学术能力

首先，我们需要考虑的是学生在学校的学习情况，我们将这一部分的权重定位40%，学生在这里的分数为A（Academics）。

具体来讲，这里我们考虑两方面因素，第一是整体的GPA，这一数值反映了学生各个方面的综合学习能力（$A_O$）。基于我们前文的综合叙述，我们不难发现，丘成桐奖实际上考察的是一个学生以科研能力为主的综合学术能力，其中包括了思维逻辑完整，语言表达，团队协作等各个方面。因此，我们首先需要考虑的是该学生整体的GPA。假设，学生的没有加权过的整体GPA为$A_O$（满分GPA为4.0，如果是100分机制的学生需要进行转换），这里学生的整体GPA占全部权重的25%, 具体可以表达为，$0.25 \times 100 \times \frac{A_O}{4.0} = 6.25 \times A_O$。

其次，我们需要考虑学生在专业课程上的学习情况（$A_S$）。这里重点考察学生在预计选择科研方向上的准备和相关基础，这里学生在专业学科的GPA（用$A_S$表示）占整体权重的15%，具体可以表达为，$0.15 \times 100 \times \frac{A_S}{4.0} = 3.75 \times A_S$。

英文能力

第二，我们需要参考学生英文的水平与能力。这里主要有两个考虑，第一，尽管丘成桐比赛预赛的论文可以用中文来提交，但由于在总决赛论文和答辩时均需要使用英文，学生需要确保英文的书面及口头表达的条例与规范。第二，在科研过程中，学生需要阅读大量英文文献，对这些文献的理解能力也直接决定了科研的进展。

因此，我们希望学生能够在考虑丘成桐奖参赛前英文能力过关，或者有书面的，比如托福或者雅思的相关成绩，英文能力的分数E（English）在整体定位的权重占比10%。这里我们以大家考的最多的托福（E为学生取得托福分数，其他测试均可换算为大概的托福分数）为例，来表达英文能力的分数情况，$0.10 \times 100 \times \frac{E}{120} = 0.0833 \times E$。

科研背景和相关经历

第三，在上述的硬性基础外，我们还需考虑学生在之前的学习过程中所具有的科研有关的背景和经历。这里包括但不局限于数理化的学科实验（比如IB物理的IA过程），计算机的竞赛，对某一学科或者课题长期的关注等等。这一部分的分数为B（Background），其整体权重为20%, 然而我们很难去用一个具体的方法去衡量，于是我们以调查问卷的方式来帮助学生明确这一部分的分数。每道问题，答案选是的话得2分，否的话0分，模棱两可在是否之间的答案统一为1分。10道问题如下所示。

1. 你是否长期（大于三年）关注某一个学科中某一个特定问题的发展与相关知识的获得？比如物理学中的黑洞问题，生物学中的DNA问题等等。

2. 你是否参加过其他形式的科研活动，并将成果以报告的形式产出？

3. 你是否觉得某一学科中过往的实验课极其有趣，并尝试过自己对上课的实验内容进行自发的扩展和思考？比如化学上Na和水的反应实验，自己想要尝试用其他物质去进行反应。

4. 你是否观察过生活中某一个现象，并希望通过自己的思考将该现象与课本中的知识做关联？比如将天空为什么是蓝色的与光学问题结合。

5. 你是否花费超过一天时间对一个数学物理难题，计算机算法实现等烧脑问题进行探究，并享受其探究过程？

6. 你是否曾经将某一个课题，知识点进行公开的讲解，并能够中各种的反馈中发现不足，保持进步？

7. 你是否参加过某一种比赛形式的竞赛，并在竞赛中体会到突破自己的乐趣？ 比如各种奥林匹克竞赛。

8. 你是否阅读过科研学术论文，并能够通过各种方式理解论文内容并学习到大量新的知识？

9. 你是否对数据比较敏感， 能够自发的去联想思考数字背后所能够带来的意义和对特定问题的解释？

10. 你是否明白科研是一个长期，枯燥，且艰辛的过程，并愿意为之去付出？

综上，我们这一部分的得分可以根据对以上问题的自省式回答得出，该调查问卷的得分即为B的分数。

时间精力

最后，也是最重要的考虑的因素，就是学生的时间与精力。大部分10-12年级的学生都会被各种各样的课业，活动，竞赛等等搞得极为充实。如果学生之前没有相关的课题学习以及科研背景的话，是需要花费很多时间和精力在丘成桐比赛的准备上的。所以，我们把整体分数的30%划分给了时间精力（T）这一部分。这里，理论上学生需要在5月到9月15号这一段期间内每天最少花费三个小时在科研有关的事情上，时间上的投入是丘成桐奖论文质量最基础的保障。如果学生没有办法去做到相对应的时间的投入，是很难在比赛中取得优异的结果的（天赋异禀，书香门第等类型除外）。因此，时间精力的分数为T（Time），T的分数具体为学生平均每天在科研上投入的时间小时数，那么其得分表达为 $0.30 \times 100 \times \frac{T}{3.0} = 10 \times T$。

