Multiplication and Factorization of Mathematical Formulas Necessary for College Entrance Examination 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 =-BA
|a-b||a|-|b| -|a|a|a|
The solution of quadratic equation in one variable -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
2-4ac=0 Note: The equation has two equal real roots.
2-4ac0 Note: The equation has two unequal real roots.
2-4ac0 Note: The equation has no real root, but a complex number of the yoke.
formulas of trigonometric functions
Two-angle sum formula
in(A+B)= Sina cosb+cosa sin(A-B)= Sina cosb-sinb cosa
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)
Double angle formula
tan2A = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
half-angle formula
in(A/2)=(( 1-cosA)/2)sin(A/2)=-(( 1-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
2 Sina cosb = sin(A+B)+sin(A-B)2 cosa sinb = sin(A+B)-sin(A-B)
2 cosa cosb = cos(A+B)-sin(A-B)-2 sinasinb = cos(A+B)-cos(A-B)
inA+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 of some series
1+2+3+4+5+6+7+8+9 ++ n = n(n+ 1)/2 1+3+5+7+9+ 1 1+ 13+ 15++(2n- 1)= N2
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 standard equation containing a circle between side A and side C (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+E2-4F0.
Parabolic standard equation y2=2px y2=-2px x2=2py x2=-2py
The side area of a straight prism is S=c*h, and the side area of an oblique prism is s = c * h.
Lateral area of regular pyramid S= 1/2c*h lateral area of 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 0 of the central angle, and the 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=SL Note: where s is the straight section area and l is the side length.
Cylinder volume formula V=s*h cylinder V=pi*r2h
The solution of the general formula:
(1) Constructing geometric series: As long as there are recurrence formulas of the last term and the previous term, the formula for finding the general term of geometric series can be constructed;
(2) Constructing arithmetic progression: When the recursive formula cannot construct geometric progression, constructing arithmetic progression;
(3) Recursion: that is, according to the corresponding law between the latter term and the former term, the corresponding formula is derived from the former term.
Common methods for finding general terms by known recursive formulas;
① when A 1 = A and an+ 1 = QAN+B are known, the key is to determine the undetermined coefficient, so that an+ 1 +=q(an+) can be obtained.
② when a 1 = a, an = an- 1+f (n) (N2) is known, when an is found, it is solved by the accumulation method, that is, an = a1+(a2-a1)+(a3-a2)+
③ When a 1 = a and an = f (n) an- 1 (N2) are known, when solving an, iterative method is used.
Senior three math review plan 1. time management
According to the number of days off, everyone should arrange their own time. This holiday is different from previous holidays, and it must be based on study. Holidays should be considered as classes at home. I suggest that everyone attend and finish classes on time according to the time standard on the schedule. The whole day is divided into morning, afternoon and evening, and mathematics is still arranged in the morning. However, the time of each class should not be too long, not exceeding 1.5 hours at most. You can relax for three days during the Spring Festival holiday, but it is not suitable for long-distance travel. You can walk around the residence, mainly to relax.
Second, the plan arrangement
Everything must be planned, which is also part of everyone's study. The winter vacation is very short. If there is no plan, it may pass quickly in the busy schedule. I also suggest that you integrate the curriculum of senior three and rearrange the subjects. Here, you should highlight your weak subjects. Don't expect a certain subject, but hope to make up for it with the results of this course? Crappy? Question, this is impossible. Math subjects are arranged at least once a day. I want to have a full understanding of math knowledge blocks, such as functions, derivatives, series, inequalities, plane vectors, analytic geometry, solid geometry, probability statistics and so on. And strengthen review and practice according to my weak links. Don't shy away from the knowledge blocks that are difficult, arrange more time and try to conquer them during the holidays.
Third, the arrangement of the summary
How to find your own weak links, it is necessary to make a good summary. Summarize the examples that the teacher said in class, the homework done after class, and the examination questions in unified training to see which knowledge you always make mistakes and which should be weak links. For the weak links, first solve the problem of basic knowledge, and then discuss with classmates and ask teachers (the school will arrange a question and answer time, and the online school will also have teachers on duty). At the same time, there must be a reflection (summary) after finishing a topic, that is, this topic examines several knowledge points, what are the mistakes, what are the similarities with the previous topic, and whether it can be done by changing conditions and summarizing the topic. It is not necessary to reflect on every topic, but it is necessary to reflect every day. This process is the process of improving one's ability.
Suggestions on improving math scores in senior three do more questions.
No matter what discipline, you need to do problems to accumulate experience, not to mention math, which is mainly based on problems.
For students with weak basic knowledge, they should first master the basic knowledge. Usually, the study is mainly based on textbooks, and the basic knowledge is consolidated by doing exercises and examples in books. Once you have mastered the foundation, you will overcome the key and difficult points.
For students who have a good grasp of basic knowledge, they should usually do more classic examples and real college entrance examination questions, accumulate experience in doing them, improve the speed of doing them, and analyze the investigation direction of college entrance examination questions over the years.
Finishing knowledge points
Comprehensive mathematics in senior high school is five compulsory courses and five optional courses, which is more troublesome to review. In order to be easy to find when reviewing, we can classify and summarize the contents of high school mathematics and review it in a targeted manner.
This not only saves reading time, but also helps to review your weak links.
Sort out the wrong problem set
Prepare a notebook, sort out your usual mistakes, solve the problem of wrong question set every once in a while, and review the wrong question set one week before the college entrance examination. This can avoid troublesome mistakes in the exam from happening again. Sorting out the wrong problem set can greatly improve the review efficiency.
Reasonable allocation of examination time