The first volume of the eighth grade mathematics syllabus of People's Education Press.
I. Polygons
1, polygon: A figure composed of many end-to-end line segments is called a polygon.
2. Polygon edge: The line segments that make up a polygon are called polygon edges.
3. Vertex of the polygon: The common * * * endpoint of each adjacent edge of the polygon is called the vertex of the polygon.
4. Diagonal line of polygon: The line segment connecting two non-adjacent vertices is called diagonal line of polygon.
5. The perimeter of a polygon: The sum of the lengths of each side of the polygon is called the perimeter of the polygon.
6. Convex polygon: Any side of the polygon extends in two directions. A polygon is called a convex polygon if all other sides of the polygon are adjacent to a straight line derived from an extension line.
Note: A polygon must have at least three sides, and the one with three sides is called a triangle. Those with four sides are called quadrilaterals; Things with several sides are called polygons. The polygons mentioned later refer to convex polygons unless otherwise specified.
7. Polygon angle: The angle formed by two adjacent sides of a polygon is called the inner angle of the polygon, which is simply called the angle of the polygon.
8. Exterior Angle of Polygon: The angle formed by the extension line opposite to one side of the corner of Polygon is called the exterior angle of Polygon.
Note: The outer angle of a polygon is the adjacent complementary angle between the inner angle and its common vertex.
9. Theorem of the sum of interior angles of polygons: the sum of interior angles of n sides is equal to (n-2) 180.
10, inference of the theorem of the sum of inner angles of polygons: the sum of outer angles of N-polygons is equal to 360.
Note: The sum of the outer angles of a polygon is a constant (independent of the number of sides), and it is simpler to solve related calculation problems by using it than by using the formula of the sum of the inner angles of a polygon and the diagonal formula. No matter which formula is used to solve the related calculation, it must be linked with solving the equation and master the calculation method.
Second, quadrilateral.
On the same plane, a figure with four line segments that are not on the same straight line connected end to end is called a quadrilateral.
Third, convex quadrilateral
If any side of a quadrilateral extends to both sides, if the other sides are on the same side of the extended line, such a quadrilateral is called a convex quadrilateral.
Fourth, diagonal line
In a quadrilateral, the line segment connecting two nonadjacent vertices is called the diagonal of the quadrilateral.
The instability of verb (verb's abbreviation) quadrilateral.
When the three sides of a triangle are determined, its shape and size are determined, which is the stability of the triangle. However, after the four sides of a quadrilateral are determined, its shape cannot be determined, which is the instability of the quadrilateral, which has a wide range of applications in production and life.
The theorem of sum of interior angles and the theorem of sum of exterior angles of quadrilateral.
Theorem of the sum of quadrilateral internal angles: the sum of quadrilateral internal angles is equal to 360.
Theorem of the sum of quadrilateral external angles: the sum of quadrilateral external angles is equal to 360.
Inference: theorem of polygon interior angle sum: the sum of n polygon interior angles is equal to 180.
Theorem of the sum of external angles of polygons: the sum of external angles of any polygon is equal to 360.
What methods are there to improve math scores?
Examination method
1, candidates with a good attitude should be confident and have objective test objectives. Pursue normal performance, don't expect your performance for a long time, so your mentality will be very peaceful. Calm and calm, but also moderately nervous, so that the brain is in the best state of activity.
2. The bad habits of "guessing" and "missing" should be avoided from the beginning of the exam, so the exam should be from word to word to sentence.
3. Learn to use calculus paper. Take the calculus test paper as a part of the test paper. To be neat and orderly, write the title number for easy inspection.
4. Correctly treating difficult problems is used to open scores. No matter what your level is, you should learn to bypass the problem and do it at last. Don't be confused by the difficult problem. Only in this way can you ensure that you can rank in the top few no matter what you take.
The habit of listening carefully.
In order to synchronize teaching and learning, teachers require students to concentrate their thoughts in class, listen attentively to the teacher's lectures, listen carefully to the students' speeches, grasp the key points, difficulties and doubts, think while listening, and encourage middle and advanced students to take notes while listening.
The habit of positive thinking.
It is an important guarantee to improve the quality and efficiency of learning to actively think about the questions raised by teachers and classmates and keep yourself in teaching activities. Students' thinking and answering questions are generally required to be well-founded, organized and logical. With the growth of age, we should gradually infiltrate mathematical ideas such as association, hypothesis and transformation when thinking about problems, and constantly improve the quality and speed of thinking about problems.
Do more questions appropriately and develop good problem-solving habits.
If you want to learn math well, it is inevitable to do more problems, and you should be familiar with the problem-solving ideas of various questions. At the beginning, we should start with the basic problems, take the exercises in the textbook as the standard, lay a good foundation repeatedly, and then find some extracurricular exercises to help broaden our thinking, improve our ability to analyze and solve problems, and master the general rules of solving problems. For some error-prone topics, you can prepare a set of wrong questions, write your own problem-solving ideas and correct problem-solving processes, and compare them to find out your own mistakes so as to correct them in time.
We should develop good problem-solving habits at ordinary times. Let your energy be highly concentrated, make your brain excited, think quickly, enter the best state, and use it freely in the exam. Practice has proved that at the critical moment, your problem-solving habit is no different from your usual practice. If you are careless and careless when solving problems, it is often exposed in the big exam, so it is very important to develop good problem-solving habits at ordinary times.
What if the math problem can't be proved?
1. Read the question carefully.
Some students write answers as soon as they see the feeling of deja vu in the front part of the question. This kind of question has not yet made clear the meaning of the topic The topic makes you understand nothing, which is very undesirable. We need to look at the conditions one by one, what is the use of the given conditions, put a question mark in our mind, and then correspond to the diagram, where to find the conclusion and where to find the position in the diagram.
remember
The record here has two meanings. The first layer means mark. When reading questions, you should mark each condition in the given chart. If the opposite sides are equal, they are represented by equilateral symbols. The second meaning is to remember that the conditions given by the topic should not only be marked, but also kept in mind, so that you can repeat it without looking at the topic.
Step 3 extend
Difficult topics often hide some conditions, so we need to be able to extend, so the extension here needs to be accumulated at ordinary times. Usually, the basic knowledge points learned in class are firmly grasped, and some special graphics that are usually trained should also be memorized. When reviewing and memorizing topics, you should think about what conclusions can be drawn from these conditions (just like clicking on the computer and the corresponding menu will pop up immediately), and then mark it next to the graph. Although some conditions may not be used when they are proved, it is such a long time.
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