1. Equation and Equivalence: An equation connected by "=" is called an equation. Note: "Equivalent value can be substituted"!
2. The nature of the equation:
Properties of equation 1: Add (or subtract) the same number or the same algebraic expression on both sides of the equation, and the result is still an equation;
Property 2 of the equation: both sides of the equation are multiplied (or divided) by the same non-zero number, and the result is still an equation.
3. Equation: An equation with an unknown number is called an equation.
4. Solution of the equation: the value of the unknown quantity that makes the left and right sides of the equation equal is called the solution of the equation; Note: "The solution of the equation can be substituted"!
5. Moving term: after changing the sign, moving the term of the equation from one side to the other is called moving term. The shift term is based on the equality attribute 1.
6. One-dimensional linear equation: An integral equation with only one unknown number, degree 1 and non-zero coefficient is a one-dimensional linear equation.
7. The standard form of one-dimensional linear equation: ax+b=0(x is unknown, a and b are known numbers, a≠0).
8. The simplest form of linear equation with one variable: ax=b(x is unknown, a and b are known numbers, a≠0).
9. General steps for solving a linear equation with one variable: sorting out the equation ... removing the denominator ... dismantling the bracket ... changing the terms ... merging similar terms ... and converting the coefficient into 1 ... (testing the solution of the equation).
10. Solving application problems by listing linear equations of one variable;
(1) reading analysis method: reading analysis method
Read the stem carefully, find out the key words that express the equal relationship, such as "big, small, many, few, yes, * * *, combination, For, completion, increase, decrease, match-",list the literal equations with these key words, and set the unknown number according to the meaning of the question. Finally, using the relationship between quantity and quantity in the question, fill in the algebraic expression and get the equations.
(2) Drawing analysis method
Analyzing mathematical problems with graphics is the embodiment of the combination of numbers and shapes in mathematics. Read the question carefully, and draw the relevant figures according to the meaning of the question, so that each part of the figure has a specific meaning. Finding the equation relationship through the graph is the key to solve the problem, so as to get the basis of concise equation. Finally, using the relationship between quantity and quantity (unknown quantity can be regarded as known quantity), filling in the relevant algebraic expression is the basis of getting the equation.
1 1. Common formulas for solving application problems with column equations:
(1) Travel Problem: Distance = Speed? Time;
(2) Engineering problem: workload = work efficiency? Working hours;
(3) Proportion: Part = All? Ratio;
(4) Downstream problem: Downstream velocity = still water velocity+water velocity, and countercurrent velocity = still water velocity-water velocity;
(5) Commodity price problem: selling price = pricing? Fold? Profit = price-cost;
(6) Perimeter, area and volume: C circle =2πR, S circle =πR2, C rectangle =2(a+b), S rectangle =ab, C square =4a,
S square =a2, S ring =π(R2-r2), V cuboid =abc, V cube =a3, V cylinder = πR2h, V cone =πR2h.
Will you review the outline?