Go back to the year of the high school entrance examination
Chapter 110 Math Difficult Math Problems
Before the math test in the afternoon, there was a sudden heavy rain. The weather was fine in the morning, but the rain immediately cooled down. The rain splashed into the corridor, so be careful when wearing slippery shoes.
Ji Shi fell asleep on the table for a while. Ten minutes before the exam started, he and Yao Meng walked to the exam room together. When they arrived, the exam room was almost full.
The invigilator also came quite early, put down the bag when the class was due, and handed out the math test papers.
Ji Shi took a piece of tissue paper and put it on the corner of the table. He felt that the table was a bit unstable during the Chinese test in the morning. It dangled during the test. In the afternoon, he had a lot of time to think about mathematics, so Ji Shi didn't want to be disturbed by the table. interference.
The unified volume was issued ahead of schedule.
Ji Shi put the draft paper aside, and started to write from the fill-in-the-blank questions with his eyes focused. The college entrance examination in Suzhou Province has not been reformed for a few years. When they were freshmen in high school, the exam still had multiple-choice questions, and later it gradually changed to only fill-in-the-blank questions.
This method has advantages and disadvantages. In short, it eliminates the possibility of cheating, but the fun of the exam is completely gone. Filling in the blanks is actually a calculation problem. Each question has to be calculated step by step. It takes a test Can make people tired enough to choke.
Overall, the fill-in-the-blank questions in this test paper are not difficult. Ji Shi went from question 1 to question 14, and he didn't encounter any questions that made him stop and think repeatedly. It was quite easy for Ji Shi to identify these pits.
Not only is he like this, he believes that all the students in the first examination room should be like this.
In the examination room, there was only the rustling of papers being turned. Everyone was staring at the papers intently. No one looked up. A pen was quickly doing calculations on the draft paper.
The atmosphere of the examination room is different from the atmosphere of the self-study. During the self-study, Ji Shi's mood is very calm, but in the examination room, he will suddenly feel a sense of tension, but this tension will not affect him to do the questions The efficiency is a kind of propulsion instead.
A sense of competition.
……
If the fill-in-the-blank questions were not too difficult, then the difficulty would naturally lie in the big questions. Ji Shi guessed this way, and the results were similar.
After all, it’s the second semester of the third year of senior high school, so there’s no need for the teacher to fool them with some simple test papers. After all, it’s impossible for the college entrance examination to be easy every year, but the difficulty of the test papers is generally distributed. It’s not interesting if they are all difficult questions. 160 points If the total score is less than 96 points in the test, can the gap be reflected?
This is obviously a dream too.
When Ji Shi did the first big question, he felt that something was wrong.
Especially when he just came out of the joy of filling in the blanks, he was a little uncomfortable when he suddenly encountered a big question.
Ji Shi took a deep breath to calm himself down.
Get it up!
The first big question is a geometry question. Ji Shi has always felt that the geometry questions that need to be demonstrated are a little easier than the algebra questions. Of course, geometry questions can be scored if you can think of a breakthrough, but if you can’t think of it, there is no way no matter how hard you try. I can only sit there and leave the questions empty. Algebra is a little better at this point, and maybe I can get a score or two according to the steps.
Ji Shi and the others had an exam before, and it seemed that the math was particularly difficult. It was said that as long as they wrote an answer, the teacher would give them one or two points. It will not appear in the college entrance examination, but he is doing the questions now, regardless of whether he will or not, first put the word "solution" on it and then talk about it.
Fortunately, this geometry argument question is the first one. Although the content is not very simple, you can still come up with the steps to solve the problem after careful consideration. Maybe the teachers don't want them to stumble on the first question, otherwise the first question will be difficult. With a bunch of points deducted, how can I answer the following questions?
After writing the first big question, Ji Shi's expression softened a little.
He continued to look at the second question, and there were actually three small questions in the second question, which is rare in their usual monthly exams. Generally speaking, the first few questions of the big question only have two small questions, and only the last question Or two questions will have three small questions.
