Qin Ke couldn't help but sigh, the school committee is really a typical hard-working academic master, and the hard work he put in is far beyond what others can appreciate.

Thanks to Ning Qingjun's "Key Points for Writing Questions" in the Chinese language notebook, he even thought of excellent entry points for composition. Although his writing skills are limited, his intention is good. A 60-point essay may get more than 45 points.

I roughly calculated the scores and found that I was confident that I could get the questions right, including the essay, and I conservatively estimated that the score would exceed 110.

This surprised Qin Ke, who had never scored more than 100 points in Chinese, for the first time he saw the hope of entering the top 50 in grade.

The afternoon test was mathematics, which was the subject that Qin Ke was least worried about.

Among the invigilators in this examination room happened to be mathematics teacher Zheng Jianzhou. Qin Ke nodded slightly to Old Zheng, then lowered his head and started writing the test paper.

Lao Zheng looked around the examination room, observing each student's reaction. When he saw that most students looked confused when they saw the first question, he couldn't help but shake his head in disappointment.

This time, he and three other mathematics teachers worked out the questions together. In the end, he made the decision to remove some simple questions, retain only the questions of medium difficulty and above, and add three extra difficult questions totaling 15 points.

The purpose of the question is naturally to select students who can participate in the Mathematical Olympiad competition - this is also Qin Ke's fault, which made Lao Zheng mistakenly believe that genius students are most likely to be buried among ordinary students who usually do not notice their talents.

Against all odds, the difficulty of this math test was increased.

Ordinary students are unlucky. When they get the test paper, the first multiple-choice question reads:

"If a natural number n is such that vertical addition n+(n+1)+(n+2) does not produce a carry phenomenon, then n is called a "happy number". For example: 32 is a "happy number" because 32+33+34 does not produce a carry phenomenon; 23 is not

"Happy numbers", because 23+24+25 produces a carry phenomenon, then the number of "happy numbers" less than 100 is ()

a.

9 b．

10 c.

11 d．

12”

They were stunned on the spot.

According to the usual "convention", aren't the first multiple-choice questions all very simple theorem and law questions that can be easily solved so that students can have some confidence to continue completing the test paper?

But what’s going on with this question now?

I don’t see the idea of ​​solving the problem at all!

The students with slightly lower math scores were put on the bus and looked at the second multiple-choice question with dull eyes:

"In a certain WeChat group, there are five people A, B, C, D, and E playing a red envelope grabbing game. There are currently 4 red envelopes. Each person can grab one at most, and all the red envelopes have been snatched up. 2 of the 4 red envelopes are 5

Yuan, one is 8 yuan, and one is 9 yuan (the same amount in the red envelope is regarded as the same red envelope), then the situation in which both A and B grab the red envelope is ()

a.

18 species b.

24 kinds

c.

36 species d.

48 types”

Scumbags: "..."

They almost overturned the table. Did they make a mistake? Are they going to let the scumbags get a point or two? This is to force them into the abyss of zero points!

The students also looked sad because the second question was so difficult. They felt that their chances of passing this time were slim.

The bad students and the bad students have nothing to love there, and the students with better math scores are also secretly frightened. The first two multiple-choice questions seem to be menacing and mean, and the subsequent questions are probably even more difficult.

Another teacher who was invigilating the exam was Xu Shichao, a newly appointed high school mathematics teacher. After he looked around at the miserable expressions of the students, he also lowered his head and looked at the exam paper, and couldn't help but murmur in his heart.

The questions in this math test paper are so murderous. Are they going to stump most students?

He walked half a circle around the examination room and found that nearly fifteen minutes had passed. Most of the students were still doing the third multiple-choice question. Many students read the examination paper from front to back and then fell asleep on the table.

, obviously gave up.

There was even a female student who secretly wiped her tears while doing the questions. She was so embarrassed that she cried.

The difficulty coefficient of this high school mathematics test is indeed obviously high...

Xu Shichao doubted that any student in this high school mathematics test could finish the paper within the specified time, let alone the three additional questions at the end.

Seeing the gloomy face of his senior, Old Zheng, Xu Shichao did not try to get involved in this bad luck. He sighed secretly, turned around and was about to walk back to the podium, but unexpectedly caught sight of something out of the corner of his eye.

He was stunned, turned around and took a closer look, and saw a male student already doing the third part of the answer question, and it was the last question!

Xu Shichao thought he was dazzled, so he took a closer look, and it turned out that he was right. The male student wrote very quickly. He finished the last question and opened the test paper to do the comprehensive questions in the fourth part.

When he turned over the test paper, Xu Shichao clearly saw that the student had completed all the multiple-choice and fill-in-the-blank questions.

So fast? The exam has only started for about fifteen minutes, right?

Could it be that he doesn’t know how to write it at all and just wrote it casually?

Xu Shichao couldn't help but stop. The student was already reading the comprehensive questions.

"Known function f(x)=xln x+ax+1,a∈r.

(1) When x>0, if the inequality f(x)≥0 about x is always true, find the value range of a;

(2) When n∈n, prove: n/(2n+4)<(ln 2)^2+(ln 3/2)^2+…+[ln (n+1)/n]^2 0),

That is, -a≤ln x+1/x is always true, that is-a≤[(ln x+1/x)]min

…

∴-a≤1, that is, a≥-1,

The value range of ∴a is [-1,+∞)"

Xu Shichao's eyes widened. This student didn't seem to be thinking at all, right? He started writing the answer the next second after reading the question?

And...this answer seems to be right!

Under Xu Shichao's shocked eyes, the male student's pen tip moved quickly, brushing, brushing, and the thirty-odd lines of solution process were completed in less than a minute and a half. The male student looked at three additional questions.

Xu Shichao couldn't help but look at these three additional questions together. The more he looked at them, the more he was astonished. These three questions were really difficult. They were all questions from the Municipal Mathematical Olympiad Preliminary Competition. The last question stumped him even more - Xu Shichao read it back then.
Chapter completed!