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Class 8
Algebraic Expressions and Identities
Operations on Algebraic Expressions
Class 8
1.
Rational Numbers
1.1.
Standard Form of a Rational Number
1.2.
Representation of Rational Numbers on the Real Line
1.3.
Addition and Subtraction of Rational Numbers
1.3.1.
Addition of Rational Numbers
1.3.2.
Properties of Addition Of Rational Numbers
1.4.
Subtraction of Rational Numbers
1.5.
Multiplication and Division of Rational Numbers
1.5.1.
Multiplication of Rational Numbers
1.5.2.
Reciprocal of Rational Number
1.5.3.
Properties of Multiplication of Rational Numbers
1.5.4.
Division of Rational Numbers
1.6.
Rational Numbers Lying between Two Rational Number
1.7.
Simplifying Rational Numbers
1.8.
Word Problems on Rational Numbers
2.
Linear Equations in One Variable
2.1.
Solving Linear Equations by the Method of Transposition
2.2.
Word Problems Based on Linear Equations
3.
Understanding Shapes
3.1.
Curve
3.1.1.
Open Curve
3.1.2.
Closed Curve
3.1.3.
Simple Closed Curve
3.2.
Polygon
3.2.1.
Understanding Polygons
3.2.2.
Name the Polygon
3.2.3.
Concave and Convex Polygon
3.2.4.
Diagonals in a Polygon with
n
Sides
3.2.5.
Interior and the Exterior Angle of a Regular Polygon with
n
Sides
3.2.6.
Finding Magnitude of Unknown Angles in the Given Polygon
3.3.
Quadrilaterals
3.3.1.
Introduction to Quadrilaterals
3.3.2.
Angle Sum Property of a Quadrilateral
3.3.3.
Special Types of Quadrilaterals
4.
Practical Geometry
4.1.
Construction of a Quadrilateral
4.1.1.
When 4 Sides and 1 Diagonal are Given
4.1.2.
When 3 Sides and 2 Diagonal are Given
4.1.3.
When 2 Adjacent Sides and 3 Angles are Given
4.1.4.
When 3 Sides and 2 Included Angles are Given
4.1.5.
Construction using Special Properties
5.
Data Handling
5.1.
Frequency Distribution
5.1.1.
Frequency Distribution of Ungrouped Data
5.2.
Bar Graphs
5.2.1.
Creating Bar Graphs
5.2.2.
Interpreting Bar Graphs
5.3.
Pie Charts
5.3.1.
Drawing Pie Charts
5.3.2.
Interpret and Present Data as Pie Charts
6.
Probability
7.
Squares and Square Roots
7.1.
Square of a Number
7.1.1.
Square of a Number
7.1.2.
Perfect Square or Square Numbers
7.1.3.
Properties of Perfect Squares
7.1.4.
Sum of First
n
Odd Natural Numbers
7.1.5.
Pythagorean Triplets
7.1.6.
Using Identities to Find the Square of a Number
7.2.
Square Root
7.2.1.
Square Root by Prime Factorization
7.2.2.
Square Root by Long-Division Method
7.2.3.
Square Root of Numbers In Decimal Form
7.2.4.
Square Root of Fractions
7.2.5.
Square Root of Product of Integers
7.2.6.
Simplifying Expressions Involving Square Roots
7.3.
Word Problems On Squares And Square Roots
8.
Cubes and Cube Roots
8.1.
Cube of a Number
8.1.1.
Cube Of A Positive Number
8.1.2.
Cubes Of Negative Integers
8.1.3.
Cube Of A Rational Number
8.1.4.
Perfect Cube or Cube numbers
8.1.5.
Properties of Perfect Cubes
8.2.
Cube Root
8.2.1.
Cube Root Of a Perfect Cube by Prime Factorization
8.2.2.
Cube Root of a Negative Perfect Cube
8.2.3.
Cube Root of Product of Integers
8.2.4.
Cube Root of a Rational Number
8.2.5.
Cube Root Of A Decimal Number
8.2.6.
Simplifying Expressions Involving Cube Roots
8.3.
Word Problems on Cubes and Cube Roots
9.
Percentage
9.1.
Conversions
9.1.1.
Convert a Fraction into Percentage
9.1.2.
Convert a Percentage into Fraction
9.1.3.
Convert Percentage into a Ratio
9.1.4.
Convert a Ratio into Percentage
9.1.5.
Convert Percentage into Decimal form
9.1.6.
Convert Decimal into Percentage
9.2.
Percentage of a Quantity
9.3.
Solving Expressions Involving Percentages
9.4.
Word Problems on Percentage
10.
Profit and Loss
10.1.
Terms Related to Profit and Loss
10.2.
Problems on Finding the Gain/Loss and Gain%/Loss%
10.3.
Problems on Finding the SP of the Article
10.4.
Problems on Finding the CP of the Article
10.5.
