#### Topics

##### Geometrical Constructions

- Constructing a Bisector of an Angle
- Drawing a Perpendicular to a Line at a Point on the Line
- The Property of the Angle Bisectors of a Triangle
- Perpendicular Bisectors of the Sides of an Acute-angled Triangle
- Perpendicular Bisectors of the Sides of an Obtuse-angled Triangle
- Construction of Triangles
- Constructing a Triangle When the Length of Its Three Sides Are Known (SSS Criterion)
- Constructing a Triangle When the Lengths of Two Sides and the Measure of the Angle Between Them Are Known. (SAS Criterion)
- Construct a Triangle Given Two Angles and the Included Side
- Construct a Right-angled Triangle Given the Hypotenuse and One Side
- Congruence Among Line Segments
- Congruence of Angles
- Congruence of Circles

##### Multiplication and Division of Integers

- Concept for Natural Numbers
- Concept for Whole Numbers
- Negative and Positive Numbers
- Concept of Integers
- Addition of Integers
- Addition of Integers on Number line
- Subtraction of Integers
- Multiplication of a Positive and a Negative Integers
- Multiplication of Two Negative Integers
- Multiplication of Two Positive Integers
- Division of Integers

##### HCF and LCM

##### Angles and Pairs of Angles

##### Operations on Rational Numbers

- Rational Numbers
- Addition of Rational Number
- Additive Inverse of Rational Number
- Subtraction of Rational Number
- Multiplication of Rational Numbers
- Division of Rational Numbers
- Rational Numbers Between Two Rational Numbers
- Decimal Representation of Rational Numbers
- BODMAS - Rules for Simplifying an Expression

##### Indices

- Concept of Exponents
- Concept of Square Number
- Concept of Cube Number
- Laws of Exponents
- Multiplying Powers with the Same Base
- Dividing Powers with the Same Base
- Taking Power of a Power
- Multiplying Powers with Different Base and Same Exponents
- Dividing Powers with Different Base and Same Exponents
- Numbers with Exponent Zero, One, Negative Exponents
- Miscellaneous Examples Using the Laws of Exponents
- Expressing Large Numbers in the Standard Form
- Finding the Square Root of a Perfect Square

##### Joint Bar Graph

##### Algebraic Expressions and Operations on Them

- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Like and Unlike Terms
- Types of Algebraic Expressions as Monomials, Binomials, Trinomials, and Polynomials
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Multiplication of Algebraic Expressions
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Binomial
- Multiplying a Binomial by a Binomial
- Equations in One Variable

##### Direct Proportion and Inverse Proportion

##### Banks and Simple Interest

##### Circle

##### Perimeter and Area

##### Pythagorasâ€™ Theorem

##### Algebraic Formulae - Expansion of Squares

##### Statistics

## Example

Solve the following equation.

2x + 2 = 8

2x + 2 = 8

∴ 2x + 2 - 2 = 8 - 2

∴ 2x = 6

∴ x = 3

## Example

Solve the following equation.

3x - 5 = x - 17

3x - 5 = x - 17

3x - 5 + 5 - x = x - 17 + 5 - x

∴ 2x = - 12

∴ x = - 6

## Example

The length of a rectangle is 1 cm more than twice its breadth. If the perimeter of the rectangle is 50 cm, find its length.

Let the breadth of the rectangle be x cm.

Then the length of the rectangle will be (2x +1)cm.

2 × length + 2 × breadth = perimeter of rectangle

2 (2x + 1) + 2x = 50

∴ 4x + 2 + 2x = 50

∴ 6x + 2 = 50

∴ 6x = 50 - 2 = 48

∴ x = 8

Breadth of rectangle is 8 cm.

Length of the rectangle = 2x + 1 = 2 × 8 + 1

∴ Length of rectangle = 17 cm.

## Example

**Solve the following equation.**

The sum of two consecutive natural numbers is 69. Find the numbers.

Let one natural number be x.

The next natural number is x + 1

(x) + (x + 1) = 69

∴ x + x + 1 = 69

∴ 2x + 1 = 69

2x = 69 - 1

∴ 2x = 68

∴ x = 34

1^{st} natural number = 34

2^{nd} natural number = 34 + 1 = 35.