Self-Paced Learning

1

- Meaning of Sets
- Finite and Infinite Sets
- Subsets and Supersets
- Equality of Sets
- The Universal Set, the Unit Set and the Empty Set
- The Cardinality of a Set
- The Intersection of Sets
- The Union of Sets
- Venn Diagrams
- Disjoint Sets
- Power Set
- Classification Involving Three Sets
- Laws of Algebra of Sets

2

- Rule of Combination
- Closure Property
- Commutative Property
- Associative Property
- Distributive Property
- The Identity Element
- The Inverse Element

3

- Notation
- Laws of Indices
- Logarithms
- Laws of Logarithsm
- Common Logarithms

4

- Surds
- Rules of Surds
- Basic Forms
- Similar Surds
- Conjugate Surds
- Rationalizing the Denominator
- Equality of Surds
- Equations in Irrational Forms

5

- Sequences
- Linear Sequence
- Exponential Sequence
- Series
- Other Progressions

6

- Notation
- Basic Rules of Inequalities
- Linear Inequalities in One Variable
- Quadratic Inequalities in One Variable
- Absolute Values
- Inequalities in Two Variables

7

- Mapping
- Function
- One-One-Mapping
- Onto-Mapping
- Graphical Representations of Mappings
- Special Mappings
- Composite Mapping
- Inverse Functions

8

- Statements
- Negation
- Conditional Statement

9

- Calculating Devices
- The Abacus
- The Slide Rule
- Pocket Calculator
- The Computer

10

- Quadrants and Angles
- Basic Trigonometric Ratios
- Ratios of the General Angle
- Ratios for Special Angles
- Graphs of Trigonometric Function
- Trigonometric Identities and Equations
- Trigonometric Equations

11

- Number Systems
- Decimal System
- Binary System
- The Octal System
- Hexadecimal System
- Conversion to Base Ten
- Conversion from Base Ten to an Arbitrary Base
- Relationship Between Binary, Octal and Hexadecimal Numbers

12

- Cartesian Co-ordinates
- Distance Between two Points
- The Mid-point of a Line Segment
- Division of a Line in a Given Ratio
- Gradients
- Equation of a Line
- Intersecting Lines
- Locus of Points
- Determination of Law

13

- The Flowchart
- The Computer Language
- Computer Programming Statements
- Flowchart Language
- Loops and Counters

14

- Scalars and Vectors
- Addition and Subtraction of Vectors
- Multiplication of a Vector by a Scalar
- Position Vectors
- Components of a Vector in Two Dimensions
- Components of a Vector in Three Dimensions

15

- Displacement
- Velocity
- Relative Velocity
- Acceleration
- Motion of Aircraft and Boat

16

- The Scalar Product of Two Vectors
- Projections
- Basic Properties of the Dot Product
- Trigonometric Applications of the Dot Product
- Geometrical Applications of the Dot Product

17

- The Subject of Statistics
- Classification of Data
- Grouped Frequency Distribution
- Cumulative Frequency Distribution
- Diagrammatic and Graphical Presentation of Data

18

- Central Tendency
- The Arithmetic Mean
- The Median
- The Mode
- Median and Mode from Interpolation Formulae
- Advantages and Disadvantages of Mean, Median and Mode

19

- Dispersion
- The Mean Deviation
- Interquartile Range
- and Semi-Interquartile Range
- Variance and Standard Deviation

20

- Meaning of Operations Research
- History and Nature of Operations Research
- Steps in operations Research
- Models in Operation Research
- Simultaneous inequalities
- Linear Programming
- Transportation Model
- Assignment Models