IB物理IA 研究问题 变量 不确定度 结论
IB 物理的内部评估是一项由你自己定题的科学探究，报告上限 3000 词，占最终成绩的 20%，SL 与 HL 用同一套评分标准。IBO 官网的科目简报把这个 10 小时的探究任务写得很清楚：满分 24 分，研究设计、数据分析、结论、评估各占 6 分。很多学生把力气全花在实验操作上，最后丢分却丢在数据表与不确定度上。下面按评分项的次序，把每个环节该写成什么样拆开讲。
The internal assessment in IB Physics is an open-ended scientific investigation that you design yourself. The report is capped at 3,000 words, carries 20% of the final grade, and is marked identically at SL and HL. Since the guide first assessed in 2025, the rubric has four criteria worth 6 marks each: research design, data analysis, conclusion and evaluation. Marks are usually lost in the tables and the uncertainties rather than in the apparatus.
研究问题要写清自变量因变量与系统
研究问题的第一句要让人看出你改了哪个量、测了哪个量。以单摆为例，写成「单摆周期如何随摆长变化」还不够，加上范围与测量方式才算合格：「摆长从 0.20 m 到 1.00 m，每 0.10 m 一档，单摆周期如何变化」。自变量是摆长，因变量是周期，系统就是一个摆角小于 10 度、忽略空气阻力的单摆。评分描述里要求研究问题放在具体背景中，这里的背景就是简谐运动与周期公式 T = 2π√(l/g)。背景不用写成长篇综述，一段话把公式与可检验的预测交代清楚即可。很多学生以为题目越宽越好写，实际上越宽的题目越难写出可比较的结论。常见的错误是把两个自变量一起改，比如同时换摆长与摆球质量，数据一出来就分不清是谁在起作用。
A workable research question names the variable you manipulate, the variable you measure and the system you are working with. Asking how the period of a pendulum depends on its length is too loose; stating that the length runs from 0.20 m to 1.00 m in 0.10 m steps makes the investigation reproducible. The system here is a simple pendulum swinging through less than ten degrees, where the small-angle approximation holds and the period follows the model T = 2 pi sqrt(l/g). Markers look for that background in one short paragraph, not in a literature review. Changing two variables at once, such as length and bob mass, leaves you unable to attribute whatever trend appears.
自变量取五档以上每组重复三次
评分描述里的范围、间隔、重复次数是具体可数的东西。物理实验常用 5 到 8 档自变量，间隔尽量等距，这样作图时横轴刻度均匀，不会全挤在一端。重复次数上，IB 的口径是把次数尽量提高，多数学校的实操按每组至少三次来安排，取平均并算出标准差，再用标准差画误差棒。单摆实验里每个摆长测三次周期，八个摆长就是 24 个测量值，写进报告已经足够。有人担心数据太多写不完，其实原始数据表只放代表性的一列或两列，其余放附录。档位太少是另一种麻烦：三个点也能连成直线，但由这条直线读出的斜率不确定度会大到无法与公认值比较。阅卷时最常见的退步是先定了结论再凑数据，斜率的百分比不确定度做到 40% 还照样宣称验证了公式。
Range, interval and the number of repeats are the concrete numbers markers count. Physics investigations usually need five to eight values of the independent variable, spaced as evenly as the apparatus allows, so the horizontal axis is not bunched at one end. Three repeats per value is the usual working minimum in most schools; you average them and use the standard deviation to size the error bars. A pendulum run with eight lengths and three repeats gives twenty-four measurements, which is plenty for a report. Too few values is worse than too many, because three points will always fit a straight line while the gradient keeps an uncertainty too wide for any comparison with an accepted value.
控制变量与系统误差要分开处理
控制变量的写法要落到具体做法，而不是列一张名词表。摆长用卷尺从悬点量到摆球球心，这一步最容易漏的是量取起点：从悬点算起还是从支架横梁算起，两次实验不一致就等于换了系统。摆角每次放球都用同一个量角器或标记线控制在 10 度以内，计时固定由同一个人完成，减少反应时间的个体差异。系统误差的特点是每次偏向同一个方向，比如计时总是晚按、米尺起始端磨掉 2 mm，做多少次平均都消不掉，只能靠校准或改用另一种测量方式把它暴露出来。随机误差正好相反，多测几次取平均能把它压小。评估部分的 5 到 6 分要求把这两类误差分开说，并说清各自对最终结果的影响。
Writing variables down as a list of nouns earns little; markers want the method attached to each one. Length is measured with a tape from the pivot to the centre of the bob, and the same reference point has to be used every time. The release angle is kept under ten degrees with a protractor or a marked line on the stand, and one student does all the timing so that reaction time stays similar across trials. Systematic errors push every reading in the same direction, so averaging cannot remove them, whereas random scatter shrinks as more readings are taken. Distinguishing the two, and saying how each one affects the final gradient, is what the top band of the evaluation criterion asks for.
