"Exam" Comprehensive math problem is done!!

Education, examination, mathematics,

Throughout the last five years of mathematics in the exam questions, we are not difficult to find that the focus of the mathematical comprehensive problem is a few points:

1, high school continue to learn the necessary functional problems. This kind of question often has the starting point not high in the examination, but the request is more comprehensive characteristic.

2, often with the number and form, algebraic calculation and geometric proof, similar triangles and four-sided shape of the determination and properties, drawing analysis and column equation solution, the Pythagorean theorem and function, circle and triangle ratio combination of comprehensive questions. At the same time, it examines the mathematical ideas of the most important mathematical methods in junior middle school mathematics, such as the thought of combination, the thought of classification and the change of geometric motion. This type of problem incorporates the change and invariant of dynamic geometry, changes the position of Schopping, flipping, and rotation of a given shape (or part thereof), and then analyzes the relationship between the graphs in the new graph. Its characteristics are: Pay attention to test students ' experiment, conjecture, proof of exploration ability. Problem solving is flexible, can test the ability of students to analyze problems and solve problems, there is a certain difficulty, but it is easy to get started. This kind of problem will often appear with a few small problems, equivalent to a few steps, this appropriate cushion to the candidates a wider entrance, conducive to the normal level of the examinee to play. And through the layers of questions, pick up the level, and gradually in-depth, can make a part of the excellent students to reflect the level of mathematics.

The key of mathematics comprehensive question is the 24th question and 25 questions, we may as well divide it into the function type comprehensive question and the geometrical type comprehensive question.

Function-Type comprehensive problem

This is usually given a Cartesian coordinate system and geometry, the analytic formula of the (known) function (that is, the type of the known function before solving), and then the study of the graph, the coordinates of the point or the study of some properties of the graph.

Junior Middle School known function has ① once function (including positive proportional function) and constant value function, their corresponding image is a straight line, ② inverse proportional function, it corresponds to the image is hyperbolic, ③ two times function, it corresponds to the image is a parabolic line.

The main method to find the analytic formula of the known function is the undetermined coefficient method, the key is to find the coordinates of the point, and the basic method of finding the coordinates is the geometrical method (graph method) and algebraic method (analytic method). This type of problem is basically in the 24th question, out of 12 points, basic points 2-3 small questions to present.

Geometrical type comprehensive problem

This is usually given the geometry, calculated according to the known conditions, and then there are moving points (or moving segments) movement, corresponding to the production line, area and other changes, to the corresponding (unknown) function of the analytic formula (that is, in the absence of finding out what the function of the analytic form) and the definition of the function domain, At last, according to the function relationship, the general types of research are as follows:

① under what conditions the triangle is isosceles triangle, right triangle;

② four-sided shape is diamond, trapezoid, etc.;

③ explore two triangles to meet what conditions are similar;

④ explore the position relationship between line segments and so on;

⑤ to explore the value of x in satisfying certain relationship between areas;

⑥ the value of the argument when the line (circle) is tangent to the circle.

The key to finding an analytic formula for an unknown function is to list the equivalent relationships between the arguments and the dependent variables (that is, to list the equations containing x and y), and the variants as Y=F (x). Generally there is direct method (directly lists the equations containing x and y) and the composite method (list the equations containing the x and Y and the third variable, then find the function relation between the third variable and x, take the third variable, get the form of y=f (x), and, of course, the parametric method, which is beyond the junior high school mathematics teaching requirements.

The way to find the same amount of relationship in junior middle school mainly use the Pythagorean theorem, parallel lines cut proportional segments, triangular similarity and so on. The definition field is mainly to find the special position of the graph (limit position) and solve it according to the analytic formula.

The final exploration problem is ever-changing, but the analysis and research of the graph is indispensable, and the value of x is calculated by means of geometry and algebra. The geometric type comprehensive question basically is in the 25th question to do as the pressure axis question appears, out 14 points, generally divide three small questions to present.

In the previous years, the mathematics comprehensive question revelation We in the comprehensive thinking time to do: The number form combination mind, the big problem small to transform, the latent condition cannot forget, the transformation is static many drawing, the equation function is the tool, the computational reasoning must be rigorous, the innovation quality improves.

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"Exam" Comprehensive math problem is done!!