1. Geometry and general logic terms
2. Complex number
3. Plane vector
4. Algorithm, reasoning and proof
5. Inequalities and linear programming
6. Permutation and Binomial Theorem
7. Images and properties of functions and basic elementary functions
8. Functions and equations, function models and their applications
9. Derivative and its application
Graphs and properties of trigonometric functions
1 1. triangle identity change and triangle solution
12. arithmetic progression
13. Sum of sequence and simple application of sequence
14. Space geometry
15. The positional relationship between spatial points, straight lines and planes
16. Space vector and solid geometry
17. Equations of lines and circles
18. Definition, Equation and Properties of Conic Curve
19. Hot issues of conic curves
probability;likelihood
2 1. Discrete Random Variables and Their Distribution
22. Statistics and statistical cases
23. The idea of function and equation, combined with the idea of mathematics.
24. Classification and integration of ideas, transformation and transformation of ideas.
25. Coordinate system and parameter equation
26. Lecture on inequality
What are the key formulas in high school mathematics?
Multiplication and factorization A2-B2 = (a+b) (a-b) A3+B3 = (a+b) (A2-AB+B2) A3-B3 = (A-B (A2+AB+B2))
Trigonometric inequality | A+B |≤| A |+B||||| A-B|≤| A |+B || A |≤ B < = > -b≤a≤b
|a-b|≥|a|-|b| -|a|≤a≤|a|
The solution of the unary quadratic equation -b+√(b2-4ac)/2a -b-√(b2-4ac)/2a
The relationship between root and coefficient x1+x2 =-b/ax1* x2 = c/a Note: Vieta theorem.
Discriminant b2-4ac=0 Note: The equation has two equal real roots.
B2-4ac >0 Note: The equation has two unequal real roots.
B2-4ac & lt； Note: The equation has no real root, but a complex number of the yoke.
The sum of the two angles of trigonometric function formula sin (a+b) = sinacosb+Cosasinbsin (a-b) = sinacosb-sinbcosa.
cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+ 1)/(ctg B-ctgA)
The angle doubling formula tan2a = 2tana/(1-tan2a) ctg2a = (ctg2a-1)/2ctg.
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
Half-angle formula sin (a/2) = √ ((kloc-0/-COSA)/2) sin (a/2) =-√ ((kloc-0/-COSA)/2).
cos(A/2)=√(( 1+cosA)/2)cos(A/2)=-√(( 1+cosA)/2)
tan(A/2)=√(( 1-cosA)/(( 1+cosA))tan(A/2)=-√(( 1-cosA)/(( 1+cosA))
ctg(A/2)=√(( 1+cosA)/(( 1-cosA))ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))
Sum-difference product 2sina cosb = sin (a+b)+sin (a-b) 2cosasinb = sin (a+b)-sin (a-b)
2 cosa cosb = cos(A+B)-sin(A-B)-2 sinasinb = cos(A+B)-cos(A-B)
sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2 cosA+cosB = 2 cos((A+B)/2)sin((A-B)/2)
tanA+tanB = sin(A+B)/cosa cosb tanA-tanB = sin(A-B)/cosa cosb
ctgA+ctgBsin(A+B)/Sina sinb-ctgA+ctgBsin(A+B)/Sina sinb
The sum of the first n terms in some sequences is1+2+3+4+5+6+7+8+9+…+n = n (n+1)/21+3+5+7+9+/kloc-0.
2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1) 12+22+32+42+52+62+72+82+…+N2 = n(n+ 1)(2n+ 1)/6
13+23+33+43+53+63+…n3 = N2(n+ 1)2/4 1 * 2+2 * 3+3 * 4+4 * 5+5 * 6+6 * 7+…+n(n+ 1)= n(n+ 1)(n+2)/3
Sine theorem a/sinA=b/sinB=c/sinC=2R Note: where r represents the radius of the circumscribed circle of a triangle.
Cosine Theorem b2=a2+c2-2accosB Note: Angle B is the included angle between side A and side C..
The standard equation of a circle (x-a)2+(y-b)2=r2 Note: (A, B) is the center coordinate.
General equation of circle x2+y2+Dx+Ey+F=0 Note: D2+E2-4f > 0
Parabolic standard equation y2=2px y2=-2px x2=2py x2=-2py
Lateral area of a straight prism S=c*h lateral area of an oblique prism s = c' * h.
Lateral area of a regular pyramid S= 1/2c*h' lateral area of a regular prism S= 1/2(c+c')h'
The lateral area of the frustum of a cone S = 1/2(c+c')l = pi(R+R)l The surface area of the ball S=4pi*r2.
Lateral area of cylinder S=c*h=2pi*h lateral area of cone s =1/2 * c * l = pi * r * l.
The arc length formula l=a*r a is the radian number r > of the central angle; 0 sector area formula s= 1/2*l*r
Conical volume formula V= 1/3*S*H Conical volume formula V= 1/3*pi*r2h
Oblique prism volume V=S'L Note: where s' is the straight cross-sectional area and l is the side length.
Cylinder volume formula V=s*h cylinder V=pi*r2h
Extracurricular reading:
As an important subject to measure a person's ability, most students from primary school to high school have a special liking for it and have invested a lot of time and energy. However, not everyone is a success. Many excellent students in primary schools and junior high schools have stumbled in mathematics since they entered the high school stage. This phenomenon is relatively common at present and should be paid attention to. Of course, there are many reasons for this phenomenon. This paper only discusses the following points from the aspects of students' learning situation:
In the face of many successful students in junior high school who become losers in senior high school, some people have conducted a research and investigation on their learning situation. The results show that the main reasons for the decline in their grades are as follows.
