Come on! There are still more than 60 days, I hope we can all do well in the exam.
PS: You can check it in Baidu Library. There are questions and formulas.
Popularization of mathematical formula in senior high school
A, set, simple logic, function
1. When studying sets, we must pay attention to the characteristics of set elements, that is, three properties (certainty, mutual difference and disorder); Given the set A={x, xy, lgxy}, the set b = {0, | x |, y} and A=B, then x+y=
2. To study a set, we must first understand the representative elements in order to understand the meaning of the set. Given the set m = {y | y = x2, x ∈ r}, n = {y | y = x2+ 1, x ∈ r}, find m ∩ n; Find the difference between m = {(x, y) | y = x2, x ∈ r}, n = {(x, y) | y = x2+ 1, x ∈ r}.
3. When assembling A and B, did you notice "extreme" situations: or; When you find a subset of a set, do you forget it? For example, when finding the constant planting range of A, have you ever discussed the situation that A = 2?
4. For a finite set m with n elements, the number of subsets, proper subset, nonempty subset and nonempty proper subset is the number of the set M*** that meets the conditions in turn.
5. The basic tool to solve the set problem is Wayne diagram; There are * * members of a literary and art group 10, each of whom can sing and dance at least, of which 7 can sing and dance well and 5 can sing and dance well. Now choose a person who can sing and dance and perform a song and dance program. How many different ways are there?
6. The relationship between two sets.
7.(CUA)∩(CU B)= CU(A∪B)(CUA)∩(CUB)= CU(A∪B)； ;
8. A statement that can be judged true or false is called a proposition.
Logical conjunctions include or, and right and wrong.
The truth table of compound propositions in P and Q forms: (true and true, identical or false)
P q P and q P or q
Really, really, really.
True or false.
False, true, false, true
Fake, fake, fake.
9. Four forms of propositions and their relationships:
Inverted easily
Interaction
Interaction
No, no, no, no.
No, no.
No, no.
There is no reciprocity.
The original proposition and the negative proposition are the same as true and false; The truth and falsehood of an inverse proposition are the same.
Several important properties of functions;
① If the function has everything or f(2a-x)=f(x), the image of the function is symmetrical about a straight line.
② Function and function image are symmetrical about a straight line;
Functions and images of functions are symmetrical about a straight line;
The function and its image are symmetrical about the origin of coordinates.
(3) If odd function is the increasing function on the interval, then it is also the increasing function on the interval.
④ If an even function is a increasing function in an interval, it is a decreasing function in an interval.
⑤ Shift the image of the function by one unit to the left along the X axis to get the image of the function; The image of the function (obtained by translating the image of the function to the right along the X axis;
The image of the function +a is obtained by translating the auxiliary image of the function by one unit along the Y axis. The image of the function +a is obtained by translating the auxiliary image of the function by units along the Y axis.
solid geometry
53. The proof of parallelism and verticality is mainly proved by the transformation of line-plane relationship: line//line//plane//plane, line ⊥ line ⊥ plane ⊥ plane, vertical common vector.
54. What is the main method to make the plane angle of dihedral angle? Three verticality method: a plane, two vertical lines and three diagonal lines, the projection is visible.
55. The dihedral angle solutions mainly include: right triangle, cosine theorem, projective area method and normal vector.
56. What is the conventional method for finding the distance from point to surface? (direct method, equal volume transformation method, normal vector method)
57. Do you still remember the three vertical theorems and their inverse theorems?
58. The solution of the spherical distance between two points on a sphere is mainly to find the angle of the center of the sphere, which is often associated with latitude and longitude. Do you remember the meaning of longitude and latitude? (Longitude is the face angle; Latitude is the angle between a line and a plane)
59. Remember the Euler formula of simple polyhedron? (V+F-E=2, where V is the number of vertices, E is the number of edges, and F is the number of faces), do you still remember the two algorithms of edges? (① If every face of a polyhedron is an N polygon, then E =；; (2) If every vertex of a polyhedron has m edges, then E=)
probability statistics
94. Solution of event probability: The probability of the event to be sought is converted into an equal probability event (often using the knowledge of permutation and combination), into the probability of one of several mutually exclusive events events, and into the probability of simultaneous occurrence of independent events by using the probability of opposing events. This probability is regarded as the probability that an event happens exactly k times in n experiments, but attention should be paid to the use conditions of the formula.
