2. Area =(π)(R2)
3. Perimeter = 2(π)r
4. The standard equation of a circle (x-a)2+(y-b)2=r2(a, B) is the center coordinate.
5. Circle X2+Y2+DX+EY+F = 0d2+E2-4f > 0
Summary and formula of high school mathematics knowledge points: elliptic formula 1, ellipse circumference formula: l=2πb+4(a-b).
2. ellipse circumference's Theorem: The circumference of an ellipse is equal to the short axis of an ellipse, and the circumference of a circle with a radius of (2πb) plus four times the difference between the long axis (a) and the short axis (b) of an ellipse.
3. Elliptic area formula: s=πab
4. Ellipse area theorem: the area of an ellipse is equal to π times the product of the major semi-axis length (a) and the minor semi-axis length (b) of the ellipse.
Although there is no ellipse πT in the above ellipse circumference sum area formula, both formulas are derived from ellipse π t. ..
Summary and formula of high school mathematics knowledge points: arithmetic progression 1 and arithmetic progression's general formula is: an = a1+(n-1) d (1).
2. The sum of the first n items is: Sn=na 1+n(n- 1)d/2 or Sn=n(a 1+an)/2(2).
It can be seen from the formula (1) that an is a linear function (d≠0) or a constant function (d = 0) of n, and (n, an) is arranged in a straight line. According to formula (2), Sn is a quadratic function (d≠0) or a linear function (d =
3. From arithmetic progression's definition and general formula, the first n terms and formulas can also be deduced: A1+an = A2+an-1= A3+an-2 = … = AK+an-k+1,k ∈ {1. Then am+an = AP+aqsm-1= (2n-1) an, s2n+1= (2n+1) an+1sk, s2k-sk, s3k-s2k. ...
Summary and formula of high school mathematics knowledge points: geometric progression 1 and geometric progression's general formula is: an = a 1 * q (n- 1).
2. The sum formula of the first n terms is: sn = [a1(1-q n)]/(1-q) and the relationship between any two terms am and an = am q (n-m).
3. A1an = a2an-1= a3an-2 = … = akan-k+1,k ∈ {1 can be deduced from the definition of geometric series, the general term formula and the first n terms. Aq equal ratio terms. If π n = A 1 A2 … an, then π 2n- 1 = (an) 2n- 1, π 2n+1= (an+1) 2n+1add. On the other hand, taking any positive number c as the cardinal number and a arithmetic progression term as the exponent, a power energy is constructed, which is a geometric series.
In this sense, we say that a positive geometric series and an arithmetic series are isomorphic. Attribute:
(1) if m, n, p, q∈N, m+n=p+q, then am an = AP * AQ；;
② In geometric series, the sum of every k term still becomes geometric series in turn. "G is a neutral term with equal proportions of A and B" and "G 2 = AB (G ≠ 0)". In geometric series, the first term A 1 and the common ratio q are not zero.
parabola
1, parabola: y=ax*+bx+c is y = ax plus bx plus c squared a>0, and the opening of parabola is upward; At a & lt0°, the parabolic opening is downward; When c=0, the parabola passes through the origin; When b=0, the axis of symmetry of parabola is the Y axis.
2. Vertex y=a(x+h)*+k means that y is equal to a times the square of (x+h) +k, -h is the x of vertex coordinates, and k is the y of vertex coordinates, which is generally used to find the maximum and minimum values.
3. Parabolic standard equation: y 2 = 2px, which means that the focus of parabola is on the positive semi-axis of X, and the focal coordinate is (p/2,0).
4. The directrix equation is x=-p/2. Because the focus of parabola can be on any half axis, there is a standard equation for * * *: y 2 = 2pxy 2 =-2pxy 2 =-2pxy.
Summary and formula of high school mathematics knowledge points: axiom of position relationship between points, straight lines and planes 1: If two points on a straight line are in a plane, then all points on this straight line are in this plane.
Axiom 2: When three points that are not on a straight line intersect, there is one and only one plane.
Axiom 3: If two non-coincident planes have a common point, then they have one and only one common straight line passing through the point.
Axiom 4: Two lines parallel to the same line are parallel to each other.
Theorem: If two sides of an angle in space are parallel to two sides of another angle, then the two angles are equal or complementary.
First, the basic properties and applications of plane
Basic properties of 1. plane
2. Equiangular theorem
Second, the positional relationship between two straight lines in space.
Classification of positional relationship between two straight lines in 1. space
2. Angles formed by straight lines on different planes
Definition of angles formed by (1) straight lines on different planes
Third, the positional relationship between spatial straight line and plane, plane and plane
1. Classification of positional relationships between straight lines and planes, and between planes.
(1) Classification of positional relationship between straight line and plane
(2) the classification of plane and the relationship between plane positions
The positional relationship between two planes has and only has the following two kinds:
(1) Two planes are parallel-have nothing in common;
(2) Two planes intersect-there is a straight line.
3. Common conclusions
(1) uniqueness theorem
① One and only one straight line is parallel to the known straight line at a point outside the straight line.
② There is one and only one plane perpendicular to the known straight line at one point.
③ One and only one plane is parallel to the known plane at a point outside the plane.
④ There is only one straight line perpendicular to the plane at a point outside the known plane.
(2) Determination method of straight lines in different planes
A straight line passing through a point in a plane and a straight line not passing through the point in the plane are non-planar straight lines.
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