Go back to the year of the high school entrance examination

After the test papers were handed out, there was a slight sound of flipping the test papers in the examination room. Ji Shi noticed that everyone's expressions were very calm at this moment, and some people rubbed their hands lightly, using small movements to resolve the uneasiness before the test.

Although I have already spent two and a half hours in the same examination room in the morning, mathematics and Chinese are still different after all. For their science students, mathematics scores are higher, and it is almost a must for them to beat their opponents in the college entrance examination examination room place.

After the exam bell rang, answering began.

The first few questions belong to the types of questions they usually take in the monthly exams, functions and sets, and a probability test. The fourth question involves intervals. From this question, Ji Shi felt that this year's college entrance examination Mathematics is indeed more difficult than their usual monthly exam questions.

In other words, it is the feeling that the topic is more lively, such as the fourth question, their teachers generally would not think of using graphs to show the frequency distribution.

The difficulty of the first 6 questions was still barely high, and Ji Shi did it fairly smoothly, but he didn't feel at ease because of this. Anyway, his mathematics has always been ranked well in Z. If a few fill-in-the-blank questions can stump him, What did he learn this year?

Later, Ji Shi wrote two more questions. The amount of calculation for these two questions was not small, and carefulness was also very important. Ji Shi wrote while looking at the time displayed by the clock, which indeed took him longer than his usual monthly exam.

As I wrote, Ji Shi became more involved.

In his mind, he no longer thinks about which teacher issued this test paper, and he no longer struggles with whether this test paper is easy or difficult. Caring about such things has no effect, but will make him hesitate.

He just needs to do what he did in every previous exam, to perform to the level he should have, and to show the results of his study in the third year of high school.

Just let yourself have no regrets.

I wrote a total of 10 fill-in-the-blank questions. Up to now, Ji Shi has not encountered a question that is really difficult for him to write. It can only be said that there is no one-step question in this test paper. Almost every question has to be carefully thought out. I think, I need to change my thinking and learn to transform. Of course, for him, these questions are relatively new forms. Fortunately, Ji Shi usually does enough questions, and the types of questions he is exposed to are quite rich.

The following questions are either clever in thinking, or the amount of calculation is relatively large, and there are no sub-questions, so it is really not smooth to solve.

Ji Shi struggled with the last two fill-in-the-blank questions for a while. He looked at question 13 first. He had no train of thought and stopped first. Then he went to question 14. He drew the picture on the draft paper, and then went slowly. calculate.

He was already mentally prepared for the difficulty of the questions, at least he had already answered many questions before, Ji Shi felt that he only had to do his best to do the questions he knew first, get the points he should get, and then slowly answer the questions later. sprint.

Fortunately, the second model produced a very difficult test paper, so difficult that now I am very relaxed when I do the college entrance examination papers.

Although the questions were difficult, he didn't have time to think about them. He didn't hesitate to do the questions he could do and the questions with ideas. Instead, he increased his speed while ensuring the correct rate.

This test paper is quite time-consuming. If you spend too much time on filling in the blanks, you will never have enough time for the subsequent calculation questions.

After writing the 14th question of Ji Shi, he turned to look at the 13th question. Unfortunately, he still has no idea so far, so he can only skip this question first.

Their teacher also emphasized before the exam that they should work out the questions first, and don’t be too persistent on the questions that they have no idea. Every minute in the exam room is precious. They should allocate time reasonably and improve the performance of each minute. cost-effective.

Ji Shi vaguely noticed that the examination room was already restless.

Although no one made a sound, the sound of the test paper being turned was much louder than during the Chinese test in the morning. Under the influence of this emotion, the sound of the invigilator's shoes seemed to be amplified.

Ji Shi continued to concentrate on answering the questions.

The amount of calculation for filling in the blanks was a bit heavy, and he spent more time than the usual monthly exams, so correspondingly, the time allocated to answering the questions was naturally less.

He flipped through the test paper quickly, and just after reading the questions, he wrote a solution on the answer sheet. The first question was okay, he knew how to write it after reading it, and time did not allow him to continue dawdling on the draft paper. , Ji Shi simply answered on the answer sheet.

The amount of questions in this question is not large, and there are not many steps. It is enough to calculate the length of the two diagonals and calculate a value.

next question.

