The positional relationship between circles:

Exterior, Tangent (inscribed and circumscribed), Intersection and Inclusion. In a plane, a closed curve formed by a moving point rotating around a certain point with a certain length is called a circle.

Method of judging the positional relationship between circles

First, let the radii of two circles be r and r respectively, and the distance between the centers be d.

1 and d & gtR+r are separated; The sum of the center distances of two circles is greater than the sum of the radii of two circles.

2.d=R+r circumscribes two circles; The sum of the distances between the centers of two circles is equal to the sum of the radii of two circles.

3.d=R-r inscribed with two circles; The sum of the center distances of two circles is equal to the difference of the radii of the two circles.

Second, the positional relationship between circles can also be judged by whether they have something in common:

1, there is no common * * * point, a circle is called external separation outside another circle, and it is called internal separation inside it.

2. If there is a common point, a circle is called circumscribed by another circle and inscribed by another circle.

There are two things in common called intersection. The distance between the centers of two circles is called the center distance.

2. Summary of Three Required Knowledge Points of Mathematics in Senior Three

1, linear inclination

Definition: The angle between the positive direction of the X axis and the upward direction of the straight line is called the inclination angle of the straight line. In particular, when a straight line is parallel or coincident with the X axis, we specify that its inclination angle is 0 degrees. Therefore, the range of inclination angle is 0 ≤α.

2, the slope of the straight line

① Definition: A straight line whose inclination is not 90, and the tangent of its inclination is called the slope of this straight line. The slope of a straight line is usually represented by k, that is. Slope reflects the inclination of straight line and axis.

② Slope formula of straight line passing through two points:

Pay attention to the following four points:

(1) At that time, the right side of the formula was meaningless, the slope of the straight line did not exist, and the inclination angle was 90;

(2)k has nothing to do with the order of P 1 and P2;

(3) The slope can be obtained directly from the coordinates of two points on a straight line without inclination angle;

(4) To find the inclination angle of a straight line, we can find the slope from the coordinates of two points on the straight line.

3. Summary of Three Knowledge Points of Compulsory Mathematics in Senior Three Part III

Chapter 1: Trigonometric function. The exam must be answered. Some properties of inductive formulas and basic trigonometric function images can be remembered as long as they can draw pictures. The difficulty lies in the amplitude, frequency, period, phase and initial phase of trigonometric function, and the calculation of the values and periods of A and B according to the maximum value, as well as the changes of images and properties when constants change. This knowledge point has more contents and takes more time. First of all, you should remember. Secondly, you should do more exercises. As long as you can do it in a down-to-earth manner, it is not difficult to master it. After all,

Chapter 2: Plane vector. Personally, I think this chapter is more difficult, and it is also the chapter I have the worst grasp. The operational properties of vectors and the rules of triangles and parallelograms are not difficult, as long as you remember the vectors with the same starting point when calculating. The mathematical expressions of vector * * * straight line and vertical line are often used in calculation. * * * Straight line theorem, basic theorem of vector and formula of quantity product. The difficulty lies in the formula of vernal equinox coordinates. First, we must remember accurately. General vectors do not appear alone in the examination process, but often appear as problem-solving tools. When using vectors, we must first find the appropriate vector. Personally, I think this is more difficult and often wrong. Students with the same situation suggest reading more pictures.

Chapter 3: Triangular identity transformation. There are many formulas in this chapter. There are also formulas of difference times and half angles, which are all used, so be sure to remember them. Because the amount is relatively large and difficult to remember, it is recommended to write it on paper and stick it on the table, and read it every day. Moreover, trigonometric function transformation has certain rules, which can be combined to remember when remembering. Besides, practice more. We should look for the law of transformation from more practice, such as simplification and so on. This chapter is also required in the exam, so we must focus on it.

4. Senior three mathematics compulsory three knowledge points summary the fourth article

Comparison of inequality properties;

(1) difference comparison method

(2) Commercial comparison method

Basic properties of inequality

① Symmetry: a & gtbb & gta

② Transitivity: a>b, b & gtca & gtc.

③ additivity: a & gtba+c & gt；; b+c

④ Integrability: a>b, c & gt0ac & gt BC.

