It means that in the process of solving the problem, the key steps are omitted and the answer is directly obtained, which is a serious deduction. Because the problem is graded strictly according to the steps, if the key steps are lost in the process of solving the problem and the knowledge points and ability points to be examined are skipped, it means that points will be lost and points will naturally be deducted.
Example1(National College Entrance Examination in 2000) Known function y = cos2x+sinxcosx+ 1, x ∈ r. 。
(i) When the function y takes the maximum value, find the set of independent variables x;
(II) What kind of translation and scaling transformation can be obtained from the image of y = sinx (x ∈ r)?
Solution: (I) You can get it from the title, y = sin (2x+)+, so there is.
When x =+k, k∈Z, the function y takes the maximum value.
(2) Omission.
Comments: In the solution of (I), the mistake of "one step in place" was made, and three points in the simplification process and 1 point when the maximum value was taken were omitted, so points were deducted.
2. Avoid "using sublimation conclusions"
It is permissible to use sublimation conclusion (the correct conclusion not given in the textbook) in solving multiple-choice questions and fill-in-the-blank questions, and it is also a simple and quick answering skill. However, it is inappropriate to use it directly (without explanation or proof) in solving problems, which is a "big problem" and should be deducted appropriately.
The theoretical basis for solving college entrance examination questions should be the definitions, theorems, axioms and formulas in textbooks, but students can't use "sublimation conclusions" to examine their abilities and processes, so they can't use questions to solve problems, nor can they directly use things outside textbooks to avoid being deducted.
Example 2 (1) (199 1 National College Entrance Examination) According to the definition of monotonicity, it is proved that the function f (x) =-x3+ 1 is a decreasing function on (-∞, +∞).
(2) (20065438+0 National College Entrance Examination) Let the focus of parabola y2 = 2px (P > 0) be F, the straight line passing through point F intersects with parabola at points A and B, and point C is on the parabola's alignment and BC∨x axis. It is proved that the straight line AC crosses the origin O.
The scoring standard points out:
For (1): "It is increasing function's property to use Y = x3 in [0, +∞]", directly write f (x 1)-f (x2) =-< 0 without proving that Y = x3 is also increasing function in (-∞, +∞), but failed to prove why.
For (2): Some candidates directly use the extended conclusion "Y 1Y2 = P2" in the textbook to skip the knowledge points and ability points to be examined, and get 2 points.
The conclusions of textbook exercises and examples can only be used directly through proof (except the conclusions in bold type), otherwise they will be "qualitative" and deducted as incomplete problem solving. Another example is 1996, item 22 (Ⅱ) of college entrance examination science and item 17 (Ⅱ) of 20065438 national college entrance examination science, which directly use the area projection theorem without proof.
3 Avoid "answering irrelevant questions"
It means that you didn't answer the question with other methods or conclusions according to the meaning of the question or didn't see the meaning of the question clearly, which will obviously be deducted.
Example 3( 1993 national college entrance examination questions) known series
Sn is the sum of its first n terms. We must observe the above results, deduce the formula for calculating Sn, and prove it by mathematical induction.
Solution: according to the meaning of the question, the formula of Sn is inferred as follows:
Sn=。
∫AK = =-，
Take k = 1, 2, 3, ..., n, and add these n expressions to get:
Sn= 1- =。
Explaining the above solution can be described as "simple and clear", but it proves that mathematical induction is not used, which is "irrelevant" and it is inevitable to deduct points. Another example is 1999' s college entrance examination question 22 (application question), which asks "how many pairs of rolls should be installed at least in a cold rolling mill". The requirement is to answer in integers, but many candidates fail to answer in integers.
(D) Understand the "scoring criteria" and grasp the scoring points.
