Summary of unit knowledge points in the first volume of seventh grade mathematics of Jiangsu Education Edition (1)
Positive and negative numbers
The concepts of positive and negative numbers
Negative number: a number less than 0. Positive number: a number greater than 0. 0 is neither positive nor negative.
Note: ① The letter A can represent any number. When a represents a positive number, -a is a negative number; When a is negative, -a is positive; When a represents 0, -a is still 0. (If it is judged that the number with a positive sign is positive and the number with a negative sign is negative, this statement is wrong. For example, +a and -a cannot make simple judgments. )
(2) Positive numbers can sometimes be added to the front? +? , sometimes? +? Omit and not write. So omit? +? The sign of a positive number is a plus sign.
2. Quantities with opposite meanings
If a positive number means a quantity with a certain meaning, a negative number can mean a quantity opposite to a positive number, such as:
8℃ above zero means:+8℃; 8 degrees below zero means 8 degrees below zero.
What does 3.0 (1) 0 mean? No? If there are 0 people in the classroom, it means there is no one in the classroom;
0 is the dividing line between positive and negative numbers, and 0 is neither positive nor negative.
Summary of Knowledge Points of Unit 1 of Grade 7 Mathematics in Jiangsu Education Edition (2)
absolute value
Geometric definition of absolute value
Generally speaking, the distance between the point representing the number A on the number axis and the origin is called the absolute value of A, which is denoted as |a|.
2. Algebraic definition of absolute value
(1) The absolute value of a positive number is itself; (2) The absolute value of a negative number is its inverse; The absolute value of 0 is 0.
Can be expressed in letters as follows:
① If a>0, then | a | = a② If A
Can be summarized as ①: a? 0，& lt═>； |a|=a (the absolute value of a non-negative number is equal to itself; A number whose absolute value is equal to itself is nonnegative. )
②a？ 0，& lt═>； |a|=-a (the absolute value of a non-positive number is equal to its inverse; A number whose absolute value is equal to its opposite number is not positive. )
3. The essence of absolute value
The absolute value of any rational number is non-negative, that is, the absolute value is non-negative. So, if a takes any rational number, there is |a|? 0。 That is, the absolute value of (1)0 is 0; A number with an absolute value of 0 is 0. That is, a = 0.
(2) The absolute value of a number is non-negative, and the number with the smallest absolute value is 0. That is: |a|? 0;
(3) The absolute value of any number is not less than the original number. Namely: |a|? a；
(4) The absolute values of two numbers are the same positive number, and they are opposite. That is, if | x | = a(a >；; 0), then x=? a；
5] The absolute values of two opposite numbers are equal. That is: |-a|=|a| or |a|=|b| If a+b = 0;
[6] Two numbers with equal absolute values are equal or opposite. That is: |a|=|b|, then a=b or a =-b;
Once, if the sum of the absolute values of several numbers is equal to 0, then these numbers are simultaneously 0. That is |a|+|b|=0, then a=0 and b=0.
(Common properties of non-negative numbers: if the sum of several non-negative numbers is 0, then only these non-negative numbers are 0 at the same time)
4. Comparison of rational numbers
⑴ Compare the size of two numbers by using the number axis: when two numbers on the number axis are compared, the left one is always smaller than the right one;
⑵ Compare the size of two negative numbers with absolute values: two negative numbers compare the size, and the absolute value is larger than the small one; Compare the sizes of two numbers with different signs, and the positive number is greater than the negative number.
5. Simplification of absolute value
1 when a? 0, | a | = a2 when a? 0，|a|=-a
6. Know the absolute value of a number and find it.
The absolute value of the number A is the distance from the point representing the number A on the number axis to the origin. Generally speaking, there are two rational numbers with the same positive absolute value, which are opposite to each other. A number with an absolute value of 0 is 0, and there is no number with a negative absolute value.
Summary of Knowledge Points of Unit 1 of Grade 7 Mathematics in Jiangsu Education Edition (3)
Use letters to represent numbers.
I. Algebraic expressions
Algebraic expression: the expression formed by connecting numbers and letters with basic operation symbols is called algebraic expression, such as n,-1, 2n+500, abc. A single number or letter is also algebraic.
Monomial: An algebraic expression that represents the product of a number and a letter is called a monomial. A single number or letter is also algebraic.
Coefficient of single item: numerical factor in single item
The number of times of a monomial: the sum of the indices of all the letters in the monomial.
Polynomial: The sum of several monomials is called polynomial. Each monomial is called a polynomial term, and the term without letters is called a constant term.
The degree of the highest degree term in a polynomial is called the degree of the polynomial. The degree of the constant term is 0.
Algebraic expression: monomials and polynomials are collectively called algebraic expressions.
Note: It is not an algebraic expression whose denominator contains letters.
Algebraic writing specification:
(1) Can the letters in numbers and letters, letters and multiplication be omitted or not used? Say, put the number in front of the letter;
(2) When there is division, it is expressed by fraction;
(3) When the band score is multiplied by letters, the band score should become a false score;
(4) If the operation result is an addition and subtraction formula, when there is a unit behind it, the whole formula should be enclosed in brackets.
Second, merge similar projects.
Similar items: items with the same letters and the same letter index are called similar items.
Rules for merging similar items: when the coefficients of similar items are added, the result will be taken as the coefficient, and the index of letters will remain unchanged.
Similar item merging steps: (1) Find similar items accurately; (2) additive commutative law is used to combine similar items after exchanging positions; (3) Using the rule, the coefficients of similar items are added, and the index of letters remains unchanged; (4) Write the merged results.
Third, the rule of removing brackets.
What is before (1) brackets? +? Number, put the brackets together with the one in front? +? Delete the number, and the symbols of the items in brackets remain unchanged;
(2) What is before the brackets? Number, put the brackets together with the one in front? After deleting the number, the symbols of the items in brackets should be changed.
Algebraic addition and subtraction: if there are brackets in algebraic addition and subtraction, remove them first and then merge similar items.
Steps to add and subtract algebraic expressions: (1) List algebraic expressions; (2) remove the brackets; (3) Merge similar items.
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2. Summary of mathematical knowledge points in the first volume of the seventh grade
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5. Induction of knowledge points in the first volume of junior one mathematics: rational number.