Three minutes later, the exam paper was sent down.

The semi-finals have finally officially begun!

After Xiao Ran got the test paper, the first thing he did was to roughly scan the overall question types.

After reading it once, he also had a score in his heart, and the type and number of question banks were still the same as before.

This is a one-test paper with a total of 3 question types.

Among them, there are 6 multiple-choice questions, each with 6 points, a total of 36 points.

There are 6 fill-in-the-blank questions, each worth 9 points, a total of 54 points.

Answer 3 questions, each question is worth 20 points, a total of 60 points.

The total score of the paper is 150 points, and the exam time is from 8 am to 9:40 am, with a total length of 100 minutes.

In addition, the top of this set of test papers is also printed with the words "A paper", as always.

Xiao Ran knows that the semi-finals or provincial competitions are the unified propositions of the Organizing Committee of the National High School Mathematics Competition, and they are the same across the country.

It's just that the test paper is divided into two papers, AB, and most areas in China use paper A, and only a few remote areas use paper B.

Paper A focuses on thinking skills, while Paper B focuses on numeracy.

Generally speaking, the difficulty of the A paper is higher than that of the B paper.

As a major education province, Qilu Province is also in a relatively advantageous location, and it is naturally a national A-volume.

These are all established conventions, and Xiao Ran is not surprised.

After reading through the questions like this, Xiao Ran also had a bottom in his heart, and he began to do the questions.

Taking advantage of the fact that he is still in good spirits now, he will be able to solve it quickly, and the longer it drags on, the more unfavorable it will be for him.

Starting from the small question, Xiao Ran adheres to the 6 proverbs taught by Teacher Han before.

Make small fuss, pay attention to clever solutions, and never waste too much time.

Xiao Ran was deeply touched by this experience, and he often warned his students in his previous life when he was an Olympiad coach.

Because, he has seen many candidates who waste too much precious time on small questions, and the gains really outweigh the losses.

In one sentence, it can be summed up as picking sesame seeds and losing watermelon!

Therefore, Xiao Ran told himself that he must not make such a mistake.

Generally speaking, the difficulty of the first test is not too high, especially the first few questions.

Therefore, Xiao Ran did it very smoothly.

It's like this problem: [Knowing that the positive real number a satisfies a^a=(9a)^8a, then the value of loga(3a) is equal to (). 】

Here are 4 options.

Xiao Ran calculates slightly, from the condition 9a=a^(1/8), so 3a=√(9a*a)=a^(9/16), so loga(3a)=9/16.

It didn't take long to come to the answer.

Small questions like this have to be done skillfully, and some questions Xiao Ran didn't calculate at all, but directly brought in the answer and did the mental arithmetic.

In this way, Xiao Ran quickly completed the fill-in-the-blank question.

Fill-in-the-blank questions are a bit more troublesome than multiple-choice questions, after all, you can't reverse the answers.

However, Xiao Ran felt that it should not be a big problem.

Theoretically, it won't be particularly difficult.

However, as soon as he came into contact with the first question, Xiao Ran felt a little troublesome.

Maybe the previous multiple-choice questions were done too smoothly, but I didn't expect the first question of the fill-in-the-blank question to be given a dismount.

[7. Arrange 1,2,3,4,5,6 in a random line, denoted as a, b, c, d, e, f, then the probability that abc+def is an even number is (). 】

Yes, it's just such a mediocre line of text, but it's really not simple.

After Xiao Ran finished reviewing the questions, he took the written test and calculated it, and after 1 minute, he made a decision.

Skip over first.

This is also an important exam technique.

That is, when you encounter a problem, don't think about it, learn to skip it, and it's not too late to come back and fight the tiger when you've finished other simple questions.

Teacher Han also talked about this, and Xiao Ran thought so.

It's been 1 minute, and I don't have a good idea to solve the problem, this is still the first problem for a small problem, and there is really no need to dwell on it.

If it affects the state of the future, it will be even more worth the loss.

Thinking of this, Xiao Ran decisively skipped it.

As it turned out, he made the right choice.

The next 5 fill-in-the-blank questions were unexpectedly not difficult, and Xiao Ran finished them all in one go.

Except for the last number problem, which took a little effort, there was little effective resistance throughout the whole process.

Even Xiao Ran was a little stunned at this.

After completing these fill-in-the-blank questions, Xiao Ran looked up at the time, 8:22.

There's still time!

So, he turned the gun and came to the first fill-in-the-blank question again.

Grind this little boss!

It's obviously not appropriate to experiment with numbers one by one, and you still have to combine them with permutations.

