📚 Multiple Choice Killer Techniques for IB and AQA Physics | IB/AQA物理选择题秒杀技巧
Multiple‑choice questions in IB and AQA Physics examinations can look intimidating, but a handful of clever strategies will often allow you to find the correct answer without grinding through full calculations. This article assembles a set of ‘killer techniques’—from dimensional analysis and unit checking to graph interpretation and limiting cases—that help you eliminate wrong options rapidly and make the most of your exam time.
在IB和AQA物理考试中，选择题虽然看起来唬人，但只要掌握几招巧妙的策略，往往无需完整演算就能直击正确答案。本文整理了一套“秒杀技巧”——从量纲分析、单位筛查到图像解读和极限情况分析——帮你快速排除错误选项，高效利用考试时间。
1. Dimensional Analysis | 量纲分析
Every valid physical equation must be dimensionally homogeneous. By expressing each option in terms of the fundamental dimensions—mass (M), length (L), time (T), electric current (I), etc.—you can instantly discard any choice whose dimensions do not match the quantity being asked for. For example, if a question requires a time period, any answer with dimensions of velocity (L T⁻¹) is impossible.
任何有效的物理方程都必须量纲一致。将每个选项用基本量纲——质量(M)、长度(L)、时间(T)、电流(I)等——表示出来，凡是量纲与所求物理量不符的选项都可以立刻排除。比如题目要求周期，量纲必须是T，若某个选项具有速度量纲 (L T⁻¹)，那就绝对不能选。
A classic illustration: the period T of a simple pendulum. The formula is T = 2π√(L/g). Checking dimensions, g is acceleration, with dimensions L T⁻², so L/g has dimensions L/(L T⁻²) = T²; taking the square root gives T. If a multiple‑choice option reads √(g/L), its dimensions would be √(L T⁻²/L) = T⁻¹—wrong term, so it is killed instantly.
经典示例：单摆周期 T = 2π√(L/g)。量纲检查：g 是加速度，量纲 L T⁻²，则 L/g 量纲为 L/(L T⁻²)=T²，开方得 T。若某选项给出 √(g/L)，其量纲成为 √(L T⁻²/L)=T⁻¹，维度错误，即刻“秒杀”。
Check: [T] = √(L / (L T⁻²)) = T
| Quantity | Common Dimensions |
| Velocity, speed | L T⁻¹ |
| Acceleration | L T⁻² |
| Force (ma) | M L T⁻² |
| Energy, work | M L² T⁻² |
| Potential difference (V) | M L² T⁻³ I⁻¹ |
2. Unit Checking | 单位排除法
Even when you don’t unfold a full dimensional analysis, a quick glance at SI units can eliminate outliers. If the question expects a force (newton, N) and an answer is presented in joules (J) or watts (W), it is immediately wrong. Similarly, be alert for mismatches such as speed in m·s⁻¹ versus m·s or acceleration in m·s⁻² versus m·s⁻¹.
哪怕不展开完整的量纲分析，快速扫一眼国际单位也能剔除异常选项。如果题目要求的是力（牛顿，N），而某个答案标的是焦耳（J）或瓦特（W），那它立刻出局。同理，留心速度单位应是 m·s⁻¹ 而非 m·s，加速度应是 m·s⁻² 而非 m·s⁻¹。
This tactic is especially handy in electricity questions. For instance, resistivity ρ has units Ω·m; if the question asks for resistivity and an option ends with Ω·m⁻¹, it can be discarded. Always remember that both sides of any equation must carry the same unit, so scanning the given expression alongside the options often reveals disjoints.
在电学题中这一招特别有用。比如电阻率 ρ 的单位是 Ω·m；若题目求电阻率，而某选项以 Ω·m⁻¹ 结尾，可以直接排除。时刻牢记任何等式两侧单位必须一致，因此将题目给出的表达式与选项单位对照，常常能暴露矛盾。
e.g. Power: P = I V → watt (W) = A · V, never A·Ω
3. Limiting Cases | 极限情况速判
A physically correct formula must behave sensibly when you push its variables to extremes. Test what happens as an angle goes to 0°, a mass approaches zero, a distance tends to infinity, or a resistance becomes enormous. Options that blow up unphysically or fail to vanish when they should can be crossed out on the spot.