To a certain extent, this is also the gentleness of the teacher who produced the paper.
The last question is usually worth 15 points, and the three small questions are worth 5 points. Those who have a similar foundation can answer 5 points. Even if they are better, there are many students who can answer 10 points. As for the students who can answer 15 points, there are not many students. , but at least most people can get scores, but once it is changed to two small questions, 7 points for each question, the difficulty of the first question will increase, and students who are slightly weak in mathematics may not get a point.
But in this exam, the first two, three, and four big questions are all three small questions, and the last five and six big questions are two small questions.
It's just... a little too much.
But Ji Shi estimated that the teachers just wanted to show the gap through the big questions. After all, the difficulty of filling in the blanks this time is really a bit small, and at least half of the students can get full marks.
In Z Middle School, it is very common to fail mathematics in the first and second grades of high school. There are about a dozen people in a class who fail in mathematics. Those students who are bad at mathematics can't pass no matter how difficult the test paper is.
This has something to do with the second and third grades gradually adapting to the mathematics teaching model, and because the second and third grades are closer to the college entrance examination, the teachers pay great attention to the distribution of difficulty when they issue papers.
Like this test paper, as long as you can get 70 points for the fill-in-the-blank questions, you only need to know two of the remaining big questions to pass.
Of course, for the students in the first examination room, the requirement of passing is contempt, and each of them will only strive for full marks.
Ji Shi is the same.
When he saw the first big question, he was already mentally prepared.
The time in the examination room is limited, he must not only allocate the time reasonably, but also get all the marks he can get on this basis.
After thinking for a few minutes on the second big question, I finally solved it without any obstacles.
Next is the third question.
The rain made the sky outside gloomy, and the lights were turned on in the examination room, but Ji Shi did not raise his head during this time, his eyes were focused on the test paper, nothing else was in his mind, and his eyes kept moving with the tip of the pen , In this process, he has to make sure that every step he writes is correct.
Because time is limited, he can't make basic mistakes, especially copying wrong numbers, which is the most time-consuming.
"Because l corresponds to..., so..."
After solving another problem, Ji Shi didn't even have time to take a deep breath. He immediately moved his gaze down to the next problem.
The moment he saw this question, Ji Shi couldn't help shouting "Yeah" in his heart.
Coincidentally, he just did this question last week, and the question itself is not difficult. I am afraid it was put up by the teachers for adjustment.
The current test-exam teachers are more scary than the other. They know that students are used to doing questions from easy to difficult, so they deliberately put the difficult questions in the front and put the easy ones in the back, waiting for the students to be overwhelmed by the previous questions , I didn't bother to read the following questions.
This question saved Ji Shi a lot of time. He almost didn't think much about it. He completed the whole question in one go, and quickly filled the answer sheet.
Of course, this kind of thing is only encountered once in ten times, and it is rare to encounter questions that have been done before in the college entrance examination. References overlap.
Their teachers often describe the situation of the college entrance examination papers to them. The teacher who produced the papers was locked up and stayed in one place to write questions. It was quite dark, so they couldn't help thinking, the reason why the college entrance examination questions can be so perverted, It must be because the teacher who produced the papers suffered inhuman torture.
There is still half an hour left for Ji Shi to finish the last two major questions, which is basically the same as the time left in his final exam, but this time is already quite tight, mainly because of the time he spent on the first few questions Too much.
He doesn't know what will happen when the college entrance examination meets the mathematician's paper, and he doesn't know if he can finish the questions, but he hopes to maintain the rhythm of the usual monthly exams, even if he can't finish the last big question, it's better than not writing it better.
The last two big questions this time are really difficult.
Ji Shi was not lucky this time either.
In the previous monthly exams, he was inspired to solve the questions at the last moment, but this time, after thinking for a long time, he still couldn't solve the second question of the last question. Half of the time is not enough, because he has no ideas at all, so he can only leave the topic empty.
