📚 Pre-U WJEC Mathematics: Key Points for the Coursework Investigation | Pre-U WJEC 数学：实验/实践考核要点
The WJEC Pre-U Mathematics investigation is a unique component that assesses your ability to carry out an independent mathematical study. It requires you to engage with practical problem-solving, data analysis, and mathematical modelling—often mirroring the work of real-world mathematicians. Success in this coursework depends on careful planning, rigorous methodology, and clear communication. This guide outlines the key points you need to master for the practical assessment.
WJEC Pre-U 数学的实验考核是一项独特的组成部分，它评估你进行独立数学研究的能力。它要求你参与实际问题解决、数据分析和数学建模——通常与现实世界中数学家的工作相似。该课程作业的成功取决于周密的计划、严谨的方法和清晰的沟通。本指南概述了你需要掌握的实验考核要点。
1. Understanding the Investigation Component | 理解实验考核组件
The investigation is worth 20% of the overall Pre-U Mathematics qualification. You will produce a written report of approximately 2000–3000 words, demonstrating your ability to explore a mathematical topic in depth. Unlike traditional exam papers, the investigation allows you to choose your own area of interest, carry out experiments or simulations, collect data, and apply mathematical techniques to analyse your findings. The assessment rewards originality, clear reasoning, and critical evaluation.
该实验考核占Pre-U数学总成绩的20%。你需要撰写一份约2000–3000词的书面报告，展示你深入探索数学课题的能力。与传统的考试试卷不同，该实验允许你选择自己感兴趣的领域，进行实验或模拟，收集数据，并运用数学方法分析你的发现。评估奖励原创性、清晰的推理和批判性评价。
The key skills assessed include mathematical modelling, data handling, use of technology, and the ability to draw and justify conclusions. You should think of yourself as a mathematical researcher who is investigating a real or simulated problem.
评估的关键技能包括数学建模、数据处理、技术使用以及得出结论并证明其合理性的能力。你应该把自己看作一名数学研究者，正在研究一个真实或模拟的问题。
2. Choosing a Suitable Topic | 选择合适的题目
Selecting the right topic is crucial. It should be accessible yet challenging, allowing for mathematical analysis that goes beyond A-Level standard. Good topics often originate from applied mathematics: population growth, projectile motion, epidemiology, or financial modelling. You might also explore pure mathematical concepts, such as convergence of sequences, provided you can incorporate practical investigation or simulation. Avoid topics that are too broad or too narrow; a focused question is essential.
选择合适的题目至关重要。题目应当既可行又具有挑战性，能够进行超出A-Level标准的数学分析。好的题目通常来自应用数学：人口增长、抛体运动、流行病学或金融建模。你也可以探索纯粹的数学概念，例如数列的收敛，但前提是能够融入实践调查或模拟。避免过于宽泛或过于狭窄的题目；一个聚焦的问题至关重要。
Discuss your ideas with your teacher before committing. They will help you refine the scope and ensure that there is enough mathematical content for high marks. Consider starting from a real-world data set or a known mathematical model and then extending it.
在确定题目之前，请与你的老师讨论想法。他们会帮助你精炼范围，确保有足够的数学内容以获得高分。可以考虑从一个真实世界的数据集或一个已知的数学模型出发，然后进行拓展。
3. Conducting Background Research | 进行背景研究
Once you have a topic, you need to research existing methods and theories. Read relevant textbooks, academic papers, or credible online resources. This review should inform your methodology and demonstrate that you understand the context of your investigation. Show that you can build on prior work rather than reinventing the wheel.
一旦确定了题目，你需要研究现有的方法和理论。阅读相关的教科书、学术论文或可靠的在线资源。这项回顾应为你提供方法论依据，并表明你理解自己实验的来龙去脉。展示你能在先前工作的基础上进一步发展，而不是重复发明车轮。
Document all sources carefully, as referencing is part of the assessment. Use a standard citation style (such as Harvard or MLA) consistently. Your background research will also help you select appropriate mathematical techniques, whether analytical, numerical, or statistical.
仔细记录所有来源，因为引用是评估的一部分。始终使用标准引用格式（如哈佛格式或MLA格式）。你的背景研究还将帮助你选择合适的数学技巧，无论是解析方法、数值方法还是统计方法。
4. Formulating a Clear Research Question | 制定清晰的研究问题
A well-defined research question turns a general topic into a focused investigation. It should be specific, measurable, and mathematically tractable. For example, instead of "population growth", you might ask: "How well does the logistic model predict the population of yeast in a controlled culture over 72 hours?" This sharpens your data collection and analysis.
一个定义明确的研究问题能将一个宽泛的题目转变为聚焦的实验。它应该具体、可衡量且数学上可处理。例如，与其研究“人口增长”，不如问：“逻辑斯蒂模型在预测72小时受控培养物中酵母种群数量方面的效果如何？” 这会使你的数据收集和分析更加清晰。
Write your research question in the introduction of your report. You should also state any hypotheses or expectations based on your background reading. Remember that a good investigation allows you to test assumptions and refine the model if needed.
在报告的引言中写出你的研究问题。你还应该基于背景阅读陈述任何假设或期望。记住，一个好的实验允许你检验假设，并在需要时修正模型。
5. Designing the Methodology | 设计方法论
Your methodology explains how you will answer the research question. If you are conducting a physical experiment (e.g., pendulum swings), detail the apparatus, measurement procedures, and controls. For simulations, describe the software, algorithms, and parameters used. Data collection must be systematic and repeatable; include sample sizes and how you will deal with outliers.
你的方法论阐释了你将如何回答研究问题。如果你进行实体实验（例如单摆摆动），请详细说明仪器、测量流程和对照。对于模拟，描述使用的软件、算法和参数。数据收集必须系统且可重复；包括样本量以及你将如何处理异常值。
Think about potential sources of error and how you will minimise them. The methodology section is not just a list of steps; it should show that you have carefully designed the investigation to produce valid results.
思考潜在的误差来源以及你将如何使其最小化。方法论部分不只是一个步骤列表；它应表明你已经精心设计了实验，以获得有效的结果。
6. Data Collection Techniques | 数据收集技术
Collect your data methodically, recording raw values in tables. Use appropriate precision based on your measuring instruments. If using secondary data, verify its reliability and cite the source. For experimental data, perform multiple trials and calculate averages to improve reliability. Always include units and clear headings in your data tables.
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