Zhang Xiaoli started the lecture: "We will start with the summary of wrong questions today - assembly.
Sets are a piece of mathematical knowledge that is both simple and error-prone. Let me emphasize the knowledge of sets again.
First, we need to understand the classification of collections.
If sets are classified according to the number of elements, they can be divided into finite sets, infinite sets, and empty sets.
I emphasize here again: the empty set is a subset of any set. In classification questions, you must not ignore this empty set.
Many students tend to make mistakes here.
This knowledge point is often used in multiple-choice questions. Generally, the questions will not directly ask about the classification of sets, but will give you 3 to 5 sets for you to classify.
Next, let’s take a look at this question that everyone easily gets wrong.
Zhang Xiaoli wrote the topic quickly, and she did not go on to talk about it...
"Which student is willing to come up and give a demonstration?" Zhang Xiaoli asked.
When Zhang Xiaoli lectures, she will ask students to do the mistakes they make when she talks about them.
First, you can know how this classmate does the questions and what his ideas are.
Secondly, if one classmate makes a mistake, others may also make it.
She told a classmate in front of the whole class, or maybe the whole class, who also made the same mistake.
"Teacher, Gu Xu is willing!" Yang Wanli said.
"Yes, Gu Xu!" Other students who stood with Yang Wanli followed suit.
Gu Xu saw it.
In this exam, his scores improved by leaps and bounds, and many classmates couldn't stand him.
This group of people had the same idea as Yang Wanli.
They thought he was cheating.
"Just do it, no big deal, Gu Xu, go up and show him your hand!" Zhang Song said.
"Yes! Gu Xu, go up and do it." Other students also shouted.
Gu Xu didn't know whether to laugh or cry. Fatty Zhang didn't mind the trouble and started making noises.
Upon seeing this, Zhang Xiaoli saw that the students were emotional.
However, this is normal, she also came from school days.
She also knew that students would compete with each other. If someone's grades suddenly improved, it would definitely arouse hostility from other students.
Especially like Gu Xu, who suddenly rose so much.
The only way is to let Gu Xu prove his strength again.
"Gu Xu, would you like to come up and do the questions?"
"No problem!" Gu Xu got up from his seat, walked directly to the podium, picked up the chalk, and started doing it very logically.
Lan Ruosi looked at Gu Xu's problem-solving ideas and steps, and there were no mistakes.
Zhang Xiaoli nodded and asked, "Gu Xu, what is the key to solving this question?"
"The key to this question lies in the empty set. The empty set is a subset of any set. Therefore, choose answer B for this question."
Zhang Xiaoli praised: "Classmate Gu Xu is right."
Yang Wanli sneered from below with great disdain: "It's just a multiple-choice question, who can't do it! It's difficult to do it if you have the ability."
Gu Xu said calmly: "How difficult a question do you want me to do?"
"Classmate Gu Xu, please go down first, and we will continue the lecture!" Zhang Xiaoli saw a conflict between the two and stopped them.
Yang Wanli subconsciously raised his eyelids and said, "Just wait, you will make a fool of yourself later."
Zhang Xiaoli continued to lecture again, and the following knowledge became more and more difficult.
Zhang Xiaoli goes from easy to difficult every time, so that she can slowly bring up the weaker students, and get up to the difficult points again at the end, without delaying the students with good grades.
Zhang Xiaoli wrote a difficult question on the blackboard: "This question is a bit difficult. Which student is willing to do it?"
"Teacher, Gu Xu!" Yang Wanli said and looked at Gu Xu, "What, do you dare?"
"Why don't I dare!" Gu Xu answered quickly.
"Then go ahead!" Yang Wanli looked like he was waiting for Gu Xu to make a fool of himself.
Gu Xu asked back: "I'll go up and do it, will you do it? Do you dare to come?"
"What are you afraid of!" Yang Wanli quickly answered.
Seeing this, Zhang Xiaoli said: "In that case, then both of you come up and do it."
The blackboard in the high school classroom almost occupies the wall of the front desk. The entire blackboard is composed of four pieces and can be pulled up and down.
Gu Xu and Yang Wanli went up to solve the problem at the same time. Gu Xu stood on the left and Yang Wanli stood on the right.
Gu Xu's font is larger than Yang Wanli's.
Yang Wanli wrote very small, almost every word was written just right and couldn't be any smaller.
He didn't want to tell others his problem-solving ideas and process, he just wanted to beat Gu Xu.
As Yang Wanli wrote, he glanced at Gu Xu from the corner of his eye, Gu Xu, you are destined to be defeated!
He continued to write and soon entered the key ideas and steps of solving the problem.
Gu Xu was focused on solving the problem without any distractions.
He didn't look at how Yang Wanli solved it, he just thought about how to solve it as fast and as simple as possible.
He clearly remembered Lan Ruosi telling him that exams should be done in the simplest and most accurate way.
Don't stick to formalities.
Zhang Xiaoli sat in Yang Wanli's seat and looked at the two of them.
This is a big question about the function evaluation domain, and is generally the most difficult.
Generally speaking, in the college entrance examination, except for those who can score 140 or above, no one else can understand it.
Students usually cry when they see questions like this. Because the question is very simple, but very difficult.
In previous college entrance examinations, it is the most difficult question.
At the beginning, the two people's problem-solving steps were the same. They had to solve the answer to the function based on known conditions. In the value range, the key was the value of the value range.
Judging from the steps Gu Xu has taken now, Gu Xu has solved the three number pairs in the value range.
So, how many pairs of values are there in this function question?
That's the difficulty.
Many people fail to do it all.
Gu Xu regarded the solved three logarithms as known conditions and set up an inverse function.
In turn, find the value range of the inverse function, use the value range of the inverse function to correspond to the domain of the original question, and quickly find the value range of the original question.
Gu Xu wrote down the value range of the original question...
Zhang Xiaoli nodded, Gu Xu's progress was really great.
She looked at Yang Wanli again.
He also solved three number pairs in the value range of the original function. However, he did not set up an inverse function. Instead, he used these three points to draw a curve based on the original function.
This solution is also a problem-solving idea. The key is that the curve of this problem cannot be drawn. The correct statement is that the blackboard is not big enough, and it may not be possible to complete the drawing even on the playground.
The two of them used different ideas to answer.
Yang Wanli saw that there was still some remaining blackboard on Gu Xu's side, so he drew the curve toward Gu Xu.
"Yang Wanli, what are you doing?" Gu Xu had already walked out. Although get out of class was over, the classmates did not leave and were all watching.
"Didn't you finish the question? I'm just connecting the rest of the solution for you."
Yang Wanli said arrogantly.
"Classmate Yang Wanli, you can write the words smaller and don't continue Gu Xu's problem solving." Zhang Xiaoli said.
"But, Teacher Zhang, my half is not enough!"
"Then use colored chalk to draw on the wall."
Yang Wanli had no choice but to use Zhang Xiaoli's method to draw curves on the wall and even on the door.
"Ding" the get out of class bell rang.
"get out of class is over! Students who want to go to the toilet can go there. Gu Xu and Yang Wanli continue to solve problems." Zhang Xiaoli said.
I happened to go to Zhang Song for cleaning today.
He was very unhappy when he saw Yang Wanli's paintings on the wall.
"Yang Wanli, you painted the door. You painted the door yourself and wiped it yourself!"
Other students also sat quietly and no one wanted to finish class.
Everyone was fascinated.
No one goes to the toilet.
