According to my experience, liberal arts mathematics is easy to learn. I can draw inferences from three sets of examples designed by teachers in class. Therefore, the best and most useful way to review and consolidate is to go through the math notes carefully, recite the formula according to the knowledge points first, then do the examples again on white paper, and then check the problem-solving steps against the norms to find out the function and significance of each step. Then do the example again until the steps are the same as the standard problem-solving steps (note: don't deliberately recall the standard problem-solving steps this time, but arrange the steps by yourself according to the correct thinking. Finally, do the teacher's homework and exercises in class. Do it once this time. If you make a mistake, repeat it. Finally, after skilled use, you can find extracurricular exercises to do. (Pay attention to buying extracurricular exercises to distinguish between arts and sciences. The difficulty of arts and sciences is different, the knowledge points are different, and the thinking direction is different. However, if you want to hit 140- 150, you can do some questions that liberal arts can answer but just have a little difficulty in thinking, so that you can broaden your mind, exercise your careful thinking, and observe your contact ability. (This is very important, and in the last few questions.

Note here: every step left by the basic teacher is very useful. If there are more steps than the teacher, it means that you are too cumbersome to solve the problem and waste time. If there are too many steps, you won't get extra points, and if there are loopholes in the extra steps (such as symbol errors). ), you will lose points. Pay more attention to the omission of some simple steps in the future The college entrance examination, because of the tension, the environment, the amount of questions in the test paper itself and the tight time, most people can finish it or not. If there are fewer steps than the teacher, you should pay more attention. There are two situations: first, your thinking is not careful (such as classified discussion). Second, you have too many short steps. There are many simple steps in the college entrance examination.

But sometimes, like this after-school problem, plane α ∩ plane β = straight line L. ABC is three points and A∈α, B∈α, C∈β, straight line AB is not parallel to L, and plane ABC ∩ β = M. Judging the positional relationship between L and M proves your conclusion. Classification discussion:

1. If point C is on straight line L, there will be a plane ABC and a plane α overlapping, then straight line L coincides with straight line M. ..

2. if point c is not on the straight line l.

∫ Plane α ∩ Plane ABC=AB, Plane ABC∩ Plane β = M.

∴AB‖m

AB and L are not parallel.

M and I are not parallel.

∵mс plane β, Lс plane β.

∴m∩L,m and I intersect in plane β.

This step "m с plane β, Lс plane β" cannot be omitted, because the conclusion of "m с l" can only be established in the same plane, otherwise it may be a straight line in different planes. When you give a short answer to a geometry or proof question, please note that either your answer is wrong or you have omitted too much, and the score will be deducted according to the importance of the omission. If you often grade papers with your teacher, you will know that the important steps of standard answers are marked with scores, and the teacher gives them according to the grading steps. If there is no grading step, points will be deducted. Take a few more steps and don't deduct points. If there are loopholes in the extra steps (such as symbol errors), points will be deducted. I have a classmate who scored seven points in geometry, omitting too much, and only gave 2 points. After class, the teacher's explanation is an important step in the answer to the test questions. The score is clearly marked, and the teacher gives 4 points according to the steps, but the symbols "∈ and с" are mixed, resulting in two points. The child was unlucky, and finally got it right! )

If you have any questions, you can contact me, Wutong6 16@yahoo.cn, but the answer time may be uncertain. Now I don't often check my email.