#### 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.