Topics
Mathematical Logic
- Statements and Truth Values in Mathematical Logic
- Logical Statements & Equivalence
- Tautology, Contradiction, and Contingency
- Quantifier, Quantified and Duality Statements in Logic
- Negations of Compound Statements
- Converse, Inverse, and Contrapositive
- Algebra of Statements
- Application of Logic to Switching Circuits
11th Std
Trigonometry - II
- Trigonometric Functions of Allied Angels
- Trigonometric Functions of Compound Angles
- Trigonometric Functions of Sum and Difference of Three Angles
- Trigonometric Functions of Multiple Angles
- Trigonometric Functions of Sub-Multiple Angles
- Conversion Formulae in Trigonometry
- Trigonometric Functions of Angles of a Triangle
- Important Identities and Standard Results
12th Std
Matrices
- Symmetric and Skew Symmetric Matrices
- Inverse of a Matrix
- Application of Matrices
- Transpose of a Matrix
- Symmetric and Skew Symmetric Matrices
- Determinant of a Matrix
- Minors and Co-factors
- Adjoint of a Matrix
- System of Homogeneous and Non – Homogeneous Equations
Straight Line
- Coordinate Geometry Foundations
- Locus
- Shift of Origin
- Concept of Slope (or, gradient)
- Equations of Line in Different Forms
- The Angle Between Two Intersecting Lines
- Distance of a Point from a Line
- Family & Concurrent Lines
- Relative Position and Standard Results of Straight Lines
Circle
- Equation of a Circle in Different Forms
- Equation of a Circle in some special cases
- Director circle
- Equation of Tangent and Condition of Tangency
- Important Results for Circles
Trigonometric Functions
- Trigonometric Equations and Their Solutions
- Solutions of Triangle
- Meaning and Interpretation of Inverse Trigonometric Functions
- Graphs and Domains & Ranges of Inverse Trigonometric Functions
- Principal Values of Inverse Trigonometric Functions
- Properties of Inverse Trigonometric Functions
Conic Sections
- Fundamentals of Conic Sections
- Parabola and its types
- Ellipse and its Types
- Hyperbola and its Types
- Equations of Tangents and Conditions of Tangency for Conic Sections
- Equations of Auxiliary Circle and Director Circle
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
Measures of Dispersion
- Range, Variance and Standard Deviation
- Coefficient of Variation
- Standard Deviation for Combined Data
- Meaning and Definition of Dispersion
- Measures of Dispersion
- Quartiles and Range in Statistics
- Variance
- Standard Deviation
- Change of Origin and Scale of Variance and Standard Deviation
- Standard Deviation for Combined Data
- Coefficient of Variation
- Mean Deviation
Probability
- Elementary Types of Events and Properties of Probability
- Addition Theorem for Two Events
- Conditional Probability
- Multiplication Theorem on Probability
- Independent Events
- Bayes’ Theorem
- Odds (Ratio of Two Complementary Probabilities)
Vectors
- Vector Algebra: Representation and Types
- Algebra of Vectors
- Collinearity and Coplanarity of Vectors
- Vector in Two Dimensions (2-D)
- Three Dimensional (3-D) Coordinate System
- Components of Vector
- Position Vector of a Point P(X, Y, Z) in Space
- Component Form of a Position Vector
- Vector Joining Two Points
- Section Formula
- Product of Vector in Algebra (Dot Product)
- Direction Ratios, Direction Cosine & Direction Angles
- Vector Product of two vectors in Algebra (Cross Product)
- Scalar Triple Product
- Vector Triple Product
Line and Plane
- Vector and Cartesian Equations of a Line
- Distance of a Point from a Line
- Distance Between Skew Lines and Parallel Lines
- Equation of a Plane
- Angle Between the Planes
- Coplanarity of Two Lines
- Distance of a Point from a Plane
Complex Numbers
- Concept of Complex Numbers
- Algebraic Operations of Complex Numbers
- Equality of Two Complex Numbers
- Conjugate of a Complex Number
- Square Root of a Complex Number
- Fundamental Theorem of Algebra
- Argand Diagram or Complex Plane
- Modulus of a Complex Number
- Argument of a Complex Number
- DeMoivre's Theorem
- Cube Root of Unity
- Set of Points in Complex Plane
- Important Result of Complex Number
Linear Programming
- Linear Inequations in Two Variables
- Linear Programming Problem (L.P.P.)