⑤ law of addition: a>b, c & gtda+c & gt；; b+d

6 Multiplication Rule: a>b>0, c>d & gt0ac & gt Missile Bottom Fuze (abbreviation of base detonating)

⑦ Power law: a>b>0, an & gtbn(n∈N)

⑧ Root rule: a>b>0

5. Summary of Three Required Knowledge Points in Senior Three Mathematics Chapter 5

1. Complex number and its related concepts;

(1) imaginary unit I, whose square is equal to-1, that is, i2=- 1.

(2) Algebraic form of complex number: z=a+bi, (where a, b∈R)

(1) real number-complex number a+bi When b=0, it is a;

② imaginary number-complex number a+bi when b≠0;

③ Pure imaginary number-the complex number a+bi when ——a = 0 and b≠0, that is, bi.

④ The real part and imaginary part a+bi-A of a complex number are called the real part of the complex number, and B is called the imaginary part (note that both A and B are real numbers).

⑤ Complex number set C-the set of all complex numbers, generally represented by the letter C. 。

⑥ Special attention: a=0 is only a necessary condition for the complex number a+bi to be pure imaginary. If a=b=0, a+bi=0 is a real number.

2. Four operations of complex numbers

If two complex numbers z 1=a 1+b 1i and z2=a2+b2i,

(1) addition: z1+z2 = (a1+a2)+(b1+B2) i;

(2) subtraction: z1-z2 = (a1-a2)+(b1-B2) i;

(3) multiplication: z 1.z2 = (a 1? a2-b 1？ b2)+(a 1？ b2+a2？ b 1)I；

(4) division

(5) Exchange rate and combined exchange rate of the four operations; The distribution rate applies to complex numbers.

Note: There is basically no difference between addition, subtraction, multiplication and division of complex numbers and the operation of real numbers. The most important thing is to combine i2=- 1 with the actual operation.

Such as (a+bi)(a-bi)=a2+b2.

5.*** Yoke Complex Number: Two real parts are equal, and the complex number with opposite imaginary part is * * * Yoke Complex Number.

6. Modules of complex numbers

According to the definition that two complex numbers are equal, let a, b, c and d∈R, let two complex numbers a+bi and c+di be equal, and define it as a+bi=c+di? A=c, b=d, especially a+bi=0? a=b=0。

The sizes of two complex numbers cannot be compared, and they can only be judged to be equal or unequal by definition.

6. Summary of Three Knowledge Points of Compulsory Mathematics in Senior Three Article 6

1, the core problem of solving inequality is the homosolution deformation of inequality, and the properties of inequality are the theoretical basis of inequality deformation. The roots, functions and images of the equation are closely related to the solution of inequality, so we should be good at connecting them organically and transforming each other. When solving inequalities, method of substitution sum and graphic method are one of the commonly used skills. By transforming elements, complex inequalities can be classified as simple or basic inequalities, and by combining constructors with numbers and shapes, the solution of inequalities can be classified as intuitive and vivid graphic relations. For inequalities with parameters, the classification criteria can be made clear by graphic method.

2. The solution of algebraic expression inequalities (mainly first-order and second-order inequalities) is the basis of solving inequalities. Using the properties of inequalities and monotonicity of functions, it is the basic idea to classify fractional inequalities and absolute inequalities as algebraic expression inequalities (groups). Classification, substitution and combination of numbers and shapes are common methods to solve inequalities. The roots of equations, the properties of functions and images are closely related to the solution of inequalities, so we should be good at connecting them organically, transforming them and changing them.

3. When solving inequalities, substitution summation method and graphic method are one of the commonly used skills. By transforming elements, more complex inequalities can be classified as simpler or basic inequalities, and by constructing functions, the solution of inequalities can be classified as intuitive and vivid image relations. For inequalities with parameters, graphic method can make the classification criteria clearer.

4. The proof methods of inequality are flexible and diverse, but comparison, synthesis and analysis are still the most basic methods to prove inequality. According to the structural characteristics and internal relations of the questions, we should choose the appropriate proof methods, be familiar with the reasoning thinking in various proof methods, and master the corresponding steps, skills and language characteristics. The general steps of comparison method are: making difference (quotient) → deformation → judging symbol (value).