First, to solve problems, we must first learn to examine questions. Many students don't pay enough attention to the questions when they are in a hurry, so they don't fully understand the conditions and problems of the questions, not to mention the hidden conditions and potential mathematical thinking mining in some questions, which leads to many students' difficulties. To solve a problem, we must first learn to examine the problem. Only by analyzing the problem in time, summarizing it in time, patiently and carefully examining the problem, and accurately grasping the key words, potential conditions and internal relations between the conditions can we get as much information as possible from the problem and quickly find the correct direction to solve the problem. Example 1: If the straight line Y = 6x+A does not pass through the fourth quadrant, the value range of a is _ _ _ _. Wrong solution: it is known that the straight line passes through the first, second and third quadrants, so when A >: 0, the straight line y = 6x+a does not pass through the fourth quadrant. Analysis: If the straight line y = 6x+a does not pass through the fourth quadrant, it may pass through the first, second and third quadrants, and then a>0; It is also possible to pass through the first and third quadrants, that is, through the origin, when a = 0. Positive solution: A ≥ 0 should be filled in.
Second, the topic can not only be done, but also be done correctly. Our students often have some situations of "meeting but not being right" and "being right but not being complete" in their usual study process. Many topics that you think you are doing right are deducted because of miscalculation and omission. , resulting in a far cry from the actual scores of students. Although multiple-choice questions and fill-in-the-blank questions only need one answer, the calculus process is presented on draft paper, and a small mistake in the process will make a mistake; It is more necessary to examine the problem-solving process and give points according to the answer points. Therefore, for solving problems, it is often overlooked by some candidates to turn the problem-solving strategies and ideas into scoring points and express them accurately and completely in mathematical language. Many students "have a good idea" but can't say clearly, and there are not a few points deducted. Example 2: The current annual profit of a welfare factory is 6.5438+0.5 million yuan, and it is planned to increase by 20,000 yuan every year in the future. (1) Write the functional relationship between the annual profit y (ten thousand yuan) and the number of years x; (2) Draw the image of the function. Wrong solution: (1) y =15+2x; (2) The drawn function image is shown in figure 1. Analysis: This question does not take into account that the value range of the independent variable X in practical problems should be 0, so drawing the image as a straight line should actually be a ray.
Third, the speed and accuracy of solving problems should be two-pronged. Only by doing the right question can you score. Only by doing the right question can you not take the time to check; Only by completing all the test questions within the specified time and improving the speed of solving problems can we get all the test scores. Both the speed and accuracy of solving problems are the result of usual training, not the problems that can be solved in the examination room. If you blindly seek speed and pursue the speed of solving problems, you will only make a lot of mistakes in the end. Moreover, the simple pursuit of accuracy will cause the problem-solving speed to be too slow and the test questions cannot be completed in time. For example, some students make mistakes in the hasty and simple calculation process, and even if they have correct thinking and take the time to calculate, they can hardly get marks. Solve math problems slowly and accurately, and you can take more; On the contrary, if you hurry up and make mistakes, you will not get points if you spend time. Fourth, after solving the problem, it is easy to get the test paper first, or it is easy to get the test paper after the first difficulty. Some candidates are used to answering it from beginning to end; Some candidates like to make things easy before they are difficult, and choose simple questions before solving difficult ones. Some candidates habitually solve all the difficult problems and solve the easy ones in turn. In fact, when you answer the exam, you should read through the whole volume to see if there are any defects in the test paper. Answer the questions in turn according to the order of the questions, and arrange the time reasonably when answering them. The finale of mathematics test questions generally appears in the small questions of the last multiple-choice question and fill-in-the-blank question, and the last two or three big questions are taken as the finale questions. There will be a clear "step" in the grand finale. Two or three small questions are gradual, with a wide entrance and easy to start. 1 The small questions are easy, the latter two are difficult to go deep, and finally solved. Therefore, for easy questions, we should try our best to get scores, and for difficult questions, we should see where the scores can go. Don't take it lightly when you see the "easy" questions in the exam. Don't be timid when you see a difficult problem. Think calmly and analyze carefully, and you will get the score you deserve. Don't fight a "protracted war" on a stuck question, it will take time and you won't get points, and the questions you can do will be delayed. Example 4:
Reflection on solving problems: This topic, named the finale of quadratic function, is difficult to comprehensively examine the image and properties of quadratic function, undetermined coefficient method, coordinate characteristics of points on the function image, parallelogram, translation transformation, graphic area calculation and other knowledge points. In problem (2), the key to solving the problem is to get MN=AC=3 according to the definition of parallelogram, thus listing the equations that require solution; In problem (3), the key to solving the problem is to find the expression of S, and pay attention to the calculation method of graphic area.