Tests for Divisibility of Numbers - Divisibility by 4

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

• Concept of Cube Number
• Concept of Cube Root
• Concept of Cube Root
• Cube Root Through Prime Factorisation Method

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

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

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

• Method of Solving a Linear Inequality
• Word Problems on Linear Equations
• Equations Reducible to Linear Equations

Linear Inequations

• Pair of Linear Equations in Two Variables
• Replacement Set and Solution Set
• Operation of Whole Numbers on Number Line
• Concept of Properties

Understanding Shapes

• Different Types of Curves - Closed Curve, Open Curve, Simple Curve.
• Basic Concept of Polygons
• Sum of Interior Angles of a Polygon
• Sum of Exterior Angles of a Polygon
• Basic Concept of Regular Polygon
• Quadrilaterals

Special Types of Quadrilaterals

• Properties of Trapezium
• Properties of a Parallelogram
• Properties of Rectangle
• Properties of Rhombus
• Property: The diagonals of a square are perpendicular bisectors of each other.

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

Area of a Trapezium and a Polygon

• Perimeter of Triangle
• Perimeter of a Rectangle
• Perimeter of Squares
• Area of Trapezium
• Area of a Parallelogram
• Area of a Rhombus
• Area of Circle

Surface Area, Volume and Capacity

• Surface Area of a Combination of Solids
• Surface Area of a Cuboid
• Surface Area of a Cube
• Surface Area of a Cuboid
• Mensuration of Cylinder
• Surface Area of a Cuboid

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

• Concept of Probability