Knowledge points in the first volume of junior high school mathematics
Binary linear equations
1. Binary linear equation: contains two unknowns, and the degree of the unknowns is 1. Such an equation is a binary linear equation. Note: Generally speaking, a binary linear equation has countless solutions.
2. Binary linear equations: two binary linear equations are put together.
3. Solution of binary linear equations: The values of two unknowns that make the left and right sides of two equations of binary linear equations equal are called the solutions of binary linear equations. Note: Generally speaking, binary linear equations have only solutions (that is, common * * * solutions).
4. Solutions of binary linear equations;
(1) substitution elimination method; (2) addition, subtraction and elimination;
(3) Note: It is the key to judge how to solve the problem simply.
5. Application of linear equation. ※:
(1) For an application problem, the more unknowns are set, the easier it may be to establish the equation, but the more troublesome it may be to solve the equation, otherwise it will be difficult to establish the equation and easy to solve.
(2) For equations, if the number of equations is equal to the number of unknowns, the value of the unknowns can generally be obtained;
(3) For equations, if the number of equations is one less than the number of unknowns, then the value of the unknowns cannot be found, but the relationship between any two unknowns can always be found.
One-dimensional linear inequality (group)
1. Inequality: A formula that connects two algebraic expressions with inequality is called inequality.
2. The basic properties of inequality:
The basic property of inequality is 1: add (or subtract) the same number or the same algebraic expression on both sides of inequality, and the direction of inequality remains unchanged;
The basic properties of inequality 2: both sides of inequality are multiplied (or divided) by the same positive number, and the direction of inequality remains unchanged;
The basic property of inequality 3: both sides of inequality are multiplied by (or divided by) the same negative number, and the direction of inequality should be changed.
3. Solution set of inequality: the value of the unknown quantity that can make the inequality hold is called the solution of this inequality; The set of all solutions of an inequality is called the solution set of this inequality.
4. One-dimensional linear inequality: an inequality with only one unknown number, degree 1 and coefficient not equal to zero is called one-dimensional linear inequality; Its standard form is ax+b0 or ax+b0, (a0).
5. Solution of one-dimensional linear inequality: The solution of one-dimensional linear inequality is similar to the solution of one-dimensional linear equation, but we must pay attention to the application of inequality property 3; Note: when representing the solution set of inequality on the number axis, we should pay attention to the empty circle and real point.
Mathematics knowledge points in the second volume of the seventh grade
Probability; possibility
I. Events:
1. Events are divided into inevitable events, impossible events and uncertain events.
2. Inevitable events: events that will definitely happen in advance. In other words, the event must happen every time, and it is impossible not to happen, that is, what may happen is 100% (or 1).
3. Impossible events: events that will definitely not happen in advance. In other words, there is no chance at all, that is, the possibility of occurrence is zero.
4. Uncertain event: it is impossible to determine whether it will happen in advance, that is, the event may or may not happen, that is, the probability of occurrence is between 0 and 1.
Second, equal possibility: refers to the equal possibility of several events.
1. probability: it is a quantity that reflects the possibility of an event. It is a proportional number, generally expressed by p, and P(A)= the number of possible outcomes of event A/all possible outcomes.
2. The probability of the inevitable event is 1, and it is recorded as p (inevitable event) =1;
3. The probability of an impossible event is 0, and it is recorded as p (impossible event) = 0;
4. The probability of uncertain events is between 0 and 1, and it is recorded as 0.
Third, geometric probability.
1, the probability of the occurrence of event A is equal to the area of the possible result of this event A (expressed by SA) divided by the area of the graph of all possible results (expressed by S total), so the geometric probability formula can be expressed as P(A)=SA/S total, because the probability of the occurrence of events in each unit area is the same.
2. Find the geometric probability:
(1) Firstly, analyze the relationship between the area occupied by events and the total area;
(2) Then calculate the area of each part;
(3) Finally, the geometric probability is obtained by substituting into the formula.
Learning methods and skills of junior one mathematics
1, get ready:
In the unit preview, we can read roughly, understand the learning content in the recent stage, read carefully in the classroom preview, pay attention to the formation process of knowledge, and record the concepts, formulas and laws that are difficult to understand, so that we can listen to the class with questions.
2. Listen carefully:
Listening to lectures should include listening, thinking and remembering. Listen, listen to the ins and outs of the formation of knowledge, listen to the key and difficult points, and listen to the answers and requirements of examples. Thinking, one is to be good at association, analogy and induction, and the other is to dare to question and ask questions. Taking notes means taking notes in class-methods, doubts, requirements and precautions.
3. Seriously solve the problem:
Classroom exercises are the most timely and direct feedback, and must not be missed. Don't rush to finish your homework, look at your notebook first, review your learning content, deepen your understanding and strengthen your memory.
4, timely error correction:
Classroom exercises, homework, tests and feedback should be consulted in time, the causes of wrong questions should be analyzed, and relevant calculation training should be strengthened when necessary. Ask your classmates and teachers if you don't understand. Don't let the problem hang in the air. Get into the good habit of doing things today.
5, learn to summarize:
Teacher Feng said: "Mathematics is closely related, and knowledge is closely related. Summing up by stages can not only play a role in reviewing and consolidating, but also find the connection between knowledge, so as to achieve a thorough understanding.
6, learn to manage:
Manage your notebook, exercise book, correction book, and all the exercises and papers you have done. Teacher Feng said that this is the most useful material for reviewing the final exam and must not be ignored.
At present, junior high school students have a serious problem in learning mathematics, that is, they are not good at reading mathematics textbooks and often memorize them. Paying attention to reading methods is very important to improve junior high school students' learning ability. To learn a new chapter, first read it roughly, that is, browse the branches of what you have learned in this chapter, then tick while reading, get a general understanding of the content of the textbook and its key points and difficulties, and mark the places you don't understand. Then read carefully, that is, according to the learning requirements of each chapter after the festival, read the content of the textbook carefully, understand the essence of mathematical concepts, formulas, laws and thinking methods and their causal relationship, grasp the key points and break through the difficulties. Read it again as a researcher, that is, discuss the context, structural relationship and arrangement intention of knowledge from the perspective of development, summarize the main points, finish reading the book, form a knowledge network and improve the cognitive structure. When students master these three reading methods and form habits, they can essentially change their learning methods and improve their learning efficiency.
To improve the quality of lectures, it is necessary to cultivate the habit of listening and understanding lectures. Pay attention to the learning emphasis emphasized by the teacher in each class, the introduction and derivation methods and processes of theorems, formulas and rules, the tips and treatment methods of key parts of examples, the explanation of difficult problems, and the final summary of a class. In this way, grasping the important and difficult points and attending classes along the process of knowledge development can not only improve the efficiency of attending classes, but also change from "listening" to "listening".
Asking questions is an effective way to improve learning efficiency. In the process of learning, when encountering problems, take the time to ask teachers and classmates, and master the knowledge that you don't understand or learn in the shortest time. Set up your own error book and read it often to remind yourself not to make the same mistake twice. So as to improve the learning efficiency.
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