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Grade 8
Algebraic Expressions
Operations on Algebraic Expressions
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
15.1.
Terms Related to Co-ordinate Geometry
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 Pakistan School Math
Operations on Algebraic Expressions
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