Topics
Rational Numbers
 Concept of Rational Numbers
 Closure Property of Rational Numbers
 Commutativity Property of Rational Numbers
 Associativity of Rational Numbers
 Distributivity of Multiplication Over Addition for Rational
 Identity of Addition and Multiplication
 Negative of a Number
 Additive Inverse of Rational Number
 Rational Numbers on a Number Line
 Rational Numbers Between Two Rational Numbers
Linear Equations in One Variable
 The Idea of a Variable
 Expressions with Variables
 Concept of Equation
 Balancing an Equation
 The Solution of an Equation
 Linear Equation in One Variable
 Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
 Some Applications Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
 Solving Equations Having the Variable on Both Sides
 Some More Applications on the Basis of Solving Equations Having the Variable on Both Sides
 Reducing Equations to Simpler Form
 Equations Reducible to the Linear Form
Understanding Quadrilaterals
 Concept of Curves
 Different Types of Curves  Closed Curve, Open Curve, Simple Curve.
 Concept of Polygons  Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal
 Classification of Polygons  Regular Polygon, Irregular Polygon, Convex Polygon, Concave Polygon, Simple Polygon and Complex Polygon
 Angle Sum Property of a Quadrilateral
 Interior Angles of a Polygon
 Exterior Angles of a Polygon and Its Property
 Concept of Quadrilaterals  Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
 Properties of Trapezium
 Properties of Kite
 Properties of a Parallelogram
 Properties of Rhombus
 Property: The Opposite Sides of a Parallelogram Are of Equal Length.
 Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
 Property: The adjacent angles in a parallelogram are supplementary.
 Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
 Property: The diagonals of a rhombus are perpendicular bisectors of one another.
 Property: The Diagonals of a Rectangle Are of Equal Length.
 Properties of Rectangle
 Properties of a Square
 Property: The diagonals of a square are perpendicular bisectors of each other.
Practical Geometry
 Introduction to Practical Geometry
 Constructing a Quadrilateral When the Lengths of Four Sides and a Diagonal Are Given
 Constructing a Quadrilateral When Two Diagonals and Three Sides Are Given
 Constructing a Quadrilateral When Two Adjacent Sides and Three Angles Are Known
 Constructing a Quadrilateral When Three Sides and Two Included Angles Are Given
 Some Special Cases
Data Handling
 Concept of Data Handling
 Interpretation of a Pictograph
 Interpretation of Bar Graphs
 Drawing a Bar Graph
 Interpretation of a Double Bar Graph
 Drawing a Double Bar Graph
 Organisation of Data
 Frequency Distribution Table
 Graphical Representation of Data as Histograms
 Concept of Pie Graph (Or a Circlegraph)
 Interpretation of Pie Diagram
 Chance and Probability  Chance
 Basic Ideas of Probability
Squares and Square Roots
 Concept of Square Number
 Properties of Square Numbers
 Some More Interesting Patterns of Square Number
 Finding the Square of a Number
 Concept of Square Roots
 Finding Square Root Through Repeated Subtraction
 Finding Square Root Through Prime Factorisation
 Finding Square Root by Division Method
 Square Root of Decimal Numbers
 Estimating Square Root
Cubes and Cube Roots
Comparing Quantities
 Concept of Ratio
 Concept of Percent and Percentage
 Increase Or Decrease as Percent
 Concept of Discount
 Estimation in Percentages
 Concepts of Cost Price, Selling Price, Total Cost Price, and Profit and Loss, Discount, Overhead Expenses and GST
 Sales Tax, Value Added Tax, and Good and Services Tax
 Concept of Principal, Interest, Amount, and Simple Interest
 Concept of Compound Interest
 Deducing a Formula for Compound Interest
 Rate Compounded Annually Or Half Yearly (Semi Annually)
 Applications of Compound Interest Formula
Algebraic Expressions and Identities
 Algebraic Expressions
 Terms, Factors and Coefficients of Expression
 Types of Algebraic Expressions as Monomials, Binomials, Trinomials Or Polynomials
 Like and Unlike Terms
 Addition of Algebraic Expressions
 Subtraction of Algebraic Expressions
 Multiplication of Algebraic Expressions
 Multiplying Monomial by Monomials
 Multiplying a Monomial by a Binomial
 Multiplying a Monomial by a Trinomial
 Multiplying a Binomial by a Binomial
 Multiplying a Binomial by a Trinomial
 Concept of Identity
 Expansion of (a + b)2 = a2 + 2ab + b2
 Expansion of (a  b)2 = a2  2ab + b2
 Expansion of (a + b)(a  b)
 Expansion of (x + a)(x + b)
Visualizing Solid Shapes
Mensuration
Exponents and Powers
Direct and Inverse Proportions
Factorization
 Factors and Multiples
 Factorising Algebraic Expressions
 Factorisation by Taking Out Common Factors
 Factorisation by Regrouping Terms
 Factorisation Using Identities
 Factors of the Form (x + a)(x + b)
 Dividing a Monomial by a Monomial
 Dividing a Polynomial by a Monomial
 Dividing a Polynomial by a Polynomial
 Concept of Find the Error
Introduction to Graphs
 Concept of Bar Graph
 Interpretation of Bar Graphs
 Drawing a Bar Graph
 Concept of Double Bar Graph
 Interpretation of a Double Bar Graph
 Drawing a Double Bar Graph
 Concept of Pie Graph (Or a Circlegraph)
 Graphical Representation of Data as Histograms
 Concept of a Line Graph
 Linear Graphs
 Linear Graphs
 Some Application of Linear Graphs
Playing with Numbers
definition
 Polyhedron: A polyhedron is a closed space figure whose faces are polygons. A polyhedron is said to be regular if its faces are made up of regular polygons and the same number of faces meet at each vertex.
 Platonic solids: A regular polyhedron is made up of regular polygons. Such solids are also known as ‘platonic solids’.
 Nonpolyhedron: A nonpolyhedron is not a closed space figure, maybe one or more of the sides is a curved surface.
notes
Polyhedron:

