Sorting out the knowledge points of compulsory mathematics in the first volume of senior one.
The positional relationship between two planes:
(1) The definition that two planes are parallel to each other: there is no common point between two planes in space.
(2) the positional relationship between two planes:
The two planes are parallel-have nothing in common; Two planes intersect-there is a straight line.
First, parallel
Theorem for determining the parallelism of two planes: If two intersecting lines in one plane are parallel to the other plane, then the two planes are parallel.
Parallel theorem of two planes: if two parallel planes intersect with the third plane at the same time, the intersection lines are parallel.
B, crossroads
dihedral angle
(1) Half-plane: A straight line in a plane divides this plane into two parts, and each part is called a half-plane.
(2) dihedral angle: The figure composed of two half planes starting from a straight line is called dihedral angle. The range of dihedral angle is [0, 180].
(3) The edge of dihedral angle: This straight line is called the edge of dihedral angle.
(4) Dihedral facet: These two half planes are called dihedral facets.
(5) Plane angle of dihedral angle: Take any point on the edge of dihedral angle as the endpoint, and make two rays perpendicular to the edge in two planes respectively. The angle formed by these two rays is called the plane angle of dihedral angle.
(6) Straight dihedral angle: A dihedral angle whose plane angle is a right angle is called a straight dihedral angle.
Esp。 The two planes are perpendicular.
Definition of two planes perpendicular: two planes intersect, and if the angle formed is a straight dihedral angle, the two planes are said to be perpendicular to each other. Write it down as X.
A theorem to determine the perpendicularity of two planes: If one plane passes through the perpendicular of the other plane, then the two planes are perpendicular to each other.
Verticality theorem of two planes: If two planes are perpendicular to each other, a straight line perpendicular to the intersection in one plane is perpendicular to the other plane.
Summary of five knowledge points of compulsory mathematics in senior one.
Arithmetic progression with a tolerance of (1) is still arithmetic progression, and its tolerance is still D. 。
⑵ For arithmetic progression whose tolerance is d, the sequence obtained by multiplying each term by the constant k is still arithmetic progression, and its tolerance is kd.
(3) If {a} and {b} are arithmetic progression, {a b} and {ka+b}(k and b are nonzero constants) are also arithmetic progression.
(4) For any m and n, arithmetic progression {a} has: a=a+(n-m)d, especially when m= 1, arithmetic progression's general formula is obtained, which is more general than arithmetic progression's general formula.
5. Generally speaking, if L, K, P, …, M, N, R, … are all natural numbers, l+k+p+…=m+n+r+… (the number of natural numbers on both sides is equal), then when {a} is arithmetic progression, there is: A+A+.
[6] arithmetic progression with a tolerance of d, from which equidistant terms are extracted, forms a new series, which is still arithmetic progression, and its tolerance is kd(k is the difference between the number of extracted terms).
(7) If {a} is a arithmetic progression with a tolerance of d, then A, A, …, A and A are also arithmetic progression with a tolerance of -d; In arithmetic progression {a}, a-a=a-a=md (where m, k,).
In arithmetic progression, from the first term, every term (except the last term of a finite series) is the arithmetic average of the two terms before and after it.
Levies when the tolerance d >. 0, the number in arithmetic progression increases with the increase of the number of terms; When d < 0, the number in arithmetic progression decreases with the decrease of the number of terms; When d=0, the number in arithmetic progression is equal to a constant.
⑽ Let A, A and A be three terms in arithmetic progression, and the ratio of the distance difference between A and A, A and a=(≦- 1), then A =.
(1) The necessary and sufficient condition for the sequence {a} to be arithmetic progression is that the sum of the first n terms of the sequence {a} can be written in the form of S=an+bn (where a and b are constants).
(2) In arithmetic progression {a}, when the number of terms is 2n(nN), S-S=nd, =; When the number of terms is (2n- 1)(n), S-S=a, =.
(3) If the sequence {a} is arithmetic progression, then S, S-S, S-S, ... are still arithmetic progression with an error of.
(4) If the sum of the first n terms of two arithmetic progression {a} and {b} is s and t respectively (n is odd), then =.
5] In arithmetic progression {a}, S=a, s = b (n >; M), then S=(a-b).
[6] In arithmetic progression {a}, it is a linear function of n, and all points (n,) are on the straight line y=x+(a-).
(7) Remember that the sum of the first n items of arithmetic progression {a} is S.① If a >；; 0, tolerance d
Four knowledge points of compulsory mathematics in senior one.
1. Regression analysis:
It is a statistical analysis method to determine the relationship form between two correlated variables and determine a related mathematical expression for estimation and prediction. The mathematical expression obtained by regression analysis method is called regression equation, which can be a straight line or a curve.
2. Linear regression equation
Let x and y be two variables with correlation, and n groups of observations corresponding to n points (xi, yi) (i = 1 ..., n) are roughly distributed near a straight line, then the equation of regression straight line is.
One of them is.
3. Linear correlation test
Linear correlation test is a hypothesis test, and the specific method to test whether there is linear correlation between y and x is given.
① Find out the critical value of correlation coefficient r0.05 corresponding to significance level 0.05 and degree of freedom n-2(n is the number of observation groups) in Appendix 3 of the textbook.
② Calculate the value of r according to the formula.
③ Test results.
If |r|≤r0.05, it can be considered that the linear correlation between Y and X is not significant, and the statistical hypothesis is accepted.
If |r| >R0.05, it can be considered that the hypothesis that there is no linear correlation between Y and X is not valid, that is, there is a linear correlation between Y and X..
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