📚 IB & CIE Science: Common Mistakes & Detailed Solutions | IB 与 CIE 科学：易错题精讲
Science examinations under IB and CIE often reveal a set of recurring misunderstandings that cost students valuable marks. Whether in Physics, Chemistry or Biology, certain concepts trip up even well-prepared candidates. This article pinpoints ten classic error types, explains the underlying correct principles, and provides clear examples to help you avoid these pitfalls in your next assessment.
在 IB 与 CIE 科学考试中，总有一些反复出现的误解让许多考生丢分。无论是物理、化学还是生物，某些概念即便准备充分的学生也容易出错。本文精选十类经典易错题，剖析错误根源，讲解正确原理，并配以清晰的例子，帮助你在下一次考试中避开这些陷阱。
1. Heat vs Temperature | 热量与温度的混淆
Students often say ‘the beaker of boiling water has more heat than the iceberg’. In Physics, heat is energy in transit due to a temperature difference, while temperature measures the average kinetic energy of particles. An object does not ‘contain’ heat; it has internal energy. A large iceberg at 0°C possesses far more internal energy than a cup of 100°C water, yet its temperature is lower. Confusing these terms leads to incorrect reasoning in calorimetry questions.
学生常说“这杯沸水比冰山含有更多热量”。在物理中，热量是由于温差而传递的能量，温度则是粒子平均动能的量度。物体并不“含有”热量，它拥有的是内能。一大块 0°C 的冰山远比一杯 100°C 的水拥有更多的内能，但它的温度更低。混淆这两个术语会导致在量热学问题中出现错误推理。
A related error appears in thermal sensation: touching metal and wood at the same room temperature, metal feels colder. Many students assume the metal is at a lower temperature. In reality, both are at the same temperature; metal conducts heat away from the hand faster, creating a stronger sensation of cold. This is about thermal conductivity, not temperature difference.
一个相关的错误出现在热感上：在相同室温下触摸金属和木头，金属感觉更冷。许多学生认为金属温度更低。实际上，两者温度相同；金属更快地将热量从手上传导出去，产生了更强烈的冷感。这关乎导热性，而不是温差。
2. Mole Calculations in Stoichiometry | 化学计量中的摩尔计算
A frequent mistake is treating gas volumes as moles directly. At standard temperature and pressure (STP), 1 mole of any ideal gas occupies 22.4 dm³. Students given 11.2 dm³ of CO₂ will sometimes write ‘11.2 mol’ instead of first dividing by 22.4 dm³/mol to obtain 0.50 mol. Similarly, when calculating the number of molecules, they may forget to multiply the amount in moles by Avogadro’s constant (6.02 × 10²³). Always convert to moles first before finding particle numbers or mass.
一个常见错误是直接把气体体积当成摩尔数。在标准状况（STP）下，1 摩尔任何理想气体占据 22.4 dm³。给出 11.2 dm³ 的 CO₂ 时，学生有时会写成“11.2 mol”，而不是先除以 22.4 dm³/mol 得到 0.50 mol。同样，在计算分子数目时，他们可能忘记将摩尔数乘以阿伏伽德罗常数（6.02 × 10²³）。在求粒子数或质量之前，务必先换算成摩尔数。
Another typical slip arises with unit conversions: using cm³ without converting to dm³. 24000 cm³ = 24 dm³ at RTP, but 24 dm³ per mole is the correct factor. Writing 24 cm³ per mole is a disaster. Always check that volume units match the chosen molar volume.
另一个典型疏忽是单位换算：使用 cm³ 却没有转换为 dm³。在常温常压下 24000 cm³ = 24 dm³，但正确比例是 24 dm³ 每摩尔。写成 24 cm³ 每摩尔会导致巨大错误。务必检查体积单位是否与所用的摩尔体积一致。
3. Misapplying Ohm’s Law | 欧姆定律的误用
Ohm’s law states V = IR, but this relationship is linear only for ohmic conductors at constant temperature. For a filament lamp, the I–V graph is curved because resistance increases with temperature. A typical mistake is to pick a single point (say 3.0 V, 0.5 A), compute R = 6 Ω, and assume the lamp always has 6 Ω. In reality, at 6.0 V the current might be 0.8 A, giving a different resistance. You must treat R = V/I as a static resistance valid only at that point, not a constant.
