📚 IGCSE CAIE Additional Mathematics: Practical Assessment Skills | IGCSE CAIE 进阶数学：实践考核要点
The CAIE IGCSE Additional Mathematics (0606) syllabus does not include a separate laboratory or practical examination paper. However, the written papers consistently assess practical mathematical skills: calculator work, graph plotting, numerical methods, modelling, and the application of calculus to real-life problems. This article summarises the key practical assessment points for candidates preparing for Papers 1 and 2, and shows how each practical habit can be converted into reliable marks.
CAIE IGCSE 进阶数学（0606）大纲不设独立的实验或实践考试试卷。但笔试持续考查实践数学技能：计算器使用、绘图、数值方法、建模以及微积分在实际问题中的应用。本文总结考生备考 Paper 1 和 Paper 2 的关键实践考核要点，并说明如何把每一个实践习惯转化为稳定得分。
1. Understanding the 0606 Assessment Structure | 了解 0606 考核结构
Both Paper 1 and Paper 2 are 2-hour written papers worth 80 marks each, and each contributes 50% of the final grade. There is no coursework, no practical file and no oral test. Nevertheless, examiners design questions that require you to demonstrate practical techniques inside a written answer: constructing a table of values, using a calculator to evaluate an expression, or sketching a graph accurately on the grid provided. Because the whole qualification is decided by these two papers, every practical habit - rounding correctly, labelling an axis, writing a concluding sentence - directly affects your final grade.
Paper 1 与 Paper 2 均为 2 小时笔试，各 80 分，各占总成绩的 50%。没有课程作业、没有实践档案、也没有口语测试。但考官设计的题目要求你在书面答案中展示实践技巧：构建数值表、用计算器求值，或在题目提供的网格上准确作图。由于整门资格完全由这两份试卷决定，每一个实践习惯——正确取近似值、标注坐标轴、写出结论句——都会直接影响最终等级。
| Component | 试卷 | Duration | 时长 | Marks | 分值 | Weighting | 占比 | Practical demand | 实践能力要求 |
| Paper 1 | 2 h | 80 | 50% | Tables of values, graph work, numerical solution of equations |
| Paper 2 | 2 h | 80 | 50% | Modelling, calculus applications, kinematics, circular measure |
Neither paper is split into a "calculator" paper and a "non-calculator" paper, and neither paper contains a compulsory drawing section: practical skills are embedded in ordinary questions and are assessed implicitly.
两份试卷都不分"计算器卷"和"非计算器卷"，也都没有强制性的作图部分：实践技能被嵌入普通题目中，以隐性方式考查。
2. Calculator Skills and Control | 计算器使用与控制
Calculators are permitted in both papers, but the rules matter. A non-programmable scientific calculator is the safe choice; graphical calculators, programmable machines and any device with symbolic algebra, internet access or a stored database are not permitted in CAIE IGCSE mathematics papers. Check your model against the current syllabus and the exam board calculator regulations before the exam, and make sure you can use it fluently without reading the manual.
两份试卷均允许使用计算器，但规则很重要。不可编程的科学计算器是稳妥选择；图形计算器、可编程机型，以及任何带符号代数、联网或存储数据库功能的设备，在 CAIE IGCSE 数学试卷中都不允许使用。考前请依据当年大纲与考试局的计算器规定核对机型，并确保你能不翻说明书就熟练操作。
Working in the correct angle mode is essential. Trigonometry in these papers is normally set in degrees, so a calculator left in radian mode gives a completely wrong value for the same key press.
选择正确的角度模式至关重要。本课程三角函数通常以角度制出题，如果计算器仍停留在弧度模式，同样的按键会给出完全错误的数值。
sin 30° = 0.5 (degree mode) vs sin 30 = −0.988 (radian mode)
Use the ANS key and the memory to carry full precision through a multi-step calculation, and round only at the end. Write down the expression you entered as well as the answer: a correct expression earns method marks even when a keying error spoils the final value.
用 ANS 键和记忆键在分步计算中保留完整精度，只在最后一步取近似值。请把输入的表达式和答案一并写出：即使按键失误导致最终数值错误，正确的表达式仍可获得方法分。
3. Constructing Tables of Values | 构建数值表
Many graph questions begin with "copy and complete the table" space beside the table. For a cubic such as y = x³ − 4x + 1 on the interval −3 ≤ x ≤ 3, a systematic table looks like this.
许多图像题以"抄写并补全下表"开头。请严格使用题目给出的 x 值，所有数值保持相同精度，并准备在表格旁边写出至少一次代入过程。对于在 −3 ≤ x ≤ 3 上的三次函数 y = x³ − 4x + 1，规范的数值表如下。
| x | −3 | −2 | −1 | 0 | 1 | 2 | 3 |
| y | −14 | 1 | 4 | 1 | −2 | 1 | 16 |
chines as −(2³), which happens to agree here but not inside every expression. Second, if the table already gives some values, do not recalculate them by hand with rounded figures - check that your method reproduces them exactly, otherwise your curve will not match the printed points.
