Academic year:

## Topics with syllabus and resources

1.00 Rational Numbers

- Introduction of Rational Numbers
- Properties of Rational Numbers
- Representation of Rational Numbers on the Number Line
- Rational Numbers Between Two Rational Numbers

- Properties of rational numbers
- Representation of rational numbers online number
- Rational number between two rational numbers

2.00 Linear Equations in One Variable

- Introduction of Linear Equation
- Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Some Applications
- Solving Equations Having the Variable on Both Sides
- Some More Applications
- Reducing Equations to Simpler Form
- Equations Reducible to the Linear Form

- Solving linear equations having variable on one side
- Application of linear equations
- Solving linear equations having variable on both sides
- Some more application of linear equations
- Reducing equations to simpler form

3.00 Understanding Quadrilaterals

- Polygons
- Convex and Concave Polygons
- Convex polygons
- Concave polygons

- Convex and Concave Polygons
- Sum of the Measures of the Exterior Angles of a Polygon
- Types of Quadrilaterals
- Introduction of Quadrilaterals
- Plane surface, Plane curve.

- Kinds of Quadrilaterals
- Some Special Parallelograms
- Concept of a Rectangle
- Property: The diagonals of a rectangle are of equal length

- Concept of a Square
- Property: The diagonals of a square are perpendicular bisectors of each other.

- Concept of a Rectangle

- Polygons
- Sum of the measures of exterior angles of polygons
- Kinds of quadrilaterals
- Properties of parallelogram
- Some special parallelograms

4.00 Practical Geometry

- Constructing a quadrilateral: when the length of four side and diagonal are given
- When two diagonals and three sides are given
- When two adjacent sides and three angles are known
- When three side and two included angles are given
- Some special cases : Square
- Some special cases : Rhombus

5.00 Data Handling

- Looking for Information
- Data is represented graphically, Pictograph, Bar graph, Double Bar Graph

- Organising Data
- Grouping Data
- Introduction of Grouping Data
- Grouped Frequency Distribution,
- Class Interval,
- Lower class limit, Upper class limit

- Bars with a Difference
- Histogram

- Introduction of Grouping Data
- Graphical Representation of Data as Histograms
- Introduction of Circle Graph Or Pie Chart
- Circle Graph Or Pie Chart - Drawing Pie Charts
- Chance and Probability - Getting a Result
- Chance and Probability - Equally Likely Outcomes
- Chance and Probability - Linking Chances to Probability
- Chance and Probability - Outcomes as Events
- Chance and Probability Related to Real Life

- Looking for information
- Organizing data, Grouping data
- Circle graph or pie charts
- Chance and probability

6.00 Squares and Square Roots

- Introduction of Square Numbers
- Properties of Square Numbers
- Some More Interesting Patterns
- Adding triangular numbers
- Numbers between square numbers
- Adding odd numbers
- Sum of consecutive natural numbers
- Product of two consecutive even or odd natural numbers
- Some more patterns in square numbers

- Finding the Square of a Number - Other Patterns in Squares
- Finding the Square of a Number - Pythagorean Triplets
- Square Roots - Finding Square Roots
- Square Roots - Finding Square Root Through Repeated Subtraction
- Square Roots - Finding Square Root Through Prime Factorisation
- Prime factorisation of a Number, Prime factorisation of its Square

- Square Roots - Finding Square Root by Division Method
- Square Roots of Decimals
- Estimating Square Root

- Square of a number
- Finding Square root of a number by repeated subtraction
- Finding Square root of a number by prime factorization method
- Finding Square root of a number by long division method
- Square root of decimals
- Estimation of square root

7.00 Cubes and Cube Roots

- Introduction of Cubes and Cube Root
- Cubes
- Introduction for Cubes
- Perfect cubes or cube numbers

- Some Interesting Patterns
- Adding consecutive odd numbers
- Cubes and their prime factors

- Introduction for Cubes
- Cube Roots

- Cubes
- Cube roots
- Cube root of a cube number

8.00 Comparing Quantities

- Calculation of Percentage
- Decimal Fraction
- Recalling Ratios and Percentages
- Finding the Increase Or Decrease per Cent
- Concept of Finding Discounts
- Discount is a reduction given on the Marked Price

- Finding Discounts - Estimation in Percentages
- Prices Related to Buying and Selling (Profit and Loss)
- Finding Cost Price/Selling Price, Profit %/Loss%
- Sales Tax/Value Added Tax
- Concept of Compound Interest
**I = `"PNR"/100`.**

In this formula I = Interest, P = Principal, N = Number of years and R = Rate of interest at p.c.p.a.**For more information :**

1. Some times the interest is calculated at an interval of six months. For the duration of N years, if rate is R and if the interest to be calculated six monthly then the rate is to be taken as `R/2` and the duration is considered as 2N stages of six months.2. Many banks charge the compound interest monthly. At that time they take the interest rate as `R/12` monthly and the duration is taken 12 x N stages of months and interest is calculated.

