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Grade 7
Volume and Surface Area
Grade 7
1.
Volume and Surface Area
1.1.
Volume and Surface Area of Cylinders
1.2.
Three-dimensional Solids
1.3.
Volume and Surface Area of Cubes
1.4.
Volume and Surface Area of Cuboids
2.
Integers
2.1.
Revisiting Basics
2.2.
Operations on Integers
2.2.1.
Addition and Subtraction of Integers
2.2.1.1.
Addition of Integers
2.2.1.2.
Properties of Addition of Integers
2.2.1.3.
Subtraction of Integers
2.2.1.4.
Properties of Subtraction of Integers
2.2.2.
Multiplication and Division of Integers
2.2.2.1.
Multiplication of Integers
2.2.2.2.
Properties of Multiplication of Integers
2.2.2.3.
Division of Integers
2.2.2.4.
Properties of Division of Integers
2.2.3.
Mixed Operations of Integers
2.2.4.
Word Problems on Integers
3.
Fractions
3.1.
Revisiting Basics
3.2.
Equivalent Fractions
3.3.
Comparing Fractions
3.3.1.
Comparing Like Fractions
3.3.2.
Comparing Unlike Fractions
3.4.
Operations on Fractions
3.4.1.
Addition of Fractions
3.4.1.1.
Addition of Like Fractions
3.4.1.2.
Addition of Unlike Fractions
3.4.1.3.
Addition of Mixed Fractions
3.4.2.
Subtraction of Fractions
3.4.2.1.
Subtraction of Like Fractions
3.4.2.2.
Subtraction of Unlike Fractions
3.4.2.3.
Subtraction of Mixed Fractions
3.4.3.
Simplify Expressions involving Addition and Subtraction
3.4.4.
Multiplication of Fractions
3.4.4.1.
Simplify Expressions involving Multiplication
3.4.4.2.
Use of 'OF'
3.4.5.
Division of Fractions
3.4.5.1.
Reciprocal of a Fraction
3.4.5.2.
Simplify Expressions involving Division
3.4.6.
Simplification by Using Operations
3.4.7.
Word Problems on Fractions
3.4.7.1.
Word Problems on Addition of Fractions
3.4.7.2.
Word Problems on Subtraction of Fractions
3.4.7.3.
Word Problems on Addition and Subtraction of Fractions
3.4.7.4.
Word Problems on Multiplication of Fractions
3.4.7.5.
Word Problems on Division of Fractions
4.
Rational Numbers
4.1.
Understanding Rational Numbers
4.2.
Equivalent Rational Numbers
4.3.
Comparison of Rational Numbers
4.4.
Representation of Rational Numbers on the Real Line
4.5.
Addition and Subtraction of Rational Numbers
4.5.1.
Addition of Rational Numbers
4.5.2.
Additive Inverse of a Rational Number
4.5.3.
Subtraction of Rational Numbers
4.6.
Multiplication and Division of Rational Numbers
4.6.1.
Multiplication Of Rational Numbers
4.6.2.
Reciprocal of Rational Number
4.6.3.
Division Of Rational Numbers
4.7.
Rational Numbers Lying Between Two Rational Numbers
4.8.
Simplifying Rational Numbers
4.9.
Word Problems on Rational Numbers
5.
Decimals
5.1.
Revisiting Basics
5.2.
Like, Unlike And Equivalent Decimals
5.3.
Ordering And Comparing Decimals
5.4.
Relate Decimals and Fractions
5.4.1.
Convert Decimals to Fractions
5.4.2.
Convert Fractions to Decimals
5.4.3.
Conversion of Metric Units Using Decimals
5.5.
Addition and Subtraction of Decimals
5.5.1.
Addition of Decimals
5.5.2.
Subtraction of Decimals
5.5.3.
Mixed Operations on Decimals: Addition and Subtraction
5.5.4.
Word Problems on Addition and Subtraction of Decimals
5.6.
Multiplication and Division of Decimals
5.6.1.
Multiplication of Decimals
5.6.2.
Division of Decimals
5.6.3.
Word Problems on Multiplication of Decimals
5.6.4.
Word Problems on Division of a Decimal
5.6.5.
Mixed Operations on Decimals
6.
Ratio and Proportion
6.1.
Ratio
6.1.1.
Terms of a Ratio
6.1.2.
Equivalent Ratio
6.1.3.
Ratio in the Simplest Form
6.1.4.
Ratio of Two Quantities by Converting Them in Same Units
6.1.5.
Comparison of Ratios
6.1.6.
Miscellaneous questions on Ratio
6.2.
Proportion
6.2.1.
Terms of a Proportion
6.2.2.
Condition for the given Numbers/Ratios to be in Proportion
6.2.3.
Find the unknown variable when four numbers are in Proportion
6.2.4.
Continued proportion
7.
Unitary Method
7.1.
Problems on Direct Variation
7.2.
Problems on Inverse Variation
8.
Percentage
8.1.
Conversions
8.1.1.
