#### Topics

##### Number System

##### Integers

- Concept of Integers
- Multiplication and Division of Integers
- Properties of Operations on Integers
- Concept for Commutativity, Associativity, Existence of Identity
- Inverse and Distributivity
- Problem Solving Using Operations on Integers
- Statement Problems on Integers Using All Fundamental Operations.

##### Rational Numbers

- Rational Numbers
- Word Problems on Rational Numbers (All Operations)
- Decimal Representation of Rational Numbers
- Concept for Problem Solving Using Operations on Rational Numbers
- Concept of Decimal Numbers

##### Fractions (Including Problems)

- Concept of Fractions
- Concept for Fraction as an Operator
- Concept for Reciprocal of a Fraction

##### Decimal Fractions (Decimals)

- Concept of Decimal Numbers
- Concept for Multiplication
- Division of Decimal Numbers

##### Exponents (Including Laws of Exponents)

- Concept of Exponents
- Concept for Exponents Only Natural Numbers.
- Laws of Exponents (Through Observing Patterns to Arrive at Generalisation.)
- Concept for Application of Laws of Exponents in Simple Daily Life Problems

##### Commercial Arithmetic

##### Ratio and Proportion (Including Sharing in a Ratio)

##### Unitary Method (Including Time and Work)

- Concept of Unitary Method (Including Time and Work)
- Unitary Method Continued, Consolidation, General Expression for Unitary Method .
- Relation Between Speed, Time and Distance

##### Percent and Percentage

- Concept of Percent and Percentage
- Concept for Understanding Percentage as a Fraction with Denominator 100
- Converting Fractional Numbers to Percentage
- Converting Decimals to Percentage

##### Profit, Loss and Discount

- Concept of Discount
- Concept for Application to Profit and Loss (Single Transaction Only)

##### Simple Interest

- Concept of Principal, Interest, Amount, and Simple Interest
- Concept for Application to Simple Interest (Time Period in Complete Years).

##### Algebra

##### Fundamental Concepts (Including Fundamental Operations)

- Fundamental Concepts
- Terms, Factors and Coefficients of Expression
- Algebraic Expressions
- Performs Operations (Addition and Subtraction) on Algebraic Expressions with Integral Coefficients Only.

##### Simple Linear Equations (Including Word Problems)

- Simple Linear Equations in One Variable
- Simple Linear Equations in One Variable
- Concept for Inequalities
- Concept for Solution of Simple Inequalities in One Variable

##### Set Concepts (Some Simple Divisions by Vedic Method)

- Concept of Set Concepts
- Concept for Revision Idea of Sets
- Universal Set
- Concept for Cardinal Property of Sets

##### Geometry

##### Lines and Angles (Including Construction of Angles)

- Introduction to Lines and Angles
- Concept for Pairs of Angles
- Properties of Parallel Lines
- Construction of a Line Parallel to a Given Line from a Point Outside It .

##### Triangles

- Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle
- Concept for Angle Sum Property
- Concept for Exterior Angle Property
- Concept for Construction of Simple Triangles.

##### Pythagoras Theorem

##### Symmetry (Including Reflection and Rotation)

- Concept of Symmetry
- Concept of Reflection Symmetry
- Concept for Idea of Rotational Symmetry, Observations of Rotational Symmetry of 2-d Objects. (900, 1200, 1800)

##### Recognition of Solids (Representing 3-d in 2-d)

- Concept of Recognition of Solids
- Faces, Edges and Vertices
- Concept for Mapping the Space Around Approximately Through Visual Estimation.

##### Congruency: Congruent Triangles

- Congruence of Triangles
- Concept for Congruence Through Superimposition
- Extend Congruence to Simple Geometrical Shapes E.G. Triangles, Circles.
- Criteria for Congruence of Triangles

##### Mensuration

- Mensuration
- Concept of Perimeter
- Circumference of a Circle
- Concept of Area
- Concept of Measurement Using a Basic Unit Area of a Square, Rectangle, Triangle, Parallelogram and Circle, Rings and Combined Figures.

##### Data Handling (Statistics)

##### Data Handling

- Concept of Data Handling
- Concept for Collection and Organisation of Data – Choosing the Data to Collect for a Hypothesis Testing
- Arithmetic Mean - Raw Data
- Arithmetic Mean - Range
- Concept of Median
- Concept of Mode
- Concept for Constructing
- Interpretation of Bar Graphs

##### Probability

- Basic Ideas of Probability
- Concept for Feel of Probability Using Data Through Experiments.
- Concept for Notion of Chance
- Concept for Tabulating and Counting Occurrences
- Comparing the Observation with that for a Coin. Observing Strings of Throws, Notion of Randomness.

## Notes

**Decimal Representation of Rational Numbers:**

**1) Write the rational number `7/4` in decimal form.**

(1) 7 = 7.0 = 7.000 (Any number of zeros can be added after the fractional part.)

(2) 1 is the quotient and 3 the remainder after dividing 7 by 4. Now we place a decimal point after the integer 1. Writing the 0 from the dividend after the remainder 3, we divide 30 by 4. As the quotient, we get now is fractional, we write 7 after the decimal point. Again we bring down the next 0 from the dividend and complete the division.

**2) Write `2 1/5` in decimal form. **

We shall find the decimal form of `2 1/5 = 11/5` in three different ways.

Find the decimal form of `1/5`.

∴ `1/5` = 0.2

**3) Write the number `2/11` in decimal form.**

∴ `2/11` = 0.1818.......

`2/11 = 0.bar18`

**4) Work out the decimal form of `5/6`.**

`5/6` = 0.833...

`∴ 5/6 = 0.8dot3`

Here, a single digit or a group of digits occurs repeatedly on the right of the decimal point. This type of decimal form of a rational number is called the recurring decimal form.

If in a decimal fraction, a single-digit occurs repeatedly on the right of the decimal the point, we put a point above it as shown here. `5/6 = 0.8dot3` and if a group of digits occurs repeatedly, we show it with a horizontal line above the digits. Thus, `2/11 = 0.bar18`.