On Saturday morning of the third week, Rococo took her first test since high school - Mathematics Compulsory I, Unit 1, and Sets and Functions Concepts Unit Test. Pen & Fun & Pavilion www.biquge.info

The math teacher is a fifty-year-old female teacher with a ponytail, and it is said that she is not bad at knowledge, but in the process of teaching students, the transmission efficiency is a little low.

Rococo has heard many people discuss in private, saying that the average score of mathematics in the classes taught by the math teacher in their class has never been in the top ten, and in the show, there are only nineteen classes in total.

Just imagine, when the students in other classes scored more than 130 points in mathematics, they were the top ten in the class, but under the teaching of this teacher, 130 points are not, 128 points are already the highest score in the class, just imagine the gap.

So when a classmate in the class was bored and suddenly mentioned that his senior brother had said this, the hearts of the other students were blocked. Since they are here in the show, of course, they hope to continue to get better results.

The exams have begun.

Question 1, how many subsets are there in the set {a,b}?

The answer is undoubtedly c, 4, because a, b, {a, b}, and empty sets are all subsets of the set {a,b}.

In the second question, let the set a={x|-4

The answer Rococo is also easy to figure out, it is (-4,2], so the answer is b.

The previous topic is basically a warm-up. The key is still later.

Let the function f(x)=ax squared + bx+1(a≠0,b∈r), if f(-1)=0, and for any real number x(x∈r) inequality f(x)≥0 is constant:

(1) Find the values of real numbers a and b;

(2) When x∈[-2,2], g(x)=f(x)-kx is a monotonic function, and the range of values of the real number k is obtained.

This is the last question of this unit test, to be honest, Rococo is not too smart because she is not too smart, so when she encountered such a question, she was very confused when she read it for the first time, and she didn't know where to start. It's just that now that she is living a new life, she has a huge advantage over many others that many people don't have.

That is, she had already done a lot of questions like this before this exam, and through the error book, she had completely mastered the routine of solving questions like this.

To be honest, Rococo admits that she is not smart at all, but she wins, and she will be one step ahead of others. She doesn't rely on talent to eat, she relies on her own sweat and the wisdom of her predecessors.

After reading the question, Rococo almost did not hesitate and began to write, because in her mind, such a topic can already be divided into several steps, as long as she follows the 'universal formula' in her mind, any difficult problem is not a problem.

The total time for the exam is two hours, and Rococo only took one hour to finish the whole paper, and there was a full hour left, and Rococo was checking whether he would make mistakes or forget something for a while.

And the math teacher on the podium ......

Although it was an invigilator, she didn't seem to care too much about whether anyone was copying it below.

In the first half hour, I held a newspaper in my hand and kept reading it on the podium, and in the second half an hour, I looked at it from time to time, but what I saw was not whether anyone was copying it, but I wanted to see the expressions of the people below doing the question.

When she saw that many boys were scratching their heads and stopping their pens there, she smiled. Of course, it's not a joke, a ridicule or anything like that, but a very optimistic attitude towards life.

However, although many boys scratched their heads, there are a few boys, and she is still very optimistic.

For example, Luo Li, as her representative of mathematics, and the high school entrance examination is still a full score in mathematics, the mathematics teacher can be said to still have great expectations for Luo Li.

Last year, the highest score in other people's classes was 140 or 145, but in their class for a year, the highest one was only 128, do you really don't care at all? That's impossible! In fact, she also hopes that her students can get better results, but how to say, she has been a teacher for nearly 30 years, and she knows that high school mathematics is still very different from junior high school mathematics.

You may not be able to imagine that there will be someone who fails such a top student in the show, but the truth is like that. Because the high school questions, the implied information, are too vague, such as today's last question.

Let the function f(x)=ax squared + bx+1(a≠0,b∈r), if f(-1)=0, and the inequality f(x)∈r≥0 is constant for any real number x(xr), can you immediately see what this means?

You can see that what it means is that when a=0, f(x) is a one-time function, which is certainly not true for the following conditions. Therefore, f(x) must be a quadratic function and have only one intersection point with the x-axis, i.e. when x=-1.

Therefore, as long as it is solved by substituting f(-1)=0, i.e., a-b+1=0 and b-squared-4a=0, it is the answer. The answer to the first question is a=1, b=2. But how does b squared -4a=0 come about? Does the title tell you? No!

That's high school math! It won't tell you directly, it's a quadratic function, it's just going to tell you a≠0; And it doesn't tell you directly, b squared -4a=0, it only tells you that the inequality f(x)≥0 is constant and f(-1)=0.

Anyway, it's all kinds of winding, as if the conditions are not hidden tightly, it can't reflect the level of the questioner, so if some people will only get the conditions on the question and substitute it, f(-1)=0, then substitute x=-1, equal to 0, and then, many people don't have it, because they can only get a-b+1=0, how do I know how much a is equal to, how much b is equal to?

However, although high school math is so twisted and turned, math teachers still believe that there are still smart students who can answer it, and the key is that they can produce a few in their class this year.

When Luo Li noticed the math teacher's gaze, he couldn't help but look up at the math teacher. But the following actions are unacceptable. Because if even Luo Li scratched his head, wouldn't the others ......

But just as there was still half an hour left before the exam, about twenty minutes or so, one person suddenly stood up.

"Teacher! I'm in a bit of a hurry today, so can I turn in my papers early? ”