Convert a Fraction into Percentage
8.1.2.
Convert a Percentage into Fraction
8.1.3.
Convert Percentage into a Ratio
8.1.4.
Convert a Ratio into Percentage
8.1.5.
Convert Percentage into Decimal form
8.1.6.
Convert Decimal into Percentage
8.2.
Percentage of a Quantity
8.3.
Solving Expressions involving Percentages
8.4.
Word Problems on Percentage
9.
Profit and Loss
9.1.
Terms Related to Profit and Loss
9.2.
Problems on Finding the Gain/Loss and Gain%/Loss%
9.3.
Problems on Finding the SP of the Article
9.4.
Problems on Finding the CP of the Article
9.5.
Problems on Finding the Number of Articles
10.
Simple Interest
10.1.
Problems on Calculating the Simple Interest
10.2.
Problems on Calculating the Rate Percent
10.3.
Problems on Calculating Time Period
10.4.
Problems on Calculating the Principal
11.
Exponents
11.1.
Introduction to Exponents
11.2.
Exponent of a Rational Number
11.3.
Express Rational Numbers in Exponential Form
11.4.
Solving Expressions Involving Exponents
11.5.
Laws of Exponents
11.6.
Finding the Unknown from the Given Exponential Equation
11.7.
Standard Form of Large Numbers
11.8.
Standard Form of Small Numbers
11.9.
Expanded Form of Large Numbers
12.
Algebraic Expressions
12.1.
Variables and Constants
12.2.
Types of Algebraic Expressions
12.3.
Finding the Value of an Algebraic Expression
12.4.
Operations on Algebraic Expressions
12.4.1.
Addition of Algebraic Expressions
12.4.2.
Subtraction of Algebraic Expressions
12.4.3.
Addition and Subtraction of Algebraic Expressions
12.4.4.
Multiplication of Algebraic Expressions
12.4.4.1.
Multiplication of Monomials
12.4.4.2.
Multiplication of a Monomial and a Binomial
12.4.4.3.
Multiplication of two Binomials
12.5.
Simplifying Algebraic Expression by Eliminating the Grouping Symbols
13.
Linear Equations in One Variable
13.1.
Solving Linear Equations by the Method of Transposition
13.2.
Word Problems Based on Linear Equations
14.
Mensuration
14.1.
Standard Units of Area
14.2.
Area and Perimeter of a Square
14.3.
Area and Perimeter of a Rectangle
14.4.
Area between Two Rectangles
14.5.
Area and Perimeter of Triangles
14.6.
Area and Perimeter of Parallelogram and Rhombus
14.7.
Circumference and Area of a Circle
14.8.
Area Enclosed Between Two Different Shapes
15.
Geometry
15.1.
Lines and Angles
15.1.1.
Types of Angles
15.1.1.1.
Complementary and Supplementary Angles
15.1.1.2.
Linear Pair of Angles
15.1.1.3.
Vertically Opposite Angles
15.1.1.4.
Angles Around a Point
15.1.2.
Angles Formed when a Transversal Cuts Two Parallel Lines
15.2.
Triangles
15.2.1.
Classification of Triangles by the Length of the Sides
15.2.2.
Classification of Triangles by the Angles
15.2.3.
Properties of a Triangle
15.2.3.1.
Angle Sum Property of a Triangle
15.2.3.2.
Exterior Angle Property of a Triangle
15.2.3.3.
Triangle Inequality
15.2.3.4.
Pythagoras' Theorem
15.3.
Congruence
15.3.1.
Understanding the Meaning
15.3.2.
Congruence of Triangles
16.
Reflection and Rotational Symmetry
16.1.
Linear Symmetry
16.1.1.
Linear Symmetry Around Us
16.1.2.
Linear Symmetry in Geometric Figures
16.1.3.
Linear Symmetry in Alphabets
16.2.
Rotational Symmetry
16.2.1.
Rotational Symmetry in Figures
16.2.2.
Rotational Symmetry in Geometric Figures
16.2.3.
Rotational Symmetry in Alphabets
17.
Three-Dimensional Shapes
17.1.
Identifying 3-D Shapes
17.2.
Faces, Edges and Vertices of 3-D Shapes (Cuboid, Cube, Cone, Cylinder, and Sphere)
17.3.
Net of a 3-D Shape
18.
Probability
19.
Data Handling
19.1.
Tabular Representation of Data
19.2.
Mean, Median, and Mode
19.2.1.
Mean
19.2.1.1.
Mean of Ungrouped Data
19.2.1.2.
Mean of Tabulated Data
19.2.2.
Median
19.2.2.1.
Median of Ungrouped Data
19.2.2.2.
Median of Discrete Series
19.2.3.
Mode
19.2.3.1.
Mode of Ungrouped Data
19.2.3.2.
Empirical Formula for Calculating Mode
19.3.
Bar Graphs
19.3.1.
Drawing Bar Graphs
19.3.2.
Interpreting Bar Graphs
Grade 7 Germany School Math
Volume and Surface Area
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