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Grade 8
Rational Numbers
Multiplication and Division of Rational Numbers
Reciprocal of Rational Number

Grade 8

1. Rational Numbers

1.1. Understanding Rational Numbers

1.2. Standard Form of a Rational Number

1.4. Comparison of Rational Numbers

1.5. Representation of Rational Numbers on the Number Line

1.6. Addition and Subtraction of Rational Numbers

1.6.1. Addition of Rational Numbers

1.6.2. Properties of Addition of Rational Numbers

1.6.3. Subtraction of Rational Numbers

1.7. Multiplication and Division of Rational Numbers

1.7.1. Multiplication of Rational Numbers

1.7.2. Reciprocal of Rational Number

1.7.3. Properties of Multiplication of Rational Numbers

1.7.4. Division of Rational Numbers

1.7.5. Rational Numbers Lying Between Two Rational Number

1.7.6. Simplifying Rational Numbers

1.7.7. Word Problems on Rational Numbers

2. Square and Square Roots

2.1. Square of a Number

2.1.1. Square of a Number

2.1.2. Perfect Square or Square Numbers

2.1.3. Properties of Perfect Squares

2.1.4. Sum of First n Odd Natural Numbers

2.1.5. Pythagorean Triplets

2.1.6. Using Identities to Find the Square of a Number

2.1.7. Product of Two Consecutive Odd or Consecutive Even Numbers

2.2. Square Root

2.2.1. Square Root by Prime Factorization

2.3. Square Root by Long-Division Method

2.3.1. Square Root of Numbers In Decimal Form

2.3.2. Square Root of Fractions

2.3.3. Square Root of Product of Integers

2.3.4. Simplifying Expressions Involving Square Roots

2.3.5. Word Problems On Squares And Square Roots

3. Cube and Cube Roots

3.1. Cube of a Number

3.1.1. Cube of a Positive Number

3.1.2. Cubes of Negative Integers

3.2. Cube of a Rational Number

3.2.1. Perfect Cube or Cube numbers

3.2.2. Properties of Perfect Cubes

3.2.3. Cube Root

3.2.3.1. Cube Root of a Perfect Cube by Prime Factorization

3.2.3.2. Cube Root of a Negative Perfect Cube

3.2.3.3. Cube Root of Product of Integers

3.2.3.4. Cube Root of a Rational Number

3.2.3.5. Cube Root of a Decimal Number

3.2.3.6. Simplifying Expressions Involving Cube Roots

3.2.3.7. Word Problems on Cubes and Cube Roots

4. Exponents

4.1. Exponent of a Rational Number

4.2. Express Rational Numbers in Exponential Form

4.3. Solving Expressions Involving Exponents

4.4. Laws of Exponents

4.5. Word Problems on Exponents

4.6. Finding the Unknown from the Given Exponential Equation

4.7. Standard Form of Large Numbers

4.8. Standard Form of Small Numbers

4.9. Operations on Large Numbers

5. Direct and Inverse Proportions

5.1. Direct Proportions

5.2. Inverse Proportions

6. Time and Work

7. Percentage

7.1. Conversions

7.1.1. Convert a Fraction into Percentage

7.1.2. Convert a Percentage into Fraction

7.1.3. Convert Percentage into a Ratio

7.1.4. Convert a Ratio into Percentage

7.1.5. Convert Percentage into Decimal form

7.1.6. Convert Decimal into Percentage

7.2. Percentage of a Quantity

7.3. Solving Expressions Involving Percentages

7.4. Word Problems on Percentage

8. Profit and Loss

8.1. Terms Related to Profit and Loss

8.2. Problems on Finding the Gain/Loss and Gain%/Loss%

8.3. Problems on Finding the SP of the Article

8.4. Problems on Finding the CP of the Article

8.5. Problems on Finding the Number of Articles

8.6. Discount

8.7. Tax

9. Compound Interest

9.1. Compound Interest Compounded Annually

9.1.1. Compound Interest Compounded Annually and Rates are Same for All the Years

9.1.2. Compound Interest Compounded Annually and Rates are Different for Different Years

9.2. Compound Interest Compounded Annually and Time is a Fraction

9.2.1. Finding Time When Compound Interest Compounded Annually