原始数据表与仪器不确定度怎么记
原始数据表里每个表头都要有物理量与单位，比如 l / m 与 t / s，不确定度写在表头或表内，不能只在正文里说一句「误差很小」。不确定度按仪器的分辨力来取：米尺最小分度 1 mm，单次读数取正负 0.5 mm；卷尺量摆长要读起点与终点两次，两端的读数不确定度相加，写成正负 1 mm 或正负 2 mm。数字秒表的分辨力是 0.01 s，但手动计时的不确定度由人的反应时间决定，通常按正负 0.2 s 到正负 0.3 s 处理，直接照抄 0.01 s 是不真实的。同一列数据的小数位数必须一致，测量精度到哪一位就写到哪一位。很多学生把仪器上显示的位数全部抄下来，秒表读数写成 2.3456 s，反而暴露自己没想过精度这件事。
Every column in a raw data table needs a quantity together with a unit, and the uncertainty belongs in the table rather than in a sentence saying the errors were small. For a metre rule the smallest division is 1 mm, so a single reading carries plus or minus 0.5 mm, while a length measured between two marks accumulates the uncertainty from both readings. Hand timing is the awkward case: a digital stopwatch displays 0.01 s, but reaction time dominates, so a realistic figure is 0.2 s rather than the last displayed digit. Decimal places must match the precision of the instrument down the whole column. Copying every digit the display offers, such as 2.3456 s, usually shows that precision was never considered.
非线性关系先线性化再读斜率
原始图像画成曲线，斜率与截距都很难读出不确定度，所以先做线性化。单摆的周期公式 T = 2π√(l/g) 两边平方得到 T^2 = (4π^2/g) l，以摆长 l 为横轴、周期平方 T^2 为纵轴作图，理论截距为零，斜率等于 4π^2/g，重力加速度 g 就是 4π^2 除以斜率。电阻丝实验里 R = ρL/A，以长度 L 为横轴、电阻 R 为纵轴，斜率给出 ρ/A。光折射实验用 sin i 对 sin r 作图，斜率就是折射率，空气到玻璃通常在 1.5 附近，空气到水在 1.33 附近。作图前先想清楚哪个量放横轴：斜率要有物理含义，横轴就得是你能直接控制的自变量。坐标标签写成 量 / 单位 的形式，刻度等间距，纵轴不要随便取对数。判断数据好坏的办法是看拟合直线的截距是否覆盖零：截距带误差棒后不包含零，说明存在没有被识别出来的系统误差。
Curved graphs make uncertainties hard to read, so the standard move is to linearise first. Squaring the pendulum period gives T squared proportional to the length, with a theoretical intercept of zero and a gradient of 4 pi squared over g, which rearranges into the value of g. Plotting resistance against wire length pays off in the same way, because the gradient is resistivity divided by cross-sectional area. For refraction, sin i against sin r gives a gradient equal to the refractive index, near 1.5 for glass and 1.33 for water. A fit whose intercept does not cover zero once error bars are considered points to a systematic offset that averaging will never remove.
不确定度传递与误差棒画法
相乘除的量，百分比不确定度相加；取幂的量，百分比不确定度按指数放大。单摆里周期的不确定度除以周期得到百分比，平方后翻倍，所以 1% 的计时误差在周期平方上变成 2%。摆长 0.50 m 上正负 1 mm 的读数误差只有 0.2%，与 2% 相比可以忽略，这解释了为什么单摆实验里时间的不确定度占主导。图像上给每个点画误差棒，误差棒的高度就是该点的不确定度；再由最陡与最平的两条合理直线读出斜率的上下限，斜率不确定度取两者差值的一半。手算斜率时至少取两个相距较远的点，用相邻两点算出来的斜率很不稳定。百分比不确定度的大小能告诉你哪个量值得花时间改仪器：把 2% 的计时误差降到 1%，比把 0.2% 的测长误差降到 0.1% 划算得多。别把不确定度写成一句「误差在可接受范围内」，那等于没写。
Percentage uncertainties add when quantities are multiplied or divided, and they multiply when a quantity is raised to a power. In the pendulum case a 1% timing uncertainty becomes 2% on the squared period, which is why timing dominates the final gradient. An error bar on each point shows that uncertainty directly, and the steepest and shallowest lines that still pass through the bars bracket the gradient, half the spread being its uncertainty. Software fits are acceptable, but a hand-drawn line must use points that are far apart. Comparing percentage uncertainties also shows where to spend effort: cutting a 2% timing uncertainty in half beats refining a 0.2% length measurement. Writing that errors were acceptable, with no numbers attached, earns nothing.
