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
1. Whole Number on the number line:
A line that graphically represents the real numbers as a series of points whose distance from an origin is proportional to their value.
The distance between these points labelled as 0 and 1 is called unit distance.
A number written on the left-hand side of the number line is the smaller number and the number written on the right-hand side of the number line is the greater number.
We take a line, mark a point on it and label it 0. We then mark out points to the right of 0, at equal intervals. Label them as 1, 2, 3,... Thus, we have a number line with the whole numbers represented on it. We can easily perform the number operations of addition, subtraction, and multiplication on the number line.
2. Operation on Number Line:
1) Addition on the number line:
Let us see the addition of 2 and 5.
Start from 2. Then move 5 places to the right will give 7. The sum of 2 and 5 is 7, i.e. 2 + 5 = 7. Addition corresponds to moving to the right on the number line.
2) Subtraction on the number line:
Let us find 9 – 6.
Start from 9. Since 6 is being subtracted, so move 6 places towards left will give 3. We get 7 – 5 = 2. Subtraction corresponds to moving to the left on the number line.
3) Multiplication on the number line:
Multiplication corresponds to making jumps of equal distance starting from zero.
Let us find 2 × 6.
Start from 0, move 2 units at a time to the right, make such 6 moves.
You will reach 12. So, we say, 2 × 6 = 12.
4) Division on a number line:
A number line can be used to divide. To work out 15 ÷ 3, count how many 'jumps' of 3 it takes to get from 0 to 15. 5 'jumps' or 'groups' of 5 means 15 ÷ 3 = 5.
