Chapter 167: Thirty-four Minutes, Math Papers Completed!

Sun Xingyi's thoughts, Lin Bei didn't know.

After all, Lin Bei didn't have the magic power of his heart, and he didn't even look back from beginning to end.

But from the very beginning, he devoted himself to the test paper, and then answered the questions quickly.

That's right, it's fast.

For others, it is like a turtle speed in doing questions, even if it is the first multiple-choice question, it is very stressful.

Including Zhou Buyi, it took four or five minutes to complete the first question, and as for the second and third questions, it took even longer.

But for Lin Bei, he doesn't say that he answers in seconds, but it's not much slower, and it's basically controlled within one minute.

Of course, it would take nearly a minute to do a multiple-choice question, which was definitely a lot slower than Lin Bei's speed of answering mental arithmetic seconds in the past.

However, Lin Bei is a group of hilarious people.

"This paper is kind of interesting."

"It's not as difficult, but at least it's much more interesting than the language paper in the morning."

"Yes, you can satisfy my cravings."

This is the most sincere evaluation that Lin Bei gave to the paper after getting it and quickly scanning the questions.

I have to say that the quality of the test papers produced by Uncle Dige himself is different.

Although the difficulty is not great, it is much more complex and novel than the questions that Lin Bei does every day.

Perhaps this kind of complexity and novelty, for others, is a headache and a sad desire to die.

Even when Zhou Buyi saw it, he trembled, couldn't control the trembling of his hands and feet, and even broke the defense.

Even a senior math teacher like Sun Xingyi commented that this paper was too difficult.

But for Lin Bei, it's excellent!

It's really superb.

The first time he saw the scroll, he was overjoyed and could not control his inner impulse.

After all, he is not afraid of difficult questions, not afraid of new questions, but afraid that the questions are too simple, too old-fashioned and boring.

For example, in the Chinese exam in the morning, he was disappointed for a while because the questions were too simple.

However, the math test in the afternoon was still very interesting, and the question type was quite novel and complex, which made people fall in love at first sight.

Without a doubt, this is definitely the most interesting test paper he has ever seen, the kind that can satisfy his cravings.

So......

When he heard that the exam had officially begun, he ignored everything in the outside world and began to answer the questions with all his heart.

For the first question, choose C.

I believe everyone has no doubt about this!

After all, although this question is somewhat innovative and seems quite complicated, in fact, the difficulty is only average.

The most formal way is to use the scaling method to compare the sizes of a, b and c, although the amount of computation is larger, but as long as you are familiar enough with the various scaling formulas, it is not a big problem.

And if you take a shortcut, it is the Taylor formula, but the formula is not learned in high school, so Lin Bei doesn't know, so naturally he won't use this formula.

But he didn't use the deflation method, he drew three figures directly in his mind, looked at the tangent slope between the three when he was very close to 1, and then estimated and compared.

Of course, there is an element of opportunism in this approach, and the answer is not necessarily accurate.

After all, I didn't even get a process.

Put it in the fill-in-the-blank solution, it must be cool.

But this is a multiple-choice question, and it doesn't require a specific process, but only needs to be answered correctly, isn't it?

To do multiple-choice questions, you can make a shortcut, you can guess, you can estimate, you can draw, and even you can use the elimination method, pay attention to a small problem, pay attention to the thinking method, and achieve both fast and accurate, not the other way around, make a big fuss, and entangle for half a day to get the answer.

Even if the answer is correct in the end, it will definitely outweigh the losses if it takes too much time and too much energy.

As for the second question, the answer is A.

Lin Bei took a little longer, close to a minute.

After all, there is really no way to solve this problem, you can only calculate it in your heart.

However, this operation is not complicated.

Nothing more than ......

[Because let x =0, we get y =-2, let y =0, get x =-2, so A (-2,0), B (0,-2), IAB|.] =(√4+4)anti=2√2anti. 】

[And since the point P is in the circle (×-2)^2+y^2=2, let P (2+√2 anticosθ, √2 antisi.】

θ), so the distance from the point P to the straight line × + y + 2 = 0 d = ......]

[Therefore, the value range of △ ABP area is: [12×2√2x√2,12×2√2×3√2]=[2,6].

[So choose A.] 】

That's right, it's that simple.

You only need to figure out the position relationship between the straight line and the circle, and this question is actually no different from giving points.

And the above is just solution 1, a little more complicated, in addition to the solution 2, you can use the method of maximum and minimum values to directly calculate the range of values.

And that way, the operation is much simpler.

So one minute, that's really enough.

If it weren't for Lin Bei's desire to control his speed and prevent this delicacy from being eaten too quickly and unable to fully enjoy it, it is estimated that half a minute would be enough.

As for the third question, there is no need to say more.

The problem of curve equations is as difficult as climbing to the sky for ordinary people, and it is often in the clouds and fog, and even if it can be done, it will take an unknown amount of time.

But for Lin Bei, that's it.

Even though the problem was a bit complicated, it took him less than a minute to get the D option.

