The real difficulty is the triangle and parallelogram in geometry (each version is different, and the parallelogram in Beijing Normal University belongs to Grade Three, but most schools will finish this part by the end of the second semester).
In triangles, besides mastering the triangle congruence method and pythagorean theorem, we should also master the properties and judgments of isosceles triangles, some conclusions of special right-angled triangles, and the properties and judgments of perpendicular lines and bisectors. So much for triangles, but these parts are all combined in the exam and need to be mastered skillfully.
It is necessary to master the judgment of triangle congruence. On the basis of the above, the method of judging right triangle (HL) is added:
The nature and judgment of triangle (this is an important and difficult point), in which the expression of "three lines in one" should be understood and skillfully used, and it will be used in many topics, as well as the nature and judgment of equilateral triangle:
In addition to Pythagorean theorem and its inverse theorem, the properties of right-angled triangles also add some other properties, especially the properties of special triangles, which can be simplified a lot if skillfully used when doing problems:
This is the nature of the general right triangle:
There is nothing to say about the properties of special right-angled triangles with angles of 45 degrees and 30 degrees. You should be skilled enough to see the relevant figures and take them as a conditioned reflex:
Properties of median vertical line and angular bisector;
Note that there will be a ruler drawing in this place, that is, drawing the middle vertical line of the line segment and the bisector of an angle. At the same time, there is an extended knowledge point, that is, the distance from the intersection of the perpendicular lines of three sides of a triangle to the vertex of the triangle is equal. This intersection point is called the outer center of the triangle and the center of the circumscribed circle of the triangle. The distance from the intersection of bisectors of three angles of a triangle to three sides is equal. This intersection is called the center of the triangle and the center of the inscribed circle of the triangle.
The above is the triangular part. If you want to pay attention, these knowledge points are all places that need attention. The test sites of many topics are a combination of several knowledge points, and there are few individual knowledge points.
As for the algebraic part, it is the multiplication and division of one-dimensional linear inequalities and fractions. In one-dimensional linear inequality, it is not difficult to solve it. As long as you can solve the linear equation of one variable, there is basically no big problem. The emphasis is on the understanding of the solution set.
The difficulty in this part lies in the multiplication and division of fractions, that is, the simplification of fractions. Factorial decomposition is an important and difficult point here, and another important and difficult point is the calculation of fraction, which involves factorial decomposition, quadratic root, simplification, general division and power operation. At the same time, the amount of calculation is relatively large, which requires computing power to pass. At the same time, you need to be careful and patient, and you need to master some conventional problem-solving methods.
In fact, there is no need to struggle with any difficulties. If you want to learn well, you are naturally not afraid of any part. If you don't learn well, the whole book will be difficult. So you just need to do your daily study tasks in a down-to-earth manner. If your current grades are not satisfactory, just try harder yourself, and don't aim too high.
Compared with the first grade, the second grade mathematics is more content and more difficult. Geometry will focus on triangle, congruent triangles, isosceles triangle, equilateral triangle, Pythagorean theorem, parallelogram knowledge will be studied in the second book; Algebra, I will learn the knowledge of multiplication, factorization, fraction, quadratic root and linear function of algebraic expressions. Each part is full of knowledge points, which can be said to occupy half of junior high school mathematics, so the importance of learning junior high school mathematics well can be seen.
There are several major difficulties. Geometric part: 1 Prove that the line segment and angle are equal with the idea of congruence, but not once or twice; Flexible use of congruence condition judgment, we should be good at discovering the implied conditions in the questions; 3. The combination of the nature of isosceles triangle (equilateral and equilateral, three lines in one) and the geometric problem of judging congruent triangles; 4. The properties of two important straight lines (angle bisector and median vertical line) and their applications in geometric problems: 5. The comprehensive application and judgment of the properties of parallelogram and special parallelogram (rectangle, diamond and square); Six important theorems about right-angled triangles (the right-angled side of 30 is equal to half of the hypotenuse; The median line of the hypotenuse is equal to half of the hypotenuse, Pythagorean theorem and inverse theorem).
Algebra part: 1 algebraic expression has many multiplication formulas, including accurate identification and ingenious application of (multiplication with the same base power, multiplication with power, product multiplication, square difference formula, complete square formula); 2 accurately understand the factorization and use the best method to factorize; It is difficult to subtract, divide, add, subtract, multiply and divide fractions. 4 understanding and operation of zero exponential power and negative exponential power; The solution of fractional equation and the final exam, as well as the correct solution of fractional equation to application problems; 6. Understanding and simplification of the simplest quadratic root formula: 7. Understanding the concept of function, accurately remembering the properties of images and elementary functions, solving the elementary resolution function with undetermined coefficient method 8. Abstracting the elementary function model from practical problems, and solving problems with relevant knowledge.
The above is my summary of the important and difficult knowledge of junior two mathematics, and I hope students will pay attention to it.
In the chapter of triangle, we only need to know the three-sided relationship of triangle, the definitions of angle bisector, midline and height, the theorems of inner angle and outer angle, the complementarity of two acute angles of right triangle, and the formula of polygon inner angle. The content is simple.
I hope my answer is helpful to you.
Welcome to junior high school mathematics paradise!
This question is somewhat general, because the current version is different, the learning content is different, and the natural emphasis and difficulty are different. Let's take the eighth grade Chinese teacher edition as an example. Chapter 1 * * contains 10: the roots of numbers, multiplication and division of algebraic expressions, congruent triangles's Pythagorean theorem, data collection and arrangement, fractions, functions and their images (inverse proportional functions of functions), parallelograms, data arrangement and preliminary processing.
Among these contents, it is difficult to prove linear function and inverse proportional function, and it is difficult to prove parallelogram geometry. Everything else is basic. Just remember, understand and apply the questions.