A polyhedron is a closed space figure whose faces are polygons.

The word polyhedron has Greek origins, meaning many faces.

A solid figure consisting of four or more plane faces (all polygons), pairs of which meet along an edge, three or more edges meeting at a vertex.

Each of these solids is made up of polygonal regions which are called its faces; these faces meet at edges which are line segments, and the edges meet at vertices which are points. Such solids are called polyhedrons.
Types of the polyhedron:

A polyhedron is said to be regular if its faces are made up of regular polygons and the same number of faces meet at each vertex. any polyhedron that does not meet these conditions is considered irregular.

Regular Polyhedron
Irregular Polyhedron
This polyhedron is regular. Its faces are congruent, regular polygons. Vertices are formed by the same number of faces.
This polyhedron is not regular. All the sides are congruent, but the vertices are not formed by the same number of faces. 3 faces meet at A but 4 faces meet at B.
Regular polyhedra:
A regular polyhedron is a polyhedron whose faces are all congruent, regular polygons. A regular polyhedron is named based on its number of faces. There are only five polyhedra that are regular polyhedra; these are referred to as Platonic solids.
The five Platonic solids
Name 
Sketch 
Number of faces 
Tetrahedron 
4  
Cube 
6  
Octahedron 
8  
Dodecahedron 
12  
Icosahedron 
20 
In the above table, each regular polyhedra is named based on its number of faces. The net below each sketch shows a 2D picture of all of the faces of the polyhedron.
NonPolyhedrons:
A nonpolyhedron is not a closed space figure, maybe one or more of the sides is a curved surface. Thus, Solids with curved faces are called Nonpolyhedrons.
Example: Sphere, Cylinder, Cone, etc.
Concave and Convex polyhedrons:
 Convex Polyhedron: If the surface of a polyhedron does not intersect itself and the line segment connecting any two points of the polyhedron lies within its interior part or surface then such a polyhedron is a convex polyhedron.
 Concave Polyhedron: A nonconvex polyhedron is termed as a concave polyhedron.