Problems on union and Intersection of Sets
Ordered Pairs
Cartesian Product of Sets
Definition of Relation
Arrow Diagram
Domain, Codomain and Range of a Relation
Function as a Special Kind of Relation from one Set to another
Pictorial representation of a Function
Domain, Codomain and Range of a Function
Real valued functions and their graphs
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
Sign of trigonometric functions
Domain and range of trigonometric functions
Trigonometric functions as periodic functions, their amplitude, argument, period and graph
Trigonometric functions of sum and difference of two angles
Express sum and difference of T-Functions as the product of T-ratios
Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x
General solution of trigonometric equations of the type sin = sin , cos = cos and tan = tan
Proof and simple applications of sine and cosine rules
Need for complex number,especially iota to be motivated by inability to solve some of quadratic equation
Standard form of complex number
Modulus and conjugate of complex number
Multiplication and division of complex numbers
Polar representation Of complex number Polar Representation of Complex number
Argand Plane
Statement of Fundamental theorem of algebra
Square root of a complex number
Solution of quadratic equations in the complex number system
Cube root of unity and its properties
De Moivre's theorem
Linear Inequations
Algebraic solutions of linear inequations in one variable
Algebraic solutions of linear in equations in two variables
Graphical solution of linear inequations in two variables
Inequations solving modulus functions
Fundamental principles of counting
Factorial n (n!)
Permutation
Combinations
Derivation of properties of combination
Types of permutations
Simple applications
Pascal's Triangle
History, statement and proof of the binomial theorems for positive integral indices
General and middle term in binomial expansion
Application of binomial theorem
Arithmetic Progression, Geometric Progression
Arithmetic Mean
Geometric Mean
Sum to n terms of an A.P.
Sum to n terms of a G.P.
Infinite G.P. and its sum
Relation between A.M. and G.M.
Brief recall of two dimensional geometry from earlier classes
Shifting of origin
Slope of a line
Angle between two lines
Various forms of equation of a line: parallel to axis, point slop form, slopintercept form, two point form, intercept form, and normal form
General equation of a line
Equation of family of lines passing through the point of intersection of two lines
Distance of a point from a line
Distance between parallel lines
Introduction to section of a cone
Circle (Standard form)
Circle (general form)
Parabola (standard form)
Parabola (general form)
Ellipse (standard form) horizontal & vertical ellipse
Ellipse (general form)
Hyperbole (standard form)
Hyperbole (general form)
Application of conic section
Co-ordinate axes and co-ordinate planes in three dimensions
Distance between two points and section formula
Some results on line in space
Limits and Continuity
Random experiment: outcomes, sample spaces (set representation)
Events: occurrence of events, 'or', 'and', & 'not' events
Exhaustive events, mutually exclusive events Axiomatic (set theoretic) probability
Probability of an event
Odds of an event
Probability of occurrence of a complementary events