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
 Cardinal Number of a Set
 Types of Sets
 Subset
 Proper Subset
 Number of Subsets and Proper Subsets of a Given Set
 Super Set
 Universal Set
 Complement of a Set
 Set Operations
 Difference of Two Sets
 Distributive Laws
 Venn Diagrams
Ratio and Proportion
Percent and Percentage
Profit, Loss and Discount
 Concept of 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
 Computation of Tax
 Goods and Service Tax (Gst)
 Gst Comprises of
Interest
 Concept of Principal, Interest, Amount, and Simple 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
 Variations
 Types of Variation
 Direct Variation
 Inverse Variation
 Concept for Unitary Method (With Only Direct Variation Implied)
 Concept of Arrow Method
 Time and Work
Algebra
Algebraic Expressions
 Algebraic Expressions
 Degree of Polynomial
 Product , Factor and Coefficient
 Like and Unlike Terms
 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
 Simple Linear Equations in One Variable
 Solving Linear Inequations
 Linear Equation in One Variable
 Equations Reducible to the Linear Form
Linear Inequations
 Linear Equation in Two Variables
 Replacement Set and Solution Set
 Operation of Whole Numbers on Number Line
 Concept of Properties
Geometry
Understanding Shapes
 Different Types of Curves  Closed Curve, Open Curve, Simple Curve.
 Concept of Polygone
 Sum of Angles of a Polynomial
 Sum of Exterior Angles of a Polynomial
 Regular Polynomial
 Concept of Quadrilaterals  Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
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 Angles of 60°,30°,90° and 45°
 Construction of Bisector of a Line
 Drawing the Perpendicular Bisector of a Line Segment
 Construction of Parallel Lines
 Constructing a Quadrilateral
 Construction of Parallelograms
 Construction of a Rectangle When Its Length and Breadth Are Given.
 Construction of Rhombus
 Construction of Square
 Concept of Reflection Symmetry
Representing 3D in 2D
 2dimensional Perspective of 3dimensional Objects
 Concept of Polyhedron
 Faces, Edges and Vertices
 Euler's Formula
 Concept of Polyhedron
 Nets for Building 3d Shapes  Cube, Cuboids, Cylinders, Cones, Pyramid, and Prism
Mensuration
Area of a Trapezium and a Polygon
Surface Area, Volume and Capacity
Data Handling (Statistics)
Data Handling
 Concept of Data Handling
 Collecting Data
 Frequency
 Raw Data, Arrayed Data and Frequency Distribution
 Constructing a Frequency Table
 Frequency Distribution Table
 Class Intervals and Class Limits
 Graphical Representation of Data
Probability
Definition
Variations: If the values of two quantities depend on each other in such a way that a change in one causes a corresponding change in the other, then the two quantities are said to be in variation.
Notes
Variations:

The value of a variable is not constant and keeps on changing. There are many quantities whose value varies as per the circumstances means variation in one quantity bringing in variation in the other quantity.

If the values of two quantities depend on each other in such a way that a change in one causes a corresponding change in the other, then the two quantities are said to be in variation.

For example:
 If the number of articles purchased increases, the total cost also increases.
 More the money deposited in a bank more is the interest earned.
 As the speed of a vehicle increases, the time taken to cover the same distance decreases.
 For a given job, the more the number of workers less will be the time taken to complete the work.
If you would like to contribute notes or other learning material, please submit them using the button below.