9.2.2. Finding Rate When Compound Interest Compounded Annually

9.2.3. Finding Principal When Compound Interest Compounded Annually

9.2.4. Compound Interest Compounded Half-Yearly

9.2.5. Compound Interest Compounded Quarterly

9.2.6. Applications of Compound Interest

10. Algebraic Expressions

10.1. Operations on Algebraic Expressions

10.1.1. Addition of Algebraic Expressions

10.1.2. Subtraction of Algebraic Expressions

10.1.3. Addition and Subtraction of Algebraic Expressions

10.1.4. Multiplication of Algebraic Expressions

10.1.4.1. Multiplication of Monomials

10.1.4.2. Multiplication of a Monomial and a Binomial

10.1.4.3. Multiplication of a Polynomial and a Monomial

10.1.4.4. Multiplication of Binomials

10.1.4.5. Multiplication of two Polynomials

10.1.4.6. Simplify Expressions Involving Multiplication of Algebraic Expressions

10.1.5. Division of Algebraic Expressions

10.1.5.1. Division of a Monomial by a Monomial

10.1.5.2. Division of a Polynomial by Another Polynomial

10.1.6. Some Special Identities

11. Linear Equations in One Variable

11.1. Solving Linear Equations by the Method of Transposition

11.2. Word Problems Based on Linear Equations

12. Factorization

12.1. Factorization by Taking Out the Common Factor

12.2. Factorization by Grouping

12.3. Factorization When the Expression is a Difference of Two Squares

12.4. Factorization When the Expression is a Perfect Square

12.5. Factorization of Quadratic Trinomials

13. Playing with Numbers

13.1. Numbers in Generalized Form

13.2. Tests of Divisibility

13.2.1. Test Divisibility by 2

13.2.2. Test Divisibility by 3

13.2.3. Test Divisibility by 4

13.2.4. Test Divisibility by 5

13.2.5. Test Divisibility by 6

13.2.6. Test Divisibility by 7

13.2.7. Test Divisibility by 8

13.2.8. Test Divisibility by 9

13.2.9. Test Divisibility by 10

13.2.10. Test Divisibility by 11

13.3. Replacing Alphabets with Suitable Numbers

14. Geometry

14.1. Curve

14.1.1. Open Curve

14.1.2. Closed Curve

14.1.3. Simple Closed Curve

14.2. Polygon

14.2.1. Understanding Polygons

14.2.2. Name the Polygon

14.2.3. Concave and Convex Polygon

14.2.4. Diagonals in a Polygon with n Sides

14.2.5. Interior and the Exterior Angle of a Regular Polygon with n Sides

14.2.6. Finding Magnitude of Unknown Angles in the Given Polygon

14.3. Quadrilaterals

14.3.1. Introduction to Quadrilaterals

14.4. Angle Sum Property of a Quadrilateral

14.5. Special Types of Quadrilaterals

15. Graphs

15.2. Coordinates of a Point on the Cartesian Plane

15.3. Identify the Coordinates of the Points on the X-axis, Y-axis, and the Origin

15.4. Identify the Quadrant of a Point

15.5. Graphs of Multiples of Different Numbers

16. Mensuration

16.1. Area of a Trapezium

16.2. Area of Polygon

16.2.1. Area of Irregular Polygons

16.2.2. Area of Regular Polygons

17. Volume and Surface Area

17.1. Volume and Surface Area of Cuboid

17.2. Volume and Surface Area of Cube

17.3. Volume and Surface Area of Cylinders

17.4. Mixed Problems on Volume and Surface Area

18. Three-Dimensional Figures

18.1. Identifying 3-D Shapes

18.2. Faces, Edges and Vertices of 3-D Shapes (Cuboid, Cube, Prism and Pyramid)

18.3. Euler's Relation for 3-Dimensional Figures

19. Probability

20. Data Handling

20.1. Introduction to Data Handling

20.2. Frequency Distribution

20.2.1. Frequency Distribution of Ungrouped Data

20.2.2. Frequency Distribution of Grouped Data

20.3. Bar Graphs

20.3.1. Drawing Bar Graphs

20.3.2. Interpreting Bar Graphs

20.4. Pie Charts

20.4.1. Drawing Pie Charts

20.4.2. Interpret and Present Data as Pie Charts

Grade 8 Brazil School Math Reciprocal of Rational Number

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