总结

我们可以根据以上的情况，将所有分数进行汇总。 $$\begin{equation*} \begin{split} \mbox{分数} = &6.25 \times A_O + 3.75 \times A_S + 0.0833 \times E + B + 10 \times T \\ & A_O : \mbox{整体GPA} \\ & A_S : \mbox{学科GPA} \\ & E : \mbox{托福分数} \\ & B : \mbox{调查问卷分数} \\ & T : \mbox{每日科研时间小时数} \end{split} \end{equation*}$$ 举例：

1. 学生A，整体GPA 3.8，物理GPA 4.0，托福105分，调查问卷分数15分，每日科研时间2小时。综合得分为： $$\begin{equation*} \begin{split} \mbox{A学生分数} & = 6.25 \times 3.8 + 3.75 \times 4.0 + 0.0833 \times 105 + 15 + 10 \times 2 \\ & = \textbf{82.5} \end{split} \end{equation*}$$

2. 学生B，整体GPA 3.3，生物GPA 4.0，托福85分，调查问卷分数13分，每日科研时间1.5小时。综合得分为： $$\begin{equation*} \begin{split} \mbox{B学生分数} & = 6.25 \times 3.3 + 3.75 \times 4.0 + 0.0833 \times 85 + 13 + 10 \times 1.5 \\ & = \textbf{70.7} \end{split} \end{equation*}$$

2. 学生C，整体GPA 3.1，数学GPA 3.7，托福96分，调查问卷分数10分，每日科研时间1小时。综合得分为： $$\begin{equation*} \begin{split} \mbox{C学生分数} & = 6.25 \times 3.1 + 3.75 \times 3.7 + 0.0833 \times 96 + 10 + 10 \times 1 \\ & = \textbf{61.24} \end{split} \end{equation*}$$

根据我们大量的以往经验，该分数能较为准确的反应出一半学生的背景与是否适合参加丘成桐奖的程度。总的来说，得分在60分以上是参加丘成桐奖的必要条件，如果想要冲击总决赛以及更高的奖项，80分以上是必不可少的。以下表格可以更好的反映各区段学生的参赛目标和相关注意事项。

Academic Ability

First, we must consider how the student is doing at school. We set the weight of this part at 40%, and the student's score here is A (Academics).

Specifically, we consider two factors. The first is the overall GPA, which reflects the student's all-round learning ability ($A_O$). From our earlier discussion it is clear that the Yau Award in fact assesses a student's comprehensive academic ability, with research ability at its core — including logical completeness of thought, verbal expression, teamwork, and so on. So we first consider the student's overall GPA. Suppose the student's unweighted overall GPA is $A_O$ (out of 4.0; a student on a 100-point system must convert). Here the overall GPA accounts for 25% of the total weight, expressed as $0.25 \times 100 \times \frac{A_O}{4.0} = 6.25 \times A_O$.

Second, we consider how the student is doing in their subject courses ($A_S$). Here we focus on the student's preparation and foundation in the intended research direction; the student's subject GPA (denoted $A_S$) accounts for 15% of the total weight, expressed as $0.15 \times 100 \times \frac{A_S}{4.0} = 3.75 \times A_S$.

English Ability

Second, we must take into account the student's level and ability in English. There are two main considerations. First, although the paper for the Yau Award's preliminary round may be submitted in Chinese, the grand-final paper and defense both require English, so the student must ensure that their written and oral English is orderly and conforms to convention. Second, during the research the student must read a great deal of English-language literature, and the ability to understand it directly determines the progress of the research.

We therefore hope the student's English ability is up to standard before considering the Yau Award, or that they have a written record such as a TOEFL or IELTS score. The English-ability score E (English) accounts for 10% of the overall weight. Here, using the TOEFL that most people take as an example (E is the student's TOEFL score; other tests can be converted to an approximate TOEFL score), the English-ability score is expressed as $0.10 \times 100 \times \frac{E}{120} = 0.0833 \times E$.

