1. The second volume of senior three mathematics requires 1 knowledge points.
The parity of 1. function (1) If f(x) is an even function, then f (x) = f (-x);
(2) If f(x) is odd function and 0 is in its domain, then f(0)=0 (which can be used to find parameters);
(3) The parity of the judgment function can be defined in equivalent form: f (x) f (-x) = 0 or (f (x) ≠ 0);
(4) If the analytic formula of a given function is complex, it should be simplified first, and then its parity should be judged;
(5) odd function has the same monotonicity in the symmetric monotone interval; Even functions have opposite monotonicity in symmetric monotone interval;
2. Some questions about compound function.
Solution of the domain of (1) composite function: If the domain is known as [a, b], the domain of the composite function f[g(x)] can be solved by the inequality a≤g(x)≤b; If the domain of f[g(x)] is known as [a, b], find the domain of f(x), which is equivalent to x∈[a, b], and find the domain of g(x) (that is, the domain of f(x)); When learning functions, we must pay attention to the principle of domain priority.
(2) The monotonicity of the composite function is determined by "the same increase but different decrease";
3. Function image (or symmetry of equation curve)
(1) Prove the symmetry of the function image, that is, prove that the symmetry point of any point on the image about the symmetry center (symmetry axis) is still on the image;
(2) Prove the symmetry of the image C 1 and C2, that is, prove that the symmetry point of any point on C 1 about the symmetry center (symmetry axis) is still on C2, and vice versa;
(3) curve C 1: f (x, y) = 0, and the equation of symmetry curve C2 about y=x+a(y=-x+a) is f(y-a, x+a)=0 (or f(-y+a,-x+a) =
(4) Curve C 1:f(x, y)=0 The C2 equation of the symmetrical curve about point (a, b) is: f(2a-x, 2b-y) = 0;
(5) If the function y=f(x) is constant to x∈R, and f(a+x)=f(a-x), then the image y=f(x) is symmetrical about the straight line x=a;
(6) The images of functions y=f(x-a) and y=f(b-x) are symmetrical about the straight line x=;
4. The periodicity of the function
(1)y=f(x) for x∈R, f(x+a)=f(x-a) or f (x-2a) = f (x) (a >: 0) is a constant, then y=f(x) is a period of 2a.
(2) If y=f(x) is an even function, and its image is symmetrical about the straight line x=a, then f(x) is a periodic function with a period of 2 ~ a;
(3) If y=f(x) odd function, and its image is symmetrical about the straight line x=a, then f(x) is a periodic function with a period of 4 ~ a;
(4) If y=f(x) is symmetric about points (a, 0) and (b, 0), then f(x) is a periodic function with a period of 2;
(5) If the image of y=f(x) is symmetrical (a ≠ b) about straight lines x = a and x = b, then the function y = f (x) is a periodic function with a period of 2;
(6) When y=f(x) equals x∈R, f(x+a)=-f(x) (or f(x+a)=, then y = f (x) is a periodic function with a period of 2;
5. Equation
(1) equation k=f(x) has a solution k∈D(D is the range of f(x));
(2)a≥f(x) considers A ≥ [f (x)] max;
A≤f(x) considers a ≤ [f (x)] min;
(3)(a & gt； 0，a≠ 1，b & gt0，n∈R+)；
logaN =(a & gt； 0，a≠ 1，b & gt0，b≠ 1)；
(4)logab symbols are memorized by the formula of "same positive but different negative";
a Logan = N(a & gt； 0，a≠ 1，N & gt0);
Step 6 draw pictures
When judging whether the corresponding relationship is a mapping, we should grasp two points:
The elements in (1)A must all have images and;
(2) All elements in B may not have original images, and different elements in A may have the same images in B;
7. Monotonicity of functions
(1) can skillfully use definitions to prove monotonicity of functions, find inverse functions and judge parity of functions;
(2) According to monotonicity, the problem of finding the range of a class of parameters can be solved by using the sign-preserving property of linear functions on intervals.
8. Inverse function
For the inverse function, we should grasp the following conclusions:
The monotone function in (1) field must have an inverse function;
(2) odd function's inverse function is also odd function;
(3) There is no inverse function for even functions whose domain is not a single element set;
(4) The periodic function has no inverse function; (5) Two mutually inverse functions have the same monotonicity;
(5)y=f(x) and y=f- 1(x) are reciprocal functions. Let the domain of f (x) be a and the domain of f(x) be b, then there is f [f- 1 (x)] = x (x ∈ b).
9. combination of numbers and shapes
Don't forget the combination of numbers and shapes when dealing with quadratic functions; Quadratic function must have a maximum in the closed interval, and the problem of finding the maximum is "two views": look at the opening direction; Second, look at the relative position relationship between the symmetry axis and a given interval.
10. the problem of constant establishment
Methods to deal with the problem of fixed establishment;
(1) separation parameter method;
(2) Solving the inequality (group) of distribution table transformed into the root of quadratic equation in one variable;
2. The second volume of senior three mathematics is a compulsory knowledge point.
1, the concept of set
Set is the most primitive undefined concept in mathematics, which can only give a descriptive explanation: some formulaic and different objects are called sets together. The objects that make up a set are called elements. The set usually uses uppercase letters A, B, C, … Elements usually use lowercase letters A, B, C, …
A set is a definite whole, so it can also be described as a set composed of all objects with certain attributes.