When the invigilator came to collect the test papers, Ji Shi was still reluctant to part with that question. Even after the invigilator had already collected the test papers, Ji Shi still sat there for a while, sketching on the draft paper, recalling the past. According to the requirements of the question, see if you can write a few more steps.
Fortunately, the difficulty of answering the additional questions later was not particularly difficult, so Ji Shi answered it from beginning to end.
When the exam was over, Ji Shi was still sitting there, not wanting to move for a while.
Until Yao Meng came to call him: "Aren't you going back?"
"Oh." Ji Shicai suddenly came back to his senses, "Let's go now. I didn't solve the last question, and I'm only thinking about that question right now."
"I didn't solve it either." Across a row of seats, Xu Lang sighed, "I thought it was quite smooth when I did the fill-in-the-blank questions, but when it came to the big questions, my brain was about to explode."
"Who isn't?" Yao Meng shrugged, "Fortunately, I gave up the second-to-last question in time, otherwise I wouldn't have time to write the last question."
"The teachers in the mathematics teaching and research group are becoming less and less friendly." Xu Liang sighed with emotion.
His grade ranking this time was much better than Ji Shi's, it seemed to be 10th, but because he didn't get too many marks in mathematics at the end of the semester, his total score didn't make it into the top 5 in the grade.
The positions of the top 10 in the two intensive classes are also unstable, and they basically take turns taking turns. Occasionally, students who rank after 30 in the class suddenly rush to the top 5. This has to do with the difficulty of each subject and the tightness of the teacher's grades. Relationship, if the teacher corrects loosely, the score difference will be small, and the degree of differentiation will not be reflected, and students with lower grades will rush to the front.
"Are you doing self-study in the classroom at night?" Yao Meng asked Ji Shi, "Let's study the last question together."
"Okay." Ji Shi took out his phone, "I'll call Zhou Weile."
"it is good."
This semester has become more and more arrogant, and they bring their mobile phones directly into the classroom, but more and more students are doing this, and the teachers basically turn a blind eye to it. No, the psychological pressure of senior high school students is the greatest in three years. If you are under a lot of pressure in study, you should relax your life.
Sure enough, Zhou Weile didn't leave either, and he agreed as soon as Ji Shi called. He said that he couldn't solve the last problem either.
"Since neither Xu Liang nor Zhou Di can figure it out, it's normal that we can't figure it out."
"This can only comfort myself?" Huang Yaqiong sighed, "I will be sad every time I take a math test. I don't know how you people who can keep the deductions below 10 points do it."
"I can't control it this time." Yao Meng sighed, "I left two empty questions on the last two questions, so I should deduct 14 or 5 points, right?"
"Not at all?"
"The penultimate question is better. I wrote a few steps, but the last question is just empty."
"Time is too tight." Ji Shi took out the draft paper, "I remember that question was asked like this, do you remember?"
Everyone gathered at his table, and wrote down the requirements of the topic on the draft paper when reading the diary. The topic was quite long, and it was not easy to recall. It took a few minutes for everyone to spell the topic completely. out.
"That's about it."
"Let's solve it."
There is more than enough time in the classroom, and Ji Shi doesn't have to worry about the teacher coming to collect the papers, so his state is much more relaxed than in the examination room.
But this question is indeed difficult, and it will be difficult to figure out how to solve it for a while.
Ji Shi calculated on the draft paper for a while, his expression was very serious the whole time, and he didn't care about the progress of other people, he devoted himself to this question with all his heart.
When it was time for dinner, he had only a few thoughts.
"Have you figured it out yet?"
"Nope." Zhou Weile complained, "So it's unreasonable for this kind of question to appear on the monthly exam paper. Which day will it be able to solve it?"
"When the teacher came up with the paper, he never thought of asking you to solve this question." Huang Yaqiong was determined.