Ji Shi really has the mentality of clearing the boss. Every time he solves a problem, he feels that he has completed a major project. Of course, he also has a sense of excitement in his heart.

After all, it is the examination room of the college entrance examination, so it is completely impossible not to be excited, right?

The math test more or less needs some passion.

What's more, he is very aware of the difficulty of this test paper. In this case, he should not be overwhelmed by the difficulty, but should face this test with a more energetic state.

He can.

The next question is a geometry proof question. The first question asks to prove that two lines are perpendicular, and the second question asks for the distance from a point to a plane.

Geometry proof questions will be given in every exam, and it doesn't take long for Ji Shi. On such questions that can be solved, Ji Shi has always been very focused. He can't make mistakes on this kind of questions, and he can't solve them. To waste time, no matter which exam it is, the time left for them for the final big question is always very limited.

But Ji Shi was no longer nervous.

The amount of calculations for the next two big questions is not small, especially the penultimate question. He suspects that the teacher who wrote this question deliberately used up their time to waste their time. The type of questions will not make people feel happy, and the more you write, the more you will feel more and more irritable.

The huge amount of questions and the clock on the blackboard became a reminder.

But he has to hold on.

Ji Shi already belongs to the kind of student who has a good foundation in mathematics, but he still feels the urgency of time. Fortunately, his practice of increasing his speed has really worked. , Of course, these are not the most important, the most important thing is thinking, it is natural to come up with an answer quickly, without thinking, no matter how fast your hand is, it is useless.

Finally, Ji Shi finished writing question 18, and came to questions 19 and 20.

Relying on his weak impression of the college entrance examination, these two questions are not easy. Anyway, after they finished the exam, many people said that the major questions of the college entrance examination were beyond the outline, and some people swore that the windows of the teacher's house were closed. Got smashed by angry parents and students.

Among the student community, this statement is widely circulated, and it is deeply believed.

Thinking about it carefully, it is generally impossible for a teacher to complete the college entrance examination papers independently. The monthly exam papers of their school are all the collective results of the mathematics teaching and research group, and the college entrance examination papers should not be made by one person.

Question 19 really made Ji Shi a little stuck.

This is a sequence question. The key point is that the sequences they usually do are a1a2, S1S2 and the like. This question directly gives the sequence a root sign, which... fully reflects the fierce temperament of the college entrance examination.

The next Mawei is coming, and then the Zhongmawei and Shangmawei?

Fortunately, the first question was kind. It is estimated that the teacher did not intend to let them get a zero for a question, but he wanted to give some points.

"Prove that the maximum value of c is..."

Ji Shi murmured silently in his heart, but the nib of his pen kept writing. In fact, the amount of solution to this question is less than that of the previous question, but the key is to have ideas.

Ji Shi struggled for a while.

Looking at the clock above the blackboard, he inevitably began to feel a sense of tension.

There are only 25 minutes left, and he still has a big question and a small question unanswered.

He knew that in this examination room, he was definitely one of the students who answered the most questions, but even so, he could still appreciate the power of this math test paper.

Have!Ji Shi narrowed his eyes, he already had an idea for this question, once he figured it out, this question was originally a troublesome one in his mind, the kind that made him confused, but after solving it now, Ji Shi discovered that the steps for this question are very short, and the key is to find the point.

By this time, Ji Shi was completely relieved.

There are still 20 minutes left in the exam, and he still has a big question to answer. This question is worth 16 points. In addition to the previous fill-in-the-blank question, he has not done the question worth 21 points.

Ji Shi couldn't guarantee that he got all 140 points correct, but the correct rate would never be too low. This is his experience in so many exams.

Taking a deep breath, Ji Shi went straight to the last big question.

Just by looking at the question, you can feel how troublesome this question is, but no matter whether it is troublesome or not, this is the last math test paper in his high school career, and it is his fate that he cannot escape.

What else can I do?

What should be written still needs to be written, Ji Shi will never let the score run away from him.

First of all, you have to write down the explanation. Maybe when it’s time to correct the test paper, the teacher who corrects the test paper finds that the score of this test paper is not good. For the sake of the candidates, can you give the score even if you write the solution?

Ji Shi caught the big and the small, and he would not let go of the possibility of scoring points.