Problems on Finding the Number of Articles
10.6.
Discount
10.7.
Tax
11.
Compound Interest
11.1.
Compound Interest Compounded Annually
11.1.1.
Compound Interest Compounded Annually and Rates are Same for All the Years
11.1.2.
Compound Interest Compounded Annually and Rates are Different for Different Years
11.1.3.
Compound Interest Compounded Annually and Time is a Fraction
11.2.
Finding Time When Compound Interest Compounded Annually
11.3.
Finding Rate When Compound Interest Compounded Annually
11.4.
Finding Principal When Compound Interest Compounded Annually
11.5.
Compound Interest Compounded Half-Yearly
11.6.
Compound Interest Compounded Quarterly
11.7.
Applications of Compound Interest
12.
Algebraic Expressions and Identities
12.1.
Operations on Algebraic Expressions
12.1.1.
Addition of Algebraic Expressions
12.1.2.
Subtraction of Algebraic Expressions
12.1.3.
Addition and Subtraction of Algebraic Expressions
12.1.4.
Multiplication of Algebraic Expressions
12.1.4.1.
Multiplication of Monomials
12.1.4.2.
Multiplication of a Monomial and a Binomial
12.1.4.3.
Multiplication of a Polynomial and a Monomial
12.1.4.4.
Multiplication of Binomials
12.1.4.5.
Multiplication of two Polynomials
12.1.4.6.
Simplify Expressions Involving Multiplication of Algebraic Expressions
12.1.5.
Division of Algebraic Expressions
12.1.5.1.
Division of a Monomial by a Monomial
12.1.5.2.
Division of a Polynomial by Another Polynomial
12.1.6.
Some Special Identities
13.
Visualising Solid Shapes
13.1.
Identifying 3-D Shapes
13.2.
Faces, Edges and Vertices of 3-D Shapes (Cuboid, Cube, Prism and Pyramid)
13.3.
Euler's Relation for 3-Dimensional Figures
14.
Mensuration
14.1.
Standard Units of Area
14.2.
Area and Perimeter
14.2.1.
Area and Perimeter of a Square
14.2.2.
Area and Perimeter of a Rectangle
14.2.3.
Area of 4 Walls of a Room
14.2.4.
Area between Two Rectangles
14.2.5.
Area and Perimeter of Triangles
14.2.6.
Area and Perimeter of Parallelogram and Rhombus
14.2.7.
Circumference and Area of a Circle
14.2.8.
Area Enclosed Between Two Different Shapes
14.2.9.
Area of a Trapezium
14.2.10.
Area of Polygon
14.2.10.1.
Area of Irregular Polygons
14.2.10.2.
Area of Regular Polygons
14.3.
Volume and Surface Area
14.3.1.
Volume and Surface Area of Cuboid
14.3.2.
Volume and Surface Area of Cube
14.3.3.
Volume and Surface Area of Cylinders
14.3.4.
Mixed Problems on Volume and Surface Area
15.
Exponents and Powers
15.1.
Exponent of a Rational Number
15.2.
Express Rational Numbers in Exponential Form
15.3.
Solving Expressions Involving Exponents
15.4.
Laws of Exponents
15.5.
Word Problems on Exponents
15.6.
Finding the Unknown from the Given Exponential Equation
15.7.
Standard Form of Large Numbers
15.8.
Standard Form of Small Numbers
15.9.
Operations on Large Numbers
16.
Direct and Inverse Proportions
16.1.
Direct Proportions
16.2.
Inverse Proportions
17.
Time and Work
18.
Factorization
18.1.
Factorization by Taking Out the Common Factor
18.2.
Factorization by Grouping
18.3.
Factorization When the Expression is a Difference of Two Squares
18.4.
Factorization When the Expression is a Perfect Square
18.5.
Factorization of Quadratic Trinomials
19.
Introduction to Graphs
19.1.
Understand the Terms Related to Co-ordinate Geometry
19.2.
Identify the Coordinates of a Point on the Cartesian Plane
19.3.
Identify the Coordinates of the Points on X-axis, Y-axis and the Origin
19.4.
Graphs of Multiples of Different Numbers
20.
Playing with Numbers
20.1.
Numbers in Generalized Form
20.2.
Tests of Divisibility
20.2.1.
Test Divisibility by 2
20.2.2.
Test Divisibility by 3
20.2.3.
Test Divisibility by 4
20.2.4.
Test Divisibility by 5
20.2.5.
Test Divisibility by 6
20.2.6.
Test Divisibility by 7
20.2.7.
Test Divisibility by 8
20.2.8.
Test Divisibility by 9
20.2.9.
Test Divisibility by 10
20.2.10.
Test Divisibility by 11
20.3.
Replacing Alphabets with Suitable Numbers
Class 8 NCERT (CBSE and ICSE)
Operations on Algebraic Expressions
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