Topics
Sets
- Sets and Their Representations
- Empty Set (Null or Void Set)
- Finite and Infinite Sets
- Equal Sets
- Subsets
- Power Set
- Universal Set
- Venn Diagrams
- Intrdouction of Operations on Sets
- Union of Sets
- Intersection of Sets
- Difference of Sets
- Complement of a Set
- Practical Problems on Union and Intersection of Two Sets
- Proper and Improper Subset
- Open and Close Intervals
- Disjoint Sets
- Element Count Set
Mathematical Reasoning
- Mathematically Acceptable Statements
- New Statements from Old
- Special Words Or Phrases
- Contrapositive and Converse
- Introduction of Validating Statements
- Validation by Contradiction
- Difference Between Contradiction, Converse and Contrapositive
- Consolidating the Understanding
Sets and Functions
Algebra
Relations and Functions
- Concept of Relations
- Concept of Function
- Some Functions and Their Graphs
- Algebra of Real Functions
- Ordered Pairs
- Equality of Ordered Pairs
- Pictorial Diagrams
- Graph of Function
- Pictorial Representation of a Function
- Exponential Function
- Logarithmic Functions
- Brief Review of Cartesian System of Rectanglar Co-ordinates
Coordinate Geometry
Trigonometric Functions
- Angles and Their Measurement in Higher Mathematics
- Trigonometric Ratios
- Signs of Trigonometric Functions
- Domain and Range of Trigonometric Functions
- Trigonometric Functions of Sum and Difference of Two Angles
- Trigonometric Equations
- Trigonometric Functions
- Truth of the Identity
- Negative Function Or Trigonometric Functions of Negative Angles
- 90 Degree Plusminus X Function
- Conversion from One Measure to Another
- 180 Degree Plusminus X Function
- 2X Function
- 3X Function
- Expressing Sin (X±Y) and Cos (X±Y) in Terms of Sinx, Siny, Cosx and Cosy and Their Simple Applications
- Graphs of Trigonometric Functions
- Transformation Formulae
- Values of Trigonometric Functions at Multiples and Submultiples of an Angle
- Sine and Cosine Formulae and Their Applications
Calculus
Complex Numbers and Quadratic Equations
- Concept of Complex Numbers
- Algebraic Operations of Complex Numbers
- Conjugate of a Complex Number
- Argand Plane and Polar Representation
- Algebra of Complex Numbers - Equality
- Algebraic Properties of Complex Numbers
- Need for Complex Numbers
- Square Root of a Complex Number
Linear Inequalities
Statistics and Probability
Mathematical Reasoning
Permutations and Combinations
- Fundamental Principles of Counting
- Permutations
- Combination
- Permutation Formula to Rescue and Type of Permutation
- Smaller Set from Bigger Set
- Derivation of Formulae and Their Connections
- Simple Applications of Permutations and Combinations
- Factorial N (N!) Permutations and Combinations
Principle of Mathematical Induction
Binomial Theorem
- Introduction of Binomial Theorem
- Binomial Theorem for Positive Integral Indices
- General and Middle Terms
- Proof of Binomial Therom by Pattern
- Proof of Binomial Therom by Combination
- Rth Term from End
- Simple Applications of Binomial Theorem
Sequence and Series
Straight Lines
- Concept of Slope (or, gradient)
- Various Forms of the Equation of a Line
- Equations of Line in Different Forms
- Distance in Lines (Point & Parallel Lines)
- Brief Recall of Two Dimensional Geometry from Earlier Classes
- Shifting of Origin
- Equation of Family of Lines Passing Through the Point of Intersection of Two Lines
Conic Sections
- Sections of a Cone
- Parabola and its types
- Latus Rectum
- Relationship Between Semi-major Axis, Semi-minor Axis and the Distance of the Focus from the Centre of the Ellipse
- Special Cases of an Ellipse
- Eccentricity
- Ellipse and its Types
- Latus Rectum
- Hyperbola and its Types
- Eccentricity
- Latus Rectum
- Standard Equation of a Circle
Introduction to Three-dimensional Geometry
Limits and Derivatives
- Intuitive Idea of Derivatives
- Introduction of Limits
- Concept of Calculus
- Algebra of Limits
- Limits of Polynomials and Rational Functions
- Limits of Trigonometric Functions
- Introduction of Derivatives
- Algebra of Derivative of Functions
- Derivative of Polynomials and Trigonometric Functions
- Derivative Introduced as Rate of Change Both as that of Distance Function and Geometrically
- Limits of Logarithmic Functions
- Limits of Exponential Functions
- Derivative of Slope of Tangent of the Curve
- Theorem for Any Positive Integer n
- Graphical Interpretation of Derivative
- Derive Derivation of x^n
Statistics
- Measures of Dispersion
- Mean Deviation
- Introduction of Variance and Standard Deviation
- Standard Deviation
- Standard Deviation of a Discrete Frequency Distribution
- Standard Deviation of a Continuous Frequency Distribution
- Shortcut Method to Find Variance and Standard Deviation
- Introduction of Analysis of Frequency Distributions
- Comparison of Two Frequency Distributions with Same Mean
- Concepts of Statistics
- Measures of Central Tendency for Different Data Types
- Basic Concept of Mode
- Standard Deviation - by Short Cut Method
- Quartiles and Range in Statistics
Probability
- Concept of Probability
- Occurrence of an Event
- Elementary Types of Events and Properties of Probability
- Axiomatic Approach to Probability
- Probability of 'Not', 'And' and 'Or' Events
Concept of Logarithmic Functions
Domain and range of this function
Related concepts
- Concept of Function - Defining a Function
- Concept of Function - Function Main
- Concept of Function - Accessing a Function
- Concept of Function - Function Prototype
- Concept of Function - Passing Arguments to a Function
- Concept of Function - Recursion
- Concept of Function - Exponential Function
- Concept of Function - Even and Odd Functions
- Concept of Function - Functions with Their Graphs
- Concept of Function - Sum, Difference, Product, Quotient of Functions
