The last question and last part of the last problem in the college entrance examination mathematics, worth 8 points.
These 8 points successfully caught Shen Qi's attention.
For any positive number a, prove that 1 < f(x) < 2
Based on the given information, Shen Qi began to verify it.
From 1/√[1+x]>1/(1+x)
1/√[1+a]>1/1+a
1/√[1+b]>1/1+b
Therefore, f(x) > 1
It's not difficult; the test points are the same as those for function monotonicity, inequalities, and the method of bounding, etc.
Shen Qi felt that the last question was somewhat like the approach used in math competitions, because it required the comprehensive application of various high school math knowledge and the application of constructive thinking.
Next, Shen Qi needs to prove that f(x) < 2.
Due to the symmetry of x, a, and b, let x ≥ a ≥ b, then 0 < b ≤ 2
Shen Qi quickly proved that f(x) < 2.
Therefore, 1 < f(x) < 2
Q. E. D.
At this point, 40 minutes had passed since the exam started.
Shen Qi didn't deliberately pursue speed in answering questions. This is the college entrance examination; what's the point of being fast?
The key is accuracy, the scoring rate, and ensuring a perfect score on the math exam.
He checked the paper again and again until the bell rang. Shen Qi handed in his paper, then went home to rest and sleep.
Nothing more was said that night.
At 9:00 AM on June 8th, the subject with the highest score—Science Comprehensive—began its exam.
Of course, the Science Comprehensive forcibly combines three separate subjects into one college entrance examination subject.
Generally speaking, in a Science Comprehensive test paper with a total score of 300, physics accounts for 110 points, chemistry accounts for 100 points, and biology accounts for 90 points.
Shen Qi is the National Champion, winning the most gold medals.
This CPhO National Final gold medal was won not long ago; it's still fresh in everyone's memory.
It can be said that, apart from mathematics, physics is the subject Shen Qi is most confident in.
But Shen Qi dared not be careless. Who the hell dares to be careless with the Science Comprehensive exam?
Moreover, in chemistry and biology, one wrong move and things can go wrong.
300 points is no small number; it was the highest score in the entire exam hall.
Math plus Chinese equals one Science Comprehensive.
Let's get started, Science Comprehensive.
Shen Qi began working on the multiple-choice questions on the Science Comprehensive exam.
The multiple-choice questions in the Science Comprehensive are intimidating; each question is worth 6 points.
Damn, that's a 6-point question!
In yesterday's math test, I have a question: how do I get full marks (6 points) if I write almost half a page?
In today's Science Comprehensive, you only need to identify one letter to get 6 points.
Of course, if you choose the wrong letter, you'll lose all 6 points.
How many perfect 6s can one afford to miss in a lifetime?
If you get three 6-point questions wrong in a row, 666, you're definitely doomed.
Some test takers' hands trembled when answering Science Comprehensive -choice questions in the science section, especially during the college entrance examination.
Look, a pretty girl next door is crying, it's scary.
The young female test-taker got nervous and tore the exam paper while flipping through it.
She cried.
Shen Qi was also saddened by what he saw. "Please accept my condolences, girl. I can't help you. I wish you good luck."
Concentrating his mind, Shen Qi conquered the Science Comprehensive exam paper.
The first question to be asked was a biology question.
"In fruit flies, the red-eye gene (R) is dominant over the white-eye gene (r) and is located on the X chromosome; the long-wing gene (B) is dominant over the vestigial-wing gene (b) and is located on an autosome. A red-eyed, long-winged fruit fly is mated with a white-eyed, long-winged fruit fly. One-eighth of the F1 males are white-eyed and vestigial-winged. Which of the following statements is incorrect?"
A. The genotype of the parent female fly is BbX^RX^r;
The probability of a long-winged male fly appearing in B. F1 is 3/16.
C. The male and female parents produce gametes containing X^r in the same proportion;
"D. White-eyed, vestigial-winged female flies can form polar bodies with the genotype bX^r."
"This biology question..." Shen Qi felt a sense of déjà vu about the question about fruit fly mating and reproduction.
So classic, so familiar.
How could the National College Entrance Examination (Gaokao) be complete without fruit flies and white mice?
These two small, even insignificant creatures are the main characters in the college entrance examination.
