#### 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

## Notes

Before we start with the introduction let us try to recall what we studied earlier about Polynomials.

1) Polynomials in one variable and their degrees. Eg `x^2+x^5+x^3+x` is polynomial in one variable i.e. variable x. And the degrees here are 2, 5, 3, 1.

2) If p(x) is a polynomial in x, highest power of x in p(x) is called degree of p(x). Take the example, here the degree of polynomial is 5, because 5 is the highest degree in p(x).

3) A polynomial of degree 1 is called a linear polynomial. Eg. x+4 is a linear polynomial as the highest degree here is 1.

4) A polynomial of degree 2 is called a quadratic polynomial. `x^2-9` is a example of Qadratic Polynomial, as 2 is the highest degree.

5) A polynomial of degree 3 is called a Cubic Polynomial. For example `x^3+5x+11` is Cubic Polynomial sicnce the highest degree is 3.

6) If p(x) is a polynomial in x, and if k is any real number, then the value obtained by replacing x by k is p(x), is called the value of p(x) at x=k, and is denoted by p(k). For example, `p(x)=x^3+1` if x=4 then `p(4)=4^3+1= 64+1= 65`

7) A real number k is said to be a zero of a polynomial p(x), if p(k)=0. Let's take a example, if `p(x)=x^3-8`, and x=2 the `p(2)= 2^3-8= 8-8= 0`. Thus any value of x that makes p(x) as 0 that is called zeros of polynomial.

Now let us understand more about Polynomials through a real life example, Manav works at three differen places to earn more money in a day. The employer at the first place pays him 2x as salary where x is the number of hours he work. At the second place Manav is paid with `x^2` while at the third place he earns `x^3`. So the total amount of money is represented as p(x) and `p(x)= 2x+x^2+x^3`

Here in this example we have only one variable i.e x

#### Video Tutorials

#### Shaalaa.com | Polynomials , Ex 2.1 Q1

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