My Identity As A Schoolmaster Has Been Exposed

In the afternoon, the mathematics test was taken, and the invigilator in other test rooms did not change. This is the normal process of invigilating.

This is generally the case in school exams, because there are not enough teachers to take turns invigilating the exams.

But Xu Cong, the teacher in the examination room, changed two strangers. Xu Cong took a look when he walked in. Although they changed, he didn't think it was too strange.

When the two teachers saw him walk in, they smiled at him, and he smiled back politely.

It's all etiquette, and mutual respect has grown.

At the beginning of the exam, a teacher sent out the math test papers and draft papers.

"The performance paper is not enough, tell me and give it to you."

However, Xu Cong looked up at him, with a smile in his bright eyes, and said faintly: "Thank you teacher, no need."

Need not?

The two teachers looked suspicious and looked at each other, thinking they had heard it wrong!

Although they knew that Xu Cong got perfect scores in all subjects in the last exam, they didn't know how Xu Cong answered the questions.

Therefore, Xu Cong's operation is a real show to them.

Xu Cong ignored them and started to answer the questions directly in line with the principle of not wasting time.

The directrix equation of the parabola y=-4x is...

If the function y=x+2cosx is the maximum value in the interval [0, T/2]

…

Given that the inequality (m-n) square + (m-Inn+λ)²≥2, for any m∈R, nE(0, +oo) is always true, the value range of the real number input is

These two invigilators looked at Xu Cong, and he didn't use the blank paper before filling in the blanks!

good!

If you don't use it, you can't use it. It can only show that your brain is very powerful! You deserve to be a classmate who can get a perfect score! You don't need this question yet?

The two teachers looked at each other and seemed to be smiling, because they were a little bit proud.

Seeing that you have done so many questions, you don't need to play the scratch paper, it seems that this is provoking people.

The school exam gives the performance paper, it is determined that the students need it, and you have not used it, which is a bit uncomfortable.

It's really uncomfortable, because seeing this kind of people appear makes them seem like they are about to retire, and it's useless.

The two teachers did feel a little uncomfortable before, but now they believe that Xu Cong has to use performance paper!

Still not obediently?

Is it possible that you can calculate the answer verbally?

impossible!

Absolutely impossible!

The two teachers have such thoughts, so they are very happy. But a minute has not passed, Xu Cong wrote the answer later:

λ≥2√2-1 or λs-2√2-1, done!

After that, he continued to look at the next question.

"This, this! This" The two teachers were dumbfounded. This is a test paper issued in the city. No one will know the answer beforehand!

It is impossible!

But at the moment there is only one process for Xu Cong to give the answer, and that is to do it by himself. They are willing to believe that Xu Cong did it himself!

But... but this question can't be answered by brain math! It's useless to play scribbles!

Do you think hard?

Is this brain still a human brain?

After they were shocked, Xu Cong had finished writing a question.

The two invigilators looked at Xu Cong's calm look, and their hearts trembled. They walked to the side and began to whisper.

"Does he do this all the time?"

"At this rate, he should be able to hand in the paper a lot of time in advance."

"I don't know! Look at his appearance, so serious, it seems that he always answers questions like this..."

"It's horrible!"

"Don't treat the subject as a topic at all."

"It's a little too disrespectful of the teacher's hard work!"

While these two people were muttering, Xu Cong solved another problem. under:

It is known that the circle C passes through the points A(5,1) and B(1,3), and the circle center C is on the x-axis.

(1) Find the standard equation of circle c;

(2) Find the chord length of the straight line 3x+4y+4=0 intercepted by the circle C;

(3) P is a point on the straight line L:x=-2, if there is a straight line passing through the point P and the circle C intersects the point M, N, and M is exactly the midpoint of the line segment NP, find the value of the ordinate of the point P Scope.

Xu Cong gets started after reading the question, writes the answer directly, and solves:

(1) Knowing that the center of the circle is on the x-axis, set the coordinates of the center of the circle to (a, 0), and the radius to be r. Then the circle equation is (x-a)²+(y-0)²=r², that is, (x-a)²+y²=r². Since (5,1) and (1,3) are rounded, the system of equations is obtained:

(5-a)²+1²=r²

(1-a)²+3²=r²

The solution is a=2, r=√10.

So the circle equation is (x-2)²+y²=10.

(2)……

Xu Cong did it very quickly, and he didn't even use the papyrus at all. After he finished writing, he paused.

Then, I went back to the first question. When the two invigilators saw him like this, they immediately walked back and looked sideways at his test paper. Are they wrong?

Found yourself doing something wrong?

But they looked at it, and Xu Cong's answer was obtained! Just when they were wondering, Xu Cong slowly wrote next to the first question: "Method 2"

Fuck!!!

What the hell?

This guy thinks of the second problem-solving idea? Be a man!

Can't it?

The two teachers almost didn't exhale.

!!!

Xu Cong's pen didn't stop.

Suppose the circle C(x, 0), by ICAI=ICBI, we get

(x-5)²+1²=(x-1)²+3², the solution is x=2, then r²=(2-1)²+3²=10,

The equation for circle C is (x-2)²+y²=10. simpler!

After Xu Cong finished writing, he didn't even take a second look or consider the feelings of the two teachers next to him. He went to the next question mercilessly.

Others are doing math problems. They have to go through mountains and ridges, and cross the mountains and the fire. But Xu Cong looks at these problems, no matter how difficult it is, put aside the paper first, and then, like Guan Yu, pass five. Cut off six generals!

One knife! Kid!

If one cut doesn't work, then two cuts!

Soon, the last question.

The two teachers reluctantly looked at the clean scribble on the side and sighed.

"Hey…"

They have a feeling of insulting themselves, helpless, very helpless!

Xu Cong continues to look at the question, the last one is the finale:

Given that the sequence {An} satisfies A1=1, A(n+1)=2An+1(n∈N*)

(1) Prove: The sequence {An+1} is a geometric sequence;

(2) Find the general term formula An;

(3) Set Bn=n, find the first n terms of {AnBn} and Tn.

Xu Cong froze for a while after reading the questions. The invigilator looked nervous, and the small heart hung up quickly.

They looked at each other, and they had never seen Xu Cong like this in the whole exam. Could it be that they couldn't?

Is it necessary to use draped paper?

I don’t know why, they are always entangled, why Xu Cong doesn’t have to play the straw paper!

You don’t need to play papyrus, can this be called an exam? This is obviously disrespect for the exam!

But Xu Cong is not not that it is not, but surprised, this question is so simple, how did it come out as the finale?

Get started!

First one: "Solution" and then

(1) Because A(n+1)=2An+1(n∈N*), A(n+1)+1=2(An+1)(n∈N*)

So (A(n+1)+1)/(An+1)=2(n∈N*) Therefore, the sequence {An+1} becomes a geometric sequence.

(2) From (1), {An+1} is a geometric sequence with A1+1=2 as the first term and 2 as the common ratio

So An+1=2*2(n-1)²=2(n²) so An=2n²-1

(3)

sn=2(n+1)²(n-1)+2 so Tn=……

Thank you for reading this story at mtlarchive.com. Your support enables us to keep the site running!