欧姆定律表述为 V = IR，但此关系仅对温度恒定的欧姆导体呈线性。对于白炽灯，I–V 图是弯曲的，因为电阻随温度升高而增大。典型错误是选取一个点（如 3.0 V，0.5 A），计算出 R = 6 Ω，并假设灯泡总是 6 Ω。实际上，在 6.0 V 时电流可能是 0.8 A，得出不同的电阻。必须将 R = V/I 视为仅在该点有效的静态电阻，而不是一个常数。
Furthermore, the slope of the I–V curve does not directly give resistance for non-ohmic components. Advanced questions may ask for dynamic resistance ΔV/ΔI; students often confuse this with static resistance V/I. Remember, for a straight line through the origin, they coincide; for a curve, they differ.
此外，对于非欧姆元件，I–V 曲线的斜率并不直接给出电阻。高级题目可能要求动态电阻 ΔV/ΔI；学生常将此与静态电阻 V/I 混淆。记住，对于通过原点的直线，两者一致；对于曲线，两者不同。
4. Genetic Probability Pitfalls | 遗传概率的陷阱
A classic error in Biology involves predicting the sex of children. Many students claim that after having two daughters, the chances of the next child being a son increase. The probability of having a boy is always close to ½, independently of previous births. The mistake lies in confusing independent events with the probability of a particular sequence.
生物中一个经典错误涉及子女性别的预测。许多学生认为在已有两个女儿后，下一胎生男孩的概率会增加。实际上，每次出生男孩的概率始终接近 ½，独立于先前的出生。错误在于混淆了独立事件与特定序列的概率。
For dihybrid crosses, a frequent slip is forgetting that the alleles assort independently. When asked ‘what is the probability of an offspring having genotype AaBb from a cross AaBb × AaBb?’, students sometimes incorrectly multiply ½ × ½ = ¼. In reality, the proportion of Aa is ½ and Bb is ½, so the combined probability is ¾? Actually careful: Aa from Aa×Aa is ½, Bb from Bb×Bb is ½, so AaBb is ½ × ½ = ¼. That is correct, but the error more often occurs when dealing with linked genes or when first calculating gametes incorrectly. Always use a Punnett square or probability rules systematically.
对于双基因杂交，常见的疏漏是忘记等位基因独立分配。当被问及“AaBb × AaBb 后代基因型为 AaBb 的概率是多少？”时，学生有时错误地相乘，例如以为 Aa 的概率是 3/4 而误算。实际上 Aa 的概率为 ½，Bb 的概率为 ½，所以 AaBb 的概率是 ½ × ½ = ¼。但错误往往在连锁基因或错误推算配子时更突出。务必系统使用庞纳特方格或概率法则。
5. Le Chatelier’s Principle Misjudgements | 勒夏特列原理的误判
Le Chatelier’s principle states that if a dynamic equilibrium is disturbed, the position of equilibrium moves to counteract the change. A widespread mistake is confusing the effect on equilibrium position with the effect on rate. For the exothermic reaction N₂ + 3H₂ ⇌ 2NH₃ (ΔH = -92 kJ), increasing temperature speeds up both forward and reverse reactions, but it favours the endothermic reverse reaction, decreasing the yield of ammonia. Students often argue ‘higher temperature → faster reaction → more product’, ignoring that the equilibrium shifts left.
勒夏特列原理指出，如果动态平衡受到扰动，平衡位置会移动以抵消这一改变。一个普遍的混淆是将对平衡位置的影响与对速率的影响混为一谈。对于放热反应 N₂ + 3H₂ ⇌ 2NH₃（ΔH = -92 kJ），升高温度既加快了正反应也加快了逆反应，但它有利于吸热的逆反应，从而降低了氨的产率。学生常争论说“温度升高 → 反应加快 → 产物更多”，却忽略了平衡向左移动。
Another common error occurs with pressure changes: adding an inert gas at constant volume does not change the partial pressures of reactants, so the equilibrium position stays the same. Many students incorrectly assume any increase in total pressure shifts the equilibrium towards fewer moles. Always identify whether the partial pressures of reacting species actually change.
