Type and difficulty ratio of the first few issues of greatest concern
Six options 24, 12 empty 48 and seven large questions 78. The difficulty ratio is 8:1:1:1: 120 sub-headings, 15 mid-sizings and 15 high-strengths. The top 15 issues were emptied 18, 24 and 25, third。
This year's math is hard
Let's not be told that this year's mid-level exam will be hard, and you'll lose. It's hard not to see that year after all these years! If it's hard, it's hard for everyone, who's afraid of who? Besides, it's only 15, even if i can't do it at all。
3 careless solutions
Being accustomed to relying on the point of knowledge, the subject is immediately written with the point of knowledge, ignoring the question of what to ask and under what conditions. The carelessness is basically to see that the subject matter is very familiar and does not want to be done, leading to errors。
It was easy to explain how it felt to be familiar with the subject matter and to think that it would start. The result was that it was not in the right direction, that it was not clear what the problem was, that it ignored the minor differences in the presentation of the subject matter and the type of subject that you had previously known, leading to mistakes. It's too much to think of, of course, and it's caught in the trap。
Four point recommendations
One, slowly, at least twice。
2. Validation of works to prevent arithmetical errors and to facilitate inspection。
Third, back check, mainly on topics that are uncertain。
4. Deepening the root causes. There is a need to streamline the relevant knowledge points。
Here comes the big one. The one-number and one-size-fits-all
Easier 1: there is a misperception of the concept of reasonable, unreasonable numbers and real numbers, and the meaning of the opposite, the penultimate and absolute values is confused. And the classification of absolute values and numbers. Every year, the examination is mandatory。
Easier 2: in real-time calculations, master the concept, nature, flexibility in the application of the various algorithms, the key is to set a good sign off; in more complex calculations, miscalculation or unreasonable use of the algorithms leads to errors。
Easier 3: the difference between square root, arithmetic square root, cube root. It's a question。
Easily no. 4: if the scoring value is zero, the easily ignored denominator cannot be zero。
Easily error point 5: when calculating the split, care is taken to change the algorithms and symbols. When a split molecular denominator is polygonal, it is decomposed until it is no longer decomposed, attention is paid to the method of calculation, which cannot be decomposed, and it is reduced to the simplest fraction. It's a question。
Easier 6: the nature of non-negative numbers: several non-negative numbers and zeros, each of which is zero; whole-form approach; complete flatness。
Easier point 7: count the first test. Calculation of five basic numbers: 0 index, trigonometric function, absolute value, negative index, condensed and triangulated。
Easier 8: scientific mode. Accuracy, valid numbers. Shanghai hasn't passed the exam yet
Easier 9: a surrogate value makes the formula meaningful. In order to master the various digital methods of calculation, care must be taken about the order of the calculations。
2 equations (groups) and variants (groups)
Easier point 1: the solution of the various equations (groups) is skilled, and the meaning of the equation (groups) is that there is no condition for establishing the equation。
Easier 2: when applying the equation, the dichotomy of the two sides by one must be sensitive to the circumstances in which it cannot be o and also to the basic idea of the equation and the equation group. The main trap is the elimination of an x-caused back-check
Easier 3: when the variable nature of 3 is used, it is easy to forget the direction of the change mark and lead to errors in the outcome。
Easier 4: the title on the range of values to be taken from a one-dollar binary equation tends to ignore the fact that the binary coefficient does not cause errors。
Easier point 5: the condition of one dollar iniquitous groups is easily ignored。
Easier 6: the first step of the decomposition equation is to denumerate the denominator, with fractions equal to brackets and easily forget the root test, leading to an error in the calculation result。
Stakeholder 7: the solution of the problem of the variable (group) is first to determine the decomposition and determine the number of axes to be used in the method of decomposition。
Easily error point 8: use a function image to seek an equilibria and equation resolution。
Function 3
Easiest point 1: meaning expressed by each to be determined factor。
Easier 2: proficiency in the resolution of functions requires several points of value for several factors to be determined。
Easier to error 3: use image-seeking equations and equations (groups) to determine increase or decrease using image nature。
Easier 4: two variables solve practical problems using a function model, paying attention to differentiating between equations, functions, iniquitous models, etc。
Effort point 5: categorize using functional images (parallel quadrilaterals, similarities, straight-angle triangles, contours triangles) and solvers of classifications。
Easy to error 6: coordinates must be requested with the axis. The method of solving the maximum size, the method of solving the smallest value of the sum of distance, and the method of solving the maximum value of the difference of distance。
Stakeholder 7: the application of the idea of digital integration should also be addressed in relation to the nature of the image. Function images combined with graphics learn how to break down complex graphics into simple graphics that provide data for images or images for graphics。
Error 8: the range of values to be taken from the variable is: the opening square is a non-negative, the fraction denominator is not zero, the index bottom is not zero, and the rest is a whole real number。
4 triangle
Permissible point 1: the concept of a triangle and the angle of a triangle, the middle line and the characteristics and differences of a high line。
Easier 2: the three sides of the triangle vary, with attention to “any one side”. The shortest possible distance。
Easier 3: the inner and inner angles of the triangles, the classification of the triangles and the internal and external angles of the triangles, with particular attention to the “unaccompanied” nature of the outer corners。