"Pervert." Zhou Weile held his head, "If I don't get full marks, my life will be meaningless."
Everyone couldn't help but look sideways: "Can you stop pretending? It's too fake."
Ji Shi fell asleep on the table for a while. Ten minutes before the exam started, he and Yao Meng walked to the exam room together. When they arrived, the exam room was almost full.
The invigilator also came quite early, put down the bag when the class was due, and handed out the math test papers.
Ji Shi took a piece of tissue paper and put it on the corner of the table. He felt that the table was a bit unstable during the Chinese test in the morning. It dangled during the test. In the afternoon, he had a lot of time to think about mathematics, so Ji Shi didn't want to be disturbed by the table. interference.
The unified volume was issued ahead of schedule.
Ji Shi put the draft paper aside, and started to write from the fill-in-the-blank questions with his eyes focused. The college entrance examination in Suzhou Province has not been reformed for a few years. When they were freshmen in high school, the exam still had multiple-choice questions, and later it gradually changed to only fill-in-the-blank questions.
This method has advantages and disadvantages. In short, it eliminates the possibility of cheating, but the fun of the exam is completely gone. Filling in the blanks is actually a calculation problem. Each question has to be calculated step by step. It takes a test Can make people tired enough to choke.
Overall, the fill-in-the-blank questions in this test paper are not difficult. Ji Shi went from question 1 to question 14, and he didn't encounter any questions that made him stop and think repeatedly. It was quite easy for Ji Shi to identify these pits.
Not only is he like this, he believes that all the students in the first examination room should be like this.
In the examination room, there was only the rustling of papers being turned. Everyone was staring at the papers intently. No one looked up. A pen was quickly doing calculations on the draft paper.
The atmosphere of the examination room is different from the atmosphere of the self-study. During the self-study, Ji Shi's mood is very calm, but in the examination room, he will suddenly feel a sense of tension, but this tension will not affect him to do the questions The efficiency is a kind of propulsion instead.
A sense of competition.
……
If the fill-in-the-blank questions were not too difficult, then the difficulty would naturally lie in the big questions. Ji Shi guessed this way, and the results were similar.
After all, it’s the second semester of the third year of senior high school, so there’s no need for the teacher to fool them with some simple test papers. After all, it’s impossible for the college entrance examination to be easy every year, but the difficulty of the test papers is generally distributed. It’s not interesting if they are all difficult questions. 160 points If the total score is less than 96 points in the test, can the gap be reflected?
This is obviously a dream too.
When Ji Shi did the first big question, he felt that something was wrong.
Especially when he just came out of the joy of filling in the blanks, he was a little uncomfortable when he suddenly encountered a big question.
Ji Shi took a deep breath to calm himself down.
Get it up!
The first big question is a geometry question. Ji Shi has always felt that the geometry questions that need to be demonstrated are a little easier than the algebra questions. Of course, geometry questions can be scored if you can think of a breakthrough, but if you can’t think of it, there is no way no matter how hard you try. I can only sit there and leave the questions empty. Algebra is a little better at this point, and maybe I can get a score or two according to the steps.
Ji Shi and the others had an exam before, and it seemed that the math was particularly difficult. It was said that as long as they wrote an answer, the teacher would give them one or two points. It will not appear in the college entrance examination, but he is doing the questions now, regardless of whether he will or not, first put the word "solution" on it and then talk about it.
Fortunately, this geometry argument question is the first one. Although the content is not very simple, you can still come up with the steps to solve the problem after careful consideration. Maybe the teachers don't want them to stumble on the first question, otherwise the first question will be difficult. With a bunch of points deducted, how can I answer the following questions?
After writing the first big question, Ji Shi's expression softened a little.
He continued to look at the second question, and there were actually three small questions in the second question, which is rare in their usual monthly exams. Generally speaking, the first few questions of the big question only have two small questions, and only the last question Or two questions will have three small questions.
To a certain extent, this is also the gentleness of the teacher who produced the paper.
