The Chinese Gaokao just happened. My Chinese social media is full of celebrities cheering on high schoolers. At the same time, since last year, I have seen an increase in criticisms of the SAT, especially about the math section. Compared to other countries’ college entrance exams, the SAT is more elementary. As a result, it does not provide as much information about the students’ abilities at the top level.
The Chinese Gaokao is often compared to the SAT. However, I have not seen a serious description of the Gaokao. In this article, I would like to give a concrete idea of how difficult the Chinese Gaokao is. This article will first introduce the Gaokao system and then analyze several test questions from the Gaokao in recent years.
The History of the Gaokao
The Gaokao, also known as the Chinese college entrance exam, stems from the Chinese civil service exam, which dates back to the 6th century during the Sui Dynasty. Before that, they used the nine-rank system which relied on a central Controller’s grading and recommendation of potential government officials. The nine-rank system had several defects such as corruption and low social mobility. Thus, the Sui Dynasty improved on the old system and was considered the start of the Chinese civil service exam.
Different dynasties had different rules on the civil service exam, but in general, there were several levels of exams to take. Successfully passing each level would grant the examinee a title. For example, in the Qing Dynasty, when the examinee passed 院试 or a prefectural exam, they gained the title “生员” and they officially entered the gentry scholars class, the highest-ranked class in ancient China.
The subjects in the Chinese civil service exam varied across dynasties as well. However, after the Ming Dynasty, it became more and more limited to Zhu Xi’s Four Books. Many students studied only the Four Books and Five Classics. It became more of a “teaching to the test” practice.
The legacy of the civil service exam remained after the Qing Dynasty. In 1938, the Nationalist government started the Gaokao, which was the first unified Gaokao of China. It only existed for three years, then it was disrupted by WWII. The first Gaokao after the CCP took power was in 1952 and then it was disrupted by political turmoil. It restarted in late 1977. The Ministry of Education standardized the test. Many legacies of the civil service exam can still be seen in today’s Gaokao. For example, today, if a student gets first place in the Gaokao in his province, he will be called xx province’s Gaokao Zhuangyuan. In the civil service examination, Zhuangyuan refers to the first place in the palace examination. For another example, today's Gaokao still balances regional differences, similar to how the civil service exam allocated quotas to each region.
The current Gaokao
Let’s get some facts about the Gaokao straight:
What subjects are there?
The compulsory subjects are Language and Literature, Mathematics, and Foreign Language. Then each student can choose electives. Usually, they choose 3 electives from Political Science, History, Geography, Physics, Chemistry, and Biology.
When/where do students take the test?
Unlike the American SAT, which happens multiple times a year, the Gaokao happens once per year, around June 7 - June 10. The Gaokao generally takes place at the location of the student's hukou registration or school registration. The municipal education bureau organizes the test centers, usually set up in local middle or high schools.
Is it a standardized test?
No, it’s not a standardized test. There are several versions of the exam and different provinces have different rules for the Gaokao as well. For example, some regions use 3+3 mode, which means that in addition to Chinese, Mathematics, and Foreign Language, students must independently choose three subjects from Political Science, History, Geography, Physics, Chemistry, and Biology as their elective subjects for the Gaokao; some regions use the 3+1+2 mode, which means in addition to Chinese, Mathematics, and Foreign Language, students must choose one subject from Physics or History, and independently select two subjects from Political Science, Geography, Chemistry, and Biology as their elective subjects for the Gaokao. Some provinces share the same exam questions on certain subjects.
The difficulty of the Gaokao varies across provinces. Here is a figure showing the difficulty of the Gaokao that has been circulating on the Chinese internet (I don’t know who made this, but if you did, please let me know and I’ll quote you properly). The easiest is red and as you go down the legend it gets harder. While I can’t verify the methodology that created this figure, I do intuitively think this figure makes sense. Firstly, impoverished areas usually have an easier version of the Gaokao — thus the western part of China is colored red and yellow. On the contrary, the eastern and southern parts of China have a harder version of the Gaokao because those areas are richer. Secondly, there are several regions that are known to have an advantage. For example, Beijing’s Gaokao is known to be easier, per online discussion.
Lastly, minority groups also receive some advantages. According to the 2009 bonus point policy for the Gaokao introduced by the Ministry of Education, minority groups get 10 bonus points. But the bonus policy also varies across provinces and is gradually decreasing. The bonus points for minority groups also caused fervid online discussions as some people see it as unfair (this sparks similar debates to affirmative action in the United States, with the exception that AA is more legible in China).
How many points do I need to get into PKU/THU?