2. The relationship between elements and sets There are two kinds of relationships between elements and sets: element A belongs to set A and is marked as A ∈ A; Element a does not belong to set a, so it is recorded as a? Answer.
3. Characteristics of elements in the set
(1) Determinism: Let A be a given set and X be a specific object, then X is either an element of A or not, and one and only one of the two situations must be true. For example, A={0, 1, 3, 4}, then 0 ∈ a, 6? Answer.
(2) Reciprocity: "The elements of a set list must be different from each other", that is, "any two elements of a given set are different".
(3) Disorder: A set has nothing to do with the arrangement order of its elements, for example, set {a, b, c} and set {c, b, a} are the same set.
4. Classification of sets
According to the number of elements it contains, set division can be divided into two categories:
Finite set: A set containing a finite number of elements. For example, "the set composed of solutions of equation 3x+ 1=0" and "the set composed of 2,4,6,8" have countable elements, so these two sets are finite.
Infinite set: a set containing infinite elements, such as "the distance between two fixed points on a plane is equal to all points" and "all triangles". The elements that make up the above set are uncountable, so it is an infinite set.
In particular, we call a set that does not contain any elements an empty set, and we remember f wrong, such as {x? R|+ 1=0} .
5. Representation of a specific set
For the convenience of writing, we stipulate that commonly used data sets are represented by specific letters. Here are several common number sets, please keep them in mind.
(1) The set of all non-negative integers is usually called the set of non-negative integers (or the set of natural numbers), and is recorded as n.
(2) A set of zeros in a non-negative integer set, also known as a positive integer set, is denoted as N_ or N+.
(3) The set of all integers is usually referred to as integer set z for short.
(4) The set of all rational numbers is usually referred to as rational number set for short, and is denoted as Q. ..
(5) The set of all real numbers is usually referred to as the set of real numbers for short, and is recorded as R. ..
3. The second volume of senior three mathematics is a compulsory knowledge point.
Chapter 1: Space geometry. It is not difficult to draw three views and look straight. However, it needs a strong sense of space to recover the object from the three views and calculate it. You should be able to slowly draw the physical objects in your mind from three plans. This requires students, especially those with a weak sense of space, to read more illustrations in books, combine physical drawings with floor plans, skillfully push forward first, and then slowly push back. When you do the problem, you should combine the sketch, not just by imagination. It's not a big problem to remember the formulas of surface area and volume of the conical cylinder behind. When calculating the surface area, pay attention to how many faces there are, and whether there is such a problem as upper and lower bottom. Chapter two: the positional relationship among points, lines and surfaces. Apart from the intersection of faces, this chapter does not have a strong requirement for the concept of space, and most of them can be drawn directly, which requires students to look at more pictures and pay strict attention to solid lines and dotted lines when sketching themselves. This is a normative problem. For the content of this chapter, keep in mind that several theorems and properties of straight line and straight line, face to face, straight line and face intersection, verticality and parallelism can be expressed by graphic language, written language and mathematical expression at the same time. As long as all this is over, this chapter will solve more than half. The difficulty in this chapter lies in the concept of dihedral angle. The difficulty lies in that we can't understand this concept, that is, we know that this concept exists, but we just can't make this angle in dihedral angle. In this case, we must start with the definition, remember the definition first, and then do more and see more. There is no shortcut.
Chapter 3: Lines and Equations. This chapter mainly talks about the relationship between slope and straight line. As long as the parallel and vertical slopes of the straight line are clear, it means that the problem is not big. Special attention should be paid to the situation that the slope does not exist when the straight line is vertical, which is a common test site. In addition, several forms of linear equations can be remembered by general formulas, and the requirements are not high. Distance between points, distance between points and straight lines, distance between straight lines, remember the formula and apply it directly.
Chapter 4: Circle and Equation. I can skillfully convert general equations into standard equations. The usual form of examination is that the equation contains a root sign once and the other side does not. At this time, we should pay attention to the definition after limitation or the limitation of value range. Judging the positional relationship between a point and a circle, a straight line and a circle, and a circle and a circle by the relationship between the distance from a point to a point and the distance from a point to a line and the radius of a circle. In addition, pay attention to the tangent and intersecting straight lines caused by the symmetry of the circle, which is also a common test site.
4. The second volume of senior three mathematics is a compulsory knowledge point.
arithmetic series
1. Definition: If the difference between each term of a series and the previous term from the second term is equal to the same constant, this series is called arithmetic progression, and this constant is called arithmetic progression's tolerance, which is usually represented by the letter D. Similarly, the geometric series of the series has something in common with arithmetic progression.
2. The necessary and sufficient condition for a sequence to be arithmetic progression is that the sum of the first n terms of the sequence can be written in the form of s = an 2+bn (where a and b are constants). Arithmetic progression practices.
3. Property 1: arithmetic progression with a tolerance of d, the series obtained by multiplying each term by the constant k is still arithmetic progression with a tolerance of kd.
4. Property 2: For arithmetic progression with tolerance of d, the sequence obtained by adding 1 to each term is still arithmetic progression, and its tolerance is still d. 。
5. Property 3: When the tolerance d >; 0, the number in arithmetic progression increases with the increase of the number of terms; When d