#### Topics

##### Number Systems

##### Real Numbers

##### Algebra

##### Polynomials

##### Pair of Linear Equations in Two Variables

- Linear Equation in Two Variables
- Graphical Method of Solution of a Pair of Linear Equations
- Substitution Method
- Elimination Method
- Cross - Multiplication Method
- Equations Reducible to a Pair of Linear Equations in Two Variables
- Consistency of Pair of Linear Equations
- Inconsistency of Pair of Linear Equations
- Algebraic Conditions for Number of Solutions
- Simple Situational Problems
- Pair of Linear Equations in Two Variables
- Relation Between Co-efficient

##### Quadratic Equations

- Quadratic Equations
- Solutions of Quadratic Equations by Factorization
- Solutions of Quadratic Equations by Completing the Square
- Nature of Roots of a Quadratic Equation
- Relationship Between Discriminant and Nature of Roots
- Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
- Application of Quadratic Equation

##### Arithmetic Progressions

##### Coordinate Geometry

##### Lines (In Two-dimensions)

##### Constructions

- Division of a Line Segment
- Construction of Tangents to a Circle
- Constructions Examples and Solutions

##### Geometry

##### Triangles

- Similar Figures
- Similarity of Triangles
- Basic Proportionality Theorem (Thales Theorem)
- Criteria for Similarity of Triangles
- Areas of Similar Triangles
- Right-angled Triangles and Pythagoras Property
- Similarity of Triangles
- Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
- Triangles Examples and Solutions
- Angle Bisector
- Similarity of Triangles
- Ratio of Sides of Triangle

##### Circles

- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Tangent to a Circle
- Number of Tangents from a Point on a Circle
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles

##### Trigonometry

##### Introduction to Trigonometry

- Trigonometry
- Trigonometry
- Trigonometric Ratios
- Trigonometric Ratios and Its Reciprocal
- Trigonometric Ratios of Some Special Angles
- Trigonometric Ratios of Complementary Angles
- Trigonometric Identities
- Proof of Existence
- Relationships Between the Ratios

##### Trigonometric Identities

##### Some Applications of Trigonometry

##### Mensuration

##### Areas Related to Circles

- Perimeter and Area of a Circle - A Review
- Areas of Sector and Segment of a Circle
- Areas of Combinations of Plane Figures
- Circumference of a Circle
- Area of Circle

##### Surface Areas and Volumes

- Surface Area of a Combination of Solids
- Volume of a Combination of Solids
- Conversion of Solid from One Shape to Another
- Frustum of a Cone
- Concept of Surface Area, Volume, and Capacity
- Surface Area and Volume of Different Combination of Solid Figures
- Surface Area and Volume of Three Dimensional Figures

##### Statistics and Probability

##### Statistics

##### Probability

##### Internal Assessment

- Decimal Representation of Rational Numbers in Terms of Terminating Or Non-terminating Recurring Decimals

## Notes

We must understand the terms Terminating and Non-terminating Recurring Decimals to learn this concept. Rational Numbers are of form `p/q` where q is not equal to 0, then the expansion is either a terminating decimal or a non-terminating recurring decimal. Terminating decimals are like 1.2, 1.3, 6.2, 6.3, etc. And Non-terminating recurring decimals are like 1.323232323232, 1.632632632632, etc.

## Theorem

1)Theorem: Let x be a rational number whose decimal expansion terminates. Then x can be

expressed in the form p, q where p and q are coprime, and the prime

factorisation of q is of the form `2^n5^m` where n, m are non-negative integers.

Example: Rational Number 1.2 can be written as `p/q=12/10`, i.e. `6/5,` here the factor for q is 5. Rational Number 1.07 can be written as `p/q=107/100`, here the factor for q is 2×5×2×5

2)Theorem: Let x=`p/q` be a rational number, such that prime factorisation of q is of form

`2^n5^m` where n, m are non-negative integers. Then x has a decimal expansion

which terminates.

Explanation: This is exactly the opposite of the previous theorem. If x=p/q=107/100 is a rational number, then here, x=1.07 is terminating.

3)Theorem: Let x=p/q be a rational number, such that the prime factorisation of q is not of

the form 2^n5^m where n, m are non-negative integers. Then, x has a decimal

expansion which is non-terminating recurring.

Explanation: Here, `x=p/q`, where p&q are coprime but in this case, q is not to the power of `2^n5^m`. Then x will always be Non-terminating Recurring. For example 3/14=0.214285714285