Mastering the "scoring point" of solving problems requires understanding the scoring standards of the college entrance examination. The grading standard for solving problems is to give points step by step, but the more you write, the higher the score. Instead, you should step on the grading point to give points, that is, according to the mathematical knowledge and mathematical thinking methods used, allowing "equivalent answers" and "jumping points". Therefore, when you answer, you should have clear steps, clear points and neat format. Give points for different problems.
1. Set several questions to score.
Testimony is usually divided into two parts, and each paragraph is graded according to the main points. There are two main points in the proof: ① the basis of judgment and reasoning of spatial position relationship (theorems and axioms in textbooks); ② What are the spatial angles and distances and their causes (closely related to the definition)? Pay special attention to the angle is not clearly written, it will deduct the distance. Writing in the process of calculation: generally speaking, calculation is to solve triangles, and the conditions and results of the solution should be clearly written. When solving problems by equal product method, we must find out the equal product relationship and calculate it. They are graded by sections, such as 1998 23 questions and 1999 22 questions.
2. Classification discussion questions score points
According to the classification, plus the inductive format (that is, in the summary, write "when ×××× year ×× month × day × month × day × month × day × month × month × day × month × month × day × month × month × day × month × day × month × month × month × day × month × month × month × month × month × month × day × month × month × month × month × month × month × month
3. Score of application questions
Score according to the setting column and the answer. Pay special attention to the deduction of 1 point for non-answer and wrong answer, pay attention to the integrity of setting columns, solving problems and answering questions, and strive for grading step by step.
4. Scoring points of reasoning proof questions
According to the reasoning format, the steps of reasoning deformation are graded. For proving monotonicity and parity of functions by definition and proving problems by mathematical induction, there are strict format scores, which should be complete to avoid losing points. Even if you can't prove the reasoning, it's better to skip the answer application format. From the two ends of the conditions and conclusions to the middle, you can write the format like this, and you can subtract points.
5. Comprehensive score
According to the process of solving, give points step by step, and each step is given points according to the main points. Write the process step by step as much as possible, try not to skip the steps, and according to the meaning of the question
List relationships and translate each condition in the problem setting. If you can count a few steps, even a few steps. Failure does not mean failure, especially those problems with clear problem-solving levels and procedural methods. You can get full marks in every step of calculation. Although the final conclusion has not been worked out, the score is already over half. Therefore, it is also a good idea to "take small points for big problems". Therefore, try to increase the chances of scoring step by step, and don't leave blank questions easily.
(e) Common problem-solving skills
1. Solutions to simple problems
For the questions that are easy to answer (usually the first three questions), it is advisable to adopt the method of "one slow and one quick", that is, slowly examine the questions, solve the problems quickly, and make quick decisions quickly, leaving time for the last three questions.
After finding a solution to the problem, the writing should be concise, fast and standardized, not slow and repetitive. In the words of the marking teacher, it is to write a "score point". Generally speaking, a principle can be written in one step. As for the transitional knowledge of the topic that is not directly examined, you can write the conclusion directly. The college entrance examination allows reasonable omission of non-critical steps, which should be detailed and appropriate.
Example 2004 Beijing Science 15
In,,,, the area of the sum of values.
Analysis: This small topic mainly examines the basic knowledge such as triangle constant deformation and triangle area formula, and examines the calculation ability.
Solution:
Say it again,
.
2. solve the problem.
For the more difficult solutions (the latter three), it is unrealistic to get all the answers in a limited time. Of course, you can't give up all of them. You should get as many points as possible. For the vast majority of candidates, what is important here is how to score from the questions that they can't get. We say that what kind of problem-solving strategy there is, what kind of scoring strategy there is. The following is four o'clock.
(1), missing step solution.
If we encounter a difficult problem, we really can't chew it. The wise strategy is to break it down into a series of steps or a sub-problem. You can count a few steps. Failure does not mean complete failure. We can get full marks at every step. Although there is no final conclusion, the score is over half. Because the characteristics of college entrance examination questions in recent years are: the entrance is easy to be perfect, and it is difficult to give up any questions easily.
