This is the formula.
Focus on the images and properties of positive and negative proportional functions, linear and quadratic functions.
☆ Summary ☆
First, the plane rectangular coordinate system
1. Coordinate characteristics of points in each quadrant
2. Coordinate characteristics of each point on the coordinate axis
3. About the characteristics of coordinate axis and symmetry point.
4. The corresponding relationship between points on the coordinate plane and ordered real number pairs.
Second, function
1. Representation method: (1) analysis method; (2) List method; (3) Image method.
2. The principle of determining the range of independent variables: (1) makes algebraic expressions meaningful; (2) The practical problems in manufacturing are as follows
Meaning.
3. Draw a function image: (1) list; (2) tracking points; (3) connection.
Third, several special functions.
(Definition → Image → Attribute)
1. proportional function
⑴ definition: y=kx(k≠0) or y/x = k.
⑵ image: straight line (through the origin)
⑶ nature: ① k > 0，…②k & lt； 0,…
2. Linear function
⑴ definition: y=kx+b(k≠0)
⑵ Image: The straight line passes through the intersection of point (0, b)- and Y axis and the intersection of point (-b/k, 0, b)- and X axis.
⑶ nature: ① k > 0，…②k & lt； 0,…
(4) Four situations of images:
3. Quadratic function
(1) Definition:
In particular, they are all quadratic functions.
⑵ Image: parabola (tracing points: first determine the vertex, symmetry axis and opening direction, and then trace points symmetrically). If the configuration method is changed to, the vertex is (h, k); The symmetry axis is a straight line x = h；; A>0, the opening is upward; A<0, opening down.
⑶ Nature: a>0, on the left and right side of the symmetry axis; A<0, on the left … and right … of the symmetry axis.
4. Inverse proportional function
⑴ Definition: or xy=k(k≠0).
⑵ Image: hyperbola (two branches)-drawn by tracing points.
⑶ nature: ① k > 0, the image is at …, y follows x …; ②k & lt； 0, the image is at …, y follows x …; ③ Two curves are infinitely close to the coordinate axis but can never reach the coordinate axis.
Fourth, important problem-solving methods
1. Use the undetermined coefficient method to find the analytical formula (solving the sequence equation [group]). To find the analytic formula of quadratic function, we should reasonably choose the general formula or vertex type, make full use of the characteristics of parabola about the axis of symmetry, and find the coordinates of new points. As shown in the figure below:
2. K and B represent the linear (proportional) function, inverse proportional function and quadratic function in the image; The symbols of a, b and C.
Six, application examples (omitted)
☆ Summary ☆
First, trigonometric functions
1. definition: in Rt△ABC, ∠C = Rt∞, then sinA =；; cosA =； tgA =； ctgA=。
2. The trigonometric function value of special angle:
0 30 45 60 90
sinα
Coase α
tgα /
ctgα /
3. The trigonometric function relation of two complementary angles: sin (90-α) = cos α; …
4. The relationship between trigonometric function value and angle change.
5. Look up the trigonometric function table
Second, solve the right triangle.
1. Definition: known edges and angles (two of which must have one side) → all unknown edges and angles.
2. Basis: ① Relationship between edges:
② Angle relation: A+B = 90.
③ Angular relation: the definition of trigonometric function.
Note: Try to avoid using intermediate data and division.
Third, the handling of practical problems.
1. Pitch and elevation: 2. Azimuth and quadrant angle: 3. Slope:
4. When both right triangles lack the conditions to solve right triangles, they can be solved by the method of column equation.