IB物理IA 研究问题 控制变量 不确定度
IB物理的内部评估在2025年首次评估的新大纲里改名成"科学探究"(scientific investigation)，评分维度、字数上限和交稿节奏都跟旧版不同。下面按研究设计、数据分析、结论、评价四条线，把一份能复现、能被评分的报告拆开写。
The Physics internal assessment is now called the scientific investigation, and the syllabus first assessed in 2025 reworked how it is judged. This article works through the four strands one at a time, focusing on the decisions that separate a report a teacher can mark confidently from one that leaves the marks undecided.
2025版把IA改成了什么样
按IB Physics Guide (first assessment 2025) 的口径，科学探究占最终成绩的20%，SL和HL用同一套标准，满分24分，分成研究设计、数据分析、结论、评价四项，每项6分。报告上限3000词，官方给的时间是10小时，含实验室采数、教师反馈和真实性核查。不少学生还在回头找旧大纲里那8分的"个人投入"，2025版已经取消这一项。图表、数据表、公式与计算、参考文献不计入词数。
The scientific investigation carries 20 per cent of the final grade, uses identical criteria at SL and HL, and is marked out of 24 across four strands worth six marks each. The report is capped at 3,000 words and the course allocates ten hours to the whole task. Tables, graphs, equations and references sit outside the word count. Personal engagement, worth eight marks in the previous guide, no longer exists as a separate criterion, so a report no longer earns credit for enthusiasm alone. Nothing in the strand descriptors is hidden from students. Read them before planning a method, not after the data are collected.
研究问题要能落到一个方程上
研究问题写不清楚，后面六分的分析就没有着力点。合格的问题要交代自变量与因变量、被研究的物理系统、测量的是什么量、检验哪条关系或哪个模型。以单摆为例，"摆长如何影响周期"可以测，但信息量太少；写成"摆长从0.20 m到1.00 m变化时周期如何改变，结果在多大程度上符合小角度单摆模型"，评委才知道你要检验什么。这里容易漏的是系统这一层：摆角超过约5度后简谐近似开始失效，问题里不交代摆角范围，方法就无法复现。
A vague question tends to collapse the analysis strand, because there is nothing precise left to analyse. A workable version names the independent and dependent variables, the physical system, the quantities being measured, and the model under test. Asking how length affects the period of a pendulum is measurable but thin. Better phrasing fixes the range, states the amplitude used, and asks how far the data agree with the small-angle model. Amplitude is the part students forget: beyond roughly five degrees the simple harmonic approximation degrades. Write the question as a single sentence. If that sentence needs a paragraph of conditions, the scope is still too wide.
自变量范围、间隔与重复次数怎么定
取值多少合适，官方没有硬性条数。考纲要求的是论证：范围要覆盖足够大的变化以便看出趋势，间隔要和仪器分辨率匹配，重复次数要足以估计随机波动。常见的错误是取五个值却全部挤在量程一端。摆长实验里，0.20到1.00 m每0.10 m一档，每档三次计时，每次计时数十个来回再平均，比十个挤在一起的取值有用得多。
No official rule fixes how many values or repeats to use, and picking five because a website said so earns nothing. The criteria reward a justification: a range wide enough to expose the trend, intervals matched to the resolution of the instrument, and enough repeats to estimate scatter. A common failure is five readings bunched at one end of the available range. For a pendulum, stepping from 0.20 m to 1.00 m in 0.10 m intervals, timing three runs per length and averaging over ten swings each, produces evidence a reader can actually work with.
控制变量要写清怎么控和为什么必须控
每个控制变量需要两句话而不是一句：用什么手段固定它，以及它一旦漂移会怎样影响因变量。只列清单不写第二句，读起来像抄来的。摆球质量就是个好例子。理想模型里周期与质量无关，很多学生因此直接跳过，可摆球重了以后受空气阻力和摆动平面倾斜的影响并不一样。写清"始终使用同一摆球"再补一句原因，和只写"控制质量"是两种得分。
Each controlled variable needs two statements rather than one: the mechanism that holds it constant, and the physical reason a drift would shift the dependent variable. A list without the second half reads like a borrowed checklist. Mass is a useful case. Period is independent of mass in the ideal model, so students often skip it, yet a heavier bob responds differently to air resistance and to tilt of the oscillation plane. Naming the same bob and explaining why that matters is what separates a described method from a justified one. Two lines per variable is enough. A page is usually padding.