有两个实践要点会被考查。第一，代入负值时必须加括号，因为 (−2)³ = −8，而某些机器把 −2³ 解析为 −(2³)，在本例中结果巧合相同，但在其他表达式里未必一致。第二，如果表格中已给出部分数值，不要用已取近似的手算值去重算——先确认你的方法能完全复现这些数值，否则你画的曲线将无法通过印刷的已知点。
4. Graph Plotting and Sketching | 绘图与草图
"Plot" and "sketch" are different instructions and are marked differently. To plot, you transfer points from your table to the grid, using the scale given, and join them with a smooth curve drawn freehand or with a flexible curve - never with a series of straight segments. To sketch, you show the shape and the key features only: intercepts, turning points, asymptotes and the general direction of the curve, without any grid or plotted points.
"作图"与"草图"是两种不同的指令，评分方式也不同。作图要求你把数值表中的点按给定比例转移到网格上，并用平滑曲线连接——徒手或用曲线尺均可，但绝不能用一段段直线拼接。草图只要求呈现形状与关键特征：截距、极值点、渐近线以及曲线的大致走向，不需要网格，也不需要描点。
curve, for example y = x³ − 4x + 1 or y = 2. Where several curves share one grid, labelling them is worth a mark on its own.
曲线上的描点应画成小十字而不是粗圆点；每张图都需要标注坐标轴与题目给定的刻度，并为每条曲线加注标签，例如 y = x³ − 4x + 1 或 y = 2。当多条曲线共用同一网格时，正确标注本身就是独立的一个得分点。
5. Reading Information from Graphs | 从图像中读取信息
ation of the form f(x) = k, draw the horizontal line y = k on the same grid and read the x-coordinates of the intersection points, giving each answer to the accuracy requested, typically 1 decimal place or 2 significant figures.
曲线画好后，题目通常要求你从中提取信息。方程的根在曲线与 x 轴的交点处读出。要解形如 f(x) = k 的方程，需在同一网格上画出水平直线 y = k，读出交点横坐标，并按题目要求的精度作答，通常为 1 位小数或 2 位有效数字。
e area under a velocity-time graph represents distance travelled. In both cases write a sentence of interpretation, not just a number: "the gradient at t = 4 is 3.2 m s⁻¹, so the velocity at that instant is about 3.2 m s⁻¹".
图像还承载变化率与累积量的信息。某点切线的斜率给出该时刻瞬时变化率的估计值，而速度—时间图像下的面积代表走过的路程。两种情况都要写出解释性语句，而不是只给一个数字："t = 4 处切线斜率为 3.2 m s⁻¹，因此该时刻速度约为 3.2 m s⁻¹"。
6. Numerical Methods and Iteration | 数值方法与迭代
When an equation cannot be solved exactly, 0606 expects a numerical approach. To show that a root lies between two values, evaluate the function at both and demonstrate a sign change, then state the continuity argument explicitly, because that statement carries the mark.
当方程无法精确求解时，0606 要求采用数值方法。要证明某根位于两个值之间，需分别求出两处的函数值并说明符号改变，然后明确写出连续性论证，因为这句结论本身就是一个得分点。
f(a) × f(b) < 0 ⇒ a root lies between a and b (f continuous)
n apply the iteration formula repeatedly from the given starting value. Lay the working out as a two-column table of n and xₙ so the examiner can see convergence, and quote each iterate to at least 5 decimal places until the final stated accuracy.
使用迭代法时，先把方程整理成 x = g(x) 的形式，再从给定初值出发反复代入迭代式。请用 n 与 xₙ 两列构成的表格呈现过程，以便考官看出收敛趋势；在给出最终精度答案之前，每个迭代值至少保留 5 位小数。
xₙ₊₁ = g(xₙ)
as x = (x³ + 1)/4 instead of a divergent one, and say in your answer that you changed the arrangement for that reason.
如果迭代值偏离预期根，说明所选整理形式不收敛：请改用代数等价的其他整理形式，例如把发散的写法换成 x = (x³ + 1)/4，并在答案中说明你因此更换了整理形式。
7. Modelling Real-Life Situations | 现实情境建模
t the algebra back in context. Start by defining every variable with its unit, for example "let t be the time in seconds after release and v the velocity in m s⁻¹" model cannot produce in real life, such as a negative length or a population that exceeds the available space.
建模题要求你把情境翻译成代数，再把代数结果翻译回情境。第一步是为每个变量下定义并标注单位，例如"设 t 为释放后的时间（秒），v 为速度（m s⁻¹）"。若模型只适用于合理范围，须写出定义域，如 0 ≤ t ≤ 12，并指出模型在现实中无法产生的值，例如负长度或超出可用空间的人口数。
Exponential models appear frequently, and the practical skill is to recognise what each constant means and how to linearise the relationship using logarithms.
