📚 Year 7 CIE Additional Mathematics: Experimental Assessment Key Points | 七年级 CIE 进阶数学：实验考核要点
In the Cambridge International curriculum, Year 7 Additional Mathematics encourages students to develop practical and investigative skills. Experimental assessments evaluate how students design, conduct, and interpret mathematical investigations. This article outlines the essential key points needed to excel in these practical tasks.
在剑桥国际课程中，七年级进阶数学鼓励学生培养实践和研究技能。实验考核评估学生如何设计、实施和解读数学探究。本文总结了在这些实践任务中取得优异成绩所需的关键要点。
1. Understanding the Experimental Assessment | 理解实验考核
The experimental assessment tests your ability to apply mathematical concepts to real-world scenarios. You might be asked to measure lengths, record temperatures, investigate number patterns, or explore geometric properties. It is not about getting the 'right' answer immediately, but about demonstrating a logical investigative process.
实验考核测试你将数学概念应用于真实场景的能力。你可能会被要求测量长度、记录温度、探究数字模式或探索几何性质。考核的重点不在于立刻得出“正确”答案，而在于展示逻辑清晰的研究过程。
Assessment criteria typically include planning, data collection, accuracy, mathematical reasoning, and communication. Examiners look for clear recording of measurements, appropriate use of units, correct calculations, and a well-structured conclusion that refers back to the aim.
评分标准通常包括计划制定、数据收集、准确性、数学推理和表达。考官看重清晰的测量记录、单位的恰当使用、正确的计算以及紧扣目标的、结构良好的结论。
Time management is also vital. You will have a limited period to complete the task, so read the instructions carefully, decide on a method, and stick to it. Leave enough time to write your analysis and check for errors.
时间管理同样至关重要。你将在有限时间内完成任务，因此仔细阅读说明、确定方法并坚持执行。留出足够时间撰写分析并检查错误。
2. Measurement and Error | 测量与误差
When taking measurements, always record values to the appropriate degree of precision. For example, a ruler marked in millimetres allows readings to the nearest 0.1 cm. Estimating between the smallest scale divisions can improve accuracy but should be done consistently.
测量时，始终以适当的精度记录数值。例如，以毫米为刻度的尺子可以读取到最接近0.1厘米。在最小刻度之间进行估计可以提高准确度，但必须一致地进行。
Understanding absolute and relative error is important. Absolute error = |measured value - true value| ative error = absolute error ÷ true value. These help you judge how reliable your data is.
理解绝对误差和相对误差很重要。绝对误差 = |测量值 - 真实值|，相对误差 = 绝对误差 ÷ 真实值。这些概念有助于判断数据的可靠性。
5 s. For an analogue instrument, it is usually half of the smallest division. Acknowledging uncertainty demonstrates scientific thinking.
始终要说明读数的不确定度。对于显示0.01秒的数字秒表，不确定度为±0.005秒。对于模拟仪表，通常为最小刻度的一半。承认不确定度体现了科学思维。
3. Graph Plotting and Interpretation | 图形绘制与解读
Plotting points accurately on a coordinate grid is a fundamental skill. Use a sharp pencil and mark points as small crosses. Do not use large blobs, as these reduce precision. Ensure the axes are labelled with the quantity and unit, such as 'Distance/m' or 'Time/s'.
在坐标网格上精确描点是基本技能。使用削尖的铅笔，将点标为小叉号。不要使用大圆点，因为这会降低精度。确保坐标轴标有数量和单位，例如“距离/m”或“时间/s”。
Choose scales that spread your data across more than half of the grid in both directions. Avoid awkward scales like multiples of 3 that make plotting difficult. The origin does not always need to be included if all data are far from zero.
选择的刻度应使数据在两个方向上都占据网格的一半以上。避免使用像3的倍数那样不易描点的别扭刻度。如果数据点都远离零点，原点就不必包含在内。
When drawing a line of best fit, do not force it through all points if they show a trend. Aim for an equal number of points above and below the line. A best-fit line can be straight or, if the pattern is curved, a smooth curve. Interpret the gradient and y-intercept in context: for a distance-time graph, the gradient represents speed.