另一个常见错误发生在压强变化时：在定容条件下加入惰性气体并不改变反应物的分压，因此平衡位置保持不变。许多学生错误地认为任何总压的增加都会使平衡向分子数减少的方向移动。务必辨别反应物种的分压是否真正发生了变化。
6. Sign Conventions in Kinematics | 运动学中的符号规定
In IB and CIE Physics, choosing a sign convention is critical for vertical motion problems. A ball is thrown vertically upward with a speed of 20 m s⁻¹. Take upward as positive; then acceleration due to gravity a = -9.8 m s⁻². A common mistake is writing v = u + at with a = +9.8 m s⁻², leading to the ball going up indefinitely. Correctly, at maximum height v = 0, so 0 = 20 – 9.8t → t ≈ 2.04 s, and max height s = 20×2.04 – ½×9.8×(2.04)² ≈ 20.4 m.
在 IB 与 CIE 物理中，选择符号规定对竖直运动问题至关重要。一个球以 20 m s⁻¹ 的初速度竖直上抛，取向上为正，则重力加速度 a = -9.8 m s⁻²。常见的错误是在 v = u + at 中写 a = +9.8 m s⁻²，导致球无休止地上升。正确作法是，在最高点 v = 0，所以 0 = 20 – 9.8t → t ≈ 2.04 s，最大高度 s = 20×2.04 – ½×9.8×(2.04)² ≈ 20.4 m。
The sign error also shows up in displacement calculations. If an object is thrown upward and returns to the starting point, the total displacement is zero, but the distance travelled is twice the maximum height. Students often substitute the total distance into kinematic equations as displacement, obtaining impossible time values. Always clarify vector vs scalar quantities.
符号错误还出现在位移计算中。若物体向上抛出后又落回起点，总位移为零，但所通过的路程是最大高度的两倍。学生常将总路程当作位移代入运动学方程，得出不可能的时间值。务必分清矢量与标量。
7. Confusing Light and Dark Reactions in Photosynthesis | 光合作用光反应与暗反应的混淆
The light-dependent reactions occur in the thylakoid membranes and produce ATP, NADPH and O₂ by splitting water. The light-independent reactions (Calvin cycle) take place in the stroma and use ATP and NADPH to fix CO₂ into glucose. A classic misconception is that ‘dark reactions’ happen only at night. In reality, they are called ‘dark’ because they do not directly require light, but they usually occur during the day as they depend on the products of the light reactions.
光反应发生在类囊体膜上，通过分解水产生 ATP、NADPH 和 O₂。暗反应（卡尔文循环）在基质中进行，利用 ATP 和 NADPH 将 CO₂ 固定为葡萄糖。一个典型误解是认为“暗反应”只在夜晚发生。实际上，它们被称为“暗反应”是因为不直接需要光，但它们通常在白天进行，因为依赖光反应的产物。
Students also mix up the locations and products. Exam questions often ask: ‘Where is oxygen produced?’ The answer is the thylakoid space during photolysis. A wrong but common answer is the stroma. Tracing the path of carbon, oxygen and energy carriers correctly is essential to scoring full marks in SAQs.
学生还常混淆场所与产物。试题常问：“氧气在哪里产生？”答案是类囊体腔内在光解水时产生。一个常见却错误的回答是基质。正确追踪碳、氧和能量载体的路径是简答题拿满分的必要条件。
8. Equivalence Point vs End Point in Titration | 滴定等当点与终点的混用
In acid-base titrations, the equivalence point is when the moles of acid equal the moles of base (stoichiometric neutralization). The end point is when the indicator changes colour. A perfect match is rare. For a strong acid – strong base titration, the equivalence point is at pH 7, and using phenolphthalein (colourless to pink around pH 8.2–10) introduces a small systematic error, though often acceptable. For a weak acid – strong base titration, the equivalence point is above pH 7; phenolphthalein is suitable, but methyl orange would change far too early, causing a huge error.