Example: (No.2 1 in Zhejiang Science in 2004) It is known that the center of a hyperbola is at the origin, the right vertex is A (1 0), points P and Q are on the right branch of the hyperbola, and the distance from branch M(m, 0) to straight line AP is1.
(i) If the slope of the straight line AP is k and the range of the real number m;
(ii) When the heart of Δ δAPQ happens to be point m, find the equation of this hyperbola.
Solution: (1) Get the equation of straight line AP from conditions.
that is
Because the distance from m point to straight AP is 1,
That is.
∵ ∴
The solution is+1≤m≤3 or-1 ≤ m ≤ 1-.
The value range of ∴m is
(ii) Based on hyperbolic equation.
Yes
And because m is the heart of δAPQ, the distance from m to AP is 1, so ∠MAP=45? The straight line AM is the bisector of ∠PAQ, and the distance from m to AQ and PQ is 1. Therefore, (we set p in the first quadrant).
The linear PQ equation is.
Equation y of straight AP = x-1,
The coordinate of ∴p is (2+, 1+), and it is substituted into the coordinate of point p.
So the hyperbolic equation is
that is
(2) Skip the answer
Problem solving cards are common in a transitional link. At this time, you can admit the intermediate conclusion first, and then push it backwards to see if you can draw a conclusion. If you can't get it, prove that this road is wrong and change direction immediately; If you can reach the expected conclusion, you can come back and concentrate on conquering this "halfway point". Due to the time limit of the college entrance examination, it is too late to conquer the "halfway point". You can write down the previous one and then write "Prove that after a certain step, there will be ...". Perhaps, later, the intermediate step was thought out again. At this time, don't make it up at random, but make it up later, which can be written as "In fact, a certain step can be proved as follows."
Some problems may have multiple problems, and the first problem cannot be solved. You can think of the first question as known, and do the second question first, which is also a solution to skip the question.
Example: (Tianjin Wenke Topic 18, 2004) Choose 3 boys and 2 girls to participate in the speech contest.
(i) Find out the probability that all three selected people are boys;
(2) Find the probability that there are exactly 1 girls among the selected three people;
(3) Find the probability that there are at least 1 girls among the three selected people.
Solution: (1) The probability that all three people are boys is
(2) The probability that there are exactly 1 girls among the three selected people is
(3) The probability that there are at least 1 girls among the selected 3 people is
These three questions can be said to be independent of each other, so if you can't do the question of 1, you can skip and do the second question directly.
(3) Reverse solution
"Retreat for progress" is an important problem-solving strategy. If you can't solve the problems raised in the question, then you can take a step back from the general to the special, from the complex to the simple, and from the whole to the part. In short, retreat to a problem that you can solve. For example, {an} is a geometric series whose common ratio is q, and Sn is the sum of the first n terms of {an}. If Sn becomes arithmetic progression, find the common ratio Q = _ _ _.
For geometric series, we need to consider two cases: q= 1 and q≠ 1. We can discuss the significance of special q= 1 satisfying the problem first, and then discuss whether q≠ 1 also satisfies the problem after finding the solution and emotional stability.
Maybe you can only complete one situation, but you didn't replace the subject with one situation. It is clear in concept and logic. In addition, "too difficult to do simple" also provides meaningful inspiration for finding correct and universal problem-solving methods.
4. Auxiliary solution
A complete solution to the problem requires not only big substantive steps, but also small auxiliary steps, such as: drawing accurately, transforming the conditions in the problem into mathematical expressions, setting the unknown quantity in the application problem, the range of variables in the function, the coordinates of moving points in the trajectory problem, and proving the value of n in the first step by mathematical induction. If handled properly, it will also add points. Don't underestimate it.
In addition, writing is also an auxiliary answer, and random alteration of the paper and unreasonable position of the correct answer will cause unnecessary loss of points.
Therefore, some people say that it is not unreasonable to write neatly and share neatly.