绘制最佳拟合线时，如果数据点呈现趋势，不必强行穿过所有点。目标是使线上方和下方的数据点数大致相等。最佳拟合线可以是直线，如果模式是曲线则为平滑曲线。根据情境解读斜率和y轴截距：对于距离-时间图，斜率代表速度。
4. Using a Scientific Calculator | 使用科学计算器
Know how to perform basic operations efficiently: brackets, the fraction key (ab/c or d/c), and exponentiation. For example, to compute 2.5³, use the power or x³ function. Familiarise yourself with your calculator's model before the assessment.
知道如何高效执行基本运算：括号、分数键（ab/c 或 d/c）和乘方。例如，要计算2.5³，使用幂函数或x³键。在考核前熟悉你的计算器型号。
Use the calculator's memory functions (STO, RCL, M+) to store intermediate results. This reduces rounding errors that can build up if you re-type rounded values. When working with large data sets, use the statistics mode to enter lists of data and find the mean, standard deviation, or regression coefficients quickly.
使用计算器的存储功能（STO、RCL、M+）保存中间结果。这可以减少因重新输入舍入值而累积的舍入误差。处理大数据集时，使用统计模式输入数据列表，快速求出平均数、标准差或回归系数。
Always double-check that your calculator is set to the correct angle mode (degrees or radians) for trigonometric calculations. For most Year 7 practical work, degrees are used. A simple test is to calculate sin 30; it should equal 0.5 in degree mode.
始终再次检查计算器是否设置为正确的角度模式（角度制或弧度制）以便进行三角计算。大多数七年级实践工作使用角度制。一个简单的测试是计算 sin 30，在角度制下应等于0.5。
5. Data Collection and Organisation | 数据收集与整理
Design a clear table to record data before you start the experiment. Include a title and column headings with units, for instance, 'Length / cm', 'Time / s', 'Temperature / °C'. This makes data entry systematic and analysis easier.
在开始实验前设计清晰的表格以记录数据。包含标题和带单位的列标题，例如“长度/cm”、“时间/s”、“温度/°C”。这使得数据录入系统化且易于分析。
Collect a sufficient number of data points to reveal a reliable pattern. For most simple investigations, at least six to eight distinct readings are needed. If you are investigating how one variable changes with another, choose a sensible range and even intervals.
收集足够数量的数据点以揭示可靠模式。对于大多数简单探究，至少需要六到八个不同读数。如果你在探究一个变量如何随另一个变化，选择合理的范围和均匀的间隔。
Be consistent with significant figures and decimal places. If you measure to the nearest 0.1 cm, all lengths in that column should be recorded to one decimal place. Simple consistency greatly improves the credibility of your data.
在有效数字和小数位数上保持一致。如果测量精确到0.1厘米，那么该列的所有长度都应记录到小数点后一位。简单的一致性会极大提高数据的可信度。
6. Statistical Diagrams | 统计图表
Choose the appropriate chart for your data type. Use a bar chart for discrete categories, a histogram for grouped continuous data, and a line graph to show trends over time or ordered sets. A scatter graph is used to investigate correlation between two numerical variables.
根据数据类型选择合适的图表。分类数据用条形图，分组连续数据用直方图，随时间或有序集合变化的趋势用折线图。散点图用于探究两个数值变量之间的相关性。
bel axes clearly and give the chart a title. Axes must show the quantity and unit, such as 'Height (cm)' sector angle as (frequency ÷ total) × 360°. Use a protractor to measure angles accurately.
始终清晰标注坐标轴，并为图表加上标题。坐标轴必须显示数量和单位，例如“高度（cm）”。绘制饼图时，每个扇区角度计算为（频数 ÷ 总数）× 360°。使用量角器准确测量角度。
When constructing a histogram, ensure bars are of equal width if class intervals are equal; for unequal intervals, the area of the bar represents frequency, not the height. This concept is often tested in practical data handling tasks.
构建直方图时，如果组距相等，确保条形宽度相等；如果组距不相等，条形的面积代表频数，而非高度。这一概念常在实践数据处理任务中考查。
7. Geometric Experiments and Constructions | 几何实验与作图
Use a compass, protractor, and ruler accurately. For constructions such as perpendicular bisectors and angle bisectors, follow the standard steps without measuring angles directly. Leave all construction arcs visible as evidence of your method.
准确使用圆规、量角器和直尺。绘制垂直平分线和角平分线等图形时，遵循标准作图步骤，不直接测量角度。保留所有作图弧线作为方法的证据。
When investigating properties of triangles, measure angles to the nearest degree and side lengths to the nearest millimetre. Verify that the sum of interior angles equals 180° and check the triangle inequality (sum of any two sides > third side).
