Further Mathematics

### What You Get

Self-Paced Learning
1

### Sets

1. Meaning of Sets
2. Finite and Infinite Sets
3. Subsets and Supersets
4. Equality of Sets
5. The Universal Set, the Unit Set and the Empty Set
6. The Cardinality of a Set
7. The Intersection of Sets
8. The Union of Sets
9. Venn Diagrams
10. Disjoint Sets
11. Power Set
12. Classification Involving Three Sets
13. Laws of Algebra of Sets
2

### Binary Operations

1. Rule of Combination
2. Closure Property
3. Commutative Property
4. Associative Property
5. Distributive Property
6. The Identity Element
7. The Inverse Element
3

### Indices and Logarithms

1. Notation
2. Laws of Indices
3. Logarithms
4. Laws of Logarithsm
5. Common Logarithms
4

### Surds

1. Surds
2. Rules of Surds
3. Basic Forms
4. Similar Surds
5. Conjugate Surds
6. Rationalizing the Denominator
7. Equality of Surds
8. Equations in Irrational Forms
5

### Sequences and Series

1. Sequences
2. Linear Sequence
3. Exponential Sequence
4. Series
5. Other Progressions
6

### Inequalities

1. Notation
2. Basic Rules of Inequalities
3. Linear Inequalities in One Variable
4. Quadratic Inequalities in One Variable
5. Absolute Values
6. Inequalities in Two Variables
7

### Mapping and Functions

1. Mapping
2. Function
3. One-One-Mapping
4. Onto-Mapping
5. Graphical Representations of Mappings
6. Special Mappings
7. Composite Mapping
8. Inverse Functions
8

### Logic

1. Statements
2. Negation
3. Conditional Statement
9

### Calculating and Processing Devices I

1. Calculating Devices
2. The Abacus
3. The Slide Rule
4. Pocket Calculator
5. The Computer
10

### Trigonometric Ratio of the General Angle, Graphs and Indentities

2. Basic Trigonometric Ratios
3. Ratios of the General Angle
4. Ratios for Special Angles
5. Graphs of Trigonometric Function
6. Trigonometric Identities and Equations
7. Trigonometric Equations
11

### Calculating and Processing Devices II

1. Number Systems
2. Decimal System
3. Binary System
4. The Octal System
6. Conversion to Base Ten
7. Conversion from Base Ten to an Arbitrary Base
8. Relationship Between Binary, Octal and Hexadecimal Numbers
12

### The Straight Line

1. Cartesian Co-ordinates
2. Distance Between two Points
3. The Mid-point of a Line Segment
4. Division of a Line in a Given Ratio
6. Equation of a Line
7. Intersecting Lines
8. Locus of Points
9. Determination of Law
13

### Calculating and Processing Device III

1. The Flowchart
2. The Computer Language
3. Computer Programming Statements
4. Flowchart Language
5. Loops and Counters
14

### Vectors I

1. Scalars and Vectors
2. Addition and Subtraction of Vectors
3. Multiplication of a Vector by a Scalar
4. Position Vectors
5. Components of a Vector in Two Dimensions
6. Components of a Vector in Three Dimensions
15

### Relative Velocity

1. Displacement
2. Velocity
3. Relative Velocity
4. Acceleration
5. Motion of Aircraft and Boat
16

### Vectors II

1. The Scalar Product of Two Vectors
2. Projections
3. Basic Properties of the Dot Product
4. Trigonometric Applications of the Dot Product
5. Geometrical Applications of the Dot Product
17

### Graphical Representation of Data

1. The Subject of Statistics
2. Classification of Data
3. Grouped Frequency Distribution
4. Cumulative Frequency Distribution
5. Diagrammatic and Graphical Presentation of Data
18

### Measures of Central Tendency

1. Central Tendency
2. The Arithmetic Mean
3. The Median
4. The Mode
5. Median and Mode from Interpolation Formulae
19

### Measures of Dispersion and Coefficient of Variation

1. Dispersion
2. The Mean Deviation
3. Interquartile Range
4. and Semi-Interquartile Range
5. Variance and Standard Deviation
20

### Operations Research

1. Meaning of Operations Research
2. History and Nature of Operations Research
3. Steps in operations Research
4. Models in Operation Research
5. Simultaneous inequalities
6. Linear Programming
7. Transportation Model
8. Assignment Models
o
Topic-by-topic coverage of the curriculum or syllabus