"In other words, to thoroughly master trigonometric functions in solving inequalities, your trigonometric function lines, inequalities and functions must have a solid foundation. You failed to do this question I asked about comparing the sizes of trigonometric functions and the domain of spherical functions.
The reason why you can't solve this question is that the knowledge about function domain and quadratic function is not solid. As long as it is transformed and degraded, it can be solved immediately."
After three days in a row, in the empty classroom, a serious and solemn voice echoed around. Yu Hua sat in his seat, with an upright posture, as solemn as a gentleman, holding a pencil in his right hand and pointing at the draft book, facing Tan next to him.
Qing explained: "The knowledge points you master now are not strong enough, especially functions. During the exam, there will be no such basic questions for you."
Tutoring Tan Qing's schoolwork was one of the original arrangements.
However, after three days of tutoring by Yu Hua, it was discovered that Tan Qing had considerable problems. His mathematical foundation was not solid, functions were not fully grasped, knowledge points were miscellaneous and incomplete, and there was no system or coherence.
Most of the high school arithmetic textbooks during the Republic of China were derived from foreign textbooks, which were almost the same as those in later high school mathematics, emphasizing the coherence and system of knowledge.
If you have not mastered the previous knowledge points, then the content described later will be completely incomprehensible and you have to go step by step.
Tan Qing's main problem is here.
As the third-last student in the science class, Tan's math score was only 60 points, just above the passing mark. He was extremely embarrassed compared to his classmates whose math scores averaged 75 points.
60 points pass.
Relative to the overall level, a score of 75 is considered excellent.
"In addition, you also have quite a big problem with your plane vectors. This question is obviously a point-based question. For the first question, you only need to draw the shape according to the triangle rule. For the second question, you can just use the parallelogram rule.
"
"There is also this definite integral. When the area of the curved trapezoid surrounded by the parabola y=2x2 and the straight line x=2, x=t (t>0), y=0, the interval [0, t], etc.
Divided into n small intervals, what are the i-1 intervals? How simple is this question? You only need to insert (n-1) points at equal intervals on [0,t], and divide the interval [0,t] and so on.
Divide it into n small intervals, and the length of each small interval is t/n, won’t the answer come out?”
"Definite integral is the key point among the key points. Did you forget it when you learned derivatives last semester? Don't forget the integral formula."
"There is also this question, which is obviously about using derivatives to find the monotonic interval of a function. It's just that the question is a little confusing and there is no change in essence."
With a serious face, Yu Hua kept pointing to the almost blank draft book and explaining each question recorded on it in turn, suppressing the helplessness in his heart.
At this moment, he could finally understand the mentality of later generations of mathematics teachers facing a group of scumbag students. They lectured seriously. During the exam, all the papers were blank. Other than that, they only had solutions at most.
"Sorry, classmate Yu Hua, I have caused trouble to you." After hearing Yu Hua's meticulous explanation, Tan Qing lowered his head in inferiority, not daring to look up at the large blank space on the desktop and the drafts that were almost full of errors.
There are ten math questions in the draft book, three questions on functions, one on basic elementary functions, one on vectors, on the rules of triangles and parallelograms, one on solving inequalities with trigonometric functions, two on derivatives, one on definite integrals, and one on using derivatives.
Find the monotonic interval of a function, one plane geometry and two analytic geometry.
Of the ten questions, Tan Qing answered two correctly and was awarded points. The rest of the questions either failed to calculate the steps or simply wrote down solutions.
"Well, let's start with the basic elementary functions. Professor Hua Luogeng once said that functions are both the foundation and the most difficult part." Looking at Tan Qing, who bowed his head submissively, Yu Hua let out a long sigh and rubbed his slightly swollen face.
Forehead, I simply calmed down my mood.
What can he do when faced with a wealthy man with such a low profile?
It’s not just about forgiving like a loving father.
Yu Hua now has two ways to make money. One is to complete the first draft of Yu Hua's version of the wrong math problem set, and the other is to tutor Tan Qing in front of him. He also hopes that after Tan Qing's math scores improve, he can increase his price.
So you can earn more tuition money.
But the question is, why can't he, Tan Qing, solve such a simple question?
Hearing Yu Hua's words, Tan Qing felt quite embarrassed, but full of hope. He raised his head and asked curiously: "How to do it, classmate Yu Hua?"
"Check the questions." Yu Hua stared at Tan Qing, and after a second, he uttered two words.
It’s decided.
Use the most direct learning method for future generations, the question-sea tactic!
Refresh the questions!
Studying questions all day long!
The stupid bird flies first, hard work can make up for the weak. The main thing is to accumulate experience by brushing the questions, supplemented by explaining the questions. The main thing is to overcome the weak knowledge. The more you brush, the more you master.
In the end, your performance will be significantly improved.
"Check the questions?" Tan Qing, who thought Yu Hua had some secret method, felt a little disappointed when he heard the two words Yu Hua said. What's wrong with the questions? It's too simple.
When Yu Hua saw Tan Qing's expression, he knew that the other party looked down on the ultimate simple and crude tactic of answering questions. He smiled and said, "Hanzhi, believe me, you will be asked to answer the questions in one month."
The score will be significantly improved, at least 70 points."
"70 points?"
Tan Qing's eyes widened for a moment, and he suspected that he heard wrongly. He swallowed his throat and stared at Yu Hua: "Is it really 70 points?"
There is no doubt in the words, only incredulity.
What is the concept of 70 points?
We need to improve it by a full ten points from the base of 60 points!
If it is raised to 70 points, Tan Qing's math score will immediately be comparable to the middle of the class and rank among the top performers.
"Hanzhi, believe me, but the process is very difficult." Yu Hua nodded affirmatively. There was a unique and magical magic in his words that made people choose to believe it.
This is confidence.
Tan Qing's eyes showed a trace of desire, the desire of a bad student. Who doesn't want to enjoy the envy from his classmates? He gritted his teeth and said: "Okay, Yu Hua, I will work hard to get a score of 70 points!"
"Look at these ten questions first and think about it." After receiving Tan Qing's answer, a smile appeared on Yu Hua's face. As long as he has confidence, it will be easy, but he is afraid that the other party will not be able to hold up the wall.
Tan Qing definitely has a lot of perseverance and talent, but he usually likes to take a break during lectures. Occasionally he would be in a daze, and when he came back to his senses, he couldn't understand what Mr. Ren was talking about. He was like the situation of countless high school students in math classes in later generations.
Completely consistent.
Now Tan Qing is confident to fight hard, Yu Hua just needs to prescribe the right medicine.
Tan Qing was asked to read ten mathematical questions first. Yu Hua took out a brand new draft book, picked up a pen and quickly wrote out a series of mathematical questions about basic elementary function types.