Mathematics 7th grade review syllabus... Fast...

In the first chapter, rational numbers are divided into positive rational numbers and negative rational numbers.

Positive rational numbers are further divided into positive integers and positive fractions.

Negative rational trees are further divided into negative integers and negative fractions.

Unary Linear Equations.

1 Equation and Equivalence: The formula formed by the "=" sign is called the equation. Note: "The same amount can be substituted"!

2 Nature of the Equation:

Equation property 1: If the same number or the same integer is added (or subtracted) on both sides of the equation, the result is still an equation;

Equation property 2: Both sides of the equation are multiplied (or divided) by the same non-zero number, and the result is still the equation.

3 Equation: An equation with unknowns, called an equation.

4. The solution of the equation: the value of the unknown 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. Shifting terms: After changing the symbol, moving the terms of the equation from one side to the other is called shifting. The basis for shifting terms is the property of equation 1

6 Unary Linear Equation: An integral equation containing only one unknown, the number of unknowns is 1, and the coefficients containing the unknowns are not zero.

7 The standard form of a unitary equation: ax+b=0 (x is an unknown number, a, b are known numbers, and a≠0)

8 The simplest form of a unary equation: ax=b (x is an unknown number, a, b are known numbers, and a≠0)

9 General steps in solving unary equations: Organize the equation ......Go to the denominator ......Remove the parentheses ......Move the item ......Merge similar items ......The coefficient is 1 ......Test the solution of the equation).

10 Columns of Unary Linear Equations Solution Problems:

1) Reading analysis method: ......It is mostly used for "sum, difference, times, and points problems".

Read the question carefully, find out the key words that represent the equality relationship, such as: "big, small, more, less, is, total, combined, for, complete, increase, decrease, matching--- use these keywords to list the literal equations, and set the unknowns according to the meaning of the question, and finally use the relationship between the quantity and the quantity in the question to fill in the algebraic formula to get the equation.

2) Drawing analysis: ....It is mostly used for "travel problems".

The use of graphs to analyze mathematical problems is the embodiment of the idea of combining numbers and shapes in mathematics, read the problem carefully, draw the relevant figures according to the meaning of the topic, so that each part of the graph has a specific meaning, find the equality relationship through the graph is the key to solve the problem, so as to obtain the basis of the cloth equation, and finally use the relationship between the quantity and the quantity (the unknown can be regarded as a known quantity), fill in the relevant algebraic formula is the basis for obtaining the equation.

Common formulas for 11 columns of equation solving problems:

1) Stroke problem: distance = speed time;

2) Engineering problems: workload = ergonomic man-hours;

3) Ratio Problem: Partial = Overall Ratio;

4) Forward and reverse flow problem: Downstream velocity = hydrostatic velocity + water velocity, countercurrent velocity = hydrostatic velocity - water velocity;

5) Commodity ** problem: selling price = pricing discount, profit = selling price - cost, ;

6) Perimeter, area, volume problems: C circle = 2 r, s circle = r2, c rectangle = 2 (a + b), s rectangle = ab, c square = 4a, s square = a2, s ring = (r2-r2), v cuboid = abc, v cube = a3, v cylinder = r2h, v cone = r2h