Topics
Number Systems
Number Systems
Polynomials
Algebra
Coordinate Geometry
Linear Equations in Two Variables
Geometry
Coordinate Geometry
Introduction to Euclid’S Geometry
Mensuration
Statistics and Probability
Lines and Angles
- Introduction to Lines and Angles
- Basic Terms and Definitions
- Intersecting Lines and Non-intersecting Lines
- Introduction to Parallel Lines
- Pairs of Angles
- Parallel Lines and a Transversal
- Angle Sum Property of a Triangle
Triangles
- Concept of Triangles
- Congruence of Triangles
- Criteria for Congruence of Triangles
- Properties of a Triangle
- Some More Criteria for Congruence of Triangles
- Inequalities in a Triangle
Quadrilaterals
- Concept of Quadrilaterals
- Properties 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
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
- 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, x2 + 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:
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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:
-
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, x2 + 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:
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, x2 + 2x + 3, the 3 is a constant term.
-
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:
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.
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.
