Topics
Relations and Functions
Mathematics
Numbers, Quantification and Numerical Applications
- Modulo Arithmetic
- Apply Arithmetic Operations Using Modular Arithmetic Rules
- Congruence Modulo
- Apply the Definition of Congruence Modulo in Various Problems
- Allegation and Mixture
- Rule of Allegation to Produce a Mixture at a Given Price
- Determine the Mean Price of Amixture
- Apply Rule of Allegation
- Solve Real Life Problems Mathematically
- Boats and Streams
- Express the Boats and Streams Problem in the Form of an Equation
- Pipes and Cisterns
- Races and Games
- Concept of Partnership
- Differentiate Between Active Partner and Sleeping Partner
- Determination of Partner's Ratio
- Volume and Surface Area of Combined Solids
- Numerical Inequalities
Applied Mathematics
Algebra
Inverse Trigonometric Functions
Calculus
Matrices
- Introduction of Matrices
- Matrices
- Matrices Notation
- Order of a Matrix
- Types of Matrices
- Equality of Matrices
- Operations on Matrices
- Addition of Matrices
- Properties of Matrix Addition
- Multiplication of a Matrix by a Scalar
- Properties of Scalar Multiplication of a Matrix
- Multiplication of Matrices
- Properties of Multiplication of Matrices
- Negative of Matrix
- Subtraction of Matrices
- Transpose of a Matrix
- Properties of Transpose of the Matrices
- Symmetric and Skew Symmetric Matrices
- Elementary Transformations of a Matrix
- Invertible Matrices
- Inverse of Matrix
- Inverse of a Matrix by Elementary Transformation
Probability Distributions
Determinants
Continuity and Differentiability
- Introduction of Continuity and Differentiability
- Concept of Continuity
- Algebra of Continuous Functions
- Concept of Differentiability
- Derivatives of Composite Functions - Chain Rule
- Derivatives of Implicit Functions
- Derivatives of Inverse Trigonometric Functions
- Exponential and Logarithmic Functions
- Logarithmic Differentiation
- Derivatives of Functions in Parametric Forms
- Second Order Derivative
- Mean Value Theorem
Index Numbers and Time Based Data
- Meaning of Index Numbers
- Construction of Index Numbers
- Test of Adequacy of Index Numbers
- Population and Sample
- Differentiate Between Population and Sample
- Representative Sample from a Population
- Parameter
- Statistics
- Relation Between Parameter and Statistic
- Limitations of Statistics to Generalize the Estimation for Population
- Statistical Significance and Statistical Inferences
- Central Limit Theorem
- Relation Between Population, Sampling Distribution, and Sample
- Time Series Analysis
- Components of a Time Series
- Time Series Analysis for Uni-variate Data
Financial Mathematics
- Perpetuity Fund
- Sinking Fund
- Calculate Perpetuity
- Differentiate Between Sinking Fund and Saving Account
- Valuation of Bond
- Calculate Value of Bond Using present Value Approach
- Concept of EMI
- Calculation of EMI
- Linear Method of Depreciation
- Interpretation Cost, Residual Value and Useful Life of an Asset
- Methods of Calculating Depreciation Amount
Applications of Derivatives
- Introduction to Applications of Derivatives
- Rate of Change of Bodies or Quantities
- Increasing and Decreasing Functions
- Tangents and Normals
- Approximations
- Maxima and Minima
- Maximum and Minimum Values of a Function in a Closed Interval
- Graph of Maxima and Minima
- Simple Problems on Applications of Derivatives
Linear Programming
Integrals
- Introduction of Integrals
- Integration as an Inverse Process of Differentiation
- Geometrical Interpretation of Indefinite Integrals
- Some Properties of Indefinite Integral
- Comparison Between Differentiation and Integration
- Methods of Integration: Integration by Substitution
- Methods of Integration: Integration Using Partial Fractions
- Integrals of Some Particular Functions
- Methods of Integration: Integration by Parts
- Integration Using Trigonometric Identities
- Definite Integrals
- Definite Integral as the Limit of a Sum
- Fundamental Theorem of Calculus
- Evaluation of Definite Integrals by Substitution
- Properties of Definite Integrals
Applications of the Integrals
Differential Equations
- Introduction of Differential Equations
- Basic Concepts of Differential Equation
- Order and Degree of a Differential Equation
- General and Particular Solutions of a Differential Equation
- Formation of a Differential Equation Whose General Solution is Given
- Procedure to Form a Differential Equation that Will Represent a Given Family of Curves
- Methods of Solving First Order, First Degree Differential Equations
- Differential Equations with Variables Separable Method
- Homogeneous Differential Equations
- Linear Differential Equations
- Solutions of Linear Differential Equation
Vectors
- Introduction of Vector
- Basic Concepts of Vector Algebra
- Vectors and Their Types
- Addition of Vectors
- Properties of Vector Addition
- Multiplication of a Vector by a Scalar
- Components of a Vector
- Vector Joining Two Points
- Section Formula
- Product of Two Vectors
- Scalar (Or Dot) Product of Two Vectors
- Projection of a Vector on a Line
- Vector (Or Cross) Product of Two Vectors
- Magnitude and Direction of a Vector
- Position Vector of a Point Dividing a Line Segment in a Given Ratio
- Scalar Triple Product of Vectors
Three-dimensional Geometry
- Introduction of Three Dimensional Geometry
- Direction Cosines and Direction Ratios of a Line
- Equation of a Line in Space
- Angle Between Two Lines
- Shortest Distance Between Two Lines
- Equation of a Plane in Normal Form
- Equation of a Plane Perpendicular to a Given Vector and Passing Through a Given Point
- Equation of a Plane Passing Through Three Non Collinear Points
- Intercept Form of the Equation of a Plane
- Plane Passing Through the Intersection of Two Given Planes
- Coplanarity of Two Lines
- Angle Between Two Planes
- Distance of a Point from a Plane
- Angle Between Line and a Plane
- Vector and Cartesian Equation of a Plane
- Vector and Cartesian Equations of a Line
Linear Programming
Probability
- Introduction of Probability
- Conditional Probability
- Properties of Conditional Probability
- Multiplication Theorem on Probability
- Bayes’ Theorem
- Random Variables and Its Probability Distributions
- Mean of a Random Variable
- Variance of a Random Variable
- Bernoulli Trials and Binomial Distribution
- Independent Events
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