Edexcel IGCSE物理 力与运动 电学 波 半衰期
4PH1 只有两张卷子，Paper 1 两小时 110 分占 61.1%，Paper 2 一小时十五分 70 分占 38.9%，Pearson 考纲从 2017 年 9 月首教、2019 年 6 月首考，2024 年 9 月已经出到 Issue 4，卷面结构一直没有改。分数差距通常不在公式背了多少，而在单位、图像读法和六分题的答题结构。下面把常考的六个板块拆开，每块给一道算例和一个高频错误，最后说六分题怎么凑够给分点。
The Pearson Edexcel International GCSE Physics (4PH1) qualification is examined in two papers. Paper 1 runs 2 hours for 110 marks and carries 61.1%, while Paper 2 lasts 1 hour 15 minutes for 70 marks and 38.9%. Both are offered in November and June, and the equation booklet is supplied with each paper. Most lost marks come from units, graph reading and unstructured six-mark answers rather than from missing formulas. This piece walks through six heavily examined areas, each with one worked example and the mistake seen most often, then closes with how to build a six-mark response that scores.
速度图像与 F=ma 计算
运动学在 4PH1 的 1.x 条目里占的分不少。距离-时间图的斜率是速度，速度-时间图的斜率是加速度，图线下面的面积是位移。这三个读法每个考季都出现，答题时要先看清纵轴写的是距离还是速度。加速度 a = (v - u) / t，合力 F = ma，重力 W = mg，卷面统一取 g = 9.8 N/kg。单位换算是最先丢分的地方: 题目给 72 km/h，先除以 3.6 得到 20 m/s 再动笔。算例是一辆车以 20 m/s 刹车，4 s 停下，减速度 5 m/s²，平均速度 10 m/s，制动距离 40 m。很多学生以为面积就是距离，却在速度-时间图上把梯形按长方形算，结果少了 20 m。Paper 2 还会把动量 p = mv 放进碰撞题，动量守恒只看碰前碰后的总量。方向要带正负号，向右记正、向左记负，符号写错整题白做。卷面给的单位有时是 km/h、有时是 cm，先统一成 SI 再算，这一步不写出来也拿不到分。
Kinematics carries real weight in the 1.x statements of the 4PH1 specification. On a distance-time graph the slope gives speed; on a velocity-time graph the slope gives acceleration and the area under the line gives displacement, and all three readings appear every session. Acceleration follows a = (v - u) / t, resultant force F = ma and weight W = mg, with g taken as 9.8 N/kg throughout the specification. Unit conversion is where marks vanish first, because a speed given as 72 km/h has to be divided by 3.6 to give 20 m/s before any calculation starts. In the worked case a car braking from 20 m/s to rest in 4 s decelerates at 5 m/s², averages 10 m/s and covers 40 m. Students routinely treat the area under a velocity-time graph as a rectangle when it is a trapezium, so their stopping distance comes out 20 m short. Paper 2 also puts momentum p = mv into collision questions, where the total before equals the total after and direction enters with a sign.
v=fλ 与全反射临界角
波的计算绕不开 v = f λ。频率由波源决定，进入另一种介质时不变，波速和波长一起变。题目给频率 250 Hz、波长 1.36 m，声速就是 340 m/s。频率换成 500 Hz 时波长只剩 0.68 m，波速仍然由介质决定。折射要先画法线，光从空气斜射进玻璃块时向法线偏折，折射角小于入射角。玻璃的折射率用 n = sin i / sin r 计算，角度从法线量起。全反射要两个条件同时成立: 光从光密介质射向光疏介质，入射角大于临界角，缺一条都不会发生。考纲里的波动实验要求用信号发生器和话筒测波长，再用 v = f λ 算波速。答实验题时要写清怎么找相邻的同相点、为什么重复测量几次、怎样用图线的斜率求波速。常见的错误是把波长 18 cm 直接代进公式，忘了先化成 0.18 m，答案差一百倍。
Wave questions come back to v = f λ every time. Frequency belongs to the source and stays fixed when a wave crosses into a new medium, while speed and wavelength change together. A 250 Hz tone with a wavelength of 1.36 m gives 340 m/s in air, and doubling the frequency halves the wavelength to 0.68 m while the speed is still set by the medium. For refraction, draw the normal first: light entering a glass block from air bends towards it, and the refractive index follows n = sin i / sin r. Total internal reflection needs both conditions at once, light travelling from a denser to a less dense medium and an angle of incidence above the critical angle. The specification's wave practical asks for wavelength measurement with a signal generator and microphone before v = f λ is applied, so an answer has to describe locating adjacent points in phase and repeating readings. The usual slip is substituting 18 cm without converting to 0.18 m, which throws the answer out by a factor of a hundred.
