1. Changes in the number of elements This is the most common question type in graphic reasoning. In fact, this kind of question type is very similar to the numerical reasoning part of mathematical operation, except that these numerical laws are relatively simple and expressed by the changes of graphic elements. In the questions with quantitative changes, the elements usually involved are points, lines, surfaces, angles, areas, graphic types, components and so on. When a given graph is rich in changes, it is suggested that candidates first consider this relationship between graphs. For example, in 2009, please choose the most suitable one from the four options given to fill in the question mark, so that it presents a certain regularity: analysis: many candidates will feel "confused" at first glance. The five figures given in the stem seem to be inconsistent, so consider them quantitatively first. First, analyze the common quantitative relations such as points, angles, lines and surfaces, and substitute them into the stem of the question, but still can't find the law. At this time, we should look at the possible quantitative laws between other graphs that many candidates may not easily think of, such as strokes of graphs and closed intervals in graphs, and then we notice that there is a closed interval in these five graphs. Because item A has no closed interval, item C and item D are two closed intervals, so the correct answer is item B. It is worth noting that in recent years, the examination of graphic closed interval numbers frequently appears in various civil service examinations, and candidates should master this problem-solving idea skillfully. For another example, please fill in the question mark with the most suitable one from the four options given in 2009, so that it shows a certain regularity: Analysis: This question feels just the opposite to the last one, and many people will see that there is a quantitative relationship between these five numbers, but the difficulty of this question is that the numbers are circles and the five-pointed stars all show a certain quantitative change: from left to right, the quantitative change of the circle is 4, 2, 0. The number of five-pointed stars is 0, 1, 2, 1, 2, (). Then it is easy to get that the number of turns in the sixth picture is 0, so options A and B can be excluded; But the number of five-pointed stars is a finite increasing sequence, so the number of five-pointed stars is 3, so the correct answer is item C. In fact, there are many solutions to this problem. In fact, through observation, we can find that the five-pointed star replaces two circles at a time, so that C can also be the correct answer. Another example is the analysis of 29 questions in Beijing in 2009: this is called analogical graphic reasoning, that is, according to the laws shown in the first three pictures, choose a graphic to make the last three pictures show similar laws. It is observed that there are two factors in the first set of graphs, a * * * has five X's and nine delta's, and in the second set of graphs, we find that there are already five ☆ s and three ● s, so there should be 9-3=6 ● s in the remaining graphs, so the correct answer is item A. It should be noted that sum and equality are also common quantitative relationships. Secondly, the change of element position can not only intuitively present the quantitative relationship, but also intuitively present the change of element position. In graphic reasoning, this change is generally manifested as rotation (clockwise and counterclockwise), symmetry, movement, tangency, superposition and cancellation. Generally, we should pay attention to whether the position of elements has changed when the number of elements remains unchanged. For example, the analysis of 65 national questions in 2007: the form of this question is "nine squares", that is, eight known figures are given, and then the ninth figure is selected according to the law between them. Because this kind of problem is not like other problems, the figures are all lined up, so the key problem to be solved first is in what order to look at the pictures, because the direction is wrong, the harder you work, the farther you will be from the goal. Generally speaking, we advise candidates to look for rules horizontally. This question is easy to make people dizzy. These figures look very similar, and the figures have not changed. But they are different, so we consider the change of element position. This problem is easy to see that the rotation direction of the center line in the diagram similar to the main shaft is different. Looking horizontally, the rotation directions of the center line of the first row are counterclockwise, clockwise and counterclockwise respectively. The second line is clockwise, counterclockwise and clockwise, so we can deduce that the rotation direction of the third picture and the first picture in each line is the same, so we know that the first picture line in the third line rotates counterclockwise, and obviously the one to be selected should also rotate counterclockwise, so the correct answer is item A. In fact, this question can be answered quickly by exclusion, because only item A among the four options rotates counterclockwise. Another example is the analysis of 27 questions in Beijing in 2009: this problem is relatively simple, as long as we can find