This also depends on which province you are from, and what subjects you chose (humanities vs. science). Here is PKU’s 2023 admission cutoff score. Taking the province I grew up in, Zhejiang, as an example, it uses 3+3 mode. Each compulsory subject is worth 150 points, and each elective is worth 100 points, summing up to a total of 750 points. PKU’s admission cutoff for Zhejiang is a little above 700. So one can lose only less than 50 points across the tests. To give you an intuitive sense of what losing 50 points off is, the last math question shown below is worth about 20 points. So you can only afford to get 2-3 questions like that wrong to get in!
Gaokao Questions
Math
Now, Imagine you are a Chinese high school kid. You just learned the basic rules of the Gaokao, and now you are ready to study by looking at Gaokao Questions. You open up past test questions, and the first question on the math test is:
Not too bad, right?
Answer:
If you get this question wrong on the exam, your teacher will probably give you a side-eye.
You think this is easy, so you decide to jump to the last question that is known for being difficult. Here is the last question:
Hmm, this is… very difficult. The answer for Q1 is:
You should try to solve Q2 and Q3. I will not post the answers here for now, considering the length of this article.
And just a reminder, if your family is willing to send you abroad for college, here is the last (thus the hardest) question on SAT math:
Language and Literature
The language and literature exam starts with readings like this one:
The whole article is too long, I’m not going to post it here. Then, for the questions:
So it kind of looks like the SAT’s reading part. But the SAT does not have prompts like “President Biden has visited xxx and done xxx, please analyze what is the importance.”
You will also be asked to analyze ancient Chinese texts:
I always find this part quite hard (but actually very useful, now that I work on economic history!)
The last question is usually an essay:
This part looks like SAT writing in my opinion. Of course, SAT writing usually doesn’t ask this kind of essay questions that glorify America:
English
Finally, you have to study a foreign language as well. The English exam contains a listening test and a writing test. Here is an example:
SAT does not require a foreign language, but I have taken Chinese and Japanese AP tests during high school. My impression is that they are at similar levels.
Conclusion
I presented here a picture of the Gaokao system and the difficulty of the Gaokao. On the one hand, I think the Gaokao is really competitive and it’s a pity to spend one’s youth preparing for an exam. Of course, this is partly due to China being a big country and the legacy of the civil service exam (it was always thought of as a fair way to change one’s social class).
On the other hand, I think there are many things from the Gaokao that the American SAT should learn from. For one, I do think the SAT’s math part is too easy. Among reasonably smart people, it’s not a test of your math ability but whether you are good at not making silly arithmetic mistakes. I got a full score on both SAT and GRE on the first try without spending time practicing the math part and so did many of my friends. I would appreciate it if the test could be more selective on pure math skills than arithmetic.
Overall, I think the Gaokao as a system has tried its best to maintain a relatively fair competition in a large country like China. The bonus points for minorities are also well-thought-through and provide a concrete idea of the affirmative action they get (in contrast to American affirmative action which is more to the school’s own discretion).
Lastly, to all the seniors everywhere who just finished high school, have a fun summer!
The math question is fun. Seems like there are two kinds of (i,j)-pairs to look for.
(1) Those that leave only segments that consist of consecutive elements in multiples of 4.
m=1 : (1,2) (1,6) (5,6)
m=2 : all those from before, and also (1,10) (5,10) (9,10)
m=3: all those from before, and also (1,14) (5,14) (9,14) (13, 14)
So the number of ``good'' combos of this sort is
1+2+ ... + m + (m+1) = (m+1)(m+2)/2 = (m^2 + 3m + 2)/m
(2) Those that allow for `skipping sequences'.
m=2 : removing (2,9) allows for arithmetic sequences (1 3 5 7) and (4 6 8 10)
m=3: removing (2,13) allows for arithmetic sequences (1 4 7 10) , (3 6 9 12) and (5 8 11 14)
BUT also, (2,9) still works and so does (6 13), which is just (2 9) shifted over by 4.
The removing pairs of the skipping type are therefore:
m=2 : (2,9)
m=3: (2,9) (6,13) and (2 13)
m=4: (2,9) (6,13) (10,17) and (2 13) (6 17) and (2 17)
So the number of ``good'' combos of this sort is
1+2+ ... + (m-2) + (m-1) = (m-1)m/2 = (m^2 - m)/m
Overall, the number of ``good'' combos is
(m^2 + 3m + 2)/m + (m^2 - m)/m = m^2 + m +1
Now, the total number of combinations is
nC2 = n! / 2!(n-2)! = (n-1)n/2 = (4m+2)(4m+1)/2 = 8m^2 + 6m+1
Therefore, the probability of drawing a ``good'' pair (i,j) is
Pm = (m^2 + m +1) / (8m^2 + 6m+1) > (m^2 + m +1) / (8m^2 + 8m+8) = 1/8
QED.
I can solve all the questions easily