Topics
Number System
Rational Numbers
- Rational Numbers
- Addition of Rational Number
- Subtraction of Rational Number
- Multiplication of Rational Numbers
- Division of Rational Numbers
- Rational Numbers on a Number Line
- Inserting Rational Numbers Between Two Given Rational Numbers
- Method of Finding a Large Number of Rational Numbers Between Two Given Rational Numbers
Exponents
- Concept of Exponents
- Law of Exponents (For Integral Powers)
- Negative Integral Exponents
- More About Exponents
Squares and Square Root
- Concept of Square Roots
- Finding Square Root by Division Method
- Finding Square Root Through Prime Factorisation
- To Find the Square Root of a Number Which is Not a Perfect Square (Using Division Method)
- Properties of Square Numbers
Cubes and Cube Roots
Playing with Numbers
- Arranging the Objects in Rows and Columns
- Generalized Form of Numbers
- Some Interesting Properties
- Letters for Digits (Cryptarithms)
- Divisibility by 10
- Divisibility by 2
- Divisibility by 5
- Divisibility by 3
- Divisibility by 6
- Divisibility by 11
- Divisibility by 4
Sets
- Concept of Sets
- Representation of a Set
- Cardinality of a Set
- Types of Sets
- Subset
- Proper Subset
- Super Set
- Universal Set
- Complement of a Set
- Difference of Two Sets
- Distributive Laws
- Venn Diagrams
Ratio and Proportion
Percent and Percentage
Profit, Loss and Discount
- Overhead Expenses
- To Find S.P., When C.P. and Gain (Or Loss) Percent Are Given
- To Find C.P., When S.P. and Gain (Or Loss) Percent Are Given
- Concept of Discount
Interest
- Calculation of Interest
- Concept of Compound Interest
- To Find the Principle (P); the Rate Percent (R) and the Time
- Interest Compounded Half Yearly
- Applications of Compound Interest Formula
Direct and Inverse Variations
- Types of Variation
- Unitary Method
- Concept of Arrow Method
- Time and Work
Algebra
Algebraic Expressions
- Algebraic Expressions
- Degree of Polynomial
- Factors and Common Factors
- Classification of Terms in Algebra
- Combining like Terms
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Polynomial
- Multiplying a Polynomial by a Polynomial
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial
- Dividing a Polynomial by a Polynomial
- Simplification of Expressions
Identities
- Algebraic Identities
- Product of Sum and Difference of Two Terms
- Expansion Form of Numbers
- Important Formula of Expansion
- Cubes of Binomials
- Application of Formulae
Factorisation
- Factorisation by Taking Out Common Factors
- Factorisation by Taking Out Common Factors
- Factorisation by Grouping
- Factorisation by Difference of Two Squares
- Factorisation of Trinomials
- Factorising a Perfect Square Trinomial
- Factorising Completely
Linear Equations in One Variable
Linear Inequations
- Pair of Linear Equations in Two Variables
- Replacement Set and Solution Set
- Operation of Whole Numbers on Number Line
- Concept of Properties
Geometry
Understanding Shapes
Special Types of Quadrilaterals
Constructions
- Introduction of Constructions
- Construction of an Angle
- To Construct an Angle Equal to Given Angle
- To Draw the Bisector of a Given Angle
- Construction of an Angle Bisector: 30°, 45°, 60°, 90°
- Construction of Bisector of a Line
- The Perpendicular Bisector
- Construction of Parallel Lines
- Constructing a Quadrilateral
- Construction of Parallelograms
- Construction of a Rectangle When Its Length and Breadth Are Given.
- Construction of Rhombus
- Square: Properties and Construction
- Reflection Symmetry (Mirror Symmetry)
Representing 3-D in 2-D
- 2dimensional Perspective of 3dimensional Objects
- Concept of Polyhedron
- Faces, Edges and Vertices of Polyhedron
- Euler's Formula
- Concept of Polyhedron
- Nets of 3D Figures
Mensuration
Area of a Trapezium and a Polygon
Surface Area, Volume and Capacity
Data Handling (Statistics)
Data Handling
- Mathematical Data Collection and Organisation
- Frequency
- Raw Data, Arrayed Data and Frequency Distribution
- Cumulative Frequency and Cumulative Frequency Table
- Frequency Distribution Table
- Class Intervals and Class Limits
- Frequency Distribution and Its Applications
Probability
- Introduction
- Exploring Different Types of Sets
- Real-Life Applications
- Key Points Summary
CISCE: Class 6
Introduction
A set is simply a group of objects that have something in common.
Think about your favourite books, the days of the week, or all your friends—you group them together because they share a common feature.
CISCE: Class 6
Exploring Different Types of Sets
| Type of Set | Definition | Example |
|---|---|---|
| Finite Set | A set with a limited number of elements that can be counted. | P = {Natural numbers less than 50 } = {1, 2, 3, ..., 49} |
| Infinite Set | A set with an unlimited number of elements that cannot be counted. | Q = Set of whole numbers ={0, 1, 2, 3, ...} |
| Empty Set (Null Set) | A set that contains no elements. | Ø (No elements) |
| Equal Sets | Two sets with identical elements. | A = {1, 2, 3, 4} B = {Natural numbers less than 5} |
| Equivalent Sets | Two sets with the same number of elements, but not necessarily identical. | A = {x, y, z} B = {Patna, Calcutta, Delhi} |
| Disjoint Sets | Two sets with no common elements. | A = {Set of students in Class X} and B = {Set of students in Class XII} |
| Overlapping Sets | Two sets with at least one common element. | A = {5, 6, 7, 8, 9, 10} and B = {4, 6, 8, 10, 12} 6, 8 and 10 are common. |
CISCE: Class 6
Real-Life Aplications
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Finite set: The set of students in your class (you can count them!)
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Infinite set: The set of numbers—counting never ends!
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Empty set: The set of green elephants in your city.
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Equal sets: Two baskets, each with a mango, a banana, and an apple.
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Equivalent sets: Your desk has {pen, pencil, eraser}; your friend’s desk has {book, sharpener, ruler}. Both have 3 items.
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Disjoint sets: Group A is kids who have cats, and Group B is kids who have dogs—if nobody has both.
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Overlapping sets: Group A is kids who play football, and Group B is kids who play chess—some kids do both!
CISCE: Class 6
Key Points Summary
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Finite set: countable.
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Infinite set: never-ending.
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Empty set: no items at all.
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Equal sets: name things.
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Equivalent sets: same number, different things.
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Disjoint sets: nothing in common.
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Overlapping sets: some things in common.