The last question is usually worth 15 points, and the three small questions are worth 5 points. Those who have a similar foundation can answer 5 points. Even if they are better, there are many students who can answer 10 points. As for the students who can answer 15 points, there are not many students. , but at least most people can get scores, but once it is changed to two small questions, 7 points for each question, the difficulty of the first question will increase, and students who are slightly weak in mathematics may not get a point.
But in this exam, the first two, three, and four big questions are all three small questions, and the last five and six big questions are two small questions.
It's just... a little too much.
But Ji Shi estimated that the teachers just wanted to show the gap through the big questions. After all, the difficulty of filling in the blanks this time is really a bit small, and at least half of the students can get full marks.
In Z Middle School, it is very common to fail mathematics in the first and second grades of high school. There are about a dozen people in a class who fail in mathematics. Those students who are bad at mathematics can't pass no matter how difficult the test paper is.
This has something to do with the second and third grades gradually adapting to the mathematics teaching model, and because the second and third grades are closer to the college entrance examination, the teachers pay great attention to the distribution of difficulty when they issue papers.
Like this test paper, as long as you can get 70 points for the fill-in-the-blank questions, you only need to know two of the remaining big questions to pass.
Of course, for the students in the first examination room, the requirement of passing is contempt, and each of them will only strive for full marks.
Ji Shi is the same.
When he saw the first big question, he was already mentally prepared.
The time in the examination room is limited, he must not only allocate the time reasonably, but also get all the marks he can get on this basis.
After thinking for a few minutes on the second big question, I finally solved it without any obstacles.
Next is the third question.
The rain made the sky outside gloomy, and the lights were turned on in the examination room, but Ji Shi did not raise his head during this time, his eyes were focused on the test paper, nothing else was in his mind, and his eyes kept moving with the tip of the pen , In this process, he has to make sure that every step he writes is correct.
Because time is limited, he can't make basic mistakes, especially copying wrong numbers, which is the most time-consuming.
"Because l corresponds to..., so..."
After solving another problem, Ji Shi didn't even have time to take a deep breath. He immediately moved his gaze down to the next problem.
The moment he saw this question, Ji Shi couldn't help shouting "Yeah" in his heart.
Coincidentally, he just did this question last week, and the question itself is not difficult. I am afraid it was put up by the teachers for adjustment.
The current test-exam teachers are more scary than the other. They know that students are used to doing questions from easy to difficult, so they deliberately put the difficult questions in the front and put the easy ones in the back, waiting for the students to be overwhelmed by the previous questions , I didn't bother to read the following questions.
This question saved Ji Shi a lot of time. He almost didn't think much about it. He completed the whole question in one go, and quickly filled the answer sheet.
Of course, this kind of thing is only encountered once in ten times, and it is rare to encounter questions that have been done before in the college entrance examination. References overlap.
Their teachers often describe the situation of the college entrance examination papers to them. The teacher who produced the papers was locked up and stayed in one place to write questions. It was quite dark, so they couldn't help thinking, the reason why the college entrance examination questions can be so perverted, It must be because the teacher who produced the papers suffered inhuman torture.
There is still half an hour left for Ji Shi to finish the last two major questions, which is basically the same as the time left in his final exam, but this time is already quite tight, mainly because of the time he spent on the first few questions Too much.
He doesn't know what will happen when the college entrance examination meets the mathematician's paper, and he doesn't know if he can finish the questions, but he hopes to maintain the rhythm of the usual monthly exams, even if he can't finish the last big question, it's better than not writing it better.
The last two big questions this time are really difficult.
Ji Shi was not lucky this time either.
In the previous monthly exams, he was inspired to solve the questions at the last moment, but this time, after thinking for a long time, he still couldn't solve the second question of the last question. Half of the time is not enough, because he has no ideas at all, so he can only leave the topic empty.
