Summary of Mathematics Knowledge Points in Senior Two of One-person Education Edition
In ancient China, mathematics was called arithmetic, also called arithmetic, and finally changed to mathematics. 1. Any angle
Classification of (1) angle:
① According to different rotation directions, it can be divided into positive angle, negative angle and zero angle.
② According to the position of the end edge, it can be divided into quadrant angle and axis angle.
(2) Angle with the same terminal edge:
An angle with the same terminal edge as the angle can be written as +k360(kZ).
(3) Curvature system:
① Angle of 1 radian: The central angle of an arc with a length equal to the radius is called the angle of1radian.
(2) the radian number of the positive angle is positive, the radian number of the negative angle is negative, and the radian number of the zero angle is zero, || =, L is the arc length when the angle is the central angle, and R is the radius.
A system that measures angles in radians is called a radian system. The ratio has nothing to do with the size of r, but only with the size of the angle.
④ Conversion between radian and angle: 360 radian; 180 radians
⑤ Arc length formula: l=||r, sector area formula: S sector =lr=||r2.
2. Trigonometric function at any angle
(1) The definition of trigonometric function with arbitrary angle;
Let it be an arbitrary angle, and the terminal edge of the angle intersects with the unit circle at point P(x, y), then the sine, cosine and tangent of the angle are: sin=y, cos=x, tan= respectively, and they are all functions with the angle as the independent variable and the coordinates of each point on the unit circle or the ratio of coordinates as the function value.
(2) The symbolic formula of trigonometric function in each quadrant is: one full sine, two sines, three tangents and four cosines.
3. Trigonometric function line
Let the vertex of the angle be at the coordinate origin, the starting edge coincide with the non-negative semi-axis of the X axis, and the final edge intersect with the unit circle at point P. If it crosses P, PM is perpendicular to the X axis. At point M, according to the definition of trigonometric function, the coordinate of point P is (cos_, sin_), that is, P(cos_, sin_), where cos=OM, sin=MP, and the unit circle and.
Summary of Mathematics Knowledge Points in Senior Two of People's Education Press
Monotonicity, parity and periodicity of functions
Monotonicity: Definition: Note that the definition is relative to a specific interval.
The judgment methods are: definition method (difference comparison method and quotient comparison method)
Derivative method (for polynomial function)
Composite function method and mirror image method.
Application: compare sizes, prove inequalities and solve inequalities.
Parity check:
Definition: Pay attention to whether the interval is symmetrical about the origin, and compare the relationship between f(x) and f(-x). F(x)-f(-x)=0f(x)=f(-x)f(x) is an even function;
F(x)+f(-x)=0f(x)=-f(-x)f(x) is odd function.
Discrimination methods: definition method, image method and compound function method.
Application: function value transformation solution.
Periodicity: Definition: If the function f(x) satisfies: f(x+T)=f(x) for any x in the definition domain, then t is the period of the function f(x).
Others: If the function f(x) satisfies any x in the domain: f(x+a) = f (x-a), then 2a is the period of the function f (x).
Application: Find the function value and resolution function in a certain interval.
Fourth, graphic transformation: function image transformation: (key) It is required to master the images of common basic functions and master 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;
Summary of Mathematics Knowledge Points of Senior Two in Three-person Education Edition
The area formula of isosceles right triangle: S=a2/2, S=ch/2=c2/4 (where A is the right side, C is the hypotenuse, and H is the height on the hypotenuse).
Assuming that the waist of an isosceles right triangle is A, B and C respectively, the available area is S=ab/2.
And from the nature of isosceles right triangle, we can know that the height of the bottom is h = c/2, then the area of the triangle can be expressed as S=ch/2=c2/4.
An isosceles right triangle is a special kind of triangle, which has all the properties of a triangle: stability, two right angles are equal, the right angles have an acute angle of 45, and the perpendicular of the median bisector on the hypotenuse is an integral.
Summary of Mathematics Knowledge Points in Senior Two of Four-person Education Edition
Lines and circles: 1. The range of linear inclination angle is
In the plane rectangular coordinate system, for a straight line intersecting the axis, if the axis rotates counterclockwise around the intersection point to the minimum positive angle when it coincides with the straight line, it is called the inclination angle of the straight line. When the straight line coincides or is parallel to the axis, the specified inclination angle is 0;
2. Slope: If the inclination of the straight line is known as α, α ≠ 90, then the slope k=tanα.
The slope of the straight line passing through two points (X 1, Y 1) and (X2, Y2) is k=(y2-y 1)/(x2-x 1), and the slope of the tangent line is obtained.
3. Straight line equation: (1) point oblique type: if the slope of the intersection of straight lines is 0, then the straight line equation is 0.
⑵ Oblique intercept type: If the intercept of a straight line on the axis is sum slope, the straight line equation is
4. The relationship between straight line and straight line:
(1) Parallel A 1/A2=B 1/B2 Attention test (2) Vertical A 1A2+B 1B2=0.
5. Distance formula from point to straight line;
The distance between two parallel lines and is
6. Standard equation of circle: .2 General equation of circle:
Note that the standard equation can be transformed into a general equation.
7. A circle must have two tangents outside the circle. If only one tangent is found, the other tangent is a straight line perpendicular to the axis.
8. The positional relationship between a straight line and a circle is usually transformed into the relationship between the center distance and the radius, or a right triangle is constructed by using the vertical diameter theorem to solve the chord length problem. ① Separation ② Tangency ③ Intersection.
9. When solving the relationship between a straight line and a circle, we should give full play to the plane geometric properties of the circle (such as radius, half chord length and chord center distance to form a right triangle), and the chord length obtained by the intersection of a straight line and a circle.