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Solving problems in senior high school mathematics college entrance examination in the national volume
Answering skills of mathematics fill-in-the-blank questions in college entrance examination
Mathematical problem-solving skills in college entrance examination
Solving problems in senior high school mathematics college entrance examination in the national volume
1, make a mountain out of a molehill;
2. Don't ignore the options;
3, can qualitative analysis, not quantitative calculation;
4. The energy characteristic method does not do conventional calculation;
5. Don't solve it directly if it can be solved indirectly;
6. Narrowing the selection range can be ruled out;
7. Choose the option directly after analyzing and calculating half;
8. Three similar choices are similar. You can answer the question in a simple way.
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Answering skills of mathematics fill-in-the-blank questions in college entrance examination
1, direct method: This is the basic method to solve the fill-in-the-blank problem. It directly starts from the problem setting conditions, uses the knowledge of definition, theorem, nature and formula, and directly obtains the result through the processes of deformation, reasoning and operation.
2. Specialization method: When the conclusion of the fill-in-the-blank question is unique or the information provided in the question setting conditions implies that the answer is a fixed value, a special value can be used to replace the variable uncertainty in the question, that is, the correct result can be obtained.
3. Number-shape combination method: For some fill-in-the-blank questions with geometric background, if you can think of the shape in the number and help the number with the shape, you can often solve the problem simply and get the correct result.
4. Equivalent transformation method: by "simplifying the complex and turning the unfamiliar into the familiar", the problem is equivalently transformed into an easy-to-solve problem, so as to get the correct result.
5. Image method: With the help of the intuitive shape of graphics, the method of making quick judgments through the combination of numbers and shapes is called image method. Venn diagram, trigonometric function lines, images of functions and curves of equations are all commonly used graphics.
6. Constructive methods: When solving a problem, sometimes it is necessary to design a new model to solve the problem according to the specific situation of the topic. This kind of design work is usually called construction pattern solution, which is called construction method for short.
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Mathematical problem-solving skills in college entrance examination
1, the properties of trigonometric transformation and trigonometric function
Solution: ① Different keratinization angles; (2) reduce the power and expand the angle; ③f(x)= Asin(ωx+φ)+h； ④ Solving by combining properties.
Answer steps:
① Simplification: the simplification of trigonometric function is summarized as the form of y=Asin(ωx+φ)+h, that is, the form of "one function at one corner".
② whole substitution: ωx+φ is regarded as a whole, and the condition is determined by the properties of y=sin x and y = cos x. ..
③ Solution: Find the conditional solution with the range of ωx+φ to get the property of function y=Asin(ωx+φ)+h, and write the result.
Step 2 solve the triangle problem
Solution:
(1) ① Simplified deformation; ② Transform it into the relationship of edges by cosine theorem; ③ Proof of deformation.
(2) ① use cosine theorem to express angle; (2) Find the range of basically unequal values; ③ Determine the value range of the angle.
Answer steps:
① Conditional: Determine what is known and what is sought in the triangle, mark it in the graph, and then determine the direction of transformation.
(2) Fixed tools: According to the conditions and requirements, reasonably select the transformation tools to realize the mutual transformation between corners.
③ Seek the result.
3. General term and sum of series.
Solution: ① Find an item first, or find the relationship of series; ② Find the general term formula; ③ Find the sequence and general formula.
Answer steps:
① Recursion: Determine the relationship between two adjacent items of a series according to known conditions, that is, find the recurrence formula of a series.
② Finding the general term: according to the recursive formula of the series, convert it into the formula of arithmetic or proportional series, or find the general term formula by accumulation or multiplication.
③ Determination method: Determination summation method (such as formula method, split term elimination method, dislocation subtraction method, grouping method, etc.). ) According to the structural characteristics of sequence expressions.
(4) Write step: standardize write sum step.
4. Mean and variance of discrete random variables
Think about solving problems:
(1)① Mark the event; (2) decomposition of events; ③ Calculation probability.
(2)① Determine the value of ξ; (2) calculating the probability; ③ Obtain the distribution list; ④ Seek mathematical expectation.
Answer steps:
① Determinant: Determine the value of discrete random variables according to known conditions.
② Qualitative: Make clear the events corresponding to the values of each random variable.
③ Finalization: Determine the probability model and calculation formula of the event.
④ Calculation: Calculate the probability of random variables taking each value.
⑤ List: List distribution list.
⑥ Solution: Solve the numerical value according to the formula of mean and variance.
5. Range problem in conic curve.
Problem-solving thinking; ① Set equations; ② solubility coefficient; ③ Draw a conclusion.
Answer steps:
① Propose relations: extract unequal relations from problem setting conditions.
(2) Find the function: use a variable to represent the target variable and substitute it into the inequality relation.
(3) Value range: By solving the inequality with the target variable, the value range of the parameter is obtained.
6. Exploratory problems in analytic geometry.
Thinking of solving the problem: ① It is generally assumed that this situation holds (point exists, straight line exists, positional relationship exists, etc. ); (2) substituting the above assumptions into known conditions to solve; ③ Draw a conclusion.
Answer steps:
① Assumption first: Assumption conclusion holds.
(2) Re-reasoning: reasoning and solving under the assumption that the conclusion is established.
Conclusion: If a reasonable result is introduced and verified, it will be accepted. Hypothesis; If the contradiction is deduced, the hypothesis is denied.
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The national volume of senior high school mathematics college entrance examination questions solving methods related articles;
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