串并联与灯丝 IV 曲线
电学部分每年至少有十五分落在电路上。I = Q / t 定义电流，V = IR 只在温度稳定时成立。P = VI 和 E = Pt 是能量题的入口，时间单位要换成秒、功率换成瓦。串联电路电流处处相同、电压相加、电阻相加; 并联电路电压相同、电流相加，总电阻比任何一条支路都小。灯丝的 IV 图不是直线，电流变大时温度升高，电阻跟着增大。曲线朝电流轴弯，阅卷时最常看到学生把它当欧姆元件画成一条直线。算例是 12 V 电源接 4 Ω 和 2 Ω 串联，电流 2 A，总功率 24 W。改成并联后干路电流 9 A，总功率 108 W。很多学生会背并联电流相加，求总电阻时却把 1/R 的倒数忘了取回来。额定功率和实际功率也别混，灯泡接在不同电压下功率按 V²/R 变化。画电路图前先标出已知量，再决定用哪一个公式，别拿总电压去除某条支路的电阻。
Electricity supplies at least fifteen marks a year, mostly on circuits. Current is defined by I = Q / t, while V = IR holds only at steady temperature and P = VI with E = Pt opens most energy questions. In series the current is the same everywhere, voltages add and resistances add; in parallel the voltage is shared, currents add and the total resistance falls below the smallest branch. A filament lamp does not give a straight IV line, because a larger current raises the temperature and therefore the resistance, so the graph curves towards the current axis, and the commonest error in scripts is drawing it as if the lamp obeyed Ohm's law. For the worked case, 4 Ω and 2 Ω in series across 12 V draw 2 A and dissipate 24 W, while in parallel the supply current is 9 A and the power 108 W. Students who remember that parallel currents add often forget to invert 1/R at the end. Rated and actual power are also easy to confuse, since a lamp run below its rated voltage follows V²/R.
E=mcΔT 与密度压强
热学题的骨架是 E = mcΔT。水的比热容按 4200 J/(kg °C) 取，金属小得多，铜大约 385。同样加热时金属升温快得多，这个对比在解释题里很好用。密度 ρ = m/V，不规则固体用排水法测体积。考纲里的密度实验要写清为什么先测质量再测体积，还要说明怎样减小读数误差。压强 p = F/A 是定义式，液体压强随深度和密度增加。回答潜水或水坝题时把 h、ρ、g 三个量逐个说清。算例: 0.5 kg 水从 20 °C 加热到 60 °C，需要 E = 0.5 × 4200 × 40 = 84 000 J。若用 1000 W 电热器且不计热损失，时间是 84 s。常见的错误是把温差算成 60 而不是 40，或者把质量按克代进去，结果多出三个数量级。气体部分常考压强与体积的关系，压缩气体时分子撞击容器壁更频繁，压强上升。比热容实验要控制加热功率和时间，用温度-时间图的斜率比较升温快慢，比只看末温可靠。
Thermal questions rest on E = mcΔT. Water is taken as 4200 J/(kg °C) and metals are far lower, copper at roughly 385, which is why a metal spoon heats up so much faster for the same energy input and makes a useful comparison in explanation questions. Density is ρ = m/V, with volume found by displacement for irregular solids, and the specification's density practical expects a reason for measuring mass before volume. Pressure is defined by p = F/A, and in a liquid it grows with depth and density, so answers about dams or divers should name h, ρ and g separately. In the worked case, heating 0.5 kg of water from 20 °C to 60 °C needs 0.5 × 4200 × 40 = 84 000 J, and a 1000 W heater with no losses would take 84 s. Two errors dominate: using 60 rather than 40 as the temperature change, and entering mass in grams, which shifts the answer by three powers of ten. Gas questions usually turn on pressure and volume, where compressing a gas makes molecules strike the walls more often and raises the pressure.
变压器匝数比与感应电流
磁与电磁感应大多出现在 Paper 2。导体切割磁感线会产生感应电流，想让它变大就加快运动、换更强的磁铁、增加线圈匝数，或者让运动方向与磁场更垂直。F = BIL 描述通电导体在磁场里受到的力，方向用左手定则判断。理想变压器的核心关系是 Vp / Vs = Np / Ns，功率不变，因此 Vp Ip = Vs Is。算例: 原线圈 4000 匝接 230 V，副线圈 200 匝，输出电压 11.5 V。这就是常见降压适配器里的结构。很多学生以为变压器能改变直流电压，实际上恒定直流在副线圈里感应不出电压。这也是它只用在交流电路的原因。回答发电机题要提到线圈转动时穿过线圈的磁通量在变化，每半圈电流方向反转一次，滑环与换向器的区别也说清楚。
Magnetism and electromagnetic induction sit mostly in Paper 2. A conductor cutting magnetic field lines develops an induced current, and it grows if the motion is faster, the magnet stronger, the coil turns more numerous, or the movement more nearly perpendicular to the field. The force on a current-carrying wire is F = BIL, with direction from Fleming's left-hand rule. An ideal transformer obeys Vp / Vs = Np / Ns with power unchanged, so Vp Ip = Vs Is. In the worked example a 4000-turn primary at 230 V with a 200-turn secondary delivers 11.5 V, the arrangement inside a typical step-down adapter. A frequent misconception is that a transformer can change a steady direct voltage; in fact a constant direct current induces nothing in the secondary, which is exactly why transformers belong in alternating circuits. Generator answers should mention the changing flux as the coil turns, the reversal of current every half rotation, and the difference between slip rings and a split-ring commutator.
