Summary of knowledge points in three chapters of mathematics elective course in senior two 1
I. Mapping and function:
The concept of (1) mapping: (2) one-to-one mapping: (3) the concept of function:
Second, the three elements of function:
The judgment method of the same function: ① correspondence rule; (2) Domain (two points must exist at the same time)
Solution of resolution function (1):
① definition method (patchwork method): ② substitution method: ③ undetermined coefficient method: ④ assignment method:
(2) The solution of functional domain:
(1) The universe with parameters should be discussed by classification;
(2) For practical problems, after finding the resolution function; We must find its domain, and the domain at this time should be determined according to the actual meaning.
(3) The solution of function value domain:
① Matching method: transform it into a quadratic function and evaluate it by using the characteristics of the quadratic function; Often converted into:;
(2) Reverse solution: the value range used to represent, and then the value range obtained by solving the inequality; Commonly used to solve, such as:
(4) Substitution method: transforming variables into functions of assignable fields and returning to ideas;
⑤ Triangular Bounded Method: Transform it into a function containing only sine and cosine, and use the boundedness of trigonometric function to find the domain;
⑥ Basic inequality methods: transformation and modeling, such as: using the average inequality formula to find the domain;
⑦ Monotonicity method: The function is monotonous, and the domain can be evaluated according to the monotonicity of the function.
⑧ Number-shape combination: According to the geometric figure of the function, the domain is found by the method of number-shape combination.
Summary of knowledge points in three chapters of mathematics elective course in senior two
I. Lines and equations
(1) inclination angle of straight line
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. At that time, at that time,; It didn't exist then.
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) Linear equation
① Point-oblique type: the slope of the straight line is k, passing through the point.
Note: When the slope of the straight line is 0, k=0, and the equation of the straight line is y=y 1. When the slope of the straight line is 90, the slope of the straight line does not exist, and its equation can not be expressed by point inclination. But because the abscissa of each point on L is equal to x 1, its equation is x=x 1.
② Oblique section: the slope of the straight line is k, and the intercept of the straight line on the Y axis is b..
③ Two-point formula: () Two points on a straight line,
④ Intercept formula: where the straight line intersects with the axis at the point and intersects with the axis at the point, that is, the intercepts with the axis and the axis are respectively.
⑤ General formula: (A, B are not all 0)
⑤ General formula: (A, B are not all 0)
Note: ○ 1 scope of application.
○2 Special equations such as: straight line parallel to X axis: (b is constant); A straight line parallel to the Y axis: (A is a constant);
(4) Linear system equation: that is, a straight line with some * * * property.
(1) parallel linear system
A linear system parallel to a known straight line (a constant that is not all zero): (c is a constant)
(2) A linear system passing through a fixed point
(i) Linear system with slope k: a straight line passes through a fixed point;
(2) The equation of the straight line system where two straight lines intersect is (as a parameter), where the straight line is not in the straight line system.
(5) Two straight lines are parallel and vertical.
When, when,; Note: When judging the parallelism and verticality of a straight line by using the slope, we should pay attention to the existence of the slope.
(6) The intersection of two straight lines
Intersection point: The coordinates of the intersection point are the solutions of a set of equations. These equations have no solution; The equation has many solutions and coincidences.
(7) Distance formula between two points: Let it be two points in the plane rectangular coordinate system, then
(8) Distance formula from point to straight line: distance from point to straight line.
(9) Distance formula of two parallel straight lines: take any point on any straight line, and then convert it into the distance from that point to the straight line to solve it.
Summary of knowledge points in three chapters of mathematics elective course in senior two 3
Function image transformation: (emphasis) It is required to master the common basic function images and the general rules of function image transformation.
Regularity of common image changes: (Note that translation changes can be explained by vector language, which is related to vector translation)
Translation transformation y = f (x) → y = f (x+a), y = f (x)+b.
Note: (1) If there is a coefficient, first extract the coefficient. For example, the image of the function y=f(2x+4) is obtained by translating the function y=f(2x+4).
(2) Combining with the translation of vector, understand the meaning of translation according to vector (m, n).
Symmetric transformation y=f(x)→y=f(-x), which is symmetric about y.
Y=f(x)→y=-f(x), which is symmetrical about x.
Y=f(x)→y=f|x|, keep the image above the X axis, and the image below the X axis is symmetrical about X.
Y=f(x)→y=|f(x)| Keep the image on the right side of the Y axis, and then make the right part of the Y axis symmetrical about the Y axis. (Note: it is an even function)
Telescopic transformation: y=f(x)→y=f(ωx),
Image transformation of Y=f(x)→y=Af(ωx+φ) reference trigonometric function.
An important conclusion: if f(a-x)=f(a+x), the image of function y=f(x) is symmetrical about the straight line x=a;
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