the changes in the position of elements in the graph, it will be solved. Through observation, it can be found that in the first group of pictures, all the black shadows and half-grid black shadows move clockwise to the next figure, while in the second group of pictures, all the black shadows and half-grid black shadows move counterclockwise. It is particularly important to note that the black shadow of the half-grid rotates exactly 90, so the correct answer is item A. Third, the change of graphic elements occurs in each graphic, and it does not appear as a fixed number change or position change. Therefore, we can only find a breakthrough from the graphic elements, and find the similarities and differences between the graphics through comparison, so as to quickly find ideas. Generally speaking, the change of graphic elements generally includes subtle differences, symmetry, superposition and so on. For example, in 2009, there were 69 questions in China. Please choose the most suitable one from the four options given and fill it in the question mark, so that it shows a certain regularity: Analysis: This question is quite difficult, because the numbers appearing in the options are not the same, and the number of numbers is irregular. Because the two numbers cover each other, it is impossible to choose the correct answer according to this law. Look at the location of coverage, there is no specific law. This requires us to look for ideas from the subtle differences between graphics. Through careful observation, we can find that all the covered figures have smooth curves, but all the covered figures, on the contrary, have no smooth curves, but are composed of straight lines. Therefore, according to this law, we can choose the correct answer as item A. This question has puzzled many candidates, because it is the first time to investigate the linearity of the line segments formed by the figures, and candidates should pay attention to this method of solving problems. For example, in 2007, please choose the most suitable one from the four options given and fill it in the question mark, so that it presents a certain regularity: analysis: the figure of this question is very regular and very similar. When there are only changes such as line segments and shadows in the picture, and the number is irregular, the law of "superposition cancellation" should be considered. The so-called "superposition and cancellation" refers to the law that the former figure and the latter figure are superimposed, and the same elements between the figures are removed, and then different elements are retained, and the third new figure is obtained, which can be simply summarized as "removing similarities while reserving differences". Graphic reasoning Middle School often examines this rule, hoping that candidates can master it skillfully. In this question, the figures are superimposed horizontally, and the same overlapping line segments are erased, leaving different parts, so it is easy to get the correct answer to item D. In addition to the three common questions mentioned above, it is more common to combine them to give questions. This problem-solving method is the superposition of the above methods, and the steps are complicated, so I won't go into details here. Fourth, the transformation of graphic space is also a common graphic reasoning question, different from ordinary graphic reasoning, which focuses on the spatial imagination of candidates. In fact, this kind of topic is not as difficult as many candidates think. Find the key problem-solving points, and then eliminate them, and you can get the answer quickly. For example, in 2008, which of the four options given in the National Question 65 can't be made of the figure given on the left () Analysis: The key to doing this kind of question is to find out the correlation between the sides of the box, that is, whether it is adjacent or relative. If it doesn't conform to the given scheme, it will naturally be easy to rule out, so don't worry about what the box will look like after folding. According to the meaning of the question, it is obvious that item C is wrong, because there is no face with only one line in the original picture, so the correct answer is item C. For example, which of the four options given in Question 70 of 2009 can be folded into the given figure on the left: () Analysis: Before the national civil service examination, all the plane figures were folded into solid figures, but in this question, the known three-dimensional figures were disassembled into plane figures, which brought troubles to many candidates. In fact, no matter from the plane to the three-dimensional, or from the three-dimensional to the plane, the laws followed are the same. So in this problem, it is obvious that the dotted line in the original picture is the key to our solution. To make the vertices of two black triangles face each other, it is obvious that these two vertices should be located on the same straight line, so items A, C and D do not meet the definition, and item B does not meet at first glance, but if folded, the vertices of two black triangles can be located on a line segment, so item B is the correct answer. /fjgwy/stfd/284173.shtml Go to this website. Some pictures can't be posted. Ask: Brother, I said Didi is a password problem. Reasoning questions, etc. Answer: I am a woman, not your brother!