(1) if events a and b are mutually exclusive events, then P(A+B)=P(A)+P(B).
(2) If events A and B are independent events, then P(A? B)=P(A)？ P(B)
(3) If events A and B are opposite events, then P(A)+P(B)= 1 In general,
(4) If the probability of an event in an experiment is p, then the probability that it happens exactly k times in n independent repeated experiments:
95. Sampling methods mainly include: simple random sampling (drawing lots, random sample table method) is often used when the population is small, and its main feature is to extract one by one from the population; Systematic sampling is often used when the total number is large, and its main feature is that it is evenly divided into several parts, and only one copy is taken from each part; The main characteristics of stratified sampling and stratified proportional sampling are mainly used for people with obvious differences. The same feature of them is that the probability of each individual being drawn is equal.
96. The method of estimating samples according to the population is to take the frequency of samples as the probability of the population.
X. Methods and skills to solve problems
97. Overall test-taking strategy: easy first, then difficult. Generally, first do multiple-choice questions, then fill in the blanks, and finally do big questions. Multiple choice questions strive to ensure speed and accuracy and save time for the big questions behind, but accuracy is the premise. For the fill-in-the-blank question, it seems that there is no clue or the calculation is too complicated, so you can give it up. For big questions, try not to leave blank. It is possible to score by transforming the conditions in the question into algebra. Learn to give up in the exam and get rid of the endless entanglement of a topic.
98. What's the special way to answer multiple-choice questions?
(Forward deduction method, estimation method, special case method, feature analysis method, intuitive selection method, reverse deduction method, combination of numbers and shapes, etc.). )
99. What should I pay attention to when answering the fill-in-the-blank questions? (specialization, diagram, equivalent deformation)
100, what are the most basic requirements when answering application questions?
10 1. Examine the questions, find out the key words in the questions, set the unknowns, list the functional relationships, substitute the initial conditions, indicate the units, and answer. Learn to skip grading skills. If you can't answer the first question, you can do the second question. When using it, just use the conclusion of the first question directly. You should learn to use "from the known", "from the meaning of the problem" and "from the plane geometry".
Skills of Mathematics College Entrance Examination
In the math exam, candidates need to pay special attention to many places. Mastering all kinds of problem-solving skills in the exam can help you catch the dragon gate at the last minute.
Precautions for the exam:
1. Five minutes before the exam is very important.
In the exam, we should make full use of the 5 minutes before the exam. After the papers are handed out, you can browse the topics. When preparing for work (fill in name, test number, etc. ) After the completion, you can turn to the answer at the back, read it through, and be aware of it.
2. Treat each topic differently.
The examination questions are divided into three types: easy, medium and difficult, and the score ratio is about 3: 5: 2. In the exam, everyone should treat it separately according to their own situation.
(1) When doing easy questions, try to finish them all at once, and don't leave blank. This kind of questions will be scored 100%.
(2) When doing intermediate questions, you should calm down and try your best to get points, and at least complete 80%.
(3) When doing difficult problems, people usually feel at a loss. What to do at this moment is:
1 Look at the questions and examine them carefully.
② Have a simple feeling about the draft.
③ Don't give up easily. Many students regard it as a difficult problem and a big problem. Without much consideration, they completely surrendered. Most of the answers are small steps, and many small problems can be solved by students. Therefore, candidates should take every question seriously.
3. Time allocation should be reasonable.
(1) The exam is mainly about grabbing time on multiple-choice questions.
⑵ Check the questions while doing them to fully ensure the correctness of each question. Don't waste too much time on the later inspection with the idea of "re-inspection after completion".
(3) Go back and check your progress 30 minutes before handing in the paper. Pay attention to filling and reading cards in time.