1. The first volume of Senior Two Mathematics requires four knowledge points.
Axiom 1: If two points of a straight line are on a plane, then all points of the straight line are on this plane.
Application: judging whether a straight line is in a plane.
Express axiom1in symbolic language;
Axiom 2: If two non-coincident planes have a common point, then they have one and only one common straight line passing through the point.
Symbol: Plane α and β intersect, the intersection line is A, and it is denoted as α ∩ β = A. 。
Symbolic language:
The role of axiom 2:
It is a method to judge the intersection of two planes.
It represents the relationship between the intersection of two planes and the common point of two planes: the intersection passes through the common point.
It can judge that a point is on a straight line, which is an important basis to prove several points.
Axiom 3: One and only one plane passes through three points that are not on the same straight line.
Inference: a straight line and a point outside the straight line determine a plane; Two intersecting straight lines define a plane; Two parallel lines define a plane.
Axiom 3 and its reasoning function: it is the basis of determining planes in space and proving the coincidence of planes.
Axiom 4: Two lines parallel to the same line are parallel to each other.
2. The first volume of Senior Two Mathematics requires four knowledge points.
Concept of complex number: a+bi(a, b∈R) number is called complex number, where I is called imaginary unit. The set formed by all complex numbers is called a complex set, which is represented by the letter C.
Representation of complex numbers:
Complex numbers are usually represented by the letter z, that is, z=a+bi(a, b∈R). This representation is called algebraic form of complex number, where A is the real part of complex number and B is the imaginary part of complex number.
Geometric meaning of complex numbers:
(1) Complex plane, real axis and imaginary axis:
The abscissa of point z is a and the ordinate is b, and the complex number z=a+bi(a, b∈R) can be represented by point Z(a, b). The plane that establishes a rectangular coordinate system to represent a complex number is called a complex plane, the X axis is called a real axis, and the Y axis is called an imaginary axis. Obviously, all points on the real axis represent real numbers, and all points on the imaginary axis represent pure imaginary numbers except the origin.
(2) Geometric meaning of complex number: the set of complex number set C has a one-to-one correspondence with all points on the complex plane, namely
This is because every complex number has a unique point on the corresponding complex plane; On the contrary, every point on the complex plane has a unique complex number corresponding to it.
This is a geometric meaning of complex number, and it is another representation of complex number, that is, geometric representation.
Modules of complex numbers:
The distance from the point Z(a, b) corresponding to the complex number z=a+bi(a, b∈R) on the complex plane to the origin is called the module of the complex number, which is denoted as |Z|, that is |Z|=
Imaginary unit I:
(1) Its square is equal to-1, that is, I2 =-1;
(2) Real numbers can be used to perform four operations, and the original laws of addition and multiplication are still valid when performing four operations.
(3) Relationship between I and-1: I is the square root of-1, that is, one root of equation x2=- 1, and the other root of equation x2=- 1 is-i.
(4) periodicity of I: i4n+ 1=i, i4n+2=- 1, i4n+3=-i, i4n= 1.
Properties of complex modulus:
The relationship between complex number and real number, imaginary number, pure imaginary number and 0;
For the complex number a+bi(a, b∈R), if and only if b=0, the complex number a+bi(a, b∈R) is a real number a; When b≠0, the complex number z=a+bi is called an imaginary number; When a=0 and b≠0, z=bi is called pure imaginary number; Z is a real number 0 if and only if a=b=0.
3. The first volume of Senior Two Mathematics requires four knowledge points.
A (1) = a, a (n) is the general formula of arithmetic progression, and the tolerance is r:
a(n)=a(n- 1)+r=a(n-2)+2r=...= a[n-(n- 1)]+(n- 1)r = a( 1)+(n- 1)r = a+(n- 1)r。
It can be proved by induction.
When n= 1, a (1) = a+(1-1) r = a.
Assuming n=k, arithmetic progression's general formula holds. a(k)=a+(k- 1)r
Then, when n=k+ 1, a (k+1) = a (k)+r = a+(k-1) r+r = a+[(k+1)-/kl.
The general formula also holds.
Therefore, through induction, arithmetic progression's general formula is correct.
Sum formula:
S(n)=a( 1)+a(2)+...+a(n)
=a+(a+r)+...+[a+(n- 1)r]
=na+r[ 1+2+。 ...+(n- 1)]
=na+n(n- 1)r/2
Similarly, the summation formula can also be proved by induction.
A (1) = a, and a (n) is the geometric series of the common ratio r(r is not equal to 0).
General formula:
a(n)=a(n- 1)r=a(n-2)r^2=...=a[n-(n- 1)]r^(n- 1)=a( 1)r^(n- 1)=ar^(n- 1).
The general formula of geometric series can be proved by induction.
Sum formula:
S(n)=a( 1)+a(2)+...+a(n)
=a+ar+...+ar^(n- 1)
= a[ 1+r+0...+r^(n- 1)]
When r is not equal to 1,
s(n)=a[ 1-r^n]/[ 1-r]
When r= 1,
S(n)=na。
Similarly, the summation formula can also be proved by induction.
4. The first volume of Senior Two Mathematics requires four knowledge points.
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.
5. The first volume of senior two mathematics requires four knowledge points.
1, learning three views analysis:
2, oblique mapping method should pay attention to the place:
(1) Take the mutually perpendicular axes Ox and Oy in the known graph. When drawing a vertical view, draw it as the corresponding axes o'x' and o'y' so that ∠ x' o' y' = 45 (or135);
(2) The length of the line segment parallel to the X axis is unchanged, and the length of the line segment parallel to the Y axis is halved.
(3) A 45-degree manuscript under direct vision is 90 degrees, and a 90-degree manuscript under direct vision shall not be 90 degrees.
3, table (edge) area and volume formula:
(1) column: (1) surface area: S=S side +2S bottom; ② Lateral area: S side =; ③ volume: V=S bottom h
⑵ Cone: ① Surface area: S=S side +S bottom; ② Lateral area: S side =; ③ volume: V=S bottom h:
⑶ Platform body: ① Surface area: S=S side +S upper bottom S lower bottom ② Side area: S side =
⑷ Sphere: ① Surface area: S =；; ② Volume: V=
4. Proof of position relationship (main method): Pay attention to the writing of solid geometry proof.
(1) Straight lines are parallel to the plane: ① Straight lines are parallel to each other; (2) Parallel lines are parallel to each other.
(2) The plane is parallel to the plane: the straight line is parallel to the plane.
(3) Vertical problem: The vertical plane of the line is vertical. The core is line-plane verticality: two intersecting straight lines in a vertical plane.
5. turning: (step-I. find or make an angle; Two. Cornering)
(1) Solution of included angle formed by straight lines on different planes: translation method: translating straight lines to construct triangles;
⑵ Angle between straight line and plane: Angle between straight line and projection.