Topics
Sets and Relations
- Fundamental Concepts of Ordered Pairs and Relations
- Representation of a Set
- Intervals
- Classification of Sets
- Relations of Sets
Functions
- Functions
- Types of Functions
- Representation of Function
- Graph of a Function
- Fundamental Functions
- Algebra of Functions
- Composite Function
- Inverse Functions
- Some Special Functions
Complex Numbers 33
- Introduction of Complex Number
- Imaginary Number
- Concept of Complex Numbers
- Conjugate of a Complex Number
- Algebraic Operations of Complex Numbers
- Square Root of a Complex Number
- Solution of a Quadratic Equation in Complex Number System
- Cube Root of Unity
Sequences and Series
- Sequence, Series, and Progression
- Geometric Progression (G. P.)
- General Term Or the nth Term of a G.P.
- Sum to' n' Terms of a Geometric Progression
- Sum to' n' Terms of a Geometric Progression
- Recurring Decimals
- Harmonic Progression (H. P.)
- Types of Means
- Special Series (Sigma Notation)
Locus and Straight Line
- Locus
- Line
- Equations of Lines in Different Forms
- Equation of a Straight Line
Determinants
- Determinants
- Properties of Determinants
- Application of Determinants
- Determinant Method (Cramer’s Rule)
- Consistency of Three Linear Equations in Two Variables
- Area of a Triangle Using Determinants
- Collinearity of Three Points
Limits
- Definition of Limit of a Function
- Algebra of Limits
- Evaluation of Limits
- Direct Method
- Factorization Method
- Rationalization Method
- Limits of Exponential and Logarithmic Functions
Continuity
- Continuous and Discontinuous Functions
- Continuity of a Function at a Point
- Definition of Continuity
- Continuity from the Right and from the Left
- Properties of Continuous Functions
- Continuity in the Domain of the Function
- Examples of Continuous Functions Whereever They Are Defined
Differentiation
- The Meaning of Rate of Change
- Definition of Derivative and Differentiability
- Derivative by the Method of First Principle
- Rules of Differentiation (Without Proof)
- Applications of Derivatives
Partition Values
- Partition Values
- Deciles
- Percentiles
- Relations Among Quartiles, Deciles and Percentiles
- Graphical Location of Partition Values
Measures of Dispersion
- Measures of Dispersion
- Quartiles and Range in Statistics
- Measures of Dispersion > Variance and Standard Deviation
- Standard Deviation for Combined Data
- Coefficient of Variation
Skewness
- Skewness
- Asymmetric Distribution (Positive Skewness)
- Asymmetric (Negative Skewness)
- Measures of Skewness
- Karl Pearson’S Coefficient of Skewness (Pearsonian Coefficient of Skewness)
- Features of Pearsonian Coefficient
- Bowley’s Coefficient of Skewness
Bivariate Frequency Distribution and Chi Square Statistic
- Bivariate Frequency Distribution
- Classification and Tabulation of Bivariate Data
- Marginal Frequency Distributions
- Conditional Frequency Distributions
- Categorical Variables
- Contingency Table
- Chi-Square Statistic ( χ2 )
Correlation
- Correlation
- Concept of Covariance
- Properties of Covariance
- Concept of Correlation Coefficient
- Scatter Diagram
- Interpretation of Value of Correlation Coefficient
Permutations and Combinations
- Introduction of Permutations and Combinations
- Fundamental Principles of Counting
- Concept of Addition Principle
- Concept of Multiplication Principle
- Concept of Factorial Function
- Permutations
- Permutations When All Objects Are Distinct
- Permutations When Repetitions Are Allowed
- Permutations When All Objects Are Not Distinct
- Circular Permutations
- Properties of Permutations
- Combination
- Properties of Combinations
Probability
- Concept of Probability
- Elementary Types of Events in Probability
- Elementary Properties of Probability
- Addition Theorem of Probability
- Conditional Probability
- Multiplication Theorem on Probability
- Independent Events
Linear Inequations
- Linear Inequations
- Method of Solving a Linear Inequality
- Representation of Inequalities
- Graphical Solution of Linear Inequality of Two Variable
- Solution of System of Linear Inequalities in Two Variables
Commercial Mathematics
- Percentage
- Profit and Loss
- Simple and Compound Interest (Entrance Exam)
- Concept of Depreciation
- Partnership
- Shares
- Introduction
- Methods of Set Representation
- Number Sets with Different Methods
- Representing Sets Using Pictures
- Representing Sets Using Brackets
- Key Points Summary
CISCE: Class 6
Introduction
Sets help us collect and organise things that share something in common—like colours, numbers, or your favourite fruits.
How Can We Represent a Set?
- Description (Statement) Method
- Roster (List) Method
- Set-Builder Method
CISCE: Class 6
Methods of Set Representation
| Method | Explanation | Example |
|---|---|---|
| Description Method | Describe the set using words. | A set of odd natural numbers less than 15 |
| Roster or Tabular Method | The elements are listed within curly braces. | {1, 3, 5, 7, 9, 11, 13} |
| Rule or Set-Builder Method | The set is defined using a rule or formula. | { x : x is an odd natural number less than 15 } |
CISCE: Class 6
Number Sets with Different Methods
| Number Set | Description Method | Roster Method | Set-builder Method |
|---|---|---|---|
| Natural Numbers (N) | A set of all counting numbers starting from 1 | {1, 2, 3, 4, ...} | {x : x is a counting number starting from 1} |
| Whole Numbers (W) | A set containing zero and all natural numbers | {0, 1, 2, 3, 4, ...} | {x : x is a whole number} |
| Integers (Z or I) | A set containing negative natural numbers, zero, and natural numbers | {..., -3, -2, -1, 0, 1, 2, 3, ...} | {x : x is an integer} |
| Even Numbers (E) | A set of natural numbers divisible by 2 | {2, 4, 6, 8, ...} | {x : x is an even natural number} |
| Odd Numbers (O) | A set of natural numbers not divisible by 2 | {1, 3, 5, 7, 9, ...} | {x : x is an odd natural number} |
CISCE: Class 6
Representing Sets Using Pictures
A set or a collection of well-defined objects may also be represented by pictures drawn inside closed figures, like a circle, a rectangle, a square, etc.
Example:
1. A set of some fruits, such as
or 
2. A set of some sports goods, such as
or 
CISCE: Class 6
Representing Sets Using Brackets
Instead of showing (drawing) these pictures inside a circle, a rectangle, etc., we can also draw them within a pair of curly braces (brackets).
The two sets shown above by pictures can also be expressed by writing their names as shown below:
(i) {banana, apple, grapes, mango}.
(ii) {cricket bat, tennis racket, football, hockey}.
CISCE: Class 6
Key Points Summary
- Curly brackets
{}are always used - Three ways to write sets: Description, Roster, and Set-Builder
- No repeated items; order doesn’t matter