1. Passive learning. After entering high school, many students, like junior high school, still have strong dependence, and they can't grasp the initiative of learning by following the inertia of teachers. It is manifested in making uncertain plans, waiting for class, not previewing before class, not knowing what the teacher will do in class, being busy taking notes in class, and not hearing the "doorway". They didn't really understand what they had learned.
You can't learn law. Teachers usually explain the ins and outs of knowledge in class, analyze the connotation of concepts, analyze key and difficult points, and highlight thinking methods. However, there are also some students who don't pay attention in class, don't hear the main points clearly or can't hear them completely, take notes in large volumes, and have many problems. After class, I can't consolidate, summarize and find the connection between knowledge in time. I just do my homework and do problems in a hurry, and I am confused about concepts, laws and questions.
3. Do not pay attention to the foundation. Some students who feel good about themselves often despise the study and training of basic knowledge, skills and methods. They often forget what to do, but they are very interested in difficult problems to show their "level", so they are too ambitious and value "quantity" over "quality" and fall into the sea of questions. Formal homework or
4. Do not have the conditions for further study. Compared with junior high school mathematics, senior high school mathematics is a leap in depth, breadth and ability. This requires that you must master basic knowledge and skills to prepare for further study. There are many difficulties, new methods and strong analytical ability in high school mathematics, such as the maximum value of quadratic function in closed interval, the solution of function value domain, the distribution of real roots and parameter equation, the deformation and flexible application of triangular formula. The formation of space concept, the arrangement and combination of application problems and practical application problems, etc. Objectively, these viewpoints are the points of differentiation, and some contents are still out of touch in the textbooks of high school and junior high school. If remedial measures are not taken, differentiation will be inevitable.
Solution: 1 Cultivate good study habits. Good study habits include making plans, self-study before class, paying attention to class, reviewing in time, completing homework independently, solving problems, systematically summarizing and studying after class. Making a plan to make the learning purpose clear, the time arrangement reasonable, unhurried and steady, is the internal motivation to promote students' active learning and overcome difficulties. But the plan must be practical, with both long-term plans and short-term arrangements. In the process of implementation, we must be strict with ourselves and temper our will to learn.
Self-study before class is the basis for students to learn new lessons well and achieve better learning results. Self-study before class can not only cultivate self-study ability, but also improve their interest in learning new lessons and master the initiative in learning. Don't go through the motions in self-study, pay attention to quality, try to understand the teaching materials before class, pay attention to the teacher's ideas in class, grasp the key points, break through the difficulties and solve the problems in class as much as possible.
Classroom is the key link to understand and master basic knowledge, skills and methods. "Lack of learning before school", students who have taught themselves before class can concentrate more in class, and they know where to be detailed and where to omit. Where to carve carefully, where to pass by and where to record, instead of copying all the records, pay attention to one thing and lose another.
Timely review is an important part of efficient learning. By reading textbooks repeatedly and consulting relevant materials in multiple ways, we can strengthen our understanding and memory of the basic conceptual knowledge system, link the new knowledge we have learned with the old knowledge, analyze and compare it, and arrange the review results in our notes at the same time, so that the new knowledge we have learned will change from "knowing" to "knowing".
Independent homework is a process in which students can analyze and solve problems flexibly through their own independent thinking, so as to further deepen their understanding of new knowledge and master new skills. This process is a test of students' will and perseverance. Through application, students can be familiar with what they have learned.
Problem-solving refers to the process of understanding the exposed knowledge errors or missing answers because of thinking obstruction in the process of independently completing homework, so as to make the thinking smooth and supplement the answers. Be persistent in solving problems and do the wrong homework again. If we don't understand the mistakes, we should rethink them. If you can't solve it, ask the teachers and classmates, often review and strengthen the mistakes, and do appropriate repetitive exercises for the teachers and classmates to do.
Systematic summarization is an important link for students to master knowledge and develop cognitive ability comprehensively and systematically through positive thinking. On the basis of systematic review, the summary should be based on teaching materials, refer to notes and related materials, and reveal the internal relationship between knowledge through analysis, synthesis, analogy and generalization, so as to master the learned knowledge. Regular multi-level summary can change what you have learned from "living" to "understanding".
Extracurricular learning includes reading extracurricular books and newspapers, participating in academic competitions and lectures, and visiting senior students or teachers to exchange learning experiences. Extracurricular learning is a supplement and continuation of in-class learning. It can not only enrich students' cultural and scientific knowledge, deepen and consolidate what they have learned in class, but also satisfy and develop students' hobbies, cultivate students' autonomous learning and working ability, and stimulate students' curiosity and enthusiasm for learning.
Step by step to prevent impatience. Because students are young and have limited experience, a large number of high school students are prone to impatience. Some students are greedy for quick results, gulping down dates, some students want to "sprint" in a few days, some students are complacent as soon as they have achieved results, and they will be devastated when they encounter setbacks. In view of these situations, students should understand that learning is a long-term consolidation of old knowledge. A very important reason why many excellent students can get good grades is that their basic skills are solid, and their reading, writing and computing abilities have reached the level of automation or semi-automation.
3. Study the characteristics of the subject and find the best learning method. Mathematics is responsible for cultivating students' computing ability, logical thinking ability, spatial imagination ability, and the ability to analyze and solve problems by using what they have learned. It is characterized by a high degree of abstraction, strong logic, wide applicability and high requirements for ability. When learning mathematics, we must pay attention to "living". We can't just read books without doing problems, and we can't bury our heads in doing problems without summarizing and accumulating. We should be able to get in and out of the textbook knowledge and find the best learning method according to our own characteristics. This is the truth in the learning process of "from thin to thick" and "from thick to thin" advocated by Mr. Hua The methods vary from person to person, but the four steps of learning (preview, class, arrangement and homework) and one step (review and summary) are indispensable.
;