3. Now a days banks calculate compound interest daily.

- Deducing a Formula for Compound Interest
- Rate Compounded Annually Or Half Yearly (Semi Annually)
- Applications of Compound Interest Formula
- Concept of Percentage

- Recalling ratio and percentage, finding the increase or decrease percentage, finding discount, Prices related to buying and selling, Sales tax/ value added tax
- Compound Interest, Deducing formula for compound interest, Rate compounded half yearly
- Application of compound interest

9.00 Algebraic Expressions and Identities

- Concept of Expression
- Number line and an expression

- Terms, Factors and Coefficients
- Monomials, Binomials and Polynomials
- Monomial, Binomial, Trinomial, Polynomial.

- Like and Unlike Terms
- Addition and Subtraction of Algebraic Expressions
- Multiplication of Algebraic Expressions: Introduction
- Multiplying a Monomial by a Monomial
- Multiplying a Monomial by a Polynomial
- Multiplying a Polynomial by a Polynomial
- Concept of Identity
- What is an Identity

- Standard Identities
- Applying Identities

- What are expressions?
- Addition and subtraction of algebraic expressions
- Multiplication of algebraic expressions: multiplication of monomial with monomial and monomial with a polynomials
- Multiplication of polynomial with a polynomial
- What is Identity? standard identities

10.00 Visualizing Solid Shapes

- Views of 3D-shapes
- Mapping Space Around Us
- Perspective is very important for drawing a picture but it is not relevant for a map

- Faces, Edges and Vertices

- Views of 3D shapes
- Mapping shapes around us
- Faces, Edges and vertices

11.00 Mensuration

- Introduction of Mensuration
- Area of Trapezium
- Area of a General Quadrilateral
- Triangulation
- Area of special quadrilaterals

- Area of a Polygon
- Concept of Solid Shapes
- Right Circular Cylinders, Cuboid, Cylinder, Cone, Cube, Pyramid

- Surface Area and Volume of Cube, Cuboid and Cylinder
- Volume of Cube, Cuboid and Cylinder
- Volume and Capacity

- Area of trapezium
- Area of general quadrilateral
- Area of polygon
- Surface area of cube, cuboid and cylinder
- Volume of cube, cuboid and cylinder
- Volume and capacity

12.00 Exponents and Powers

- Powers with Negative Exponents
- Laws of Exponents
- Use of Exponents to Express Small Numbers in Standard Form
- Comparing Very Large and Very Small Numbers

- Numbers with negative and positive exponents
- Law of exponents, use of exponents to express very small and very big numbers

13.00 Direct and Inverse Proportions

- Direct proportion
- Inverse Proportion

14.00 Factorization

- Factors of Natural Numbers
- Factors of Algebraic Expressions
- Factorisation
- Division of Algebraic Expressions - Division of a Monomial by Another Monomial
- Division of Algebraic Expressions - Division of a Polynomial by a Monomial
- Division of Algebraic Expressions Continued (Polynomial รท Polynomial)
- Concept of Find the Error

- "What is Factorization? method of common factors
- Factorization by regrouping terms"
- Factorisation using identities
- Division of algebraic expression

15.00 Introduction to Graphs

- Concept of Bar Graph
- Concept of Pie Graph (Or a Circle-graph)
- Concept of Histogram
- Concept of a Line Graph
- Linear Graphs - Location of a Point
- Linear Graphs - Coordinates
- Some Applications
- Independent variable
- Dependent variable
- Quantity and Cost
- Principal and Simple Interest
- Time and Distance

- Bar graphs, pie graph and line graph
- Linear graphs
- Applications of linear graphs

16.00 Playing with Numbers

- Numbers in General Form
- Games with Numbers
- Letters for Digits
- Tests of Divisibility - Divisibility by 10
- Tests of Divisibility - Divisibility by 5
- Tests of Divisibility - Divisibility by 2
- Tests of Divisibility - Divisibility by 9 and 3

- Numbers in general form, reversing the digits of number
- Letters for digits
- Test for divisibility by 2,3
- Test for divisibility by 5, 9, 10

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