Research Background and Relevant Experience

Third, beyond the hard foundations above, we must consider the research-related background and experience the student has gained in their earlier studies. This includes, but is not limited to, science experiments in mathematics, physics, and chemistry (such as the IA process in IB Physics), computer-science competitions, long-term attention to a subject or topic, and so on. The score for this part is B (Background), with an overall weight of 20%. Since it is hard to measure with a concrete method, we use a questionnaire to help the student establish this part's score. For each question, "yes" scores 2 points, "no" scores 0, and an answer ambiguously between yes and no scores 1. The 10 questions are as follows.

1. Have you, over the long term (more than three years), followed the development of and acquired knowledge about a particular problem in some discipline? For example, the black-hole problem in physics, the DNA problem in biology, and so on.

2. Have you taken part in other forms of research activity and produced the results as a report?

3. Have you found a past lab class in some subject extremely interesting and tried, on your own initiative, to extend and reflect on the experiment? For example, with the experiment on the reaction of Na with water in chemistry, wanting to try the reaction with other substances yourself.

4. Have you observed some phenomenon in everyday life and wanted, through your own thinking, to connect it with knowledge from your textbooks? For example, connecting why the sky is blue with optics.

5. Have you spent more than a day exploring a brain-teasing problem — a hard math or physics problem, the implementation of a computer algorithm, and the like — and enjoyed the process of exploration?

6. Have you ever given a public explanation of some topic or knowledge point and been able, from various feedback, to find your shortcomings and keep improving?

7. Have you taken part in some competition and felt the joy of surpassing yourself in it? For example, the various Olympiads.

8. Have you read academic research papers and been able, by various means, to understand their content and learn a great deal of new knowledge?

9. Are you fairly sensitive to data, able to spontaneously associate and ponder the meaning numbers can carry and their explanation of specific problems?

10. Do you understand that research is a long, tedious, and arduous process, and are you willing to commit to it?

In sum, the score for this part can be obtained from an introspective answering of the questions above; the questionnaire's score is the B score.

Time and Energy

Finally — and most importantly — comes the student's time and energy. Most students in grades 10–12 are kept extremely busy by all kinds of coursework, activities, competitions, and the like. If a student has no prior topic study or research background, they will need to spend a great deal of time and energy on preparing for the Yau Award. So we allot 30% of the total score to time and energy (T). In principle, a student needs to spend at least three hours a day on research-related matters during the period from May to September 15; the investment of time is the most basic guarantee of a Yau Award paper's quality. If a student cannot make the corresponding time commitment, it is hard to achieve an excellent result in the competition (exceptionally gifted students or those from scholarly families excepted). So the time-and-energy score is T (Time); the T score is the number of hours per day the student invests in research on average, expressed as $0.30 \times 100 \times \frac{T}{3.0} = 10 \times T$.

Summary

From the above, we can sum all the scores. $$\begin{equation*} \begin{split} \mbox{Score} = &6.25 \times A_O + 3.75 \times A_S + 0.0833 \times E + B + 10 \times T \\ & A_O : \mbox{overall GPA} \\ & A_S : \mbox{subject GPA} \\ & E : \mbox{TOEFL score} \\ & B : \mbox{questionnaire score} \\ & T : \mbox{daily research hours} \end{split} \end{equation*}$$ Examples:

1. Student A: overall GPA 3.8, physics GPA 4.0, TOEFL 105, questionnaire score 15, 2 hours of research a day. Overall score: $$\begin{equation*} \begin{split} \mbox{A score} & = 6.25 \times 3.8 + 3.75 \times 4.0 + 0.0833 \times 105 + 15 + 10 \times 2 \\ & = \textbf{82.5} \end{split} \end{equation*}$$

2. Student B: overall GPA 3.3, biology GPA 4.0, TOEFL 85, questionnaire score 13, 1.5 hours of research a day. Overall score: $$\begin{equation*} \begin{split} \mbox{B score} & = 6.25 \times 3.3 + 3.75 \times 4.0 + 0.0833 \times 85 + 13 + 10 \times 1.5 \\ & = \textbf{70.7} \end{split} \end{equation*}$$

3. Student C: overall GPA 3.1, mathematics GPA 3.7, TOEFL 96, questionnaire score 10, 1 hour of research a day. Overall score: $$\begin{equation*} \begin{split} \mbox{C score} & = 6.25 \times 3.1 + 3.75 \times 3.7 + 0.0833 \times 96 + 10 + 10 \times 1 \\ & = \textbf{61.24} \end{split} \end{equation*}$$

From our extensive past experience, this score fairly accurately reflects the background of about half of students and how well-suited they are to entering the Yau Award. In general, a score above 60 is a necessary condition for entering; to make a run at the grand final and higher prizes, a score above 80 is indispensable. The table below better reflects each band's competition goals and related cautions.