Easier 4: full equation, complete triangle and its nature, triangle full equivalent. The emphasis is on demonstrating the fullness of the triangle, the combined application of the same triangle and the equivalent of the line, the multipleness of the segment being similar and the combination of similarity and a triangle function. The two triangles on the edge are not necessarily equal。
Effort point 5: the equal and parallel of two angles is often a similar basic component, and the ratio of a similar triangle to a high is equal to a similar ratio, the corresponding segment is proportional and the ratio of size is equal to the square of a similar ratio。
Easier 6: the definition of the contour triangle and the determination and nature of the contour triangle, using the determination and nature of the contour triangle to solve the problem of calculation and proof, require attention to the infiltration of the notion of classification discussion。
Evident point 7: longness of segments calculated using the theorem of tiding and its reverse theorem, proof of the quantitative relationship of the segments, resolution of problems related to area and simple practical problems. (25 points in 2012)
Easier 8: combining straight-angled triangles, straight-angled coordinate systems, functions, open-ended questions, exploratory questions, using a combination of solutions。
Easier 9: middle point, median line, median line, summary of half the theorem and their respective properties。
Error prone 10: arcular triangle determination method: determination of the area of the triangle and height above the bottom (especially the blunt angle triangle)
Error prone 11: the corresponding line in the definition of a trigonometric function is more frequent than the error and the trigonometric value of a special angle。
5 quadrilateral
Easier 1: the nature and determination of parallel quadrilaterals, how to apply them flexibly and appropriately. Triangular stability and quadrilateral instability。
Easier 2: the parallel quadrilateral pays attention to the distinction between triangular sizes. Translating relationships between parallel quadrilaterals and special parallel quadrilaterals。
Easier 3: using a parallel quadrilateral is a central symmetrical graphic, which is divided into two parts equal in size over a straight line of symmetrical centres. The diagonal line divides the quadrilateral into four parts equal in size。
Easier 4: knowledge solvers using full-equivalent and similar triangles in parallel quadrilaterals to highlight the penetration of conversion ideas。
Faultable point 5: rectangular, diamond, square concepts, nature, determination and relationship between them, primarily looking at the calculation of the length of the edge, the length of the diagonal, size, etc. Rectangular and square folding
Error 6: hand-in-hand operational issues such as flipping, smoothing, spinning, cutting, etc. In the quadrilaterals, mastering some of the same and rotating properties. (18th question)
Easier 7: 25 questions may be used) the main way to perform guides for ladder problems。
Six
Easier point 1: the concepts of arc, string, circle, etc. Are not well understood. In particular, there are two types of situations in which strings are directed, and the distance between the two strings is considered. (last examination on selected topic)
Easier 2: there is not enough understanding of the acoustic theorem to correct the problem by using a straight-angle triangle。
Easier 3: there is little understanding of the definition and nature of cutting lines, the failure to accurately decipher the nature of cutting lines, and the inexperienced use of both methods for determining cutting lines。
Easier 4: when examining the position of the circle and the circle, there are both internal and external tangents, including the intersection of the two circles, both on the side of the public string and on the other side, one of which is easily ignored by students. (25 topics for classification discussion)
Easier to error 5: the position related to the circle is managed by the relationship between r and r+r, r-r and the above-mentioned method of resolution。
Easier 6: the round angle is the key, the round angle is the same for the same arc, and the diameter is the straight angle. The round angle of the straight angle is the string of the diameter, and the round angle of an arc is equal to half the corner of the center。
Erasing point 7: several formulas must bear in mind: triangle, parallel quadrilateral, diamond, rectangle, square, ladder, round size formula, round-length formula, arc long, sector size, side size of a cone and full volume and length of arc to the bottom, the transformational relationship between the length of the parent line and the radius of the sector。
7 symmetric graphics
Error point 1: axis symmetry, axis symmetry, and central symmetry, the concept and nature of the symmetry. (question 5 of 2014)
Error point 2: the axial symmetry or rotation problem of the graphic is fully resolved using its nature, i. E., the " no change " of the graphic, the same size of the axis symmetry and the middle angle of the rotation and the same length of the line。
Easier 3: convey the axle symmetry with the whole, and the straight symmetry with the axle symmetry。
8 statistics and probability
Easier 1: the concept of medians, numbers, averages is not well understood, and the medians, numbers, averages are incorrect。
Easier 2: when obtaining information from statistical maps, the accuracy of the maps must be judged first. Irregular statistical maps often create the illusion that inaccurate information is available。
Visibility 3: errors are caused by the lack of clarity about the concepts of censuses and sample surveys and their scope of application。
Easier 4: extremely poor, differential concepts are not well understood, thus preventing the correct extraction of a very poor set of data。
Stakeholder 5: the meaning of probability and frequency is not clearly understood and the probability of an event cannot be correctly derived。
Error prone 6: the relationship between averages, weighted averages, differential formulas, circular angles in sector statistical maps and frequency, frequency, frequency, total. Weighted average weights can be data, points, percentages or probability (or frequency)
Error point 7: probability approach: (1) simple events (2) two steps and probability of simple events more than two steps: use a tree or list to indicate the ratio between the various possible scenarios and the likelihood of events. (3) the probability method for complex events uses frequency to estimate probability。
Stakeholder 8: whether or not a fair approach applies the same probability, focusing on the integration of frequency and probability。
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