Try the calculation again, and at this time, Xiao Ran found that the workload of directly calculating the probability of even numbers is indeed too large.

Conversely, if the probability is odd, it seems simpler to calculate.

It seems that the method of counter-evidence must be used!

Thinking like this, Xiao Ran slowly wrote on the scratch paper.

[If abc + def is an odd number, then abc, def is an odd and even, if abc is an odd number, then a, b, c are the permutations of 1, 3, 5, and d, e, f are the permutations of 2, 4, 6.

At this time, there are a total of 3! ×3！ = 36 cases, by symmetry, then abd+def is odd 36×2 = 72 cases.

Then, the probability that abc+def is an even number is 1-72/6! =1-72/720=9/10。 】

Call!

It's finally done!

Xiao Ran breathed a long sigh of relief, and at the same time, he couldn't help but want to greet the teacher who came out of the paper.

What is the intention to make the first fill-in-the-blank question so cumbersome, but the rest of it is so simple.

In case the candidate's psychological quality is poor, this will collapse the person's mentality.

O iniquity!

Xiao Ran sighed in his heart, but he also knew that now was not the time to complain, so he turned his attention to solving the question.

That's the highlight of a try!

Xiao Ran wanted to take advantage of the victory to chase after and face these big problems with his current state of excitement.

Maybe it was really a competitive state, Xiao Ran found that he made the first big question very easily.

It took only 12 minutes.

It was so easy that Lin Yu doubted himself a little.

Mo is not participating in a fake try.

But after reviewing the question stem and the solution method, there is no problem, which he dares to pack.

Seeing this, Xiao Ran couldn't help but start laughing at himself, how could he easily do the question and be a little unconfident!

This is a problem, and it must be changed in the future!

At this time, the time came to 8:38, and there was still a full hour and 2 minutes before the end.

There are still two unanswered questions.

It should be enough!

Thinking like this, Xiao Ran is ready to continue to charge, come on Ollie!

So, Xiao Ran turned to question 2 and began to examine the question carefully.

But at this moment, a voice suddenly came from behind him.

"Hello teacher, give me another piece of scratch paper."

It's Nie Feng!

What kind of moth is he going to do, Xiao Ran's heart jumped.

Sure enough, then I heard Nie Feng muttering to himself:

"Alas, the first big question just finished using up all the scratch paper, I'm really a waste of paper, not good, not good."

It sounds very casual, but it stinks!

As it was the time of the exam, the entire test room No. 1 was very quiet.

In addition, Nie Feng's muttering was not small, so everyone in the entire examination room heard it.

At this moment, many people immediately looked at Nie Feng in shock.

All kinds of OS began to play out in their minds constantly.

", I've just just started reviewing the question, and you've already finished writing your first big question!!"

"It's really fake, I'm only halfway done, you're already done!"

"Cry, what kind of monster is this, did you grow up eating Olympiad math problems?"

"Hmph, grandstanding, pretending to be B was struck by lightning!"

“……”

For a time, there was envy, jealousy, worship, disdain, and so on!

But what is common is the shock of unity.

After all, it's only 8:40 a.m., and the speed is amazing!

Nie Feng naturally felt the "envious" gazes of the people around him, but he didn't care.

He kept staring at Xiao Ran, who was sitting in front of him.

Hmph, little sample, know my speed, tremble, ignorant mortal!

At this time, Nie Feng really wanted to go to the front to take a look at Xiao Ran, presumably it must be interesting to see the other party trembling.

Xiao Ran naturally heard Nie Feng's muttering, and he estimated that Nie Feng had deliberately said it to him.

What a vengeful bear child.

But, brother, in front of me, you are really destined to be only a younger brother!

Because, you're really not fast enough!

Xiao Ran decided not to pay attention to Nie Feng, who was crazy behind him.

For the second big question, he already has a preliminary idea.

It doesn't seem to be as difficult as it might be to solve the inequality problem.

He began to do the math according to the ideas he had.

The result was unexpectedly smooth, and it only took 16 minutes for Xiao Ran to solve the problem.

In other words, only one last big question remains.

Whether you can completely take it a try depends on this last trembling.

This is the finale of analytic geometry.

[In the planar Cartesian coordinate system xOy, let AB be the chord of the parabola y^2=4x crossing point F(1,0), and △AOB's circumscribed circle intersection parabola at the point P.]

Point P is different from point O, A, B, if PF bisects ∠APB, find |All possible values of PF|. 】

The topic is not very long, and there are no dazzling graphics.

But Xiao Ran knew that this question could really be called the finale of this test paper.

Because it's really hard to do!