半衰期计算与放射线穿透
放射性题分两块，一块是半衰期，一块是三种射线的性质。α 粒子电离最强、穿透最弱，一张纸就能挡住。β 能穿过几毫米铝板，γ 需要厚铅或混凝土。考纲里的穿透实验用不同吸收材料加计数器，答题时要写背景计数先测、再扣除。半衰期计算只有一条思路: 先数经过几个半衰期，再把活度或剩余原子数除以 2 的相应次方。算例: 初始活度 800 Bq，半衰期 6 小时，18 小时后剩 100 Bq。反过来问多久降到 50 Bq，答案是 24 小时。常见的错误是把半衰期当成线性递减，或者把质量减半和活度减半混为一谈。天体部分会问红移与宇宙膨胀的关系，星系谱线向红端移动说明它在远离我们，距离越远退行速度越大。计数器读数先减本底、再除以测量时间，得到的才是活度，顺序弄反数值会偏大。
Radioactivity questions divide into half-life arithmetic and the properties of the three emissions. Alpha ionises strongly but barely passes through paper, beta needs a few millimetres of aluminium, and gamma requires thick lead or concrete; the specification's penetration practical uses absorbers with a counter, so an answer should mention measuring and subtracting background counts. Half-life work has one route: count how many half-lives have passed, then divide the activity or the number of nuclei by two that many times. A source starting at 800 Bq with a six-hour half-life falls to 100 Bq after 18 hours, and asking when it reaches 50 Bq gives 24 hours. Treating decay as a straight-line decrease is the standard error, and confusing a halved mass with a halved activity belongs to the same habit. Astrophysics questions link redshift to expansion: lines shifted towards the red end mean the galaxy is receding, and the further away it is, the faster it recedes.
六分题给分点与实验设计
六分开放题的给分点按物理表述逐条给，不按字数给。动笔前先在草稿上列三句: 现象或规律、背后的原因、题目给的证据怎么支持结论。三句清楚的话就能覆盖六分里的大部分。实验设计题要交代自变量、因变量、控制变量，还要写重复测量取平均、用图线而不是单点下结论。有效数字一般保留两到三位，答案必须带单位。单位错了整道小题的分都会打折。Equation Booklet 在 4PH1 两张卷子里都会随卷附上，公式不用死背，但要练熟变形。比如从 v = f λ 求 f、从 P = VI 求 I、从 E = mcΔT 求 c。阅卷时最常看到的是把六分题写成一大段描述，没有一句正面回答题目问的那个物理量。这一块练两周就能稳住，比再刷十套卷子的收益高得多。
Marks in a six-mark open response are awarded per physics statement, not per word of prose. Before writing, plan three lines: the pattern or law, the reason behind it, and how the evidence in the question supports the conclusion, which together usually cover most of the available marks. Practical design answers need the independent variable, the dependent variable and the controls, plus repeated readings averaged and a graph rather than a single point. Give two or three significant figures, always attach units, and treat a missing unit as marks lost across the whole part. The equation booklet comes with both 4PH1 papers, so memorising formulas matters less than rearranging them fluently, for instance getting f from v = f λ or I from P = VI. The script pattern that loses most marks is one long descriptive paragraph that never states the quantity the question asked for. Two weeks of practice on that single habit moves a grade more reliably than ten extra papers.
复习节奏与错题归因
4PH1 的八个板块里，力与运动、电学、波这三块占分最多，复习时间可以按 4:3:2 分配，剩下留给热学、磁与放射。每做完一套真题，把错题按三类归档: 概念不清、单位或计算失误、没读懂题干。前一类回去看考纲对应的条目，后两类只需要在下一套卷子里刻意检查。错题本别抄整道题，只写清错在哪一步、正确思路是什么。一周后再做一遍同一道题，能做对才算过。十一月和六月都有考次，两次之间隔半年，重考的人要把上次失分的板块单独列出来。
Across the eight topic areas of 4PH1, forces and motion, electricity and waves carry the most marks, so revision time can follow roughly 4:3:2 with the remainder for thermal physics, magnetism and radioactivity. After each past paper, sort every lost mark into three piles: unclear concepts, unit or arithmetic slips, and misread questions. The first pile sends you back to the relevant specification statement, while the other two only need a deliberate check on the next paper. An error log should record the step that went wrong and the correct reasoning rather than a full copy of the question, and the same question should be attempted again a week later. Exams run in both November and June, so a retake six months on should start from the topics that cost the most marks last time.
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