Topics
11th Std
Mathematical Logic
- Concept of Statements
- Truth Value of Statement
- Logical Connective, Simple and Compound Statements
- Statement Patterns and Logical Equivalence
- Tautology, Contradiction, and Contingency
- Duality
- Quantifier and Quantified Statements in Logic
- Negations of Compound Statements
- Converse, Inverse, and Contrapositive
- Algebra of Statements
- Application of Logic to Switching Circuits
Conics
11th Std
Trigonometry - II
- Compound Angle
- Trigonometric Functions of Sum and Difference of Angles
- Trigonometric Functions of Allied Angles
- Trigonometric Functions of Multiple Angles
- Trigonometric Functions of Double Angles
- Trigonometric Functions of Triple Angle
- Factorization Formulae
- Formulae for Conversion of Sum Or Difference into Product
- Formulae for Conversion of Product in to Sum Or Difference
- Trigonometric Functions of Angles of a Triangle
12th Std
Straight Line
Matrices
Sets
Sequences and Series
Circle
Trigonometric Functions
Measures of Dispersion
- Range, Variance and Standard Deviation
- Coefficient of Variation
- Standard Deviation for Combined Data
- Meaning and Definition of Dispersion
- Measures of Dispersion
- Range of Data
- Variance
- Standard Deviation
- Change of Origin and Scale of Variance and Standard Deviation
- Standard Deviation for Combined Data
- Coefficient of Variation
Pair of Straight Lines
- Combined Equation of a Pair Lines
- Homogeneous Equation of Degree Two
- Angle between lines represented by ax2 + 2hxy + by2 = 0
- General Second Degree Equation in x and y
- Equation of a Line in Space
- Formation of Joint Equation and Separation of Equations from a Given Equation
- Sum and Product of Slopes
- Acute Angle Between a Pair of Straight Lines
- General 2nd Degree Equation to Represent a Pair of Lines
Probability
Vectors
- Representation of Vector
- Vectors and Their Types
- Algebra of Vectors
- Collinearity and Coplanarity of Vectors
- Vector in Two Dimensions (2-D)
- Three Dimensional (3-D) Coordinate System
- Position Vector of a Point P(X, Y, Z) in Space
- Components of Vector
- Component Form of a Position Vector
- Vector Joining Two Points
- Section Formula
- Scalar Product of Vectors (Dot)
- Vector Product of Vectors (Cross)
- Scalar Triple Product of Vectors
- Vector Triple Product
- Direction Angles
- Direction Ratios
- Direction Cosines
- Addition of Vectors
Complex Numbers
- Introduction of Complex Number
- Concept of Complex Numbers
- Algebra of Complex Numbers
- Equality of Two Complex Numbers
- Conjugate of a Complex Number
- Powers of i
- Square Root of a Complex Number
- Fundamental Theorem of Algebra
- Modulus of a Complex Number
- Argument, Polar Form and Exponential Form of a Complex Number
- Argand Diagram Or Complex Plane
- Cube Root of Unity
- DeMoivre's Theorem
- Set of Points in Complex Plane
Line and Plane
Linear Programming
- Linear Inequations in Two Variables
- Linear Programming Problem (L.P.P.)
- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Formulation of LPP
- Terminologies Related to the Solution of LPP
- Graphical Method of Solving Linear Programming Problems
- Special Cases of LPP
- Linear Programming Problem in Management Mathematics
Permutations and Combinations
- Factorial Notation
- Fundamental Principles of Counting
- Invariance Principle
- Factorial Notation
- Permutations
- Permutations When All Objects Are Distinct
- Permutations When Repetitions Are Allowed
- Permutations When Some Objects Are Identical
- Circular Permutations
- Properties of Permutations
- Combination
- Properties of Combinations
Differentiation
Functions
Applications of Derivatives
Limits
Continuity
- Continuous and Discontinuous Functions
- Continuity of a Function at a Point
- Discontinuity of a Function
- Types of Discontinuity
- Continuity in the Domain of the Function
- Algebra of Continuous Functions
- Continuity in Interval - Definition
- Continuity of Some Standard Functions - Polynomial Function
- Continuity of Some Standard Functions - Rational Function
- Continuity of Some Standard Functions - Trigonometric Function
Indefinite Integration
Definite Integration
Application of Definite Integration
Differential Equations
Probability Distribution
Binomial Distribution
description
- `int1/(x^2 + a^2) dx = 1/a tan^-1 (x/a) + c`
- `int1/(x^2 - a^2) dx = 1/(2a) log ((x - a)/(x + a)) + c`
- `int1/(a^2 - x^2) dx = 1/(2a) log ((a + x)/(a - x)) + c`
- `int1/sqrt(a^2 - x^2) dx = sin^-1 (x/a) + c`
- `int1/sqrt(x^2 - a^2) dx = log ( x + sqrt(x^2 - a^2))+ c`
- `int1/sqrt(x^2 + a^2) dx = log ( x + sqrt(x^2 + a^2))+ c`
- `int1/(xsqrt(x^2 - a^2)) dx = 1/a sec^-1(x/a) + c`
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