According to preliminary estimates, the mathematical theories that may be used include the circumscribed circle theorem, the angle bisector theorem, and the Vedic theorem.

This is still possible, as for how to use it, and which step to use, it is still unknown.

It's very complicated!

Xiao Ran guessed that this question is bound to become the biggest pull item for the first attempt, and it may also directly affect the belonging of province 1 and province 2.

After all, the second test is too difficult, and if you can get a high score as much as possible in the first test, or even a full score, then it is really not a big problem to win a prize.

You must know that in the past two years, the provincial second score line of Qilu Province is only in the early 100s, and the full score of the first attempt is 120 points.

So, while it's relatively easy, it's really important.

At the very least, it should be stable to keep it and take a province two.

This is also the reason why Mr. Han did everything possible to calm down the candidates of the Caozhou team before the game.

Because, for most candidates in Caozhou, it is really profitable to be able to get a provincial two.

Of course, this does not include Xiao Ran.

After Xiao Ran finished reviewing the question, he started the trial calculation as soon as possible, and tried all the theories that he had a hunch to use.

Although this question is difficult, Xiao Ran is not a vegetarian.

After several attempts, he finally succeeded in finding a solution.

Then, in one go, Xiao Ran wrote every step seriously, and did not give the marking teacher the opportunity to deduct points.

In this way, 20 minutes later, Xiao Ran had already written the test paper and got the final answer.

√13-1。

When he put pen to paper and wrote down this final answer, Xiao Ran couldn't help but breathe a sigh of relief.

He slowly put down the pen and paper and checked the answer again from beginning to end.

Well, it should be stable!

At this time, the clock in the test room showed 9:20 a.m., and there were 20 minutes left before the end of the test.

This time, it seems that the difficulty is really good.

Thinking like this, Xiao Ran looked around, he wanted to see if everyone felt the same way.

But at this time, he found that many people were still writing hard there, some frowning, some smiling, with different expressions.

The only thing that is the same is that none of them are done yet!

Even Nie Feng behind him, Xiao Ran could hear that he was still "swishing" and writing, and he shouldn't have finished it.

This......

Is there not many masters in this exam room?

Or did I get so strong before I knew it!

Or is it said that having a cold can really make people play extraordinarily!

Xiao Ran sighed in his heart, but no matter what, it was finally done, and there was no moth in his body, and Xiao Ran's whole person relaxed.

But as the saying goes, the more fortunate you are that nothing comes, then what will happen in the next second.

As soon as his body relaxed, Xiao Ran suddenly felt a little wrong.

Maybe it was because of the high-intensity suppression of the question just now, or maybe because the attention was diverted from being too excited to do the question, Xiao Ran didn't feel any special discomfort.

But now that it was done, as soon as his spirit relaxed, Xiao Ran immediately felt a wave of exhaustion in his body, and a sense of weakness and sleepiness welled up in his heart.

The body seems to be hollowed out, and it can't be supported a little!

When he noticed this, Xiao Ran couldn't help but secretly rejoice, fortunately, he didn't come up until he had done this cold sequelae.

If you come early, you'll be in trouble.

But then he smiled bitterly, because there was a second test at 10 o'clock, which was even more important.

Moreover, both the intensity and the difficulty are much higher than they are now.

Therefore, now I can only rest as soon as possible to recuperate.

But here is not familiar with the place, where is there a good place to rest, when you go out, you may only have to find a random place to work, it is better to rest in place.

At least there's everything here.

Thinking of this, Xiao Ran had a preliminary idea in his heart.

But at first, he saw that the people around him were still fighting there, and he wanted to continue to work hard.

He also wanted to check the exam paper again.

However, before he could read the two questions, a wave of discomfort came to him, Xiao Ran smiled bitterly, and had to lie down temporarily.

Rest now for a better fight afterward!

Slow down for a moment and check back later!

Xiao Ran, who was lying on his stomach, naturally attracted the attention of the invigilator in the No. 1 examination room.

He hurriedly walked over and wanted to inquire about the candidate.

But when he got closer and saw that Xiao Ran was just lying down to sleep, he couldn't help but sigh in his heart.

Alas, another baby driven crazy by the Olympiad!

In his eyes, he felt that Xiao Ran must have given up answering the question.

Every year, there are many such candidates, and some even cry during the exam.

The scene of crying and taking the exam is still fresh in his memory.

Therefore, at this time, he saw that Xiao Ran was just lying down to sleep, and there was no extra movement, so he naturally didn't care.

After all, no one is allowed to sleep in the Olympiad exam room!

People's mentality has collapsed, can't people heal their injuries for a while!

Silence!