一个物理上正确的公式在变量取极限时必须表现得合理。试试看角度趋于0°、质量趋近于零、距离趋于无穷大、或电阻极大时会发生什么。那些在这些情况下无端发散、或者该消失却不消失的选项，可以当场划掉。
Example: The electric field due to an infinite line of charge has magnitude E = λ/(2π ε₀ r). As r → ∞, E → 0; an option giving E → constant or ∞ at large r is clearly wrong. Similarly, in projectile motion, range R = (u² sin 2θ)/g. When θ → 0°, sin 2θ → 0 so R → 0; an alternative reading (u² cos 2θ)/g would give a non‑zero range for θ=0, which contradicts experience.
示例：无限长线电荷的电场大小 E = λ/(2π ε₀ r)。当 r → ∞，E → 0；若某个选项在大 r 下给出常值或无穷大，显然错误。又如抛体运动射程 R = (u² sin 2θ)/g，当 θ → 0°，sin 2θ → 0，R → 0；若某选项写成 (u² cos 2θ)/g，θ=0 时所得射程非零，与经验矛盾，即可秒杀。
4. Special Values | 特殊值代入法
When the answer choices are algebraic expressions, substitute simple numerical values for the variables and evaluate which option reproduces a known physical outcome. Often θ = 0, m = 1 kg, or a resistance set to zero will give a straightforward benchmark. The option that matches the benchmark is the survivor.
当答案选项是代数式时，给变量代入简单的数值，看看哪个选项能复现已知的物理结果。通常取 θ=0、质量 m=1 kg、或让某个电阻为零，就能得到一目了然的基准。符合基准的那个选项就是存活者。
Consider a box sliding down a smooth incline: acceleration a = g sin θ. Substitute θ = 30°, sin 30° = 0.5, so a = 0.5 g. Competing options such as g cos θ, g tan θ, or g/ sin θ will give different numbers—quickly exposing the imposter. Never forget to check the sign if direction matters.
考虑光滑斜面上下滑的滑块：加速度 a = g sin θ。代入 θ=30°，sin 30°=0.5，得 a = 0.5 g。其他选项如 g cos θ、g tan θ、g/ sin θ 会给出不同数值，迅速让假答案现形。如果方向重要，切勿忘记核对正负号。
Test: a = g sin 30° = 0.5 g → cos 30° would give ≈0.866 g → wrong
5. Estimation & Order of Magnitude | 估算与数量级
Physics multiple‑choice frequently sets up questions where the correct answer differs from distractors by several orders of magnitude. Round off constants (π ≈ 3, g ≈ 10 m·s⁻²) and use powers of ten to get a rapid rough figure. Even a one‑significant‑figure estimate can uniquely pick the right option.
物理选择题中，正确答案经常与干扰项相差几个数量级。把常数取整（π ≈ 3, g ≈ 10 m·s⁻²），用10的幂次快速得出一个粗略数值。即便只保留一位有效数字的估算，也足以唯一锁定正确选项。
Example: Estimate the wavelength of red light. c ≈ 3×10⁸ m·s⁻¹, f ≈ 4×10¹⁴ Hz → λ = c/f ≈ (3×10⁸)/(4×10¹⁴) ≈ 0.75×10⁻⁶ m = 7.5×10⁻⁷ m. Choices listed as 10⁻⁹ m, 10⁻⁷ m, 10⁻³ m make 10⁻⁷ m the clear winner. There is no need to compute 6.32×10⁻⁷ m precisely.
示例：估算红光波长。c ≈ 3×10⁸ m·s⁻¹，f ≈ 4×10¹⁴ Hz，λ = c/f ≈ (3×10⁸)/(4×10¹⁴) ≈ 0.75×10⁻⁶ m = 7.5×10⁻⁷ m。选项若列出 10⁻⁹ m、10⁻⁷ m、10⁻³ m，10⁻⁷ m 明显胜出。根本无需计算到 6.32×10⁻⁷ m。
6. Graph Interpretation | 图像斜率与截距巧解
Straight‑line graphs are a gift in multiple‑choice: the gradient and y‑intercept often directly yield the desired physical quantity. Determine what has been plotted on each axis, link to the linear equation y = mx + c, and read off the answer. Options that confuse the gradient with the reciprocal or the intercept can be eliminated instantly.
直线图是选择题中的送分题：斜率和 y 轴截距往往直接给出所求的物理量。明确两轴各表示什么，与直线方程 y = mx + c 挂钩，答案就清楚了。那些把斜率与其倒数混淆、或错误解读截距的选项可以被立即排除。
Classic cases: a graph of V against I gives resistance R as the gradient; an extension–force graph gives the spring constant k as the gradient of force against extension. If a question asks for resistivity from a resistance‑length graph, keep in mind R = ρL/A, so slope = ρ/A. An option claiming slope = ρ A is dimensionally wrong—kill it.