在酸碱滴定中，等当点是酸的摩尔数与碱的摩尔数相等（化学计量中和）的时刻。终点则是指示剂变色之时。两者完美重合很少见。对于强酸–强碱滴定，等当点在 pH 7，使用酚酞（无色到粉红约 pH 8.2–10）会引入小的系统误差，尽管通常可接受。对于弱酸–强碱滴定，等当点 pH > 7，酚酞是合适的，而甲基橙则会过早变色，造成巨大误差。
A frequent mistake is choosing an indicator simply based on its colour change rather than the pH range of the change relative to the equivalence point. Always sketch the pH curve and select an indicator whose range lies entirely within the steep part of the curve.
常见错误是仅根据指示剂的颜色变化来选择，而不是考虑其变色 pH 范围相对于等当点的位置。务必勾画 pH 曲线，选择变色范围完全落在曲线陡峭区间的指示剂。
9. Conditions for Interference in Waves | 波动干涉条件的错误理解
Two-source interference requires the sources to be coherent – meaning they have the same frequency, a constant phase difference, and the same (or nearly the same) amplitude for clear fringes. Many students state only ‘same frequency’ and forget that a constant phase relationship is key. Two speakers emitting the same frequency but with randomly varying phase difference will not produce a stable interference pattern.
双源干涉要求波源具有相干性——即具有相同的频率、恒定的相位差，并且振幅相同或相近才能得到清晰的条纹。许多学生只表述为“相同频率”，却忘了恒定的相位关系才是关键。两个发出同样频率但相位差随机变化的扬声器不会产生稳定的干涉图样。
In explaining the double-slit experiment with light, candidates often incorrectly say that bright fringes are points where waves ‘meet in phase’ and dark fringes where they ‘meet out of phase’ without mentioning path difference. The precise condition for a bright fringe is that the path difference equals a whole number of wavelengths, nλ; for a dark fringe it is (n + ½)λ. A qualitative description loses marks when quantitative reasoning is required.
在解释光的双缝实验时，考生常错误地说亮纹是波“同相相遇”，暗纹是“反相相遇”，却未提及路程差。亮纹的精确条件是路程差等于波长的整数倍 nλ；暗纹则是 (n + ½)λ。当题目要求定量推理时，仅作定性描述会丢分。
10. Individual vs Population Evolution | 个体进化与种群进化的谬误
A deeply rooted misunderstanding in Biology is that individual organisms evolve during their lifetime in response to environmental pressures, such as ‘giraffes stretched their necks and passed this length to offspring’. This Lamarckian view is incorrect. Natural selection acts on heritable variation within a population; individuals with longer necks survive better and reproduce more, shifting the population’s gene pool over generations. It is the population that evolves, not the individual.
生物学中一个根深蒂固的误解是生物个体在其一生中为了应对环境压力而进化，例如“长颈鹿伸长脖子，然后将这个长度遗传给后代”。这种拉马克式观点是错误的。自然选择作用于种群内的可遗传变异；脖子更长的个体存活得更好、繁殖更多，经过世代逐渐改变种群的基因库。进化的是种群，而非个体。
Antibiotic resistance in bacteria is often described as ‘bacteria become resistant when exposed to the antibiotic’. The resistant alleles already exist in the population by random mutation; the antibiotic acts as a selective agent, killing susceptible bacteria and leaving the resistant ones to multiply. The individual bacterium does not deliberately develop resistance; the population’s allele frequency changes over time.
细菌的抗生素耐药性常被描述为“接触抗生素后细菌变得耐药”。实际上，耐药等位基因通过随机突变早已存在于种群中；抗生素充当选择剂，杀死敏感的细菌，留下耐药的个体繁殖。细菌个体并不会主动产生耐药性；改变的是随时间推移种群中的等位基因频率。
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