Seven-grade mathematics knowledge points
real number
First, the concept and classification of real numbers
1, classification of real numbers, positive rational number, rational number, zero finite decimal number and infinite cyclic decimal number.
Negative rational number
Positive irrational number
Irrational number infinite acyclic decimal
Negative irrational number
Integers include positive integers, zero and negative integers.
Positive integers are also called natural numbers.
Positive integer, zero, negative integer, positive fraction and negative fraction are collectively called rational numbers.
2. Irrational number
When understanding irrational numbers, we should grasp the moment of "infinite non-circulation", which can be summarized into four categories:
(1) An inexhaustible number, such as 7, 2, etc. ;
π(2) a number with a specific meaning, such as pi, or a simplified number containing pi, such as+8; three
(3) Numbers with specific structures, such as 0.101001001… etc.
Second, the reciprocal, reciprocal and absolute value of real numbers.
1, reciprocal
A real number and its inverse are a pair of numbers (only two numbers with different signs are called inverse numbers, and the inverse of zero is zero). Seen from the number axis, the points corresponding to two opposite numbers are symmetrical about the origin. If a and b are opposites, then a+b=0, A =-B, and vice versa.
2. Absolute value
The absolute value of a number is the distance between the point representing the number and the origin, |a|≥0. When the absolute value of zero is itself, it can also be regarded as its inverse. If |a|=a, then a ≥ 0; If |a|=-a, then a≤0. Positive numbers are greater than zero and negative numbers are less than.
Zero, positive number is greater than all negative numbers, two negative numbers, the larger absolute value is smaller.
Step 3 count down the seconds
If A and B are reciprocal, there is ab= 1, and vice versa. The numbers whose reciprocal equals itself are 1 and-1. Zero has no reciprocal.
4. The relationship between real numbers and points on the number axis:
Every irrational number can be represented by a point on the number axis.
Some points on the number axis represent rational numbers and some represent irrational numbers.
Real numbers correspond to points on the number axis one by one, that is, each real number can be represented by a point on the number axis; On the contrary, every point on the number axis represents a real number.
Junior one mathematics knowledge points
Knowledge network:
Concept, definition:
1, which is the product of numbers or letters, is called a monomial, and a single number or letter is also a monomial.
2. The numerical factor in a single item is called the coefficient of the item.
3. In the monomial, the sum of the indices of all letters is called the number of times of the monomial.
The sum of several terms is called polynomial, in which each term is called polynomial term ($ TERM) and the term without letters is called constant term (constancy)
Terminology).
5. The degree of the degree term in the polynomial is called the degree of the polynomial.
6. Merging similar terms in polynomials into one term is called merging similar terms.
After merging similar items, the coefficient of the obtained item is the sum of the coefficients of similar items before merging, and the letter part remains unchanged.
7. If the factor outside the brackets is positive, the symbols of the items in the original brackets are the same as the original symbols after removing the brackets;
8. If the factor outside the brackets is negative, the symbols of the items in the original brackets are opposite to those after the brackets are removed.
9. Generally speaking, several algebraic expressions are added and subtracted. If there are brackets, remove them first, and then merge similar items.
Mathematics learning methods of junior high school grade one
preview
For science study, preview is essential. In the preview, we should read the contents of the book, try our best to understand, mark the problems that cannot be solved, consult the teacher or listen to the class to solve them, and try our best to do exercises after the book to test the preview effect.
Second listening and speaking
This link is the most important, because the teacher concentrates the essence of knowledge in the classroom, and he should master the teacher's ideas and methods when listening to the math class. Write down the problem, sort it out after class and solve it. We must think positively in math class and do it according to the teacher's ideas.
review
Experience the examples in the teacher's class, organize your own thinking, think about your own ideas, what are the similarities and differences with the teacher's ideas, think about the test sites of each question, try to solve as many questions as possible, and make inferences.
Four assignments
Seriously finish the exercises left by the teacher, and appropriately select some extracurricular exercises as exercises, but don't blindly pursue digression and strange questions, let alone play "sea tactics".
Five summaries
This step is to better master what you have learned. After learning a piece of knowledge or doing a typical problem, you can sum up: summarize the mathematical knowledge of the topic; Summarize where you are stuck; Summarize how you are wrong, where you are wrong, where the "trap" of the topic is, and what you or others think.
How to choose and deal with exercises
There are countless problem sets in the market, most of which are copied from each other and full of loopholes, which makes students waste time and effort in the process of practice. I think the real problem of the calendar is an exercise, which is closely related to the exam outline and has moderate difficulty, so there will be no strange problems. At the same time, it also allows students to firmly grasp the direction of the exam and avoid detours.
Second, some students like "crowd tactics". They just do problems and never sum them up. They feel that the more they do, the higher their grades will be. This is one of the disadvantages of learning mathematics.
Remember: the problem is not much but the essence. It is essential to do exercises, but after each exercise, we should seriously reflect on what the test center of this exercise is, how many solutions there are, and which one is the simplest. We should repeatedly think about the wrong exercises, find out the reasons for the mistakes, and ensure that we can master this knowledge point.
Many students like to ask difficult questions outside the topic. But it ignores the understanding of definitions, concepts and formulas in books. As a result, mistakes in "basic questions" often appear in exams.
Therefore, in the usual math practice, we should deeply understand every knowledge point in the book and find out the possible test sites and traps. In the exam, we should make sure that the basic questions are all right, that the intermediate questions are not wasted, and that the high-scoring questions are fully attacked, even if they are wrong.
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