MindMap Gallery Formulas and equations
This mind map elaborates on the related concepts of equations and equations in mathematics in detail, helping you to familiarize yourself with the key points of knowledge and strengthen memory. Students in need can bookmark it.
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Formulas and equations
Basic concepts of equations
Definition of equations
Equations with unknown numbers
Unknown numbers are represented by letters
Solutions to equations
The value of the unknown number that makes the equation true
The process of solving equations is called solving
Classification of equations
One-element equation
Contains only one unknown number
The maximum number of unknown numbers is 1
Binary equations
Contains two unknown numbers
The maximum number of unknown numbers is 1
Multivariate equation
Contains more than two unknown numbers
The maximum number of unknown numbers is 1
One-element equation
Solutions to equations
Transfer method
Move unknown terms to one side of the equation
Move the constant term to the other side of the equation
Merge similar items
Merge similar terms on both sides of the equation
Test the correctness of the solution
Substitute the obtained solution into the original equation
Make sure both sides of the equation are equal
Application of equations
Mathematical modeling of practical problems
Transform practical problems into equations
Find answers to the problem by solving equations
Solve practical problems
Calculate cost, profit, distance, etc.
Involves speed, time, quantity and other relationships
System of first-order equations
Definition of system of equations
Consisting of two or more single-element equations
The unknown number in the system of equations is the same
solution
Substitution method
Solve an unknown number from an equation
Substitute another equation to solve
Elimination method
Eliminate an unknown number through addition and subtraction operations
Solve the value of another unknown number
Graphics
Draw an image of each equation in the coordinate system
The intersection point of the image is the solution of the system of equations
Application of system of equations
Solve the actual problem of two unknown numbers
Related to the relationship between two variables
Such as product purchase issues, itinerary issues, etc.
Inequality and its properties
Definition of inequality
Mathematical formula that represents two expressions that are not equal
Contains inequality signs ">", "<", "≥", "≤"
Solution to inequality
Principles of addition and subtraction
Add or subtract the same number on both sides at the same time
Unchanged relationship
Multiplication and division principle
Multiply or divide by positive numbers on both sides at the same time
Unchanged relationship
When multiplication and division of negative numbers, the inequality sign is reversed
Application of inequality
Solve constraints in practical problems
Such as budget restrictions, time restrictions, etc.
Determine the range of values of variables
Scale and scale
The concept of proportion
Represents two equal equations
The form is a:b = c:d or a/b = c/d
Properties
Cross multiplication principle
a/b = c/d can be converted to ad = bc
Properties of proportional terms
If a:b = c:d, then b is the medium ratio of a and c
Application of scale bar
The relationship between distance on the map and actual distance
Calculate the actual distance by scale
Suitable for map reading and drawing
Proportional equations and proportional problems
Solution to proportional equations
Solve equations using properties of proportions
Convert proportional equations into univariate equations to solve the solution
Apply the principle of cross multiplication
Simplify the calculation process
Practical application of proportional issues
Solve practical issues involving proportions
Such as mixture ratio, speed and time issues, etc.
A proportional relationship involving two or more variables
Comprehensive application of equations and inequality
Solve complex practical problems
Solve the equation and inequality
Such as optimization problems, cost control, etc.
It is necessary to consider both equal and unequal relationships
Solutions between system of equations and inequality groups
Solve multiple equations and inequality simultaneously
Find solutions that meet all conditions
Intersection area that may involve graphics
Modeling and solving practical problems
Transform complex problems into mathematical models
Use equations and inequality to describe problems
Find solutions by mathematical methods