- Formal Definitions and Solution of L.P.P
- Formal Definitions and Solution of L.P.P
- Methods to Find the Solution of L.P.P> Graphical Method
- Methods to Find the Solution of L.P.P> Corner - Point Method
Permutations and Combinations
- Factorial Notation
- Fundamental Principles of Counting
- Invariance Principle
- Permutations
- Circular Permutations
- Combination
- Important Result for Permutation and Combination
Functions
- Domain and Range of a Function
- Types of Functions
- Representation of Function
- Special Type of Function
- Algebra of Functions
- Composition of Functions
Differentiation
- Introduction & Derivatives of Some Standard Functions
- Derivative of Composite Functions
- Geometrical Meaning of Derivative
- Derivative of Inverse Functions
- Derivatives of Inverse Trigonometric Functions
- Logarithmic Differentiation
- Derivative of Implicit Functions
- Derivative of Parametric Functions
- Higher Order Derivatives
- Successive Differentiation
Limits
- Concept of Limits
- Algebra of Limits
- Methods to Find Limit of Rational Function>Factorization Method
- Methods to Find Limit of Rational Function> Rationalization Method
- Methods to Find Limit of Rational Function> Substitution Method
- Limits of Exponential and Logarithmic Functions
- Limits of Trigonometric Functions
- Limit at Infinity
Applications of Derivatives
- Application of Derivative in Geometry
- Derivative as a Rate Measure
- Velocity, Acceleration and Jerk
- Approximations
- Rolle's Theorem
- Lagrange's Mean Value Theorem (LMVT)
- Increasing and Decreasing Functions
- Maxima and Minima
Continuity
- Continuous and Discontinuous Functions
- Types of Discontinuity
- Continuity Over an Interval
- Intermediate Value Theorem
- Algebra of Continuous Functions
Indefinite Integration
- Indefinite Integration with Standard Indefinite Integral Formulae
- Methods of Integration> Integration by Substitution
- Methods of Integration> Integration by Parts
- Methods of Integration> Integration Using Partial Fraction
- Integrals of Trignometric Functions
- Some Special Integrals
Definite Integration
- Definite Integral as Limit of Sum
- Fundamental Theorem of Integral Calculus
- Properties of Definite Integrals
Conics
- Double Cone
- Fundamentals of Conic Sections
- Parabola and its types
- Ellipse and its Types
- Hyperbola and its Types
Application of Definite Integration
- Area Under Simple Curves
- Area Bounded by Two Curves
- Symmetrical Area
Sets and Relation
- Concept of Sets
- Classification of Sets
Differential Equations
- Order and Degree of a Differential Equation
- Solution of a Differential Equation
- Formation of Differential Equations
- Equations in Variable Separable Form
- Homogeneous Differential Equations
- Linear Differential Equations
- Applications of Differential Equation
Sequences and Series
- Sequence, Series, and Progression
- nth Term of A.G.P
- Expressing Recurring Decimals as Rational Numbers
- Arithmetic Progression (A.P.)
- Geometric Progression (G. P.)
- Sum to' n' Terms of a Geometric Progression
- Harmonic Progression (H. P.)
- Types of Means
- Arithmetico Geometric Series
- Power Series
Probability Distribution
- Random Variables
- Probability Distribution of Discrete Random Variables
- Probability Mass Function (P.M.F.)
- Cumulative Distribution Function (c. d. f. )
- Expected Value and Variance of a Random Variable
- Probability Distribution of a Continuous Random Variable
- Probability Density Function (P.D.F.)
- Cumulative Distribution Functions (c. d. f.)
Methods of Induction and Binomial Theorem
- Principle of Mathematical Induction
- General Term in Expansion of (a + b)n
- Middle term(s) in the expansion of (a + b)n
Binomial Distribution
- Bernoulli Trial
- Binomial Distribution
- Mean and Variance of Binomial Distribution
Determinants and Matrices
- Minors and Cofactors of Elements of Determinants
- Properties of Matrix Multiplication
- Jump Discontinuity
- Removable Discontinuity
- Infinite Discontinuity
