The system development of a scholar

Chapter 33 Learning Makes Me Happy
Xu You deeply agrees with Zhang Wen's statement that "your thinking is imprisoned in textbooks".

Because the exams in junior and senior high schools are all about testing students' understanding and mastery of textbook knowledge, the teacher's method of marking papers is also given step by step. It is not that you only need the final answer to be correct. full marks.

Even if you play tricks, the result may be 8-0.

You are not convinced, take the paper and ask the teacher, my question is obviously well-founded, the result is not wrong, why only give me half of the mark?Please give me a reasonable explanation.

The teacher will definitely point to the question and tell you that the test points of this question include the application of the theorem of sine and cosine, the conversion of elliptic parameter equations, and the application of eccentricity and focal distance formulas.But in your problem-solving steps, how many of these knowledge points are used?

For example, this question.

Let the focus of parabola C: y^2 is equal to 4x be F, the straight line l passing through F with slope k (k greater than 0) and C intersect at two points A and B, |AB| is equal to 8, find the equation of l.

The standard answer is this:
From the meaning of the title, the coordinates of F are 1 and 0, and the equation of l is: y is equal to k times x minus 1, provided that k is greater than 0.

Let the coordinates of A be x and y (subscript 1), and the coordinates of B be x and y (subscript 2),
联合l和C的方程，解得：k^2乘x^2减去小括号内2倍的k^2加4，再加k^2等于0。

Delta is equal to 16 times k^2 plus 16 and greater than 0,

所以x1加x2等于（2k^2加4）除以k^2，所以|AB|等于|AF|加|BF|，等于（x1加1）乘以（x2加1），等于（4k^2加4）除以k^2，【x后面的1和2都是下角标】

由题设知：（4k^2加4）除以k^2等于8，解得k等于正负1，因为负1不合题意，所以舍去。

So the equation is: y equals x minus 1.

Sao operation is like this:

Because the focal radius and intersecting chord formula of a parabola passing through the focus are: |AB| is equal to 2p divided by sin^2x (x is the inclination angle of passing through the focus).

Directly bring in 2p/sin^2x equal to 8;

So 4/sin^2x is equal to 8;

sin^2x is equal to 1/2;

sinx is equal to root 2 of 2, x is equal to 4th,

k equals tanx equals 1,

So, the equation for l is: y equals x minus 1.

There are two ways to do the questions. The first method is very easy for the teacher to give marks according to the steps, but the second method, how to give?
Some teachers think you are good enough and give you half points; some teachers will think that your behavior is cheating and give you zero points directly.

How to score depends on the mood of the teacher...

However, when these two problem-solving methods are applied to the competition field, they can get full marks.

Because the mathematics competition is a place where everyone can show their strengths. As long as your operation is reasonable, you can show off no matter how much you show off.

It is precisely because of the limitations of textbook knowledge on thinking that various competitions are held to select elite talents...

Although Xu You has taken the pills and has a solid foundation for pioneering thinking, he still needs someone to guide him to expand and diverge infinitely.

Therefore, Xu You was looking forward to this training camp.

Zhang Wendao: "You are actually very good in terms of mathematical foundation and mathematical thinking, but when it comes to competitions, you have to improve, because the opponents you face are outstanding students from various universities across the country. Among them, many of you are better than you. ! There are even some Mathematical Olympiad prodigies and geniuses.”

"Competing on the same stage with them, you have no advantage at all, let alone get a ranking."

He pointed at himself with a thumbs up, "So my next task is to elevate your mathematical thinking to the same level as those students who have been in Math Olympiad classes for several years in a short period of time."

"Is it so awesome? Then where do you put the MMPs of those students who spend huge tuition fees?"

Xu You can only wait and see Big Brother Zhang's coquettish operation with anticipation...

Zhang Wen raised his hand and patted a moth that flew in front of him, saying: "Tonight's class, although there is not much content, is very important."

"So, you must listen carefully, and even remember every word I say."