不确定度从哪里来、怎么传递
仪器不确定度一般取最小分度的一半，数字显示仪表按末位一个字，带采样率说明的数据采集器又要按说明书来。百分比不确定度在乘除运算里相加，只有这样不同量级之间才有可比性。周期与摆长的关系是T = 2π√(L/g)，处理成T²对L作图，梯度等于4π²/g。摆长的不确定度来自米尺的±0.5 mm，周期的不确定度来自反应时间除以摆动次数，两者常差一个数量级，写清哪个占主导，评价那段自然有内容。
Instrument uncertainty is usually half the smallest division on an analogue scale, one unit in the last digit for a digital readout, and whatever the specification states for a datalogger. Percentage uncertainties add when quantities are multiplied or divided, which is why a table of percentages without propagation rarely earns credit. For a pendulum the linearised form plots the square of the period against length, giving a gradient of four pi squared over g. Length uncertainty comes from a metre rule, timing uncertainty from reaction time divided by the number of swings, and naming which dominates gives the evaluation something concrete to discuss. Quote the percentages in the same table as the raw values. Readers should not have to recompute them.
线性化之后梯度才是物理量
只有当图画成直线，梯度才能直接读出一个物理量并拿去与公认值比较。检验单摆模型画T²对L，梯度给出g，再与9.81 m s⁻²对照；检验胡克定律画力对伸长量，梯度就是劲度系数。这里反复出现的两个错误，一是对弯曲的数据硬做直线拟合，还拿拟合优度当证据；二是坐标轴没有从零起却去解释截距的含义。把残差图画出来，系统性弯曲一眼可见，这一步最容易省掉，也最容易丢分。
A gradient yields a physical quantity only when the graph is linear, so linearising belongs to the design rather than the presentation. Squaring the period turns a square-root relation into a straight line whose gradient is four pi squared over g, while force against extension returns the spring constant directly. Two mistakes recur. One is fitting a straight line to data that bend, then quoting a high coefficient of determination as if it settled the matter. The other is interpreting an intercept when the axes never started at zero. A residual plot exposes both at once and takes two minutes to draw.
结论要回答什么
结论那6分看的是数据能否回答问题，不是把过程再讲一遍。要写出梯度的数值与单位、由梯度推出的物理量、与公认值的差，以及这个差是否落在传递后的不确定度范围内。若落在范围之外，要指出可能的方向性偏差，比如米尺总从同一端量起、计时总滞后于过零点。很多学生以为结论越长越稳，其实三句话讲完差异与原因，比一页复述更有说服力。
The conclusion strand asks whether the data answer the question, not whether the report restates the procedure. State the gradient with units, the physical quantity derived from it, the accepted value, and whether the difference falls inside the propagated uncertainty. If it does not, name the likely direction of the bias, such as a rule always read from the same end or a stopwatch always started late. Length is not the variable that earns marks here: three sentences that compare and explain beat a page of summary. Put the number first, the accepted value second, the judgement third. That order is easy to mark.
评价部分要把随机误差和系统误差分开
评价那6分看两件事：能不能指出具体的局限，以及能不能解释它对结果的影响有多大。随机误差可以通过更多重复与平均削弱，系统误差不能，只能识别出来再设法补偿或声明。改进建议要落到操作上，"使用更精密的仪器"这种写法太空泛；"改用光电门计时以消除反应时间，把周期的百分比不确定度从约1%降到0.1%以下"才可评。延伸研究也写具体，比如把摆角作为第二个自变量重做一轮。
Evaluation rewards limitations tied to their consequences rather than a list of generic complaints. Random error shrinks with repetition and averaging; systematic error does not, and has to be identified and either compensated for or declared. Proposals belong at the level of procedure. Replacing hand timing with a light gate removes reaction time and changes the percentage uncertainty in the period from around one per cent to a tenth of that, which a reader can assess. Vague advice about better equipment says nothing about which measurement was actually limiting the result.
三千词怎么分配
3000词听着紧，按功能分配就不紧。研究问题与物理背景约350到450词，变量与方法600到700，数据处理与图表分析700到900，结论350到450，评价450到600。原始数据表、样算、图与文献不计入。真正该省的是照抄课本推导的段落，评委对标准物理的复述不给分。很多学生把一半篇幅用在背景上，方法只剩三行，分析被压缩到半页，那6分就悬了。
Three thousand words is comfortable once the budget follows function. Roughly 350 to 450 for the question and the physics behind it, 600 to 700 for variables and method, 700 to 900 for processing and graph work, 350 to 450 for the conclusion, and 450 to 600 for evaluation. Tables, sample calculations, figures and references do not count. The savings come from cutting textbook derivations, which earn nothing. A frequent imbalance is half the report spent on background, a three-line method, and a squeezed analysis, exactly where six marks sit. Draft the analysis before the introduction if the budget is tight. The analysis is what the marks depend on.
模拟与数据库类探究的额外要求
用模拟采数仍属一手数据，但模拟必须能产生变异。输入相同就返回相同结果的模型不能用，替学生把变量选好的模型也不能用。数据库路径属于二手数据，重点转到抽样上：哪些行被排除、依据是什么、样本量与覆盖范围如何限制结论的适用范围。这两条路考纲都写明了，动手前先跟老师确认设备与数据可得性，比写到一半换题省事。
A simulation still produces primary data, but only if it generates variability. A model returning identical output for identical input is not acceptable, and neither is one that selects the variables on the student's behalf. Database work counts as secondary data, and the design strand then shifts to sampling: which records were excluded, on what grounds, and how sample size and coverage limit what the conclusion can claim. Both routes are described in the guide, and clearing them with a teacher before the ten hours are spent saves a rewrite. Both routes also change what counts as a control variable. Check which one you are on before designing the method.
