#### Topics

##### Number Systems

##### Number Systems

##### Algebra

##### Polynomials

##### Linear Equations in Two Variables

##### Coordinate Geometry

##### Geometry

##### Coordinate Geometry

##### Mensuration

##### Introduction to Euclid’S Geometry

##### Lines and Angles

- Introduction to Lines and Angles
- Basic Terms and Definitions
- Intersecting Lines and Non-intersecting Lines
- Parallel Lines
- Pairs of Angles
- Parallel Lines and a Transversal
- Lines Parallel to the Same Line
- Angle Sum Property of a Triangle

##### Statistics and Probability

##### Triangles

##### Quadrilaterals

- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Angle Sum Property of a Quadrilateral
- Types of Quadrilaterals
- Another Condition for a Quadrilateral to Be a Parallelogram
- Theorem of Midpoints of Two Sides of a Triangle
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram

##### Circles

- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Angle Subtended by a Chord at a Point
- Perpendicular from the Centre to a Chord
- Circles Passing Through One, Two, Three Points
- Equal Chords and Their Distances from the Centre
- Angle Subtended by an Arc of a Circle
- Cyclic Quadrilateral

##### Areas - Heron’S Formula

##### Surface Areas and Volumes

##### Statistics

##### Algebraic Expressions

##### Algebraic Identities

##### Area

##### Constructions

- Introduction of Constructions
- Basic Constructions
- Some Constructions of Triangles

##### Probability

## Notes

A particular type of algebraic expression, called polynomial. The letters x,y,z etc. to denote variables where as 2x , 3x , -x , `-1/2`x are algebric expressions. . The values of the constants remain the same throughout a particular situation, that is, the values of the constants do not change in a given problem, but the value of a variable can keep changing.

Now, consider a square of side 3 units in following fig.

The perimeter of a square is the sum of the lengths of its four sides. Here, each side is 3 units. So, its perimeter is 4 × 3, i.e., 12 units. The perimeter is 4 × 10, i.e., 40 units. In case the length of each side is x units in following fig.

the perimeter is given by 4x units. So, as the length of the side varies, the perimeter varies.

It is `x × x = x^2` square units. `x^2` is an algebraic expression. You are also familiar with other algebraic expressions like 2x, `x^2` + 2x, `x^3` – `x^2` + 4x + 7. Note that, all the algebraic expressions we have considered so far have only whole numbers as the exponents of the variable. Expressions of this form are called polynomials in one variable.

In the polynomial `x^2 + 2x`, the expressions `x^2` and 2x are called the terms of the polynomial.There are many terms of the polynomial.Each term of a polynomial has a coefficient. So, in `–x^3 + 4x^2 + 7x – 2`, the coefficient of `x^3` is –1, the coefficient of `x^2` is 4, the coefficient of x is 7 and –2 is the coefficient of `x^0` (Remember, `x^0` = 1).

2 is also a polynomial. In fact, 2, –5, 7, etc. are examples of constant polynomials. The constant polynomial 0 is called the zero polynomial.

If the variable in a polynomial is x, we may denote the polynomial by p(x), or q(x), or r(x), etc. for example : `p(x) = 2x^2 + 5x – 3`

`q(x) = x_3 –1`.

A polynomial can have any (finite) number of terms.

Polynomials having only one term are called monomials (‘mono’ means ‘one’). example : 2x , 2.

Polynomials having only two terms are called binomials (‘bi’ means ‘two’) example : p(x) = x + 1, `q(x) = x^2 – x` .

Polynomials having only three terms are called trinomials (‘tri’ means ‘three’). example : `p(x) = x + x^2 + π`, `q(x) = sqrt2 + x – x^2`

The highest power of the variable in a polynomial as the degree of the polynomial.

For example `3x^7` the term with the highest power of x in this term is 7.

The degree of a non-zero constant polynomial is zero.

A polynomial of degree two is called a quadratic polynomial.

For example : `4y + 5y^2` , `5 – y^2`

A polynomial of degree three a cubic polynomial.

For example : , `5x^3 + x^2` , `2x^3 + 1`.