"This biology question... although simple, it still has a trap. The person who set the question is so cunning! Are you perhaps the legendary king of trick questions?"
Shen Qi was very cautious. Although he was more than 99.999% sure he could answer immediately, he still reviewed the question again.
In fact, Shen Qi was somewhat worried that he might make a careless mistake on the multiple-choice questions in the Science Comprehensive.
Short answer questions involve derivation and calculation processes. As long as Shen Qi performs the derivation and calculation on paper, he generally won't make mistakes.
Those who master the Science Comprehensive subjects will conquer the world.
In the Science Comprehensive, each multiple-choice question is worth 6 points and cannot be wrong, nor can it be wrong.
The accuracy rate on multiple-choice questions is a major nightmare for improving Science Comprehensive scores throughout the senior year of high school.
"Therefore, when long-winged individuals mate, and vestigial wings appear in the offspring, all long-winged individuals are heterozygous (Bb)... A is correct."
"The probability of a long-winged male fruit fly appearing in F1 is 3/4 × 1/2 = 3/8, so the description in B is incorrect."
"C and D are also correct, so choose B."
Shen Qi reviewed the document with extreme caution, and ultimately chose B.
Next, the multiple-choice questions in chemistry and physics came at once.
Shen Qi spent an hour answering the multiple-choice questions, carefully considering each one before making his selection.
Finally, Shen Qi finished the multiple-choice questions and breathed a sigh of relief. He should have no problem getting them all right.
The following short answer questions, well, those were complete idiots.
In no time, Shen Qi finished the short answer questions, checked them several times, and then handed in his paper when the bell rang.
The last exam this afternoon is English.
Having completed numerous English mock exams, Shen Qi achieved a perfect score of 150, a minimum score of 130, and an average score in the 140s.
Before the English exam in the college entrance examination, Shen Qi was not entirely confident of getting a perfect score, and could only set a small goal of getting 145 and striving for 150.
But Shen Qi was in exceptionally good form this afternoon, and he was really into English, there was no stopping him.
The teacher is right, in the exam room, your presence determines everything!
At 5:00 PM on June 8th, the bell rang to signal the end of the English exam.
"Holy crap, I'm finally free!"
"I'm going to sleep forever, until the end of the world!"
The test takers jumped and skipped around, letting loose and enjoying themselves.
These past three years have been tough, it's time to let loose and have some fun.
Shen Qi blended in unnoticed in the crowd. Inspired by the group of peers around him, he shouted a couple of times, "We're free! We're at home! Time to collect the laundry!"
Just to fit the occasion.
Suddenly, Shen Qi noticed a group of people carrying video cameras and other equipment scattered around the entrance of the school where the exam was being held.
He knew that this group of people were definitely not the parents of the test takers.
The reporters are here! Run!
Shen Qi took a shortcut, slipped through the bushes, and secretly left the No. 1 Middle School examination hall.
He hates reporters the most, and he often gets tricked by them.
After being tricked by a reporter, the story was even adapted by a comedian.
So he made a hasty retreat and went home to guard the tower.
In reality, the college entrance examination is not truly over yet.
The exam is over; what determines a candidate's fate are their scores and the admission cutoff score.
The marking of college entrance examination papers in Nanyue Province began the following day, and the results will be released two to three weeks later, at the end of June.
Students in Nanyue Province will fill out their college application forms after checking their college entrance examination scores.
Candidates can rest for two to three weeks, but they are not really able to relax.
Shen Qi didn't feel as much pressure; he knew exactly which university he would be enrolling in in September.
His purpose in taking the college entrance examination was to rack up achievements and accumulate academic points.
On the same day that the marking work began, Shen Qi returned to Nangang Second High School. He had some personal belongings stored with Zhang Wanbang, and he went back to the school to retrieve them.
Upon entering the gate of Nangang Second High School, Shen Qi was astonished to see white snowflakes dancing in the air, a dazzling display of colors.
It doesn't snow on a hot day; the "snowflakes" falling from the sky are made of scraps of paper.
"They've gone mad, they've all gone mad, students!" Shen Qi discovered that the senior students were tearing up books, textbooks, test papers, and exercise books.
"This is all knowledge! Don't do this, students!" Shen Qi was heartbroken. He immediately ran up to the teaching building and tried to stop the students' crazy behavior of destroying knowledge.