The arrangement of mathematics knowledge points in the first day of junior high school in People's Education Press
Collection and arrangement of data
1, Census and Sample Survey
A comprehensive survey of all topics for a specific purpose is called a census. Among them, all the inspected objects are called the whole, and each inspected object that constitutes the whole is called the individual.
Selecting some individuals from the population for investigation is called sampling investigation, and selecting some individuals from the population is called the sample of the population.
2, vermicelli map
Sector statistical chart: the relationship between the whole and the part is represented by circles and sectors, and the size of the sector reflects the percentage of the part in the whole. This kind of statistical chart is called departmental statistical chart. (The sum of percentages of each sector is 1)
Degree of central angle = 360× the percentage. (The sum of the degrees of the central angle of each part is 360)
3. Frequency histogram
Frequency histogram is a special bar chart, which groups data with the horizontal axis as the statistical object, and the vertical axis represents the frequency of each group of data.
4, the characteristics of various statistical charts
Bar chart: The specific figures of each item can be clearly displayed.
Broken line statistical chart: it can clearly reflect the changes of things.
Department statistical chart: it can clearly show the percentage of each part in the total.
Summary of knowledge points in the second volume of mathematics in the first day of the People's Education Press
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 and 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.
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.
The second volume of the first day of junior high school mathematics tutoring review materials
1. Geometry: Points, lines, surfaces and bodies can help people effectively describe the complex world. It's all called geometry. All kinds of figures abstracted from objects are collectively called geometric figures. Geometric figures with parts not in the same plane are called three-dimensional figures. Some geometric figures are all in the same plane, which is called plane figures. Although solid figure and plane figure are two different geometric figures, they are interrelated.
2. Classification of geometric figures: Geometric figures are generally divided into three-dimensional figures and plane figures.
3. Straight line: The basic concept of geometry is the trajectory of a point in space moving in the same or opposite direction. From the point of view of plane analytic geometry, a straight line on a plane is a graph represented by a binary linear equation in a plane rectangular coordinate system. To require the intersection of two straight lines, we only need to solve these two binary linear equations simultaneously. When simultaneous equations have no solution, two straight lines are parallel. When there are infinite solutions, two straight lines coincide; When there is only one solution, two straight lines intersect at one point. The angle between a straight line and the positive direction of the X axis (called the inclination angle of the straight line) or the tangent of the angle (called the slope of the straight line) is often used to indicate the inclination of the straight line on the plane (for the X axis).
4. Ray: In Euclidean geometry, the figure formed by a point on a straight line and its edge is called a ray or a semi-straight line.
5. Line segment: refers to a continuous or discontinuous figure composed of one or more different line elements, such as a real line segment or a two-point long line segment composed of "long stroke, short interval, point, short interval, point and short interval".
The line segment has the following properties: the line segment between two points is the shortest.
6. Distance between two points: The length of the line segment connecting two points is called the distance between these two points.
7. Endpoint: Two points on a straight line and the part between them are called line segments, and these two points are called the endpoints of line segments.
A line segment is represented by letters or lowercase letters representing its two endpoints. Sometimes these letters also represent the length of a line segment, which is recorded as line segment AB or line segment BA and line segment A .. where AB represents any two points on a straight line.
8. The difference between straight lines, rays and line segments: straight lines have no distance. Ray has no distance. Because a straight line has no end point, a ray has only one end point and can extend indefinitely.
9. Angle: A graph composed of two non-overlapping rays with a common endpoint is called an angle. This common endpoint is called the vertex of the angle, and these two rays are called the two sides of the angle.
The figure formed by the rotation of light from one position to another around its endpoint is called an angle. The endpoint of the rotated ray is called the vertex of the angle, the ray at the starting position is called the starting edge of the angle, and the ray at the ending position is called the ending edge of the angle.
10. Static definition of angle: A graph composed of two non-coincident rays with a common endpoint is called an angle. This common endpoint is called the vertex of the angle, and these two rays are called the two sides of the angle.
1. monomial: in algebraic expressions, if only multiplication (including power) operations are involved. Or algebraic expressions that contain division but do not contain letters in division are called monomials; The product of numbers or letters is called a monomial (a single number or letter is also a monomial).
2. Coefficient: The numerical factor in a single item is called the coefficient of this single item. The sum of the exponents of all letters is called the degree of this monomial. The zeroth power of any nonzero number is equal to 1.
3. Polynomial: The sum of several monomials is called polynomial.
4. Number and degree of polynomials: the number of monomials contained in a polynomial is the number of polynomial terms, and each monomial is called a polynomial term; In polynomials, the degree of the degree term is called the degree of polynomials.
5. Constant term: the term without letters is called constant term.
People's education edition arranges related articles on the knowledge points of mathematics in the first day of junior high school;
★ Summary of knowledge points of the first-year mathematics people's education edition
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★ Knowledge points of the first volume of mathematics in the first day of People's Education Edition
★ Induction of knowledge points in the first volume of junior high school mathematics.
★ Summary of the knowledge points in the first volume of mathematics in the first grade education edition.
★ Summarize the knowledge points in the first volume of junior high school mathematics.
★ People's Education Edition Senior One Mathematics Knowledge Points
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★ Summary of knowledge points in the first volume of junior high school mathematics (2)
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