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.
Summary of knowledge points in the second volume of junior one mathematics
Chapter 1: Lines, rays and line segments
(1) Representation methods of lines, rays and line segments
① Straight line: represented by a lowercase letter, such as straight line L, or represented by two uppercase letters, such as straight line AB.
② Ray: a part of a straight line, represented by lowercase letters, such as ray L; It is represented by two capital letters, with the endpoint in front, such as ray OA. Note: When it is represented by two letters, the endpoint letter comes first.
③ Line segment: A line segment is a part of a straight line, which is represented by lowercase letters, such as line segment A; It is represented by two letters representing the endpoint, such as line segment AB (or line segment BA).
(2) The positional relationship between a point and a straight line:
(1) point through a straight line, said the point in a straight line;
(2) The point does not pass through the straight line, which means that the point is outside the straight line.
Chapter 2: the distance between two points
(1) Distance between two points: The length of the line segment connecting two points is called the distance between two points.
(2) There is a certain distance between any two points on the plane, which refers to the length of the line segment connecting these two points. When learning this concept, pay attention to the last two words "length", that is, it is a quantity with size, which is different from a line segment, which is a figure. The length of a line segment is the distance between two points. It can be said that it is a line segment, not a distance.
Chapter 3: Cubes
(1) The general method to solve this kind of problem is to fold the paper according to the diagram, or directly imagine it on the basis of understanding the unfolded diagram.
(2) It is the key to solve this kind of problem to distinguish the geometric expansion diagram from the real object, and to establish the concept of space by combining the transformation between the three-dimensional figure and the plane figure.
(3) There are 1 1 cases in the cubic expansion diagram. After analyzing various situations in the plane expansion diagram, carefully judge which two surfaces are relative.
Chapter 4: Solving one-dimensional linear equations.
Definition: The value of an unknown quantity that makes the left and right sides of a linear equation equal is called the solution of a linear equation.
Substituting the solution of the equation into the original equation, the left and right sides of the equation are equal.
13, solving a linear equation:
1. General steps for solving linear equations with one variable
Removing the denominator, removing brackets, moving terms, merging similar terms, and converting the coefficient into 1 are just the general steps to solve the linear equation with one variable. According to the characteristics of the equation, all the steps are to gradually transform the equation into the form of x = a.
2. When solving a linear equation with one variable, first observe the form and characteristics of the equation. If there is a denominator, generally go to the denominator first; If there are both denominators and brackets, and the denominator can be eliminated after the items outside the brackets are multiplied by the items inside the brackets, the brackets should be removed first.
3. When solving an equation similar to "ax+bx=c", merge the left side of the equation into one term according to the method of merging similar terms, that is, (A+B) x = C.
The equation is gradually transformed into the simplest form of ax=b, which embodies the idea of reduction.
When the coefficient of ax=b is changed to 1, the calculation should be accurate. Once it is clear whether the two sides of the equation are divided by a or b, especially when a is a fraction; Second, we must accurately judge symbols. The same sign X of A and B is positive, and the different sign X of A and B is negative.
14, the application of one-dimensional linear equation
1. Types of applied problems for solving linear equations of one variable
(1) Explore the problem of regularity;
(2) Quantity;
(3) Sales problem (profit = selling price-purchase price, profit rate = profit purchase price ×100%);
(4) engineering problems (① workload = per capita efficiency × number of people × time; (2) If a job is completed in several stages, the sum of workload in each stage = total workload);
(5) Travel problem (distance = speed × time);
(6) the problem of equivalent transformation;
(7) Sum, difference, multiplication and division;
(8) Distribution problem;
(9) Competition score;
(10) Current navigation problem (downstream speed = still water speed+current speed; Water velocity = still water velocity-water velocity).
2. The basic idea of solving practical problems by using equations:
First, find out the unknown quantity and all known quantities in the problem through examination, set the required unknown quantity as X directly or indirectly, and then use the formula containing X to express the related quantity, find out the equation between them, and solve it to get the answer, that is, set, column, solution and answer.
List five steps of solving application problems by linear equations of one variable.
(1) Examination: Carefully examine the questions, determine the known quantity and the unknown quantity, and find out the equivalent relationship between them.
(2) Assumptions: Assumptions about the unknown (X). According to the actual situation, it can be directly unknown (ask whatever you want) or indirectly unknown.
(3) Column: list the equations according to the equivalence relation.
(4) Solution: Solve the equation to obtain the value of the unknown quantity.
(5) Answer: Check whether the unknown value is correct and write a complete answer.
Seventh grade second volume math final review plan
Review objectives (including key points and difficulties)
According to the learning level of the whole class, the initial review goal is to improve the academic performance of the whole class, improve the excellent rate and average score, and improve students' ability to solve practical problems by using basic knowledge.
Review the key points and difficulties:
Chapter 5 focuses: review-the positional relationship between intersection and parallelism of two straight lines in a plane, and the comprehensive application of intersection and parallelism. Difficulties: the nature of vertical parallelism and the comprehensive application of judgment. The sixth chapter focuses on: in the plane rectangular coordinate system, the position of this point is determined by the coordinates of the known point, and the coordinates of this point are determined by the position of the known point and the application of the plane rectangular coordinate system. Difficulties: establish a one-to-one correspondence between points on the coordinate plane and ordered real number pairs, and explore the changes between graphs from coordinate changes.
Chapter 7 focuses on: plane rectangular coordinate system, focusing on understanding the related concepts of plane rectangular coordinate system, drawing plane rectangular coordinate system, finding points according to the coordinates in plane rectangular coordinate system, and finding coordinates from points; Deepen the understanding of the idea of combining numbers with shapes. The difficulty is the practical application of plane rectangular coordinate system.
The eighth chapter focuses on: binary linear equations and related concepts, elimination ideas and substitution methods, solving binary linear equations with addition and subtraction, and solving practical problems with binary linear equations. Difficulties: using equations as a tool to analyze problems and solve many unknown problems.
Chapter 9 focuses on the solution and application of one-dimensional linear inequalities (groups). Difficulties: the solution set of one-dimensional linear inequality (group) and the application of one-dimensional linear inequality (group) to solve practical problems
Chapter 10 focuses on data collection, classification and description.
Difficulties: sampling and drawing histogram of frequency distribution.
Review strategy (measures)
Default 1. The review strategy of "divide first and then summarize" is to review chapter by chapter first and then summarize the review;
2. The strategy of "learning while practicing", while reviewing knowledge, firmly grasp the practice link;
3. The strategy of "link detection" is to detect every link once, and solve the problem in time when it is found;
3. "Simulation" review strategy, in the general review, conduct simulation tests for many times, find problems and solve them in time, and promote the improvement of students' learning quality.
4. The strategy of "summarizing" in time. For a knowledge link or related knowledge points, it is necessary to summarize them in time so that students can master knowledge systematically and improve their ability.
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