#### 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

**The perpendicular bisector of a line segment:**

Fold a sheet of paper. Let `bar"AB"` be the fold. Place an ink-dot X, as shown, anywhere.

Find the image X' of X, with AB as the mirror line.

Let `bar"AB"` and `bar"XX’"` intersect at O.

This means that `bar"AB" "divides" bar"XX’"` into two parts of equal length.

`bar"AB" "bisects" bar"XX’" or bar"AB" "is a bisector of" bar"XX’"`.

Hence, `bar"AB" "is the perpendicular bisector of" bar"XX’"`.

**Construction using ruler and compasses:**

**Step 1:** Draw a line segment `bar"AB"` of any length.

**Step 2:** With A as the centre, using compasses, draw a circle. The radius of your circle should be more than half the length of `bar"AB"`.

**Step 3: **With the same radius and with B as centre, draw another circle using compasses. Let it cut the previous circle at C and D.

**Step 4:** Join `bar"CD". "It cuts" bar"AB"` at O.

Use your divider to verify that O is the midpoint of `bar"AB"`.

Therefore, `bar"CD" "is the perpendicular bisector of" bar"AB".`