Mathematics in the college entrance examination 1 problem-solving skills for multiple choice questions. Special value test method:
For a general mathematical problem, we can specialize the problem in the process of solving it, and use the principle that the problem does not hold in special circumstances and does not hold in general circumstances to achieve the purpose of removing the false and retaining the true.
Example: the three vertices of △ABC are on the ellipse 4x2+5y2=6, where the two points A and B are symmetrical about the origin O. Let the slope of the straight line AC be k 1 and the slope of the straight line BC be k2, then the value of k 1k2 is
A.-5/4 B.-4/5 C.4/5 D. 2√5/5
Analysis: Because the value of k 1k2 is required, we can know from the stem that the value of k 1k2 is a fixed value. There is no specific location of a, b and c, because it is a multiple-choice question, so there is no need to solve it. Through simple drawing, we can get the most easily calculated value. We might as well make A and B two vertices on the long axis of the ellipse and C one vertex on the short axis of the ellipse, so we can directly confirm the intersection point and simplify the problem, so we choose B.
2. Extreme principle:
Analyze the problem to be studied to the extreme state, so that the causal relationship becomes more obvious, thus achieving the purpose of solving the problem quickly. Extreme value is mainly used to find extreme value, range and analytic geometry. Many problems with complicated calculation steps and large amount of calculation can be solved instantly once extreme value analysis is adopted.
3. Elimination method:
Using the known conditions and the information provided by the selection branch, three wrong answers are eliminated from the four options, so as to achieve the purpose of correct selection. This is a common method, especially when the answer is a fixed value or has a numerical range, special points can be used instead of verification to exclude it.
4. Number-shape combination method;
According to the conditions of the topic, make a graph or image that conforms to the meaning of the topic, and get the answer through simple reasoning or calculation with the help of the intuition of the graph or image. The advantage of the combination of numbers and shapes is intuitive, and you can even measure the result directly with a square.
5. Recursive induction:
Through the conditional reasoning of the topic, we can find the law and sum up the correct answer.
6. Forward pyrolysis method:
Using mathematical theorems, formulas, rules, definitions and meanings, the method of obtaining results through direct calculus and reasoning.
Example: The bank plans to invest part of its funds in Project M and Project N for one year, of which 40% will be invested in Project M, 60% in Project N, and the annual income of Project M will be 65,438+00%, and the annual income of Project N will be 35%. At the end of the year, banks should withdraw funds and pay depositors at a certain rebate rate. In order to make the annual profit of the bank not less than 65,438 of the total investment of M and N ..
A.5% B. 10%
Analysis: Let * * have funds as α and the depositor's rebate rate χ, and we can get 0.1α≤ 0./kloc-0 /× 0.4α+0.35× 0.6α-χ α≤ 0.15α from the meaning of the question.
The solution is 0. 1≤χ≤0. 15, so choose B.
7. Reverse verification method (dry verification method):
Substitute the selected branch into the stem for verification, so as to deny the wrong selected branch and get the correct method of selecting branch.
Example: Let both sets M and N be positive integer sets N*, and map f:M→ map the element N in set M to the element 2n+n in set N, then under the map F, the original image of image 37 is
a3 b . 4 c . 5d . 6
8. If there are difficulties, it will violate the law:
When it is difficult to solve the problem from the front, we can find a qualified conclusion step by step from the choice of expenditure, or draw a conclusion from the opposite side.
9. Characteristic analysis method:
Analyze the characteristics of topic setting and branch selection, find the law and summarize the correct judgment method.
For example, 256- 1 may be divisible by two numbers between 120 and 130, which are:
A. 123， 125 B. 125， 127 C. 127， 129 D. 125， 127
Analysis: The square difference formula of junior middle school is from 256-1= (228+1) (228-1) = (228+1) (21).
10. Appraisal selection method:
Some problems cannot (or are not necessary) be accurately calculated and judged due to the limitation of subject conditions. At this time, we can only get the correct judgment method from the surface by means of estimation, observation, analysis, comparison and calculation.
Summary: Multiple-choice questions in college entrance examination are generally easy or intermediate, while individual questions are more difficult. Most of the answers can be quickly selected by special methods. Such as valuation selection method, special value test method, forward deduction method, combination of numbers and shapes, feature analysis method and reverse deduction method are all commonly used solutions. When solving problems, we should pay special attention to the fact that only one of the four branches of multiple-choice questions is correct, so it is very important to compare the branches when solving problems, which is the basic premise of quick choice and correct answer.