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
Squares and Square Root
Cubes and Cube Roots
Playing with Numbers
Sets
Ratio and Proportion
Percent and Percentage
Profit, Loss and Discount
Interest
Direct and Inverse Variations
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
Factorisation
Linear Equations in One Variable
Linear Inequations
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 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 3-D in 2-D
Mensuration
Area of a Trapezium and a Polygon
Surface Area, Volume and Capacity
Data Handling (Statistics)
Data Handling
Probability
notes
Divisibility by 4:
A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.
Take 212 as an example and think of another four-digit example which is 1936. Observe the number formed by the ones and tens places of 212. It is 12; which is divisible by 4. 212 is also divisible by 3. For 1936 it is 36, again divisible by 4.
More Examples:
Is the number 98731812 divisible by 4?
Take the last two digits in the given number,
Last two digit is 12, which is divisible by 4,
So 98731812 is divisible by 4.
Is the number 3426941365 divisible by 4?
The last two digits of the number is 65, which is not divisible by 4,
So the number 3426941365 is not divisible by 4.
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