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Grade 7
Unitary Method
Problems on Direct Variation
Grade 7
1.
Integers
1.1.
Revisiting Basics
1.2.
Operations on Integers
1.2.1.
Addition and Subtraction of Integers
1.2.1.1.
Addition of Integers
1.2.1.2.
Properties of Addition of Integers
1.2.1.3.
Subtraction of Integers
1.2.1.4.
Properties of Subtraction of Integers
1.2.2.
Multiplication and Division of Integers
1.2.2.1.
Multiplication of Integers
1.2.2.2.
Properties of Multiplication of Integers
1.2.2.3.
Division of Integers
1.2.2.4.
Properties of Division of Integers
1.2.3.
Mixed Operations of Integers
1.2.4.
Word Problems on Integers
2.
Fractions
2.1.
Revisiting Basics
2.2.
Equivalent Fractions
2.3.
Comparing Fractions
2.3.1.
Comparing Like Fractions
2.3.2.
Comparing Unlike Fractions
2.4.
Operations on Fractions
2.4.1.
Addition of Fractions
2.4.1.1.
Addition of Like Fractions
2.4.1.2.
Addition of Unlike Fractions
2.4.1.3.
Addition of Mixed Fractions
2.4.2.
Subtraction of Fractions
2.4.2.1.
Subtraction of Like Fractions
2.4.2.2.
Subtraction of Unlike Fractions
2.4.2.3.
Subtraction of Mixed Fractions
2.4.3.
Simplify Expressions involving Addition and Subtraction
2.4.4.
Multiplication of Fractions
2.4.4.1.
Simplify Expressions involving Multiplication
2.4.4.2.
Use of 'OF'
2.4.5.
Division of Fractions
2.4.5.1.
Reciprocal of a Fraction
2.4.5.2.
Simplify Expressions involving Division
2.4.6.
Simplification by Using Operations
2.4.7.
Word Problems on Fractions
2.4.7.1.
Word Problems on Addition of Fractions
2.4.7.2.
Word Problems on Subtraction of Fractions
2.4.7.3.
Word Problems on Addition and Subtraction of Fractions
2.4.7.4.
Word Problems on Multiplication of Fractions
2.4.7.5.
Word Problems on Division of Fractions
3.
Rational Numbers
3.1.
Understanding Rational Numbers
3.2.
Equivalent Rational Numbers
3.3.
Comparison of Rational Numbers
3.4.
Representation of Rational Numbers on the Real Line
3.5.
Addition and Subtraction of Rational Numbers
3.5.1.
Addition of Rational Numbers
3.5.2.
Additive Inverse of a Rational Number
3.5.3.
Subtraction of Rational Numbers
3.6.
Multiplication and Division of Rational Numbers
3.6.1.
Multiplication Of Rational Numbers
3.6.2.
Reciprocal of Rational Number
3.6.3.
Division Of Rational Numbers
3.7.
Rational Numbers Lying Between Two Rational Numbers
3.8.
Simplifying Rational Numbers
3.9.
Word Problems on Rational Numbers
4.
Decimals
4.1.
Revisiting Basics
4.2.
Like, Unlike And Equivalent Decimals
4.3.
Ordering And Comparing Decimals
4.4.
Relate Decimals and Fractions
4.4.1.
Convert Decimals to Fractions
4.4.2.
Convert Fractions to Decimals
4.4.3.
Conversion of Metric Units Using Decimals
4.5.
Addition and Subtraction of Decimals
4.5.1.
Addition of Decimals
4.5.2.
Subtraction of Decimals
4.5.3.
Mixed Operations on Decimals: Addition and Subtraction
4.5.4.
Word Problems on Addition and Subtraction of Decimals
4.6.
Multiplication and Division of Decimals
4.6.1.
Multiplication of Decimals
4.6.2.
Division of Decimals
4.6.3.
Word Problems on Multiplication of Decimals
4.6.4.
Word Problems on Division of a Decimal
4.6.5.
Mixed Operations on Decimals
5.
Ratio and Proportion
5.1.
Ratio
5.1.1.
Terms of a Ratio
5.1.2.
Equivalent Ratio
5.1.3.
Ratio in the Simplest Form
5.1.4.
Ratio of Two Quantities by Converting Them in Same Units
5.1.5.
Comparison of Ratios
5.1.6.
Miscellaneous questions on Ratio
5.2.
Proportion
5.2.1.
Terms of a Proportion
5.2.2.
Condition for the given Numbers/Ratios to be in Proportion
5.2.3.
