Introduction to Gaokao Notes - Wyatt's Notes

The Gaokao (高考, formally the National College Entrance Examination) is the standardised examination used for university admission in China. It is widely regarded as one of the most competitive and consequential examinations in the world, taken by approximately 10–12 million students each year across the country.

The Gaokao is administered annually in early June over a period of two to three days, depending on the province. The examination results determine university placement, with top-tier universities (e.g., Tsinghua University, Peking University, Fudan University) requiring exceptionally high scores.

Key features of the Gaokao:

• A single examination with no repeated attempts within the same year (though students may re-sit in subsequent years)
• Results are the primary criterion for university admission in most provinces
• Content and format vary by province, though a national framework is maintained
• The system has undergone significant reforms in recent years, with many provinces adopting the 3+1+2 model

Historically, most provinces followed the 3+X model:

• 3 (mandatory subjects): Chinese (语文), Mathematics (数学), and a Foreign Language (外语) — most commonly English
• X (elective subjects): Students choose from a set of electives depending on their province and stream (Arts/Humanities or Science). In the traditional system:
  • Science stream: Physics (物理), Chemistry (化学), Biology (生物)
  • Arts stream: History (历史), Geography (地理), Politics (政治)

Under this model, the total score is in most cases 750 points:

• Chinese: 150 points
• Mathematics: 150 points
• Foreign Language: 150 points (including a 30-point listening component)
• Comprehensive Science / Comprehensive Arts (combined paper): 300 points

As of 2024, most provinces have transitioned to the 3+1+2 model, which offers greater flexibility in subject selection:

• 3 (mandatory): Chinese, Mathematics, Foreign Language
• 1 (preferred elective): Students choose one subject from Physics or History. This choice determines the broad category of programmes they can apply to at university.
• 2 (free electives): Students choose two subjects from the remaining four: Chemistry, Biology, Geography, Politics

This model allows up to 12 different subject combinations, compared to only 2 under the traditional system (Science or Arts). It better accommodates students with cross-disciplinary interests and reduces the rigid Arts vs Science divide.

Scoring under the 3+1+2 model:

• Chinese: 150 points (original score)
• Mathematics: 150 points (original score)
• Foreign Language: 150 points (original score)
• Preferred elective (Physics or History): 100 points (original score)
• Two free electives: Each scored out of 100, but converted to a scaled score based on provincial rank. This scaling mechanism ensures that the difficulty of different subjects does not disadvantage students who choose harder electives.
• Total: 750 points

Some provinces (e.g., Zhejiang, Shanghai) adopted an earlier reform using the 3+3 model:

• 3 (mandatory): Chinese, Mathematics, Foreign Language
• 3 (free electives): Students choose any 3 from 7 options: Physics, Chemistry, Biology, History, Geography, Politics, and (in some provinces) Technology (技术)

This offers up to 35 subject combinations. Each elective is scaled similarly to the 3+1+2 model.

The Gaokao”s total score of 750 points is distributed across the mandatory subjects and electives as described above. Understanding how scores are reported and used is critical:

• Original score (卷面分): The raw mark a student receives on the exam paper. Used directly for Chinese, Mathematics, Foreign Language, and the preferred elective (Physics or History) in the 3+1+2 model.
• Scaled score (等级赋分): Under the reformed system, the two free electives are converted from raw marks to scaled scores. The scaling is based on the student’s percentile rank in that subject within the province, ensuring fair comparison across subjects of different difficulty.
• Provincial rank (省排名): In many provinces, students receive a percentile-based rank rather than an absolute score. University admission is often based on rank position within the province.

Students receive their scores approximately 2–3 weeks after the exam, in most cases in late June. The score report includes:

• Individual subject scores
• Total score
• Provincial rank or percentile band

China’s Gaokao system has significant provincial variation in several areas:

Notable examples:

• Beijing, Tianjin, Shanghai, Zhejiang: Use their own provincial papers and have been at the forefront of reform, adopting flexible subject selection models earlier than other provinces.
• Henan, Shandong, Guangdong: Among the provinces with the highest number of Gaokao candidates, making competition extremely intense.
• National papers (全国卷): Used by the majority of provinces and come in several versions (全国I卷, 全国II卷, 全国甲卷, 全国乙卷) to reduce the risk of leakage and accommodate regional curriculum differences.

This site provides comprehensive revision notes for the following Gaokao subjects:

• Mathematics — covers both the Arts (文科数学) and Science (理科数学) streams, including all topics tested on national and provincial papers
• Physics — mechanics, electromagnetism, thermodynamics, optics, and modern physics
• Chemistry — stoichiometry, chemical bonding, reaction kinetics, equilibrium, organic chemistry, and electrochemistry
• Biology — cell biology, genetics, ecology, human physiology, and evolution
• English — reading comprehension, writing, vocabulary, grammar, and listening strategies

Each subject page covers key concepts aligned with the Gaokao syllabus, worked examples, exam-style questions, and detailed solutions.

• Master the fundamentals. The Gaokao emphasises deep understanding of core concepts. Ensure you have a solid grasp of foundational knowledge before tackling advanced problems.
• Practise extensively. Complete as many past papers as possible. The Gaokao has a large bank of published past questions available from various provinces. Aim to solve problems from multiple provinces to expose yourself to different question styles.
• Time management is critical. The Gaokao is a timed examination with strict time limits for each paper. Practise completing papers under timed conditions to build speed and accuracy.
• Analyse your mistakes. Keep an error log to track recurring mistakes. Review and correct mistakes systematically to avoid repeating them on the actual exam.

