1. Rational Numbers
Basic Properties
Commutative Property
a+b=b+a
a×b=b×a
Associative Property
(a + b) + c = a + (b + c)
(a × b) × c = a × (b × c)
Distributive Property
a × (b + c) = ab + ac
2. Linear Equations in One Variable
General form of a linear equation:
ax + b = 0
Solution:
x = −b / a
Example:
2x + 4 = 0
x = −
x = −2
3. Understanding Quadrilaterals
Sum of interior angles of a quadrilateral
= 360°
Polygon Interior Angle Formula
Sum of interior angles:
(n − 2) × 180°
Where n = number of sides
4. Practical Geometry
There are construction methods used for drawing shapes:
Important constructions:
, Constructing quadrilaterals
Constructing polygons
Constructing triangles
Tools used:
Compass
Ruler
Protractor
5. Data Handling
Mean
Mean = Sum of observations / Number of observations
Probability
Probability =
Number of favorable outcomes / Total number of outcomes
6. Squares and Square Roots
Square
Square of a number:
n² = n × n
Example:
7² = 49
Square Root
√n × √n = n
Example:
√64 = 8
7. Cubes and Cube Roots
Cube
n³ = n × n × n
Example:
3³ = 27
Basic Properties
Commutative Property
a+b=b+a
a×b=b×a
Associative Property
(a + b) + c = a + (b + c)
(a × b) × c = a × (b × c)
Distributive Property
a × (b + c) = ab + ac
2. Linear Equations in One Variable
General form of a linear equation:
ax + b = 0
Solution:
x = −b / a
Example:
2x + 4 = 0
x = −
x = −2
3. Understanding Quadrilaterals
Sum of interior angles of a quadrilateral
= 360°
Polygon Interior Angle Formula
Sum of interior angles:
(n − 2) × 180°
Where n = number of sides
4. Practical Geometry
There are construction methods used for drawing shapes:
Important constructions:
, Constructing quadrilaterals
Constructing polygons
Constructing triangles
Tools used:
Compass
Ruler
Protractor
5. Data Handling
Mean
Mean = Sum of observations / Number of observations
Probability
Probability =
Number of favorable outcomes / Total number of outcomes
6. Squares and Square Roots
Square
Square of a number:
n² = n × n
Example:
7² = 49
Square Root
√n × √n = n
Example:
√64 = 8
7. Cubes and Cube Roots
Cube
n³ = n × n × n
Example:
3³ = 27
