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 to Basic Concepts in 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 = 42 is at 4th position. similarly, 25 = 52 is at the 5th position; 49 = 72 is at the 7th 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 a1,a2,a3,a4,..... then a1 is first, a2 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 f1, f2, f3, . . . 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 a1 = 2, a2 = 11, a3 = -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,........`
