Summary of Mathematics Knowledge Points in Volume II of Grade One of Beijing Normal University Edition
First of all, the monomial
1, an algebraic expression of the product of numbers and letters, is called a monomial.
2. The single numerical factor is called the single coefficient.
3. The index of all the letters in the monomial and the number of times called the monomial.
4. A single number or letter is also a monomial.
5. The coefficient of monomial with only letter factor is 1 or-1.
6. A number is a monomial, and its coefficient is itself.
7. The degree of a single nonzero constant is 0.
8. A single item can only contain multiplication or power operation, and cannot contain other operations such as addition and subtraction.
9. The coefficient of the monomial includes the symbol before it.
10, when the coefficient of the monomial is a fraction, it should be turned into a false fraction.
When 1 1 and the single coefficient is 1 or-1, the number "1" is usually omitted.
12, the number of monomials is only related to letters, and has nothing to do with the coefficient of monomials.
Second, polynomials
The sum of 1 and several monomials is called a polynomial.
2. Each monomial in a polynomial is called a polynomial term.
3. The term without letters in polynomial is called constant term.
4. A polynomial has several terms, which are called polynomials.
5. Every term of polynomial includes the symbol before the term.
6. Polynomials have no concept of coefficient, but have the concept of degree.
7. The degree of the degree term in a polynomial is called the degree of the polynomial.
Seven-grade mathematics knowledge points
First, the knowledge network structure
Second, the main points of knowledge
1. In the same plane, there are two kinds of positional relationships between two straight lines: intersecting and parallel, and verticality is a special case of intersection.
2. On the same plane, two disjoint straight lines are called parallel lines. If two straight lines have only one common point, they are said to intersect; If two straight lines have no common point, they are said to be parallel.
3. Among the four angles formed by the intersection of two straight lines, two angles with a common vertex and a common edge are
The properties of adjacent complementary angles: complementary adjacent complementary angles. As shown in figure 1, they are complementary angles,
Fill the corner with neighbors. += 180 ; += 180 ; += 180 ;
+= 180 。
4. Among the four corners formed by the intersection of two straight lines, two sides of one corner are opposite extension lines of two sides of the other corner, so the two corners are opposite. The nature of antipodal angle: antipodal angle is equal. As shown in figure 1, and they are opposite to each other. =; =。
5. If one of the angles formed by the intersection of two straight lines is a right angle or 90, the two straight lines are said to be perpendicular to each other.
One of them is called the perpendicular of the other. As shown in Figure 2, when = 90, ⊥.
Nature of vertical line:
Property 1: There is one and only one straight line perpendicular to the known straight line.
Property 2: Of all the line segments connecting a point outside the straight line and a point on the straight line, the vertical line segment is the shortest.
Property 3: As shown in Figure 2, when a ⊥ b = = = 90.
Distance from point to straight line: The length from a point outside a straight line to the vertical section of this straight line is called the distance from point to straight line.
6. The basic characteristics of congruent angle, internal dislocation angle and ipsilateral internal angle:
(1) is on the same side of two straight lines (cut lines) and the same side of the third straight line (cut lines), so that
These two angles are called isosceles angles. In Figure 3, * * * has a pair of isosceles angles; And is an isosceles angle;
And are at the same angle; And are at the same angle; And it's the same angle.
(2) Between two straight lines (secant) and on both sides of the third straight line (secant), such two angles are called inscribed angles. In figure 3; * * has a pair of inner corners; Is the inner corner; And is an inner corner.
(3) Between two straight lines (intersecting lines), both are on the same side of the third straight line (intersecting line), and such two angles are called ipsilateral inner angles. In figure 3; * * There are a pair of inner corners on the same side; And are internal angles on the same side; And it is the same inner angle.
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:
The fifth chapter focuses on: review. The position relationship of two straight lines intersecting and parallel in the plane, and the comprehensive application of intersecting and parallel. 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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