探究三角形性质时，角度精确到度，边长精确到毫米。验证内角和为180°，并检查三角不等式（任意两边之和大于第三边）。
For experiments involving area and perimeter of irregular shapes, use a grid to count squares or trace the outline with string and then measure its length. This gives a practical sense of approximation and limits of accuracy.
涉及不规则图形的面积和周长实验时，使用网格数方格，或用细绳描出轮廓再测量其长度。这让你对近似和准确度极限有实际感受。
8. Pattern Investigation and Conjecture | 模式探究与猜想
Many experimental tasks ask you to find a rule or formula. Begin by organising data in an ordered table and look for differences between consecutive terms. For sequences, check if the first differences are constant (linear) or second differences are constant (quadratic).
许多实验任务要求你发现规则或公式。从将数据整理成有序表格开始，并观察连续项之间的差。对于数列，检查一次差是否恒定（线性），或二次差是否恒定（二次）。
Express the nth term in words first, then using algebraic symbols. For example, 'start at 5 and add 7 each time' can be written as t = 7n - 2, where n is the position number. Always define the variable clearly.
先用文字表达第n项，然后用代数符号。例如，“从5开始，每次加7”可写成 t = 7n - 2，其中n是位置序号。始终清晰地定义变量。
Test your conjecture with at least two additional cases that you did not use to find the rule. If it fails, refine your hypothesis. Be prepared to explain how you arrived at the formula, showing intermediate steps in your report.
用至少两个未用于发现规则的额外例子检验猜想。如果不成立，修正你的假设。准备好解释你是如何得出公式的，并在报告中展示中间步骤。
9. Writing the Report | 撰写实验报告
Structure your report with clear sections: Aim, Method, Results, Analysis, and Conclusion. The aim should state what you are investigating. The method should be a step-by-step description clear enough for someone else to repeat your experiment.
报告结构应包含清晰的章节：目的、方法、结果、分析和结论。目的应说明你正在探究什么。方法应是逐步的描述，足够清晰，使他人能够重复你的实验。
In the results section, present your data in a neat table and show a graph where appropriate. Label and refer to tables and graphs as 'Table 1', 'Figure 1', etc. In the analysis, look for trends and use mathematical vocabulary such as 'directly proportional', 'inversely proportional', or 'increases at a constant rate'.
在结果部分，以整洁的表格展示数据，并在适当处显示图表。将表格和图表分别标注并称为“表1”、“图1”等。在分析中，寻找趋势并使用数学词汇，如“成正比”、“成反比”或“以恒定速率增加”。
A strong conclusion directly answers the aim and is supported by your data. Discuss any anomalies, sources of error (human, instrumental, environmental), and suggest realistic improvements. This demonstrates high-level thinking and can earn top marks.
强有力的结论直接回应目的，并以数据支撑。讨论任何异常值、误差来源（人为、仪器、环境），并提出切实的改进建议。这展示了高层次思维，可以赢得高分。
10. Collaboration and Communication | 合作与交流
If working in a group, agree on roles at the start: who will measure, who will record, and who will check calculations. Rotate roles so everyone gains hands-on experience. Clear communication avoids duplicated work and errors.
如果小组合作，在开始时商定角色：谁测量、谁记录、谁检查计算。轮换角色使每个人都能获得动手经验。清晰的沟通可以避免重复工作和错误。
Present your findings using precise language and correct mathematical notation. Practise explaining your reasoning aloud to a partner; this helps you identify gaps in your logic. In the report, use short sentences and check your spelling of key terms like 'hypotenuse', 'quadrilateral', or 'circumference'.
使用精确的语言和正确的数学符号展示你的发现。练习向同伴口头解释推理过程，这有助于发现逻辑中的漏洞。在报告中，使用简短的句子，并检查关键术语的拼写，如“斜边”、“四边形”或“圆周”。
Listen carefully to feedback from your teacher or peers and revise your work accordingly. The experimental assessment is as much about the process as the final answer. Showing you can refine your ideas is a marker of a true mathematician.
仔细听取老师或同伴的反馈，并相应地修改你的工作。实验考核既看重过程，也看重最终答案。展示你能改进自己的想法，这正是一名真正数学家的标志。
Published by TutorHao | Additional Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图