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 assumption that there is no linear correlation between Y and X is not true, that is, there is a linear correlation between Y and X..
Mathematics learning methods and skills
Do your homework and pay attention to norms.
It is also necessary to cultivate good homework habits in classroom and extracurricular exercises. In homework, we should not only do it neatly, but also cultivate aesthetic feeling, which is an effective way to cultivate logical ability and must be done independently. At the same time, it can cultivate a sense of responsibility to think independently and solve problems correctly. When doing homework, we should advocate efficiency, and homework that should be completed in ten minutes should not be delayed for half an hour. Tired homework habits make the thinking loose and the energy unfocused, which is harmful to the cultivation of mathematical ability. To master the study habits of mathematics, we must start from the first year of high school and cultivate the study habits from the psychological characteristics of age growth and the requirements of different learning stages.
Write a summary and grasp the law.
A person can constantly improve by constantly accepting new knowledge, encountering setbacks, having doubts and summing up. "Students who can't summarize will not improve their ability, and frustration experience is the cornerstone of success." The biological evolution process of the survival of the fittest in nature is an example. Learning should always sum up the rules, with the aim of further development. Through the usual contact and communication with teachers and classmates, the general learning steps are gradually summarized, including: making a plan, self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and extracurricular learning, which are simply summarized as four links (preview, class, sorting and homework) and one step (review summary). Each link has profound content, strong purpose and pertinence, and should be put in place. Adhere to the study habit of "two before and two after a summary" (preview first, then listen to lectures, review first, then do homework, and write a summary of each unit). Be good at summing up the connections between knowledge.
Learning mathematics is not that I can get good grades by doing problems, but that I should spend my energy on summing up. Especially for the examples in textbooks or classes, as long as you are good at summarizing, you can know what kinds of questions there are in this section of mathematics content, and what are the approximate solutions and ideas of each question, so as to improve your ability to analyze and solve problems by using what you have learned. At the same time, every time you finish learning a unit, you should establish the knowledge framework of this unit and turn the main ideas, reasoning methods and application skills of this chapter into your own practical skills.
Pay attention to reflection and improve ability
Learning should pay attention to reflection and practice understanding. Teachers usually explain the ins and outs of knowledge in class, analyze the connotation and extension of concepts, analyze key points and difficulties, and highlight thinking methods. But some students don't pay attention in class, don't hear the main points clearly or can't hear them completely, take a lot of notes and have a lot of problems. After class, I can't consolidate, summarize and find the connection between knowledge in time, but I am busy with homework and confused questions, and I know little about concepts, laws, formulas and theorems. Mathematics discipline must cultivate the ability of calculation, logical thinking, spatial imagination and the important task of analyzing and solving problems by using the learned knowledge. Its characteristics are high abstraction, strong logic, wide applicability and high requirements for ability. Mathematical ability can only be cultivated and improved through continuous reflection on the application of mathematical thinking methods. The content of mathematics changes greatly, and the learning method is backward. In the process of learning high school mathematics, you will certainly encounter many difficulties and problems. Students should have the courage and confidence to overcome difficulties, be proud of victory, be indomitable in failure, and never let problems pile up and form a vicious circle. Instead, we should seek solutions to problems under the guidance of teachers and cultivate the ability to analyze and solve problems. This is our understanding.
Learn to find problems and pay attention to questioning students who often see good grades in their studies. There are always many questions to ask the teacher. Asking questions is not only the starting point of discovering true knowledge, but also the beginning of invention and creation. The process of improving academic performance is the process of finding, asking and solving problems. Boldly questioning the teacher is not a manifestation of stupidity, but a manifestation of pursuing true knowledge and being proactive. In class, we should not only "know why", but also "know why", so that problems can continue to arise, and then we can analyze and think about solving problems and make progress in learning.
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