Find the unknown variable when four numbers are in Proportion
5.2.4.
Continued proportion
6.
Unitary Method
6.1.
Problems on Direct Variation
6.2.
Problems on Inverse Variation
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
9.
Simple Interest
9.1.
Problems on Calculating the Simple Interest
9.2.
Problems on Calculating the Rate Percent
9.3.
Problems on Calculating Time Period
9.4.
Problems on Calculating the Principal
10.
Exponents
10.1.
Introduction to Exponents
10.2.
Exponent of a Rational Number
10.3.
Express Rational Numbers in Exponential Form
10.4.
Solving Expressions Involving Exponents
10.5.
Laws of Exponents
10.6.
Word Problems on Exponents
10.7.
Finding the Unknown from the Given Exponential Equation
10.8.
Standard Form of Large Numbers
10.9.
Standard Form of Small Numbers
10.10.
Expanded Form of Large Numbers
11.
Algebraic Expressions
11.1.
Variables and Constants
11.2.
Types of Algebraic Expressions
11.3.
Finding the Value of an Algebraic Expression
11.4.
Operations on Algebraic Expressions
11.4.1.
Addition of Algebraic Expressions
11.4.2.
Subtraction of Algebraic Expressions
11.4.3.
Addition and Subtraction of Algebraic Expressions
11.4.4.
Multiplication of Algebraic Expressions
11.4.4.1.
Multiplication of Monomials
11.4.4.2.
Multiplication of a Monomial and a Binomial
11.4.4.3.
Multiplication of two Binomials
11.5.
Simplifying Algebraic Expression by Eliminating the Grouping Symbols
12.
Linear Equations in One Variable
12.1.
Solving Linear Equations by the Method of Transposition
12.2.
Word Problems Based on Linear Equations
13.
Mensuration
13.1.
Standard Units of Area
13.2.
Area and Perimeter of a Square
13.3.
Area and Perimeter of a Rectangle
13.4.
Area of 4 Walls of a Room
13.5.
Area between Two Rectangles
13.6.
Area and Perimeter of Triangles
13.7.
Area and Perimeter of Parallelogram and Rhombus
13.8.
Circumference and Area of a Circle
13.9.
Area Enclosed Between Two Different Shapes
14.
Geometry
14.1.
Lines and Angles
14.1.1.
Types of Angles
14.1.1.1.
Complementary and Supplementary Angles
14.1.1.2.
Linear Pair of Angles
14.1.1.3.
Vertically Opposite Angles
14.1.1.4.
Angles Around a Point
14.1.2.
Angles Formed when a Transversal Cuts Two Parallel Lines
14.2.
Triangles
14.2.1.
Classification of Triangles by the Length of the Sides
14.2.2.
Classification of Triangles by the Angles
14.2.3.
Properties of a Triangle
14.2.3.1.
Angle Sum Property of a Triangle
14.2.3.2.
Exterior Angle Property of a Triangle
14.2.3.3.
Triangle Inequality
14.2.3.4.
Pythagoras' Theorem
14.3.
Congruence
14.3.1.
Understanding the Meaning
14.3.2.
Congruence of Triangles
15.
Reflection and Rotational Symmetry
15.1.
Linear Symmetry
15.1.1.
Linear Symmetry Around Us
15.1.2.
Linear Symmetry in Geometric Figures
15.1.3.
Linear Symmetry in Alphabets
15.2.
Rotational Symmetry
15.2.1.
Rotational Symmetry in Figures
15.2.2.
Rotational Symmetry in Geometric Figures
15.2.3.
Rotational Symmetry in Alphabets
16.
Three-Dimensional Shapes
16.1.
Identifying 3-D Shapes
16.2.
Faces, Edges and Vertices of 3-D Shapes (Cuboid, Cube, Cone, Cylinder, and Sphere)
16.3.
Net of a 3-D Shape
17.
Probability
18.
Data Handling
18.1.
Tabular Representation of Data
18.2.
Mean, Median, and Mode
18.2.1.
Mean
18.2.1.1.
Mean of Ungrouped Data
18.2.1.2.
Mean of Tabulated Data
18.2.2.
Median
18.2.2.1.
Median of Ungrouped Data
18.2.2.2.
Median of Discrete Series
18.2.3.
Mode
18.2.3.1.
Mode of Ungrouped Data
18.2.3.2.
Empirical Formula for Calculating Mode
18.3.
Bar Graphs
18.3.1.
Drawing Bar Graphs
18.3.2.
Interpreting Bar Graphs
Grade 7 Pakistan School Math
Problems on Direct Variation
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