Super academic master: start with low adjustment scores!

Very soon!

The test paper was handed out.

There were ten questions in total.

Eight fill-in-the-blank questions, 8 points each, a total of 64 points.

Two problem-solving questions, question 9 has two questions, a total of 16 points, and question 10 has only one question, a total of 20 points.

Jiangnan had to control his score to 88 points.

Under the premise that all questions must be completed and no blanks can be left, the simplest way is...

Deliberately fill in a fill-in-the-blank question incorrectly, deduct 8 points, and then write the first question of question 9 incorrectly, deduct 4 points.

Well!

Perfect.

Jiangnan made up his mind and prepared to start working.

First, the first question.

"Given real numbers: x, y, satisfying x^2-xy-2y^2=1, then the minimum value of 2x^2+y^2 is..."

Jiangnan: "..."

Looking at this question, he couldn't help but laugh.

Damn!

Are Olympiad math questions so simple?

Solution 1...

Because x^2-xy-2y^2=1.

So (x+y)(x-2y)=1.

Let x+y=m, x-2y=n (at this time: mn=1).

At this time x=（2m+n）/3, y=（m－n）/3.

Then 2x^2+y^2=1/9(9m^2+3n^2+6mn）=1/9(9m^2+3/m^2+6）...

Greater than or equal to (2+2√3)/3, if and only if m=……, n=……...

...

Solution 2...

From the known, we can draw an ellipse and a hyperbola, prove that the two are tangent, and we can get the answer...

"（2+2√3）/3."

...

There is no need to think too much.

Jiangnan immediately thought of two solutions.

The first one is a conventional solution, which is nothing more than transforming the equation and then setting up another equation to find the minimum value.

The second one is to change the way of thinking and transform a function problem into a hyperbola and circle tangency problem.

Tsk tsk!

It couldn't be simpler.

Jiangnan filled in the answer and continued with the second question.

It took a few seconds.

Then the third question.

The fourth question!

…

Question 8…

“It is known that {an} is an arithmetic progression, satisfying a1, 3, a4, 12, and the sequence {bn} satisfies b1, 4, b4, 20, and {bn,,an} is a geometric progression (find the general formula of the sequences {an} and {bn}: find the sum of the first n terms of the sequence {bn}…”

Jiangnan: “…”

Okay!

It’s really speechless.

In less than a minute.

He finished the eighth fill-in-the-blank question in one go.

And as soon as he saw this question.

He almost instinctively wrote down the answer.

Tsk tsk!

It’s really too simple.

There shouldn’t be anyone who can’t do this kind of question, right?

Anyone who has read books in daily life.

Nine out of ten can do it.

But he...

Oh!

He had to complete the score control task.

He couldn't do all of them right.

It's really pitiful.

Finally!

Jiangnan gritted his teeth and resisted the urge to write the correct answer, and filled in a wrong answer.

Then...

He turned the paper.

He did the last two questions.

That is, Question 9 and Question 10.

Question 9 is still very simple, it is a trigonometric function. The first question is to find the value range of an angle a, and the second question is to find the maximum and minimum values ​​of the function.

One minute.

Jiangnan finished the question.

And the reason It took so long.

It was purely because he had to get the first question wrong, even wrong to the point where he couldn't get any points, and he didn't want the examiner to see that he got it wrong on purpose.

So...

It only took one minute.

Otherwise!

Give him half a minute.

Just like the last question.

It only took half a minute.

He got it done.

And at this time...

The radio hanging in the corner of the classroom was beeping a few times, "Now let's start reading the rules of the Mathematical Olympiad exam: 1: The exam duration is two and a half hours, 2..."

"6: During the exam, candidates cannot leave their seats or go to the toilet unless they hand in their papers in advance..."

" ..."

Jiangnan: "? ? ?"

What?

Can I hand in my paper early?

Really?

This is a pleasant surprise.

He originally thought that this competition was the same as the monthly exam, and that I couldn't hand in my paper early unless I waited until the last 15 minutes.

He was ready to clean up the table and go to bed.

But the result...

The broadcast said that I couldn't leave my seat to go to the bathroom, but I could hand in my paper early, and I could leave after handing in my paper.

So...

Jiangnan put his pen in his pocket and stood up.

"Dear candidate, didn't you hear the broadcast clearly? During the exam, you can't leave your seat to go to the bathroom."

"Besides, the exam has just started, how can you answer"What? Didn't you solve it beforehand?"

An invigilator called Jiangnan seriously.

"Teacher, don't be nervous!"

Jiangnan waved his hand and said calmly: "I listened to the broadcast, I don't want to go to the toilet."

"Then what do you want to do?"

"I've finished it, hand it in early!"

Invigilator: "? ? ? ? "

His head was full of question marks, and he was a little confused.

What?

What?

What?

What did Jiangnan say?

Did he hear it right?

Didn't you see that the pens in the hands of other students in the examination room seemed to be as heavy as a thousand pounds, and they couldn't write at all?

Didn't you see that most of the more than 30 people in the examination room were gritting their teeth and scratching their heads?

Even...

Even I, the invigilator, could only barely finish the first question and hadn't found a solution.

But you said you had finished all of them?

You said you wanted to hand in the paper?

Could it be that your level is hundreds of thousands of times better than mine?

No!

Even if you are hundreds of thousands of times better than me.

Don't even think about finishing the paper so quickly.

"This candidate, I hope you can take every exam seriously and be responsible for your own grades."

"If you are not ready or don't want to take the exam, don't come to waste your quota and time."

"But since you are here, you should go all out. ”

‘Even if the questions are difficult, so difficult that you can’t answer any of them, you shouldn’t give up right after the exam. At least you should write down some steps, so you don’t get 0 points, right?”

The tone of the invigilator was quite unfriendly.

Just because…

He had concluded that Jiangnan had not finished the test paper, but his level was too poor, and the test paper was difficult, so he gave up the test directly.

However…

“What?”

“Is this question difficult?”

“No!”

“It’s as simple as it can be. I can understand it after just one look. Although I can’t get full marks, I won’t get 0 points either.”

“Anyway…”

“I can still get 87 or 8 points.”

“…”

Jiangnan answered very seriously.

"Oh, 87 or 8 points?"

The invigilator sneered, "Student, you are so arrogant, you actually want to get 87 or 8 points?"

"You know..."

"This is not an ordinary exam, but an Olympic Mathematical Competition."

"Although it is only the preliminary round, the difficulty is not low. The first place in previous years was only 87 or 8 points."

"Not to mention that I just looked at the paper. The overall difficulty this year is much higher than in previous years."

"It is estimated..."

"The first place will be at most 85 or 86 points."

"If you can get 87 or 8, doesn't that mean you are the first in this year's preliminary round?"