Senior two mathematics knowledge points
Position and coordinates
1, determine the location
In a plane, two data are usually needed to determine the position of an object.
2. Plane rectangular coordinate system
Meaning: In a plane, two mutually perpendicular axes with a common origin form a plane rectangular coordinate system.
(2) Usually, the two number axes are placed in horizontal and vertical positions respectively, and the right and upward directions are the positive directions of the two number axes respectively. The horizontal axis is called X axis or horizontal axis, and the vertical axis is called Y axis and vertical axis, both of which are collectively called coordinate axes, and their common origin O is called the origin of rectangular coordinate system.
③ Establish a plane rectangular coordinate system, and the points on the plane can be represented by a set of ordered real number pairs.
(4) In the plane rectangular coordinate system, two coordinate axes divide the coordinate plane into four parts, the upper right part is called the first quadrant, and the other three parts are called the second quadrant, the third quadrant and the fourth quadrant counterclockwise, and the points on the coordinate axes are not in any quadrant.
⑤ In the rectangular coordinate system, for any point on the plane, there is an ordered real number pair (that is, the coordinates of the point) corresponding to it; On the contrary, for any ordered real number pair, there is a point on the plane corresponding to it.
3. Axisymmetry and coordinate changes
Regarding the coordinates of two points about the axis symmetry of X, the abscissa is the same, and the ordinate is opposite; With regard to the coordinates of two points symmetrical about the Y axis, the ordinate is the same, and the abscissa is opposite.
Eighth grade mathematics review materials volume one
linear function
20. The concept of1linear function
1. Generally, a function with an analytical formula similar to ykxb(kb is a constant, k0) is called a linear function; The domains of linear functions are all real numbers.
2. Generally, we call the function yc(c is a constant) a constant function.
20.2 linear function image
1. List, drawing and connection
2. The ordinate of the intersection of a straight line and the Y-axis is called the intercept of the straight line on the Y-axis.
3. The coordinate of the intersection of a general straight line ykxb(kb is constant, k0) and the Y axis is (0, b), and the intercept of the straight line is b..
4. the image of linear function ykxb(b≠0) can be translated from the image of proportional function ykx to get the image when b >: 0 and b unit moves up, and when b
5. The relationship between linear inequality and linear function (see figure)
20.3 Properties of Linear Functions
1. linear function ykxb(kb is constant, k? 0) has the following properties:
When k>0, the function value y increases with the value of the independent variable x.
When k < 0, the function value y decreases with the increase of independent variable X.
(1) As shown in the figure, when k>0, b>0, the straight line passes through the first, second and third quadrants (the straight line does not pass through the fourth quadrant); ② As shown in the figure, when k>0, b-o, the straight line passes through the first, third and fourth quadrants (the straight line does not pass through the second quadrant); ③ As shown in the figure, when k￠O, b>0, the straight line passes through the first, second and fourth quadrants (the straight line does not pass through the third quadrant);
④ As shown in the figure, when k￠O and b￠O, the straight line passes through the second, third and fourth quadrants (the straight line does not pass through the first quadrant). The application of 20.4 linear function.
1. Using linear functions and images to solve practical problems
Math review method in junior two
orderly
Mathematics is an interlocking subject, and any link will affect the whole learning process. Therefore, don't be greedy when studying. You should pass the exam chapter by chapter, and don't leave questions that you don't understand or understand deeply easily.
Emphasize understanding
Concepts, theorems and formulas should be memorized on the basis of understanding. Every time you learn a new theorem, first try to do an example without looking at the answer to see if you can correctly apply the new theorem; If not, compare the answers to deepen the understanding of the theorem.
basic skill
You can't learn mathematics without training. Usually do more exercises with moderate difficulty. Of course, don't fall into the misunderstanding of dead drilling questions, be familiar with the questions of the college entrance examination, and be targeted in training.
Pay attention to mistakes
Booking the wrong book and collecting the wrong questions by yourself is often your weakness. When reviewing, this wrong book has become a valuable review material.
Mathematics learning is a step-by-step process, and it is unrealistic to dream of reaching the sky in one step. After reciting the contents of the book, carefully write the exercises at the back of the book. Some students may think that the exercises after the book are too simple to do. This idea is highly undesirable. The function of the exercises after the book is not only to help you remember the contents in the book, but also to help you standardize the writing format, make your problem-solving structure compact and tidy, make proper use of formulas and theorems, and reduce unnecessary marks in the exam.
The usual mathematical research:
○ 1 preview carefully before class. The purpose of preview is to listen to the teacher better. Through preview, the mastery level should reach 80%. Listen to the teacher answer these questions with questions that you don't understand in the preview. Preview can also improve the overall efficiency of attending classes. Specific preview method: finish the topics in the book and draw the knowledge points. The whole process lasts about 10.
○2 Let math class combine with practice. It's no use just listening in math class. When the teacher asks the students to do calculus on the blackboard, they should also practice on the draft paper. You must ask questions you don't understand, or you may not do it if you encounter similar problems in the exam. When listening to the teacher's lecture, you must concentrate on the details, otherwise, "the embankment of a thousand miles will collapse in the ant nest."
○3 Review in time after class. After finishing your homework, sort out what the teacher said that day, and you can do extracurricular problems for about 25 minutes. You can choose the extracurricular books that suit you according to your own needs. The content of the extracurricular problem is probably today's class.
The fourth unit test is to test your recent study. In fact, the score represents your past. The key is to sum up and learn from each exam so that you can do better in the mid-term and final exams. Teachers often take exams without notice and review them in time after class.
Second year of high school, Shanghai science edition, the first book of mathematics, related articles on knowledge points;
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