A survey of knowledge points 1 (1) in the second volume of seventh grade mathematics. Understand the meaning of the question. Find out what is a known quantity, what is an unknown quantity, and what is the equivalent relationship between problems and problems.

(2) Set the element (unknown).

① Direct unknowns ② Indirect unknowns (often both). Generally speaking, the more unknowns, the easier it is to list the equations, but the more difficult it is to solve them.

(3) The related quantities are expressed by algebraic expressions containing unknowns.

(4) Find the equation relationship (some are given by the topic, some are given by the equivalence relationship involved in this topic) and list the equations. Generally speaking, the number of unknowns is the same as the number of equations.

(5) Solving equations and testing.

(6) the answer.

To sum up, the essence of solving application problems by column equations (groups) is to first transform practical problems into mathematical problems (setting elements and column equations), and then the solutions of practical problems (column equations and writing answers) are caused by the solutions of mathematical problems. In this process, the column equation plays a role of connecting the past with the future. Therefore, the column equation is the key to solve the application problem.

Knowledge points in the second volume of seventh grade mathematics 21. Algebraic expressions

1. Single item. ※

An algebraic expression consisting of the product of numbers and letters is called a monomial. A single number or letter is also a monomial.

② The coefficient of a single item is a numerical factor of a single item. As a monomial coefficient, you must add the ` attribute symbol before the number. If the monomial is just a product of letters, it is not without coefficients.

In a monomial, the sum of the exponents of all the letters is called the degree of the monomial.

2.※ Polynomial

The sum of several monomials is called polynomial. In polynomials, each monomial is called a polynomial term. Among them, items without letters are called constant items. In a polynomial, the degree of the term with the highest degree is called the degree of this polynomial.

(2) Both monomials and polynomials have degrees, monomials with letters have coefficients, and polynomials have no coefficients. Every term of a polynomial is a monomial, and the number of terms of a polynomial is the number of monomials with the polynomial as the addend. Each term in a polynomial has its own degree, but their degrees cannot all be regarded as the degree of this polynomial. Polynomials have only one degree, which is the highest degree of inclusion.

3. Algebraic expressions Monomials and polynomials are collectively called algebraic expressions. ※ 。

2. Addition and subtraction of algebraic expressions

The addition and subtraction of 1. algebraic expression is essentially the combination of similar items after removing brackets, and the operation result is a polynomial or a single item.

There is a "-"sign before the brackets. When the brackets are deleted, the symbols of the items in the brackets should be changed. When a number is multiplied by a polynomial, it should be multiplied by all the items in brackets.

Three. Same base power multiplication

Same base powers's multiplication rule: (m, n are all positive numbers) is the most basic rule in power operation. Pay attention to the following points when applying regular operations. ※:

① The preconditions for using this rule are: when the bases of powers are the same and multiplied, the base a can be a specific numeric letter or a term or polynomial;

② When the index is 1, don't mistake it for no index;

③ Don't confuse multiplication with addition of algebraic expressions. Multiplication, as long as the base is the same, the indexes can be added; For addition, not only the radix is the same, but also the exponent needs to be added;

(4) When three or more bases are the same, the rule can be generalized as (where m, n and p are all positive numbers);

⑤ The formula can also be reversed: (M and n are positive integers)

4. Power and products.

1. power law: (m, n are both positive numbers) is derived from the power multiplication law, but the two cannot be confused. ※ 。

※2 ..

3. When the base has a negative sign, it should be noted that when the base is a and (-a), it is not the same base, but it can be converted into the same base by power law. ※,

If (-a)3 is replaced by -a3.

4. The base sometimes has different forms, but it can be replaced with the same one. ※ 。

5. Pay attention to the difference between (ab)n and (a+b)n, and don't mistake (a+b) n = an+bn (both a and b are not zero). ※ 。

6. Power law of product: the power of product is equal to each factor of product multiplied by power respectively, that is, (n is a positive integer). ※ 。

7. Power and product power rules can be applied in reverse. ※ 。

Verb (abbreviation for verb) division with the same radix power

1. same base powers's division rule: same base powers divides, the base number is unchanged, and the exponent is subtracted, that is, (a≠0, m, n is a positive number, m >；; n)。

2. Pay attention to the following points when applying. ※:

(1) The prerequisite for using the rule is "divisible by same base powers" and 0 is not divisible, so a≠0 is included in the rule.

② Any number that is not equal to 0, whose power of 0 is equal to 1, that is, if (-2.50= 1), 00 is meaningless.

(3) The power of any number not equal to 0 is -p (p is a positive integer) which is equal to the reciprocal of the power of this number, that is, (a≠0, p is a positive integer), 0- 1, 0-3 is meaningless; When a>0, the value of a-p must be positive;