Topics
Number Systems
Number Systems
Algebra
Polynomials
Linear Equations in Two Variables
Algebraic Expressions
Algebraic Identities
Coordinate Geometry
Geometry
Introduction to Euclid’S Geometry
Lines and Angles
 Introduction to Lines and Angles
 Basic Terms and Definitions
 Intersecting Lines and Nonintersecting Lines
 Parallel Lines
 Pairs of Angles
 Parallel Lines and a Transversal
 Lines Parallel to the Same Line
 Angle Sum Property of a Triangle
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
Area
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
Constructions
 Introduction of Constructions
 Basic Constructions
 Some Constructions of Triangles
Mensuration
Areas  Heron’S Formula
Surface Areas and Volumes
Statistics and Probability
Statistics
Probability
 Variable
 Constant
 Algebraic Expressions
 Value of Expression
 Number line and an expression
Definition
 Variable: Variable means something that can vary, i.e. change.
 Constant: Constant term is a term in an algebraic expression that has a value that is constant or cannot change because it does not contain any modifiable variables.
 Algebraic expressions: Algebraic expressions are formed from variables and constants. We use the operations of addition, subtraction, multiplication, and division on the variables and constants to form expressions.
Notes
Algebraic Expressions:
1. Variable:

The word variable means something that can vary, i.e. change.

A variable takes on different numerical values; its value is not fixed.

Variables are denoted usually by letters of the alphabets, such as x, y, z, l, m, n, p, etc.

From variables, we form expressions.
2. Constant:

A constant term is a term in an algebraic expression that has a value that is constant or cannot change because it does not contain any modifiable variables.

Example, x^{2} + 2x + 3, the 3 is a constant term.
3. Algebraic expressions:

Algebraic expressions are formed from variables and constants. We use the operations of addition, subtraction, multiplication, and division on the variables and constants to form expressions.

For example, the expression 4xy + 7 is formed from the variables x and y and constants 4 and 7. The constant 4 and the variables x and y are multiplied to give the product 4xy and the constant 7 is added to this product to give the expression.
4. Value of an expression:

The expressions are formed by performing operations like addition, subtraction, multiplication, and division on the variables.

From y, we formed the expression (10y – 20). For this, we multiplied y by 10 and then subtracted 20 from the product.

The value of an expression thus formed depends upon the chosen value of the variable.
when y =15, 4 y + 5 = 4 × 15 + 5 = 65;
when y =0, 4 y + 5 = 4 × 0 + 5 = 5.
6. Number line and an expression:
1) Consider the expression x + 5.
Let us say the variable x has a position X on the number line; X may be anywhere on the number line, but it is definite that the value of x + 5 is given by a point P, 5 units to the right of X.
2) What about the position of 4x and 4x + 5?
The position of 4x will be point C; the distance of C from the origin will be four times the distance of X from the origin. The position D of 4x + 5 will be 5 units to the right of C.