结论要与公认值定量比较
结论不是把图像念一遍，而是回答研究问题并给出数字。写法可以是：由斜率得到 g = 9.6 正负 0.3 m/s^2，公认值 9.81 m/s^2 落在不确定度区间内，因此数据支持周期公式的预测。这种定量比较往往决定 3 到 4 分与 5 到 6 分之间的差距。百分比差异同时算出来：|9.6 - 9.81| 除以 9.81 约等于 2.1%，小于斜率的百分比不确定度，说明差异可以由随机误差解释。若差异明显超出不确定度，就要回到数据找原因，比如摆球质量与支架质量之比不够大，或者摆角超过 10 度之后周期公式本身开始偏离。结论里还要写清有没有数据点偏离趋势、是否把它们剔除过，剔除的理由要经得起追问。不确定度区间要写全，只写 9.6 一个数字等于放弃了比较的依据。
A conclusion answers the research question with a number rather than a description of the graph. A usable statement reads: the gradient gives g = 9.6 plus or minus 0.3 m/s^2, and the accepted value of 9.81 m/s^2 lies inside that interval, so the data support the model. Showing the same comparison as a percentage difference, here about 2.1%, makes the argument much harder to dismiss. When the gap is far larger than the uncertainty, the reason has to be traced in the data: a bob whose mass is not negligible against the stand, or an amplitude past ten degrees where the period formula itself drifts. Any point you discarded needs a stated reason, and quoting the interval in full is what makes the comparison meaningful.
评估要排优先级并给出对应改进
评估部分的分档很清楚：笼统的弱点只能拿 1 到 2 分，写出具体的弱点能到 3 到 4 分，说明每个弱点对结果影响多大才够 5 到 6 分。笼统的写法是「秒表有误差」；具体的写法是「手动计时的反应时间约 0.2 s，对应 1% 到 2% 的周期误差，平方后放大成 2% 到 4%，是斜率不确定度的主要来源」。把弱点按影响大小排个序，先说最大的那个，再说可以忽略不计的，分类时明确写出随机误差与系统误差各自的处理方式。改进要与弱点一一对应，比如改用光电门自动计时，把计时不确定度降到毫秒量级。环境因素也要提：空调气流带动摆球、桌面振动、温度改变电阻丝的长度与阻值。评估里不要写「下次我会更小心」，这句话对分数没有任何贡献。
The evaluation bands are explicit: a generic weakness reaches only 1 or 2 marks, a specific weakness 3 or 4, and an explanation of its relative impact is what unlocks 5 or 6. Saying the stopwatch was imprecise earns little; stating that reaction time adds roughly 0.2 s, about 1% to 2% on the period and 2% to 4% after squaring, shows how that weakness reaches the gradient. Ranking the weaknesses by impact, and naming which are random and which are systematic, keeps the paragraph focused. Each improvement should answer the weakness it targets, for instance a light gate that cuts timing uncertainty to the millisecond level. Air currents, bench vibration and the temperature dependence of a wire belong in the same section, and promising to be more careful next time contributes nothing.
写作顺序与各部分字数分配
报告 3000 词的上限看着宽裕，写完方法与数据处理往往只剩几百词留给评估。按评分项分配比较稳：研究设计约 700 词，数据分析约 800 词，结论约 600 词，评估约 700 词，剩下留给引言与背景。考纲里这四个评分项是等权的，评估与研究设计一样值钱，没有理由把它们留到最后草草收尾。写作顺序与阅读顺序相反：先把方法、数据表与图表做出来，再写引言与背景，最后写结论与评估，这样引言不会偏离数据本身。图表每一张都要能在正文里被引用到，没有引用的图表不占分。很多学生以为评估只是客气几句，其实它是四个评分项里最容易拿满的一项。常见的时间安排失误是先做完实验再动笔，写到一半发现数据不足以回答研究问题，只能补做，而 10 小时的时间早已用光。
Three thousand words sounds generous until the method and the data processing are written up. A workable split is roughly 700 words for research design, 800 for data analysis, 600 for the conclusion and 700 for evaluation, with the remainder left for the introduction. The four criteria carry equal weight, so evaluation deserves the same effort as research design. Write the method, the tables and the graphs first, then the introduction, and finish with conclusion and evaluation, so the opening cannot drift away from what the data show. Every figure needs to be referred to in the text, since an unreferenced graph carries no marks. The common misjudgement is treating evaluation as a polite formality, when in fact it is often the easiest criterion to fill.
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