First, the basic steps of solving the moving point trajectory equation 1. Establish a suitable coordinate system and set the coordinates of the moving point m;

3. Write a set of points m;

3. List the equation = 0;

2. Simplify the equation to the simplest form;

5. test.

Second, the common methods to solve the trajectory equation of the moving point: There are many methods to solve the trajectory equation, such as literal translation, definition, correlation point method, parameter method, intersection method and so on.

1. Literal translation method: the conditions are directly translated into equations, and the trajectory equation of the moving point is obtained after simplification. This method of solving trajectory equation is usually called literal translation.

3. Definition method: If it can be determined that the trajectory of the moving point meets the definition of the known curve, the equation can be written by using the definition of the curve. This method of solving trajectory equation is called definition method.

13. Associated point method: use the coordinates x and y of the moving point q to represent the coordinates x0 and y0 of the associated point p, and then substitute them into the curve equation satisfied by the coordinates (x0, y0) of the point p to obtain the trajectory equation of the moving point q simply and clearly. This method of solving trajectory equation is called correlation point method.

3. Parametric method: When it is difficult to find the direct relationship between the coordinates of the moving point X and Y, the relationship between X and Y and a variable T is often found first, and then the parameter variable T is eliminated to get the equation, which is the trajectory equation of the moving point. This method of solving trajectory equation is called parameter method.

5. Trajectory method: eliminate the parameters in the two dynamic curve equations, and get the equation without parameters, that is, the trajectory equation of the intersection of the two dynamic curves. This method of solving trajectory equation is called trajectory method.

* Literal translation method: the general steps to find the trajectory equation of the moving point

(1) Establish a system-establish a suitable coordinate system;

② set point-set any point on the trajectory P(x, y);

(3) Formula —— List the relationship that the moving point P satisfies;

④ Substitution-according to the characteristics of conditions, the distance formula and slope formula are selected, converted into equations about X and Y, and simplified;

⑤ Proof —— Prove that the equation is a moving point trajectory equation that meets the requirements.

Sorting out the important knowledge points of mathematics in senior two and senior three.

1. There are nine chapters in college entrance examination mathematics, including function, sequence, trigonometric function, plane vector, inequality and solid geometry.

Mainly test functions and derivatives, which are the core plates of our whole high school stage. In this section, we focus on two aspects: the properties of the first function, including monotonicity and parity of the function; The second is the solution of function, focusing on quadratic function and higher order function, fractional function and some distribution problems, but this distribution also includes two analysis problems, that is, the distribution of quadratic equation, which is the first plate.

Second, plane vectors and trigonometric functions.

Focus on three aspects: first, subtraction and evaluation; The other is to master formulas and five basic formulas. Secondly, the images and properties of trigonometric functions. This paper focuses on the properties of sine function and cosine function. Thirdly, the triangle is solved by sine theorem and cosine theorem. The difficulty is relatively small.

Third, the order.

This series focuses on two aspects: a common term; One is summation.

Fourthly, space vector and solid geometry, in which we focus on two aspects: one is proof; One is calculation.

Fifth, probability statistics.

This part mainly belongs to the category of mathematical application problems. Of course, we should master the following aspects: first, possible probability, second, events, and third, the probability of independent events and independent repeated events.

Sixth, analytic geometry.

This is a headache for us, and it is also a difficult and computationally intensive problem in the whole paper. Of course, for this kind of questions, I have summarized the following five types of frequently asked questions, including:

The positional relationship between straight lines and curves mentioned in the first category is the most testing content. Candidates should master its general methods;

The second kind of moving point problem we talk about;

The third category is the chord length problem;

The fourth category is symmetry, which was passed in the college entrance examination in 2008;

The fifth key question often feels thoughtful, but there is no answer.

Of course, what I'm saying here is that although this problem has a large amount of calculation, the reason for the large amount of calculation is often this reason, and the method we choose is not very appropriate. Therefore, in this chapter, we need to master a better algorithm to improve the accuracy of our questions, which is the sixth section we talked about.

Seventh, the issue of gambling axis.

Candidates should focus on learning the calculation method of inequality when preparing for the exam. Although it is difficult, I suggest that candidates grade the whole test paper in sections, and don't leave blank. This is the core test site of the seven sections of the college entrance examination.

Sort out the important knowledge points of mathematics in grade three and grade three.