Zhang Wen said seriously: "Because next, I want to change your way of thinking!"

He clicked the mouse, and a math problem appeared on the screen.

"Come on, use your best skills to solve this problem as quickly as possible."

Everyone read the questions first, then took out their notebooks and started to solve them.

Seeing that everyone started to write, Zhang Wen took a sip from the water glass on the desk, then walked off the podium to check the students' problem-solving methods.

As expected, Qian Le is the first in the grade, and his thinking is very quick. Only through the guidance of Zhang Wen's question just now, he is trying to overthrow his original thinking of solving the problem and explore Zhang Wen's thinking...

Chen San obviously attended the Mathematical Olympiad class, and his problem-solving skills have the embryonic form of "quick questions", but they are still immature, so the problem-solving steps are a bit messy...

Zhao Yuxiang is completely using textbook knowledge to forcibly show off the operation...

Ye Jin's operation and awareness are better than Zhao Yuxiang's, and he has also been inspired by Zhang Wen's thinking in solving problems, but his thinking is still not divergent enough...

As for Xu You...

Zhang Wen felt that this son definitely had his former demeanor!
Not only is the consciousness slippery enough, but the operation is even more coquettish.

The problem-solving method is simply brilliant!

Directly use a magic formula, substitute the conditions in the question stem, and the answer will be revealed immediately.

Simple and brutal.

"Yes, Not Bad."

Zhang Wen nodded in satisfaction, and confirmed the look in his eyes, it was the man I fell in love with...

Xu You put down his pen and looked at his own steps to solve the problem, feeling very happy in his heart.

Simply thriving.

Of course, this is all due to the effect of the pills, which poured a large number of mathematical conclusions and formulas into his mind, otherwise he could only play basic operations, at most a little better than Ye Jinxiu, but with Qian Le, Chen Sanbi, definitely not as good as...

After waiting for about 10 minutes, everyone came up with their answers. Zhang Wen walked up to the podium and said, "Let's see the solution method for this question."

Click the mouse, and the concise problem-solving steps will appear in front of everyone.

"Is there such a formula?"

Ye Jin looked at half a page of his derivations and calculations, feeling so tired and his body hollowed out...

Zhang Wen clicked the mouse again, and a whole page of formulas appeared in everyone's eyes.

"These formulas are not in your textbooks, but they are commonly used magic formulas to solve most math problems. They can be easier than ordinary problem-solving methods and save time. Everyone, take out your small notebooks and write down the key points."

Seeing that everyone started to take notes, Zhang Wen continued: "In the examination room, you are racing against time. Even if you can save a second of time, you must fight for it. Maybe you are only one second behind on a certain question. thinking in it."

Although these formulas were firmly imprinted in Xu You's mind, he followed everyone else and wrote them down in the notebook, even if it deepened his memory. After all, a good memory is not as good as a bad pen.

For the two and a half hours of evening self-study, Zhang Wen only gave you five questions to do, but with these five questions, the thinking mode constructed for you is huge...

In the first 10 minutes of the next night's self-study, Zhang Wen finished his lecture and asked everyone to go back to the classroom to pack their things and get ready for school.

Building a thinking model is a long-term process. Although the time is tight, it is necessary to help Xu You and others build a framework that can withstand the wind and rain within a month, but there is no rush, and we can only guide it step by step.

When going downstairs, Xu You asked Ye Jin: "How is it? Is there a sudden enlightenment, and learning makes me happy like flying?"

Ye Jin rolled his eyes at him and said, "I only have a feeling of powerlessness that my consciousness can't keep up with the operation..."

Although the boss gave her a "strategy", how to apply it proficiently to various question types still has a long way to go.

Alas, I can only continue to brush up the questions, and slowly get used to it.

god annoyed...

PS: Thank you: support the author, Ezealic's reward, sprinkle flowers...

　Ask for a recommendation ticket and collect it!
　　


(End of this chapter)