For a triangle, there are four ways to judge which chapter is the congruence of the triangle. A right triangle has a special judgment method. From the beginning, according to the requirements and progress of the textbook, there is no problem at all with one kind of learning, one kind of practice, basic problems and memory-understanding-practice. Pay attention to the correspondence of two triangles in the proof of congruence and write them in the corresponding positions, otherwise they don't correspond.
In short, one or two sentences like this are not clear, and only in the specific content can we explain the precautions in detail.
A little humble opinion, welcome criticism and correction.
# Education #
Compared with Grade One, the knowledge content of junior high school mathematics has increased significantly. As students gradually adapt to the basic learning mode of junior high school, there are more mathematical symbol languages and more abstract contents in algebra. The logical reasoning proof of geometry part requires higher requirements and wider contents. Generally speaking, there are two main difficulties in learning in senior two: first, how to form a knowledge system in the brain by memorizing mathematical knowledge? Most senior two students who find math difficult have one thing in common:' I have a clear impression of what I just learned, and the chapters I learned before are vague, so I feel that I can't answer some questions that evaluate double basics in the math exam'. Therefore, the first difficulty is to remember knowledge! Many people think that memorizing knowledge is very simple, and memorizing is a natural ability, which can be solved by reading more books and doing more problems. In fact, everyone's memory talent is different. No matter how talented you are, the length of your memory information can reach more than 8 characters. Faced with a huge amount of mathematical knowledge, you can only look at the ocean and sigh! What should I do? There are inherent logical connections between mathematical knowledge, which determines that learners need to find these logical connections. For example, have you ever thought about the connection between a linear equation and a quadratic equation? After factorizing the latter, two linear equations can be obtained. Another example is a linear inequality, a linear equation and a linear function. Have you considered the relationship between them? I call this kind of thinking activity the processing of knowledge, which can be more vividly called: branding yourself. In the mythical world, if someone else's magic weapon or instrument can be used for himself, he must put his own brand on it. The same is true in mathematics. Massive mathematical knowledge is the public wealth of mankind. If you want to be your own, you have to put your own brand. Among the junior high school students I contacted, there is a common phenomenon of' paying attention to brushing questions and ignoring the processing and arrangement of knowledge'. It is not surprising that we ignore or lack the processing and arrangement of knowledge, and feel that mathematical knowledge is difficult to remember, can't remember, and can't remember accurately! Second, it is difficult to solve the problem. Reflected in the large amount of exercise and slow speed of solving problems. I feel that mathematics is rare, and junior high school students often solve problems slowly and have a high error rate. In fact, our learning process is divided into three parts: new knowledge learning, review and consolidation, and comprehensive testing. Any chapter of mathematics is this step-by-step learning mode. When learning new knowledge, students often turn to books to do exercises, and most of them can be done correctly. In the review and consolidation stage, exercises combining old and new knowledge often appear, and students' error rate will increase. Finally, in the comprehensive test, there are many chapters of knowledge, so it is entirely possible that a comprehensive question involves three or more chapters of knowledge, and it is necessary to accurately call these knowledge to get the answer. My advice to junior two students when they usually do problems is: Don't do problems for the sake of doing problems, but know the real purpose of doing problems-consolidate knowledge and synthesize knowledge! With this understanding, I will design my own practice strategy next. My strategy is shared as follows: first, read all the homework exercises patiently and divide them into' basic knowledge, basic ability, simple synthesis and complex synthesis'. Basic courses insist on not turning over the books or closing the books. If you can't remember the knowledge involved in comprehensive courses, you must stop and patiently check your memory. The above difficulties are the training ground for students to acquire mathematical literacy and ability. There are solutions to the dilemma, but students have to work hard on their own! I hope my two opinions can help you!
1. Tandem knowledge, lay a solid foundation, and remember many theorems and formulas.
2. Three points, three sides and three corners. Add a few special triangles. Actually, that's all.
What can't be done is difficulty; What is written in the book is what you should pay attention to
As a freshman majoring in mathematics, it is a distant thing to mention Grade Two in my mind.
Generally speaking, my junior high school mathematics at that time was relatively simple, and the requirements for students' mathematical literacy were not so high. More importantly, students' ability to accept knowledge and use it to solve simple problems.
But after all, everything will change. I also know that junior high school mathematics is also very flexible and has many sharp corners. If we want to talk about the difficulties of junior two mathematics, I think more aspects involve some abstract and unspecific knowledge points. That is, students are only 13. 14 years old, and they don't have high ability to solve problems. In the second day of junior high school, it is more important to attend classes and do problems after class. The senior high school entrance examination is not very difficult.
As for the content of the triangle chapter, congruent triangles and similar triangles and the special points in the triangle are more important, such as the center of gravity, center, center of gravity and so on. It can be proved by the judgment theorem, and the congruence (similarity) of triangles can be judged, and then some angles or edges can be obtained to further solve the problem.
In a word, the difficulty of triangle lies in the nature of its heart, and there are many common angles or sides in the triangle in specific topics, which brings great trouble to students in solving problems, and the marked angles and sides are chaotic, which requires students to be careful. For example, at the end of the senior high school entrance examination, I remember very clearly that it was a triangular topic. Many corners and sides of a triangle are all in one figure, and when they are found, they will be chaotic. Therefore, this is the most troublesome thing for students in the triangle.
Finally, I wish you progress in your study. Come on, as long as you study hard, the difficulties will eventually be broken. Come on!
It is necessary to flexibly hold congruent similar triangles to meet the requirements, that is, to prove the satisfying conditions when demonstrating.
Judging consistent and similar conditions should be combined with reality.