That's it......

He kept the speed of less than a minute, about forty or fifty seconds, and it took only ten minutes to complete 12 multiple-choice questions and come to the fill-in-the-blank question.

Fill-in-the-blank questions, like multiple-choice questions, are quite novel and have a certain degree of complexity, which can make people shine.

So much so that Lin Bei controlled his speed as much as possible, not to let himself go too fast, and it was done all at once.

After all, if you want to encounter such an interesting question next time, you don't know when, you have to savor it!

So, it's basically one question per minute.

I saw that at 2:14, there were four fill-in-the-blank questions.

Then it's time to answer questions 17-21.

The answer question is definitely more complicated than the choice fill-in-the-blank question, but it is not beyond Lin Bei's scope.

Probably, that's a 3-minute piece!

The five questions add up to 15 minutes, and if you add 4 minutes to fill in the blanks, it is 19 minutes.

Well, less than 20 minutes.

If you add 10 minutes to the multiple-choice question, it is 29 minutes, and it is not more than 30 minutes.

The time is 2:29.

It was also the time for the invigilator Zhou Xingyi to make sure that Lin Bei's multiple choice questions were all correct and return to Lin Bei's side.

Seeing this scene, Zhou Xingyi was completely stunned.

However, Lin Bei didn't care at all, and only started the solution of the last big axis question with great interest.

"22: The known functions f(x)=e^2-ax and g(x)=ax-l

x has the same minimum value. ”

"1: Ask for A."

"2: Prove that there is a straight line y=b, which has three different intersections with two curves y=f(x) and y=g(x), and that the abscissa of the three intersections from left to right is in an equal difference series."

Is this a difficult question?

It is estimated that the vast majority of people do not know.

Because, they can't understand it, how can they know if this question is difficult or not?

However, Lin Bei only looked at it for three seconds, and then couldn't help laughing, "Giggles, this question is really good, not only can it satisfy my cravings, but it seems that I can also eat a little full." ”

"After all, the test points are much more complicated than the previous questions, and they are worthy of being the last big axis questions."

"I'm afraid I can't handle it in three minutes, I guess it will take a little time, well, that's five minutes!"

"( ̄y▽ ̄)~*Cover your mouth and snicker."

Lin Bei snickered and began to answer the question.

It is worth mentioning that the difficulty of this question is really much higher than the previous ones.

After all, the derivative is fused with sequences and inequalities, and it is still very complicated to solve the comprehensive problem of transcending the hidden zero point of the equation by constructing a special function.

If you are an ordinary person, if you have time, you can do the first question, and the second question is best not to even look at it.

After all, it's really a waste of time, and it will lead to a bad personal mentality, which is too difficult.

Isn't it fragrant to have this time, do the front with your heart, and strive to get all the points that you should get in front of you?

Of course.

Lin Bei, who has completed all the previous questions and is confident that he can get a full score, must be excepted.

This big axis question is quite complicated, but it is precisely because of its complexity that it has aroused Lin Beibei's great interest.

Without saying a word, I just got to work.

"Solution: f'(x)=e^x-a, g'(x)=a-1/x, since f(x) has a minimum, so a>0."

"So x belongs to (0,1/a), f'(x)0, f(x) monotonically increasing. ”

"x belongs to (0,1/a), g'(x) > 0, g(x) has to be monotonically increased for g(x), x belongs to (1/a,+∞), g'(x) <0, then g(x) is monotonically decreasing."

"So f(x)mi

=f(l

a)=e^l

a-al

a=a-l

a; g(x)mi

=g(1/a)=1-l

1/a=1+l

a。 ”

"If you create an inequality between the two and let it be the third function h(a), we can calculate a=1."

The pen walks the dragon snake.

It's definitely a pen and a snake.

There's really not much to say about this first question.

Although the value of a is further required in terms of monotonicity, everything can be changed, as long as the monotonicity is no problem, just follow the steps, which is very simple.

As long as you have a better mentality, don't be afraid of difficulties and be serious, this part can be done.

So......

After Lin Bei only took a minute to get it done, he stopped looking at it, and started to ask the second question without stopping.

Comparatively.

The second question is much more complicated, after all, it is a question that distinguishes the gap between the top geniuses and the geniuses.

And the second question of the big axis question this time is much more difficult than the second question of the big axis question in the last monthly exam.

After all, the last monthly exam was an independent proposition by the teacher of the third middle school, but this joint examination was made by Uncle Ge.

There is no comparison between the two.

But it only took Lin Bei four minutes to get it done.

The last question, which added up to five minutes, was exactly the same time he expected.

So far.

Lin Bei finished the second math test, looked up at the blackboard, and found that the clock hands were located at 2:34.

Well, more than half an hour, it took two minutes more than the last monthly math test.

And at present, Lin Beidu's strength is many times stronger than the strength of the last monthly exam.

But even if he has such a strong strength, it actually took 34 minutes, which shows the difficulty of this paper.

~( ̄▽ ̄~)(~ ̄▽ ̄)~。