• Mathematics: Focus on problem-solving strategies and pattern recognition. The Gaokao mathematics paper includes questions of increasing difficulty — ensure you can solve the standard questions quickly to allocate time for the more challenging final problems.
• Sciences (Physics, Chemistry, Biology): Understand the underlying principles and their applications. The Gaokao often tests concepts in novel contexts. Practise interpreting experimental data and drawing conclusions.
• English: Build vocabulary systematically. Practise reading comprehension with a variety of text types. For the writing section, learn and practise common essay structures and transitional phrases.

• Answer every question. In the Gaokao, there is generally no penalty for guessing on multiple-choice questions. Never leave a blank answer.
• Show all working for calculation questions. Partial marks are awarded for correct methods, even if the final answer is incorrect.
• Read the entire paper before starting. Quickly scan the paper to identify easy and difficult questions. Start with questions you are confident about to secure marks and build momentum.
• Manage stress effectively. The Gaokao is a high-pressure examination. Develop healthy coping strategies: adequate sleep, regular exercise, and balanced nutrition in the weeks leading up to the exam are as important as academic preparation.

The Gaokao is like a marathon, not a sprint. You would not expect to run 26 miles without months of training, and the same applies to this exam. Each subject you study is a training session: some days you build endurance with long practice sets, other days you work on speed with timed drills. The key is consistent effort over the months leading up to the exam, not cramming in the final week.

Strategy is like a game plan in sports. You would not enter a basketball game without knowing which plays to run in different situations. Similarly, knowing which sections to tackle first, which questions to skip and return to, and how to allocate your time across subjects is the difference between a good performance and a great one. The best athletes and the best students both succeed because they prepare their strategy as carefully as their skills.

The key principles covered in this topic are linked in the sub-pages above. Focus on understanding the definitions, applying the formulas or frameworks, and evaluating strengths and limitations of each approach.

题目： 从集合 $\{1, 2, 3, 4, 5, 6\}$ 中随机抽取两个不同的数字 $a$ 和 $b$，求 $a + b$ 为偶数的概率。

解答：

步骤1：总取法数为 $\binom{6}{2} = 15$ 种。

步骤2：$a + b$ 为偶数当且仅当 $a$ 和 $b$ 同奇或同偶。

• 奇数集合：$\{1, 3, 5\}$，取法数 $\binom{3}{2} = 3$
• 偶数集合：$\{2, 4, 6\}$，取法数 $\binom{3}{2} = 3$

步骤3：有利取法数 $= 3 + 3 = 6$。

步骤4：概率 $P = \dfrac{6}{15} = \dfrac{2}{5}$。

答案： $P = \dfrac{2}{5}$

题目： 已知函数 $f(x) = x^3 - 3x^2 + 1$，求 $f(x)$ 在区间 $[-1, 4]$ 上的最大值和最小值。

解答：

步骤1：求导：$f'(x) = 3x^2 - 6x = 3x(x - 2)$。

步骤2：令 $f'(x) = 0$，得 $x = 0$ 或 $x = 2$，均为区间内的驻点。

步骤3：计算端点值和驻点值：

• $f(-1) = (-1)^3 - 3(-1)^2 + 1 = -3$
• $f(0) = 0 - 0 + 1 = 1$
• $f(2) = 8 - 12 + 1 = -3$
• $f(4) = 64 - 48 + 1 = 17$

步骤4：最大值为 $f(4) = 17$，最小值为 $f(-1) = f(2) = -3$。

答案： 最大值为 $17$，最小值为 $-3$

题目： 在标准状况下，将 $2.24\,\text{L}$ 的 $\text{CO}_2$ 通入 $100\,\text{mL}$ $1\,\text{mol/L}$ 的 $\text{NaOH}$ 溶液中，求所得溶液中溶质的物质的量之比。

解答：

步骤1：计算物质的量：

• $n(\text{CO}_2) = \dfrac{2.24}{22.4} = 0.1\,\text{mol}$
• $n(\text{NaOH}) = 0.1 \times 1 = 0.1\,\text{mol}$

步骤2：分析反应：

• $\text{CO}_2 + 2\text{NaOH} \rightarrow \text{Na}_2\text{CO}_3 + \text{H}_2\text{O}$（需 $n(\text{NaOH}) = 0.2\,\text{mol}$）
• $\text{CO}_2 + \text{NaOH} \rightarrow \text{NaHCO}_3$（需 $n(\text{NaOH}) = 0.1\,\text{mol}$）

步骤3：$n(\text{NaOH}) : n(\text{CO}_2) = 1:1$，恰好完全反应生成 $\text{NaHCO}_3$。

步骤4：溶质为 $\text{NaHCO}_3$，物质的量为 $0.1\,\text{mol}$。

答案： 溶质为 $\text{NaHCO}_3$，物质的量为 $0.1\,\text{mol}$

• Confusing terminology or concepts that appear similar but have distinct meanings.
• Overlooking key assumptions or boundary conditions that limit applicability.

• Algebra - Core algebraic concepts including sets, logic, and inequalities tested in gaokao
• Functions - Fundamental function types and transformations that underpin many exam problems
• Inorganic Chemistry - Essential inorganic chemistry topics including equilibrium and electrochemistry