经典案例：V–I 图，斜率是电阻 R；力‑伸长图，F 对 Δx 的斜率是劲度系数 k。若题目要从电阻‑长度图求电阻率，牢记 R = ρL/A，故斜率=ρ/A。若某选项声称斜率=ρ A，量纲就不对——秒杀。
Gradient = Δy/Δx, never x/y unless playing with axes
7. Conservation Laws & Symmetry | 守恒律与对称性
In collision, explosion, and circuit problems, always check whether an option respects conservation of momentum, charge, or energy. If a choice suggests final kinetic energy greater than the initial total, it violates conservation. Symmetry arguments can also halve the possibilities—for instance, in a balanced Wheatstone bridge, the galvanometer current is zero.
在碰撞、爆炸和电路问题中，始终检验选项是否遵守动量、电荷或能量守恒。若某个选项暗示末态动能大于初始总动能，那就违反了守恒。对称性论证也能让可能选项减半——比如平衡惠斯通电桥中，检流计电流为零。
Take a one‑dimensional elastic collision of two identical masses where one is initially at rest. After collision, the incident mass stops and the target moves off with the original velocity. Any option in which both move with half the original speed conserves momentum but not kinetic energy—it corresponds to a perfectly inelastic collision, not elastic. Spotting this difference saves valuable minutes.
考虑两个相同质量的一维弹性碰撞，一个初始静止。碰撞后，入射小球停下，被撞小球以原速度运动。任何选项给出两者都以一半速度运动，动量守恒但动能不守恒——那对应完全非弹性碰撞，而非弹性碰撞。辨别这种区别可节省宝贵时间。
8. Formula Manipulation | 公式变形直接选
Many multiple‑choice items simply test whether you can rearrange an equation correctly. Instead of fully solving from first principles, scan the algebraic form of each option. Check the operation: has the square been taken properly? Is the required variable isolated on one side? Be especially wary of sign mistakes, e.g., missing a minus sign in lens formula or forgetting to invert fractions.
许多选择题实际上只是在考察你是否能正确变换公式。与其从头推导，不如直接扫视每个选项的代数形式。检查运算：平方开得对吗？所求变量是否被正确隔离在一侧？尤其要当心符号错误，比如透镜公式漏掉负号，或者忘记将分数取倒数。
Example: For an ideal gas, pV = nRT, to solve for T, T = pV/(nR). An option showing T = pnR/V or T = pV nR would be dimensionally implausible. In gravitation, F = GmM/r² gives r = √(GmM/F). The distractors r = √(F/GmM) or r = GmM/F² can be swiped away after a quick rearrangement check.
示例：理想气体 pV = nRT，求 T 得 T = pV/(nR)。若某选项出现 T = pnR/V 或 T = pV nR，量纲就不对。万有引力 F = GmM/r² 变形得 r = √(GmM/F)，干扰项 r = √(F/GmM) 或 r = GmM/F² 通过快速变形检查即可扫除。
9. Common Traps & Misconceptions | 常见陷阱辨析
Examiners love predictable traps: mass vs weight, average speed vs instantaneous speed, distance vs displacement, and current as a scalar with direction in circuit loops. Read the question stem carefully—does it ask for the magnitude or the vector? Energy or power? Average or peak? Lenz’s law is another notorious pitfall: the induced emf opposes the change in flux, often requiring a negative sign.
考官喜欢反复使用的陷阱：质量与重量、平均速度与瞬时速度、路程与位移、电流是标量但在回路中有方向。仔细审题——它问的是大小还是矢量？能量还是功率？平均值还是峰值？楞次定律是另一个臭名昭著的坑：感应电动势反抗磁通量的变化，经常需要带上负号。
A common blunder: a stone falls under gravity. The distance travelled in the 2nd second is not the same as the displacement after 2 s. The phrase “in the nth second” requires u + ½g(2n‑1), while “after n seconds” uses s = ut + ½gt². Options deliberately offer both values, so check the wording. Likewise, in nuclear physics, distinguish mass number from atomic number carefully.
常见错误：石块自由落体，“第2秒内的位移”与 “2秒内的位移”不同。“第n秒内”要用 u + ½ g (2n‑1) 计算，“n秒后”则用 s = ut + ½
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