College entrance examinations

The **college entrance examinations** is an event that happens every year at the end of June. It is composed of Chinese Literature, Mathematics, English Language, Arts, and Science exams.

## Schedule

* Day 1 - Morning: English
* Day 1 - Afternoon: Arts and Science
* Day 2 - Morning: Chinese Literature
* Day 2 - Afternoon: Mathematics

## Beijing College Entrance Examinations

### **Reform**

The Beijing college entrance exams have been infamously easy compared to other provinces' entrance exams, so the Beijing Higher Education Entrance Examination Board wanted to add more difficulty to the exams.

### **Question Setting Teams**

#### Mathematics

* Supervisor: Pan Yang (Peking University)

* Members:
	+ Zhang Ye (Peking University)

#### Chinese Literature

* Supervisor: Yan Fu

* Members:
	+ Zhang Ye (Peking University)
	+ Su Na (Peking University)
	+ Liao Qi (Tsinghua University)
	+ Li Rui (Renmin University)
	+ Ma Qi (Beijing Normal University)

### **Operation "Send Zhang Ye Home"**

When the Beijing Higher Education Entrance Examination Board announced that Zhang Ye will be joining the question setting team for Mathematics and Chinese Literature, many Beijing college entrance examinees and parents protested due to Zhang Ye's infamous wondrous math problems. They launched a massive boycott against Zhang Ye labeled as "Send Zhang Ye Home". Not only were the examinees and parents caught off-guard, but even the high school teachers were also blindsided as they have no idea what questions Zhang Ye will set.

### **Examination Day**

Despite the Beijing Higher Education Entrance Examination Board's reform, the first day's exams were only slightly more difficult than the previous year's. Many of the Beijing examinees went home joyfully with their parents and their faces beaming. However, on the second day, barely anyone was able to answer the Chinese Literature exam questions. An online media outlet and many teachers and education industry insiders later analyzed that since the Chinese Literature exam is already very difficult, then the Mathematics exam will likely only be moderate or slightly above average difficulty. However, the Mathematics exam turned out to be at least two times harder than the Chinese Literature exam. They were dubbed as the most difficult exams in history.

#### Sample Questions

* Confucius and Laozi are fighting, who will you help?
* If the complex number z satisfies the equation z(2 - 3i) = 6 + 4i (where i is the imaginary unit), then the modulus of z is \_\_\_\_\_.
* There are 3 small balls of similar size in a box. One of them is a black ball. If two balls are randomly picked from the box, what is the probability of the two balls being different in color?
* To better understand the quality of a batch of cotton, a cotton mill randomly extracted 100 lengths of cotton fiber (the length of a cotton fiber is an important indicator of the quality of cotton). The resulting data falls between [5, 40]. Its appearance frequency is indicated in the distribution histogram below. [image] In the sampling of 100 lengths of fiber, there are \_\_\_\_\_ lengths that are shorter than 20mm.
* In the Chinese Literature and Mathematics subjects, the results are graded into 3 tiers of either "Excellent," "Pass," or "Fail." Assuming Student A's results are all not lower than Student B's, with at least one subject scoring better than Student B's, then the statement "Student A's results are better than Student B's" is valid. If among some students no one scored better than each other, and neither did any two students score the same points as another, with their Mathematics results also not the same. Then: What is the maximum number of students that fulfill the conditions?

### **Aftermath**

After the Chinese Literature and Mathematics exams, many Beijing examinees were brought to tears by the difficulty. Not long after, a call to "severely punish the question setter" was making rounds across the Internet. Countless Beijing examinees and their parents were participating in it. When Zhang Ye went online on Weibo, he was besieged by countless people cursing at him which made him go offline and lie low.

The Beijing Higher Education Entrance Examination Board later exposed the names of the question setters of the most difficult questions in the various subjects' exams and even revealed some details in regard to how a question should be written. The press release revealed that all the insane questions in the Chinese Literature and Mathematics exams were all set by Zhang Ye.

The low average of the Beijing examinees caused the admission cutoff scores to drop drastically. Later, the supervisor of the national college entrance examination question setting team praised the standard of Beijing's exams and wished to invite Zhang Ye to the question setting task in the national college entrance exam the following year.

### **Results**

#### Average scores

* Beijing Municipality Chinese Literature Examination Average Score: 72 points
* Beijing Municipality Mathematics Examination Average Score: 59 points

#### Cut-off scores

* Arts Subjects Tier 1 Grade cutoff score: 467
* Science Subjects Tier 1 Grade cutoff score: 464
* Arts Subjects Tier 2 Grade cutoff score: 425
* Science Subjects Tier 2 Grade cutoff score: 421

## Trivia

* Question setters can't return to their homes or contact the outside world even after finishing their work
* The Chinese Literature examination's average score of Beijing examinees was lower than the national average by nearly 30 points
* The Mathematics examination's average score of Beijing examinees was lower than the national average by nearly 40 points
* The total scores that the Beijing examinees got were lower than the national average by more than 70 points
* Zhang Ye's Beijing Mathematics test is the most difficult in the history of the national college entrance exam
* Huang Lingling was the only one who got a perfect score in the Mathematics exam

## References

1. ↑ Chapter 696: The Higher Education Entrance Examination Board's Invitation!
2. ↑ Chapter 618: Philosophy behind the math problem!
3. ↑ Zhang Ye's Classroom