有效数字与不确定度怎么写才一致
有效数字的规则不复杂，执行起来容易前后不一致。不确定度一般保留一位有效数字，首位是1时可留两位；测量值的末位要与不确定度的末位对齐，写成(0.842 ± 0.003) s 是自洽的，写成0.8420 ± 0.003 s 就不自洽。平均值由三次读数取来时，先写清每次读数的仪器不确定度，再讨论读数之间的离散是否超过它。样算只贴一到两组，代入的数值、单位、结果一并写清，其余注明按同一方法处理即可。
Significant figures are simple in principle and messy in practice. Quote uncertainty to one significant figure, or two when the leading digit is one, and align the last digit of the measured value with it. A period written as 0.842 plus or minus 0.003 seconds is consistent; 0.8420 carrying the same uncertainty is not. When a mean comes from three readings, state the instrument uncertainty first, then discuss whether the spread between readings exceeds it. Show one or two complete sample calculations with substituted numbers and units, and note that the remaining rows follow the same steps.
安全、伦理与环境要落到装置上
研究设计那6分明确要求处理安全、伦理与环境问题，写法要贴着装置，而不是在文末加一句。摆长实验涉及支架配重，要写清底座压重和防倾倒措施；用激光或强光源要写护目与光路遮挡；弹簧拉伸要设限位，防止越过弹性限度后弹飞。环境项也不是套话，大功率加热器的耗电、汞或化学废弃物的处置，都能写成具体条目。只写"已注意安全"不构成内容，评委看不到任何可评的判断。
Criterion A asks for safety, ethical and environmental issues, and the answer has to attach to the apparatus instead of sitting in a closing sentence. A pendulum rig needs its base weighted against toppling. A laser or an intense source needs eye protection and beam containment. A spring extension needs a stop that keeps the load inside the elastic limit. Environmental points can be concrete too: power drawn by a heater left running between trials, or disposal of mercury and chemical waste. A line stating that safety was considered gives a marker nothing to credit.
教师反馈与真实性核查的边界
10小时里包含教师反馈和真实性核查的时间，但反馈有边界。老师可以就研究问题是否可行、方法有哪些风险、数据是否够用给出意见，不能替你改数据或替你写分析。讨论后改动的方法，在报告里要呈现为你自己的决定，并说明为什么改。定稿前留一次通读，检查报告是按四个维度组织的，还是按你做事的时间顺序写下来的。评委按标准找证据，不按你的日程找。
The ten hours include teacher feedback and authenticity checks, and feedback has limits. A teacher can comment on feasibility, on the risks in a method, and on whether the data are sufficient; a teacher cannot rewrite the data or supply the analysis. Any method change that came out of a discussion should appear in the report as your decision, with a reason attached. Leave one read-through before submission to check that the report is organised by the four strands rather than by the order in which the work happened, because marking looks for evidence against criteria and not along a timeline.
扣分最集中的几个地方
阅卷时看到的失分很集中。研究问题里没有变量，方法读者跟不下来，不确定度只在表格里出现一次就消失，坐标轴没有单位，结论只写"符合理论"而不给数值，评价把人为误差当成唯一原因。还有一个隐性问题是排版：图片过大挤掉分析篇幅，或者把样算整页贴上去而正文没写清步骤。这些都不涉及物理难度，是取舍和表达的问题。
Marking notes cluster around a small set of failures. Questions with no named variables, methods a reader cannot follow, uncertainties that appear once in a table and then vanish, axes without units, conclusions that say the result agrees with theory but give no number, evaluations that blame human error and stop there. A quieter problem is layout: oversized images crowding out the analysis, or pages of pasted arithmetic standing in for an explanation. None of this concerns the difficulty of the physics, which is why it is worth fixing early.
十小时大概怎么排
官方给的10小时里，大部分花在实验室。一种可用的排法是选题与文献一小时，方法与安全核查一小时，采数三到四小时含试做，处理与作图两小时，写作与修改两到三小时。试做那一次很关键，它能在正式采数前暴露量程不够、仪器漂移或读数不稳。跳过试做直接采正式数据，做到一半发现间隔太密或太疏，只能整段重来。
Most of the ten allocated hours belong in the laboratory. A workable split is an hour on topic selection and background reading, an hour on method and safety checks, three to four hours collecting data including a pilot, two hours processing and plotting, and two to three hours drafting. The pilot run is what students skip, and it is what reveals an inadequate range, instrument drift or unstable readings before the real data are wasted. Discovering halfway through that the intervals were too coarse costs the entire session. Book the laboratory slot early. A rig left half-built on the last afternoon produces data nobody can defend.
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