#### Topics

##### Rational Numbers

- Rational Numbers
- Closure Property of Rational Numbers
- Commutative Property of Rational Numbers
- Associative Property of Rational Numbers
- Distributive Property of Multiplication Over Addition for Rational Numbers
- Identity of Addition and Multiplication of Rational Numbers
- Negative Or Additive Inverse of Rational Numbers
- Reciprocal Or Multiplicative Inverse of Rational Numbers
- Rational Numbers on a Number Line
- Rational Numbers Between Two Rational Numbers

##### Linear Equations in One Variable

- The Idea of a Variable
- Expressions with Variables
- Concept of Equation
- Balancing an Equation
- The Solution of an Equation
- Linear Equation in One Variable
- Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Some Applications Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Solving Equations Having the Variable on Both Sides
- Some More Applications on the Basis of Solving Equations Having the Variable on Both Sides
- Reducing Equations to Simpler Form
- Equations Reducible to the Linear Form

##### Understanding Quadrilaterals

- Concept of Curves
- Different Types of Curves - Closed Curve, Open Curve, Simple Curve.
- Concept of Polygons - Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal
- Classification of Polygons
- Angle Sum Property of a Quadrilateral
- Interior Angles of a Polygon
- Exterior Angles of a Polygon and Its Property
- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Properties of Trapezium
- Properties of Kite
- Properties of a Parallelogram
- Properties of Rhombus
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Property: The adjacent angles in a parallelogram are supplementary.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Property: The diagonals of a rhombus are perpendicular bisectors of one another.
- Property: The Diagonals of a Rectangle Are of Equal Length.
- Properties of Rectangle
- Properties of a Square
- Property: The diagonals of a square are perpendicular bisectors of each other.

##### Practical Geometry

- Introduction to Practical Geometry
- Constructing a Quadrilateral When the Lengths of Four Sides and a Diagonal Are Given
- Constructing a Quadrilateral When Two Diagonals and Three Sides Are Given
- Constructing a Quadrilateral When Two Adjacent Sides and Three Angles Are Known
- Constructing a Quadrilateral When Three Sides and Two Included Angles Are Given
- Some Special Cases

##### Data Handling

- Concept of Data Handling
- Interpretation of a Pictograph
- Interpretation of Bar Graphs
- Drawing a Bar Graph
- Interpretation of a Double Bar Graph
- Drawing a Double Bar Graph
- Organisation of Data
- Frequency Distribution Table
- Graphical Representation of Data as Histograms
- Concept of Pie Graph (Or a Circle-graph)
- Interpretation of Pie Diagram
- Chance and Probability - Chance
- Basic Ideas of Probability

##### Squares and Square Roots

- Concept of Square Number
- Properties of Square Numbers
- Some More Interesting Patterns of Square Number
- Finding the Square of a Number
- Concept of Square Roots
- Finding Square Root Through Repeated Subtraction
- Finding Square Root Through Prime Factorisation
- Finding Square Root by Division Method
- Square Root of Decimal Numbers
- Estimating Square Root

##### Cubes and Cube Roots

##### Comparing Quantities

- Concept of Ratio
- Concept of Percent and Percentage
- Increase Or Decrease as Percent
- Concept of Discount
- Estimation in Percentages
- Concepts of Cost Price, Selling Price, Total Cost Price, and Profit and Loss, Discount, Overhead Expenses and GST
- Sales Tax, Value Added Tax, and Good and Services Tax
- Concept of Principal, Interest, Amount, and Simple Interest
- Concept of Compound Interest
- Deducing a Formula for Compound Interest
- Rate Compounded Annually Or Half Yearly (Semi Annually)
- Applications of Compound Interest Formula

##### Algebraic Expressions and Identities

- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Types of Algebraic Expressions as Monomials, Binomials, Trinomials, and Polynomials
- Like and Unlike Terms
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Multiplication of Algebraic Expressions
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Binomial
- Multiplying a Monomial by a Trinomial
- Multiplying a Binomial by a Binomial
- Multiplying a Binomial by a Trinomial
- Concept of Identity
- Expansion of (a + b)2 = a2 + 2ab + b2
- Expansion of (a - b)2 = a2 - 2ab + b2
- Expansion of (a + b)(a - b)
- Expansion of (x + a)(x + b)

##### Visualizing Solid Shapes

##### Mensuration

##### Exponents and Powers

##### Direct and Inverse Proportions

##### Factorization

- Factors and Multiples
- Factorising Algebraic Expressions
- Factorisation by Taking Out Common Factors
- Factorisation by Regrouping Terms
- Factorisation Using Identities
- Factors of the Form (x + a)(x + b)
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial
- Dividing a Polynomial by a Polynomial
- Concept of Find the Error

##### Introduction to Graphs

- Concept of Bar Graph
- Interpretation of Bar Graphs
- Drawing a Bar Graph
- Concept of Double Bar Graph
- Interpretation of a Double Bar Graph
- Drawing a Double Bar Graph
- Concept of Pie Graph (Or a Circle-graph)
- Graphical Representation of Data as Histograms
- Concept of a Line Graph
- Linear Graphs
- Linear Graphs
- Some Application of Linear Graphs

##### Playing with Numbers

## Notes

**Applications of Compound Interest Formula:**

There are some situations where we could use the formula for calculation of amount in CI. Here are a few.

- Increase (or decrease) in population.
- The growth of bacteria if the rate of growth is known.
- The value of an item, if its price increases or decreases in the intermediate years.

## Example

The population of a city was 20,000 in the year 1997. It increased at the rate of 5% p.a. Find the population at the end of the year 2000.

There is 5% increase in population every year, so every new year has new population.

Population in the beginning of 1998 = 20000

Increase at 5% = `5/100` × 20000 = 1000

Population in 1999 = 20000 + 1000 = **21000**

Increase at 5% = `5/100` × 21000 = 1050

Population in 2000 = 21000 + 1050 = **22050**

Increase at 5% = `5/100` × 22050 = 1102.5

At the end of 2000 the population = 22050 + 1102.5 = 23152.5

Population at the end of 2000 = 20000 `(1+5/100)^3`

`= 20000 xx 21/20 xx 21/20 xx 21/20`

= 23152.5

So, the estimated population = 23153.

## Example

A TV was bought at a price of ₹ 21,000. After one year the value of the TV was depreciated by 5% (Depreciation means reduction of value due to use and age of

the item). Find the value of the TV after one year.

Principal = ₹ 21,000

Reduction = 5% of ₹ 21000 per year

= ₹ `(21000 xx 5 xx 1)/100`

= ₹ 1050

Value at the end of 1 year = ₹ 21000 - ₹ 1050 = ₹ 19,950.

Value at the end of 1 year = ₹ `21000(1 - 5/100)`

= ₹ `21000 xx 19/20`

= ₹ 19,950.

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