#### 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

- general term of the AP

## Notes

nth term of an AP is also known as last term or general term.

Let a be the first term of an AP and d be the common difference then a standard form of an AP will be a, a+d, a+2d, a+3d,............. and so on upto nth term.

In an AP terms can also be written as `a_1, a_2, a_3, a_4,........, a_n`

`a_1= a+ (1-1)d`

`a_2= a+d= a+ (2-1)d`

`a_3= a+2d= a+ (3-1)d`

`a_4= a+3d= a+ (4-1)d`

And so on...

So if we generalize this pattern we get

`a_n= a+ (n-1)d`

Example- In an AP 2, 7, 12, ........... Then find a20

`a= 2, n=20, d= a_2-a_1= 7-2= 5`

`a_20= 2+ (20-1)5`

= `2+ 19(5)`

= `2+ 95`

`a_20= 97`

Now, what will do if we are asked find nth term form the end? So, we will use a different approch.

Let a be the first term of an AP and d be the common difference then a standard form of an AP will be `a, a+d, a+2d, a+3d, ......, l ` where `l` is a last term.

If the last term is `l` then the term before l will be `l-d`, and if the second last term is `l-d` then `l-d-d` i.e `l-2d` will be the term before it and so on.

First term from the end`= l= l- (1-1)d`

Second term from the end`= l-d= l- (2-1)d`

Third term form the end`= l-2d= l- (3-1)d`

And so on...

So if we generalize this pattern we get

nth term from the end= `l- (n-1)d`

Example- 4, 9, 14, ....., 254 Find the 10th term from the end

`a= 4, n=10, d= a_2-a_1= 9-4= 5, l=254`

nth term from the end=` l- (n-1)d`

10th term from the end= `254- (10-1)5`

= `254- (9)5`

= `254-45`

10th term from the end= `209`