Super Scholar: Start with a low regulatory score!

Chapter 108 There should be no one who can't understand such a simple question, right?

quickly!

The paper was sent out.

There are ten questions in total.

Eight fill-in-the-blank questions, each worth 8 points, totaling 64 points.

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

Jiangnan needs to control 88 points.

On the premise that all the questions have to be finished and no blanks can be left, the easiest way is...

If you deliberately fill in a blank question, 8 points will be deducted, and if the first question of question 9 is wrongly written, 4 points will be deducted.

Ah!
perfect.

After Jiang Nan settled down, he was ready to start work.

First is the first question.

“已知实数：x，y，满足x^2-xy-2y^2=1，则2x^2+y^2的最小值为……”

Jiangnan: "..."

Looking at this topic, he couldn't help laughing.

Nima!

Are Olympiad 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.

则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...

The answer can be obtained by proving that an ellipse and a hyperbola are known to be tangent to each other...

"(2+2√3)/3."

……

No need to think too much.

Jiang Nan instantly thought of two solutions.

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

The second way is to change the way of thinking and transform a function problem into a hyperbolic and circle tangent problem.

Gee!

It couldn't be easier.

Jiang Nan filled in the answers and continued to the second question.

It took a few seconds.

Followed by the third question.

The fourth question!
……

The eighth question...

"It is known that {an} is an arithmetic sequence, which satisfies a1, 3, a4, 12, and the sequence {bn} satisfies b1, 4, b4, 20, and {bn,, an} is a geometric sequence (find the sequence {an} The general term formula of sum {bn}: Find the sum of the first n terms of the sequence {bn}..."

Jiangnan: "..."

Ok!

Really speechless.

Less than 1 minutes.

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

And look at this question.

He almost instinctively wrote the answer.

Gee!

It's so simple.

With such a question, there should be no one who can't, right?

As long as people who have read books on weekdays.

Nine times out of ten they will do it.

But he...

Hey!
It just happened to complete the task of controlling points.

Can't get it all right.

What a pity.

finally!
Jiang Nan gritted his teeth and resisted the urge to write the correct answer, but abruptly filled in the wrong answer.

then……

Turn over the paper.

Then I went to do the last two questions.

That is, questions 9 and 10.

Among them, the ninth question is still very simple, which 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.

1 minutes.

Jiang Nan finished the question.

And why it took so long.

It's purely because he had to do the first question wrong, even so wrong that he couldn't get a point, and he didn't want the marking teacher to see that he did it on purpose.

and so……

It only took 1 minute.

otherwise!

Give him half a minute.

Just like the last question.

That's half a minute.

And he did it.

And this time...

The radio hanging in the corner of the classroom was bluffing a few times, "Now start to read the rules of the Mathematical Olympiad examination room: [-]: The exam will last for two and a half hours, [-]..."

"Six: During the exam, candidates are not allowed to leave their seats and cannot go to the toilet unless they hand in the papers in advance..."

"..."

Jiangnan: "???"

What?
Can I hand in the papers in advance?

Really?
This is a pleasant surprise.

Originally, he thought that this competition was the same as the monthly exam, and that the papers could not be handed in in advance unless they waited until the last 15 minutes.

Now he was ready to clear the table and go to sleep.

The result can be...

The radio said that you can't leave your seat to go to the bathroom, but you can hand in the papers in advance, and you can leave after handing in the papers.

and so……

Jiang Nan put the pen in his pocket and got up straight away.

"Candidate, didn't you hear the broadcast clearly just now? During the exam, you are not allowed to leave your seat to go to the toilet."

"What's more, the exam has just started. What's the matter with you? Didn't you solve it beforehand?"

An invigilator stopped Jiang Nan very seriously.

"Teacher, don't be nervous!"

Jiang Nan waved his hand and said calmly, "I've listened to the content of the broadcast, and I don't want to go to the toilet."

"Then what do you want?"

"I'm done, hand in the paper ahead of time!"

Invigilator: "????"

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

What?
What?
What?
What did Jiang Nan say?
Did he hear it right?
Didn't you see that the pens in the hands of other students in the examination room seem to be so heavy that they can't write at all?

Didn't you see more than thirty people in the examination room, most of them are gnashing their teeth, scratching their ears and cheeks?
even……

Even me, the invigilator, barely read the first question, but I haven't found a way to solve it.

But you said it was all done?
Said to hand in the paper?

Could it be that your level is hundreds of times better than mine?
Do not!
Even if it surpasses me by a thousand times.

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

"Candidate, I hope you will take every exam seriously and be responsible for your own results."

"If you're not ready, or don't want to take the test, don't come to waste places and time."

"But since you're here, you should go all out."

'Even if the questions are so difficult that you can't even do a single question, you shouldn't give up right after the exam starts. At least you have to write some steps, so you won't get 0 points, right? "

The invigilator's tone was rather unfriendly.

just because...

He had concluded that Jiangnan hadn't finished the papers, but that his level was too low, but the papers were difficult, so he gave up the exam directly.

however……

"What?"

"Is this topic difficult?"

"No!"

"It couldn't be simpler, just look at it. Although I can't get full marks, I won't get 0 points in the test."

"anyway……"

"87 and eight points are still available."

"..."

Jiang Nan answered very seriously.

"Heh, 87 eight points?"

The invigilator sneered, "Student, you are really brazen, and you still want to get 87 points in the exam?"

"To know……"

"This is not an ordinary exam, but a Mathematical Olympiad competition."

"Although it is only a preliminary round, the difficulty is not low. No. 1 in previous years was only 87 eight points."

"Not to mention that I read the paper just now, the overall difficulty of this year is much higher than previous years."

"Estimated..."

"No.1 is only 85 six points."

"If you can get 87 in the exam, doesn't it mean that you are the number one in this year's preliminary competition?"

……

sp: Today's [-] words are over, I just want to ask, who else?
The poor dog author has already suffered from three terminal illnesses at a young age, aphthous sores + herpes simplex + sweat herpes, as long as he stays up all night, all of them will come out, but please give some good comments and small gifts for support and comfort!

(End of this chapter)