This question is said to have two questions, but the first question also includes two small questions, which means that there are a total of three small questions to be answered. The first small question is a proof question. This question is not difficult. it came out.

4 points to hand.

Ji Shizhen felt that the teacher was a bit picky about the exam. Two questions were made into three questions. The first two small questions were only worth 8 points, and the second most difficult question was also worth 8 points. The score was too high.

The first question and the second question took several minutes, mainly because the process should be discussed on a case-by-case basis, not a single answer.

There is only one last question left.

The reminder sound of the examination room radio had already sounded, and the moment the radio sounded, the already agitated examination room became louder. From the seat Ji Shi was sitting in, he could hear the rattling of the test papers in the back row, as well as faint sobs.

That's right, there was indeed someone crying in their examination room, although he didn't know who that person was.

But Ji Shi didn't want to pay attention to other people's affairs. He first turned the test paper to question 13 and filled in the blanks. After being sharpened by the big questions, it seemed that it would not be so troublesome to come back and look at the multiple-choice questions.

But it still took Ji Shi a few minutes to smooth out the train of thought for this fill-in-the-blank question. When he filled in the answer on the answer sheet, there were 6 minutes left in the exam.

The last big question is absolutely too late.

When Ji Shi saw the last big question, he knew it was difficult, because it had x1x2, m, α and β, and it was difficult to straighten out the question just by reading it once.

If it is in the monthly exam, you may give up when you see this kind of question paper, because it is too time-consuming, and you can never finish writing.

But now it is the college entrance examination, and the other questions are almost written. He doesn't need to save time to do other questions, he can deal with this question until the last moment.

Ji Shi read the question carefully, first copied down the formula in the question, and then wrote it according to the nature of f(x) in the question stem. Anyway, he would definitely not be able to solve it all. He also relaxed a little and was able to write How much is how much, can get 1 point is 1 point, whatever.

Ji Shi was writing quickly on the answer sheet. In fact, his train of thought was not smooth for the time being, but he wrote everything he could think of on the answer sheet. Anyway, the answer sheet was large enough, so he might not have room to write it. I'm trying my luck to see if what I wrote touches a certain point of the answer.

It's a pity that he only wrote a few lines before the exam bell rang.

Next is the additional questions section.

Ji Shi didn’t have any impression of the additional questions. 21 questions were optional, and the four ABCD questions given were not too difficult. Ji Shi chose two question types that he was usually better at, and hurriedly finished writing them.

He couldn't remember whether the extra questions this year were easy or difficult, but he felt that the unified papers were all produced in that way, and the teacher who produced the extra questions might not be too kind. Anyway, he would write the questions he knew first Alright, buy time for the next questions.

Question 22 is a purely calculation question, and the amount of calculation is not bad. Ji Shi is not afraid of doing this kind of question, because he is not afraid of doing calculations, and he is also careful in calculation. The usual mistakes in calculation questions are the calculation process. Zhou Weile will occasionally do this kind of question Lost points in the game, but basically not like this in Ji Shi.

Question 23...

how to say?It is true that he has never done the problem of proving that cosA is a rational number, but the person who made the test did it like this.

However, he had just finished the unified paper, and when he wrote the additional questions, the first two questions were relatively simple, which surprised Ji Shi a little. For one question, Ji Shi immediately... As expected of you, as worthy of 2010.

This question is really not easy. When Ji Shi wrote it, he was not sure whether he could prove it. The main reason was that the angle of the question was too tricky, and ordinary teachers would not test it this way.

In the end, he was not sure whether his proof process was correct.

But what should be written still needs to be written, Ji Shi kept writing with this uncertain state of mind until the exam bell rang again.

After putting down his pen, Ji Shi didn't dare to write any more, because writing at this time could be judged as cheating, but in the examination room, after the bell rang, there were still many people who didn't put down their pens. After the invigilator reminded them , everyone reluctantly put down their pens.

Compared with the state after the Chinese test in the morning, the mathematics in the afternoon is completely gloomy.

Even after the invigilator collected the test papers and reminded them that they could leave the examination room, many people still sat in the examination room with stiff expressions.

They guessed many kinds of situations during the college entrance examination, but they didn't expect that mathematics would end up in this situation. When doing this test paper, they even felt that their three years of high school were completely wasted.

If not, why are they only at a loss when they see those topics?