Many junior high school students are deductions of mathematics, which are not low-capacity at all, but rather do not take a problem-solving model。
The inverse function looks simple, it's a formula, but there's a lot of variation in the medium test. Many of our students have written so many questions, and are confronted with new ones or with cardboard, which are simply dead and do not solve them with fixed models。
I've been teaching math in junior high schools for many years, combing out four core models of the mid-level inverse function, 90% of the test models match, mastering direct seconds, and not re-engineered every time
Model i: k-value geometric area model (baseline, hf)
This is one of the most frequent models of test papers, none。
Core conclusion: at any point in the image of the inverse function, line up to the axis of the coordinates, with a rectangle area equal to |k| and a diameter triangle equal to |k|/2。
The test spectrometry technique: see the area for k, see the area for k, apply the conclusions directly and eliminate the equation calculation of the column. The only detail: the positives and negatives of k based on the image are that many of our classmates are trapped in a symbol trap。
Model ii: medium point coordinate model (air filler)
A lot of axle questions, the point of entry is never a function calculation, but a middle-point connection pattern。
Core conclusion: if the two points of the inverse function are connected, the midpoint is placed on the axis or line of the coordinates, the medium point formula can be used directly and the function is resolved quickly, without multiple unknown numbers。
Operational use: the subject appears with the key words “medium point, flat fraction, past original point”, giving priority to this model, which saves half of the time on a question-and-answer basis compared to the conventional method of entry, and is dedicated to the problem of filling the space axis。
Model iii: parallel segment equivalent model (substantiation)
Many students do the inverse function, and the total card is on the online section, area equivalent。
Core law: on the same inverse function image, parallel to the line segment of the axis, the corresponding graphic area is always equal; the two parallel lines intersect with the hyperbolic curve and the corresponding triangle area is constant。
The solution to the problem is that, without a point-by-point search for coordinates, parallel lines, an equal area, a k-value formula, simple steps that do not make mistakes, perfect fit for the big points。
Model iv: symmetric model (image flip, offset exclusive)
In recent years, the ccp has added new hot spots, with images smoothing, turning, symmetrical variants, all of which have been solved by this model。
Core conclusion: the inverse function is a reverse number of k values after the axial symmetry of the point, the coordinates; the lateral function requires the replacement of the coordinates according to the axial rule。
The focus of the pit escape: many students only count static hyperbolic questions, encounter dynamic symmetry, smoothing problems, crashing through the model, and all dynamic variants can easily be broken。
The inverse function wants to get a full score without a crazy brush, and the core is modeling, problem-setting, set of conclusions。
The basics are killed in size model seconds, the fillings are speeded by medium-point model, the larges are balanced in size, and dynamic questions are symmetrical. It's not like you're going to have to think about the four models, and you're going to get answers when you see them。
Which one of the four inverse models you're the easiest to confuse? Do you want me to do a special practice tape? Welcome to the comment section