Test center 1: set and simple logic

The collection part generally appears in the form of multiple-choice questions, which belongs to easy questions. The key point is to know and understand the relationship between sets. In recent years, the examination questions have strengthened the examination of the simplification ability of set calculation, and developed to the infinite set to examine the abstract thinking ability. When solving these problems, we should pay attention to the intuition of geometry and the transformation and simplification of set representation method. There are two forms of simple logical examination: one is to directly examine propositions and their relations, logical conjunctions, "necessary and sufficient relations", to judge the truth value of propositions, and to deny full-name propositions and proper-name propositions. In answering questions, the other is to thoroughly examine the mathematical problem-solving process and logical reasoning expressed by common logical terms.

Test Site 2: Functions and Derivatives

Function is the key content of college entrance examination. Taking multiple-choice questions and fill-in-the-blank questions as carriers, the definition and scope of functions, the nature of functions, functions and equations, and the application of basic elementary functions (linear and quadratic functions, exponential, logarithmic and power functions). , the score is about 10, and the properties of the function are investigated when the solution meets the derivative. On the one hand, the derivative part examines the operation and geometric meaning of derivative, on the other hand, it examines the simple application of derivative, such as finding the monotonous interval, extreme value and maximum value of function, which usually appears in the form of objective questions and belongs to easy and intermediate questions. Third, the comprehensive application of derivatives mainly appears in the form of solving problems, such as some inequalities, the range of parameters, the number of roots of equations, and the proof of inequalities.

Test site 3: trigonometric function and plane vector

Generally, there are 2 small questions, 1 comprehensive answer. One of them examines the concept and operation of plane vector, and the other supplements the knowledge of triangle. If the application of sine theorem and cosine theorem is not involved in the big topic, it may be a problem of the image, properties or trigonometric identity transformation of trigonometric functions that complement each other, or it may be a problem of examining plane vectors. Attention should be paid to the application of the idea of combining numbers with shapes in solving problems. Vector focuses on the concept and application of plane cross product. It is a "new hot topic" to combine vector with straight line, conic curve, sequence, inequality and trigonometric function to solve problems such as angle, verticality and * * * line.

Test site 4: sequence and inequality

Inequality mainly examines the solution of one-dimensional quadratic inequality, one-dimensional quadratic inequality group and simple linear programming problem, the application of basic inequality and so on. , and usually set 1 to 2 questions in the small questions. The instrumental application of inequality in solving problems such as sequence, analytic geometry and function derivative is investigated. In selecting and filling in the blanks, the concept, properties, general formula and summation formula of geometric series are investigated. Most of the problem-solving skills highlight the ability to solve problems by using sequence knowledge as a tool and comprehensively using functions, equations, inequalities and so on. All belong to middle and high-end problems.

Test site 5: solid geometry and space vector

Firstly, the structural characteristics, direct view and three views of space geometry are investigated. The second is to investigate the positional relationship between points, lines and surfaces in space; The third is to investigate the use of space vectors to solve solid geometry problems: using space vectors to prove that straight lines are parallel and perpendicular to planes, and to find space angles. (Not required by liberal arts). In college entrance examination papers, there are generally 1~2 objective questions and 1 solution questions, most of which are intermediate questions.

Test Site 6: Analytic Geometry

Generally, there are 1~2 objective questions and 1 analytical questions, in which the objective questions mainly examine the slope of a straight line, the equation of a straight line, the equation of a circle, the relationship between a straight line and a circle, the definition and application of a conic curve, the solution of a standard equation, the calculation of eccentricity and so on. And solving problems mainly examines the relationship between straight lines and ellipses, parabolas, etc. And often intersect with plane vectors, functions and inequalities to examine some existing problems.

Test site 7: complex reasoning and algorithm proof

In the college entrance examination, the algorithm is examined in the form of multiple-choice questions or fill-in-the-blank questions, or the solution questions are put on a coat. The focus of the exam is the identification of flow chart and the reading comprehension of algorithm language. The network intersection proposition of algorithm and sequence knowledge is the mainstream of examination. The re-examination focuses on the related concepts of complex numbers, the algebraic form of complex numbers, and the geometric significance of operations and operations. Generally, multiple-choice questions and fill-in-the-blank questions are not difficult. Reasoning proves that the direction of some propositions will be mainly in functions, triangles and sequences. For science, mathematical induction may be used as a short problem to solve problems.