The first volume of eighth grade mathematics induces the linear function of knowledge points.
(1) proportional function: the general shape is y=kx(k is a constant, k? 0) is called the proportional function, where k is called the proportional coefficient.
(2) Image features of proportional function: some straight lines passing through the origin.
(3) Image attributes:
(1) when k >; 0, the image of function y=kx rises from left to right through the first and third quadrants, that is, y also increases with the increase of x; ② when k
(4) Find the analytic expression of the proportional function: just know a non-origin point.
(5) Drawing the image of the proportional function: passing through the origin and point (1, k); (or another non-origin).
(6) linear function: the general shape is y=kx+b(k and b are constants, k? 0) is called a linear function.
(7) Proportional function is a special linear function; (because when b=0, y=kx+b is y=kx).
(8) Linear function image features: partial straight lines.
(9) Nature:
(1) y=kx and y=kx+b have the same inclination angle, and y=kx+b can be regarded as y=kx translation |b| unit length; (When b>0, translate upward; When b<0, translate downward)
2 when k >; 0, the straight line y=kx+b rises from left to right, that is, y increases with the increase of x;
③ When k < 0, the straight line y=kx+b decreases from left to right, that is, Y decreases with the increase of X;
4 when b>0, the intersection of the straight line y=kx+b and the positive semi-axis of the y axis is (0, b);
⑤ When b
(10) Find the analytical formula of linear function: that is, find the values of k and b;
(1 1) Draw the image of the function once: two points are known.
On Equations (Groups) and Inequalities from the Perspective of Functions
(1) Solving a linear equation with one variable can be transformed into: when the value of a linear function is 0, find the value of the corresponding independent variable; From the image, this is equivalent to knowing the straight line y=kx+b and determining the value of the abscissa of its intersection with the x axis;
(2) Solving the linear inequality of one variable can be regarded as: when the linear function value is greater than (less than) 0, find the value range corresponding to the independent variable;
(3) Each bivariate linear equation corresponds to a univariate linear function, so it also corresponds to a straight line;
(4) Generally, each binary linear equation group corresponds to two linear functions, so it also corresponds to two straight lines. From the "number" point of view, solving equations is equivalent to considering the values of two functions when the independent variables are equal. What is the value of this function? From the perspective of "shape", solving equations is equivalent to determining the coordinates of the intersection of two straight lines.
Extended reading: What are the methods for reviewing mathematics in Grade Two? First, overcome psychological fatigue.
First, we should have a clear learning purpose. Learning is like pumping water from a river. The more power, the greater the water flow. Motivation comes from the purpose, and only by establishing the correct learning purpose can we have a strong learning motivation;
Second, we should cultivate a strong interest in learning. The formation of interest is related to the excitement center of cerebral cortex, accompanied by pleasant, cheerful and positive emotional experience. Psychological fatigue is caused by the negative emotion of cerebral cortex resistance. Therefore, cultivating one's interest in learning is the key to overcome psychological fatigue. With interest, learning will have enthusiasm, consciousness and initiative, and psychology will be in a good competitive state;
Third, we should pay attention to the diversification of learning. Book learning itself is boring and monotonous. If you study a course or a chapter repeatedly, it is easy to suppress the cerebral cortex, resulting in psychological saturation and boredom. Therefore, candidates may wish to review each course alternately.
Second, overcome the plateau phenomenon.
The plateau phenomenon in review refers to the phenomenon that when reviewing for a certain period, it often stagnates, not only making no progress, but also regressing. The platform period is not that there is no progress in learning, but that some progress and some retrogression are balanced with each other, which makes the review effect not fundamentally changed and makes people frustrated and disappointed. When candidates encounter plateau in the process of reviewing for the exam, don't be impatient or lose confidence, but find out the reasons for learning methods and enthusiasm. Adjust the review progress in time, make more efforts to use your brain scientifically and improve the review efficiency.
Third, pay attention to reviewing "mistakes"
If you are not good at coming out of mistakes in review, there will be more and more defects and loopholes. If left unchecked, the ant nest will eventually burst. During the preparation period, in order to reduce the error rate, in addition to timely revision and comprehensive and solid review, the key issue is to find out the reasons and constantly review the mistakes. That is, read the wrong questions regularly, recall the reasons for the mistakes, and sort out all kinds of wrong questions and reasons. For those problems that are repeatedly wrong, you can consider doing it again to avoid "future troubles." The reasons for the mistakes are: problems in conceptual understanding, problems caused by carelessness, and illusions caused by sloppy writing, so as to effectively avoid making similar mistakes in the exam.
Fourth, grasp the psychological characteristics and do a good job in reviewing before the exam.
Practice has proved that a person's temperament, personality, psychological stability and other factors will also affect the review before the exam. In the process of preparing for the exam, candidates should make an exam review plan according to their own psychological characteristics, adjust the review progress according to their own mentality, choose and use the review methods well, and make their exam review achieve the expected results.
1, textbooks can not be ignored.
For junior two students, they are all learning new lessons, and textbooks are important review materials that are easy to ignore. Usually, everyone takes notes in class at school, and basically doesn't read textbooks. Students are advised to read and understand the knowledge points repeatedly according to the textbook while reading notes, and to think, ponder and integrate exercises in after-school exercises to deepen their understanding of the knowledge points. We should also focus on memorizing the key contents and key examples in the textbook.
2. Wrong title
I believe that students with good study habits should have a wrong book, copy down the wrong questions in each exercise, homework and exam, make the answers clear, find out the reasons for the mistakes, find out the weak points in their knowledge and ability, and take them out and look at them often. When you encounter repeated mistakes, you should take the initiative to discuss with your classmates and ask the teacher to thoroughly understand the problem and avoid making similar mistakes again.