#### Topics

##### Relations and Functions

- Introduction of Relations and Functions
- Ordered Pair
- Cartesian Product
- Concept of Relation
- Concept of Functions
- Representation of Functions
- Types of Functions
- Special Cases of Functions
- Composition of Functions
- Identifying the Graphs of Linear, Quadratic, Cubic and Reciprocal Functions

##### Numbers and Sequences

- Introduction of Numbers and Sequences
- Euclid’s Division Lemma
- Euclid’s Division Algorithm
- Fundamental Theorem of Arithmetic
- Modular Arithmetic
- Sequence
- Arithmetic Progression
- Series
- Geometric Progression
- Sum to n Terms of a Geometric Progression
- Special Series

##### Algebra

- Introduction to Algebra
- Simultaneous Linear Equations in Three Variables
- GCD and LCM of Polynomials
- Rational Expressions
- Square Root of Polynomials
- Quadratic Equations
- Graph of Variations
- Quadratic Graphs
- Matrices

##### Geometry

- Introduction of Geometry
- Similarity of Triangles
- Thales Theorem and Angle Bisector Theorem
- Right-angled Triangles and Pythagoras Property
- Converse of Pythagoras Theorem
- Circles and Tangents
- Concurrency Theorems

##### Coordinate Geometry

- Coordinate Geometry
- Area of a Triangle by Heron's Formula
- Area of a General Quadrilateral
- Inclination of a Line
- Straight Line
- General Form of a Straight Line

##### Trigonometry

##### Mensuration

- Mensuration
- Surface Area of Cylinder
- Surface Area of a Right Circular Cone
- Surface Area of a Sphere
- Frustum of a Cone
- Volume of a Cylinder
- Volume of a Right Circular Cone
- Volume of a Sphere
- Volume of Frustum of a Cone
- Surface Area and Volume of Different Combination of Solid Figures
- Conversion of Solids from One Shape to Another with No Change in Volume

##### Statistics and Probability

- Introduction of Statistics and Probability
- Measures of Dispersion
- Coefficient of Variation
- Probability
- Algebra of Events
- Addition Theorem of Probability

## Definition

A set of numbers where the numbers are arranged in a definite order, like the natural numbers, is called a **sequence**.

## Notes

We write numbers 1, 2, 3, 4, . . . in an order. In this order we can tell the position of any number. For example, number 13 is at 13th position. The numbers 1, 4, 9, 16, 25, 36, 49, . . . are also written in a particular order. Here 16 = 4^{2} is at 4^{th} position. similarly, 25 = 5^{2} is at the 5^{th} position; 49 = 7^{2} is at the 7^{th} position. In this set of numbers also, place of each number is detremined.

In a sequence a particular number is written at a particular position. If the numbers are written as a_{1},a_{2},a_{3},a_{4},..... then a_{1} is first, a_{2} is second, . . . and so on. It is clear that an is at the nth place. A sequence of the numbers is also represented by alphabets f_{1}, f_{2}, f_{3}, . . . and we find that there is a definite order in which numbers are arranged.When students stand in a row for drill on the playground they form a sequence.We have experienced that some sequences have a particular pattern.Complete the given pattern

Look at the patterns of the numbers. Try to find a rule to obtain the next number from its preceding number. This helps us to write all the next numbers. See the numbers 2, 11, -6, 0, 5, -37, 8, 2, 61 written in this order.

Here a_{1} = 2, a_{2} = 11, a_{3} = -6, . . . This list of numbers is also a sequence. But in this case we cannot tell why a particular term is at a particular position ; similarly we cannot tell a definite relation between the consecutive terms.

In general, only those sequences are studied where there is a rule which determines the next term.

For example (1) 4, 8, 12, 16 . . . (2) 2, 4, 8, 16, 32, . . . (3)`1/5,1/10,1/15,1/20,........`