When the invigilator came to collect the test papers, Ji Shi was still reluctant to part with that question. Even after the invigilator had already collected the test papers, Ji Shi still sat there for a while, sketching on the draft paper, recalling the past. According to the requirements of the question, see if you can write a few more steps.
Fortunately, the difficulty of answering the additional questions later was not particularly difficult, so Ji Shi answered it from beginning to end.
When the exam was over, Ji Shi was still sitting there, not wanting to move for a while.
Until Yao Meng came to call him: "Aren't you going back?"
"Oh." Ji Shicai suddenly came back to his senses, "Let's go now. I didn't solve the last question, and I'm only thinking about that question right now."
"I didn't solve it either." Across a row of seats, Xu Lang sighed, "I thought it was quite smooth when I did the fill-in-the-blank questions, but when it came to the big questions, my brain was about to explode."
"Who isn't?" Yao Meng shrugged, "Fortunately, I gave up the second-to-last question in time, otherwise I wouldn't have time to write the last question."
"The teachers in the mathematics teaching and research group are becoming less and less friendly." Xu Liang sighed with emotion.
His grade ranking this time was much better than Ji Shi's, it seemed to be 10th, but because he didn't get too many marks in mathematics at the end of the semester, his total score didn't make it into the top 5 in the grade.
The positions of the top 10 in the two intensive classes are also unstable, and they basically take turns taking turns. Occasionally, students who rank after 30 in the class suddenly rush to the top 5. This has to do with the difficulty of each subject and the tightness of the teacher's grades. Relationship, if the teacher corrects loosely, the score difference will be small, and the degree of differentiation will not be reflected, and students with lower grades will rush to the front.
"Are you doing self-study in the classroom at night?" Yao Meng asked Ji Shi, "Let's study the last question together."
"Okay." Ji Shi took out his phone, "I'll call Zhou Weile."
"it is good."
This semester has become more and more arrogant, and they bring their mobile phones directly into the classroom, but more and more students are doing this, and the teachers basically turn a blind eye to it. No, the psychological pressure of senior high school students is the greatest in three years. If you are under a lot of pressure in study, you should relax your life.
Sure enough, Zhou Weile didn't leave either, and he agreed as soon as Ji Shi called. He said that he couldn't solve the last problem either.
"Since neither Xu Liang nor Zhou Di can figure it out, it's normal that we can't figure it out."
"This can only comfort myself?" Huang Yaqiong sighed, "I will be sad every time I take a math test. I don't know how you people who can keep the deductions below 10 points do it."
"I can't control it this time." Yao Meng sighed, "I left two empty questions on the last two questions, so I should deduct 14 or 5 points, right?"
"Not at all?"
"The penultimate question is better. I wrote a few steps, but the last question is just empty."
"Time is too tight." Ji Shi took out the draft paper, "I remember that question was asked like this, do you remember?"
Everyone gathered at his table, and wrote down the requirements of the topic on the draft paper when reading the diary. The topic was quite long, and it was not easy to recall. It took a few minutes for everyone to spell the topic completely. out.
"That's about it."
"Let's solve it."
There is more than enough time in the classroom, and Ji Shi doesn't have to worry about the teacher coming to collect the papers, so his state is much more relaxed than in the examination room.
But this question is indeed difficult, and it will be difficult to figure out how to solve it for a while.
Ji Shi calculated on the draft paper for a while, his expression was very serious the whole time, and he didn't care about the progress of other people, he devoted himself to this question with all his heart.
When it was time for dinner, he had only a few thoughts.
"Have you figured it out yet?"
"Nope." Zhou Weile complained, "So it's unreasonable for this kind of question to appear on the monthly exam paper. Which day will it be able to solve it?"
"When the teacher came up with the paper, he never thought of asking you to solve this question." Huang Yaqiong was determined.
"Pervert." Zhou Weile held his head, "If I don't get full marks, my life will be meaningless."
Everyone couldn't help but look sideways: "Can you stop pretending? It's too fake."
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