IGCSE物理 1P 2P 公式手册 力学 电学 半衰期
Edexcel IGCSE 物理（代码 4PH1）的备考难点不在知识量，而在两卷 180 分里的答题口径：公式手册随卷发放，公式不用默写，失分大多出在选式、单位与作图这几个环节。这篇按八个主题的顺序，把 1P 与 2P 的分工、计算题写法、力学电学波与能量、放射性到天体物理逐块拆开，每一块都给出可以马上用的检查动作。文中出现的规格与数字来自 Pearson 官方 spec 的 Issue 4（2024 年 9 月发布，2017 年 9 月首次施教、2019 年 6 月首次考试），可以对照自己手上的 syllabus 核对。
A common assumption about Edexcel IGCSE Physics (4PH1) is that it is mostly memorisation; in practice the Equation Booklet is supplied with every paper, so the marks are lost in choosing the right relationship, keeping units consistent and drawing graphs properly. The sections below follow the eight specification topics and turn each one into a check you can run during practice, from the split between Paper 1P and Paper 2P through mechanics, circuits and waves to radioactivity and astrophysics. Specification details quoted here come from Pearson's official specification, Issue 4, published September 2024, with first teaching from September 2017 and first assessment in June 2019.
1P 考 110 分、2P 考 70 分：两卷的分工与时间
Edexcel IGCSE 物理是线性证书，两卷必须在同一个考季考完，总分 180 分，分数不做折算。Paper 1（4PH1/1P）考 2 小时、110 分，占 61.1%，只考不加粗、没有 P 标记的核心内容；Paper 2（4PH1/2P）考 1 小时 15 分钟、70 分，占 38.9%，把加粗的 P 内容一并考到。两卷都不分层，等级从 9 到 1，计算器都允许带进考场。很多学生以为 Paper 2 时间短所以更轻松，算一下每分钟的分数就知道不对：110 分摊到 120 分钟是每分钟 0.92 分，70 分摊到 75 分钟是每分钟 0.93 分，两边一样紧。试卷封面写明要带直尺、计算器和随卷附上的公式手册，公式手册在答题开始前就发到手上。
The qualification is linear, so both papers are taken in the same series; the two papers total 180 marks and the marks are not scaled. Paper 1 assesses core content only, while Paper 2 assesses everything including the bold P statements reserved for the Physics-only specification; calculators and rulers are allowed in both, and grades run from 9 to 1 with no tiering. What catches candidates out is the pace rather than the depth: 110 marks in 120 minutes is about 0.92 marks a minute, and 70 marks in 75 minutes is 0.93, so the shorter paper buys no extra thinking time.
公式手册先看单位：量纲与换算的检查顺序
公式手册（Equation Booklet）随卷发放，失分因此不再来自背不出公式，而来自选错关系式和单位不统一。常见的错误是算出密度 2.7 g/cm^3 之后直接代进用 SI 单位写的压强式，中间少了一次 1000 倍的换算。厘米、毫米、克、毫安、千帕这些单位在题目里随处可见，动笔时先把每一个量改写成 SI 基本单位，再代入公式，最后检查量纲能不能对上。速度用 m/s、力用 N、功与能量用 J、功率用 W、电荷用 C、电阻用 ohm，这几个单位之间的组合关系本身就是自查工具。很多学生以为单位换算是小事，阅卷时看到数量级差 1000 的答案，通常整题的分都没有了。时间类题目里 1 小时 15 分钟要写成 75 分钟或 4500 秒，别把 1.15 小时当成 75 分钟。
Because the Equation Booklet is supplied with the paper, marks are lost on choosing the wrong relationship and on mixing units rather than on recall. Convert every quantity into SI units before substituting, then check whether the units of the answer match the quantity being asked for; speed in m/s, force in N, energy in J, power in W, charge in C and resistance in ohms form a self-checking set. Marks are commonly thrown away on order-of-magnitude slips of 1000, and a paper lasting 1 hour 15 minutes must be entered as 75 minutes or 4500 seconds, never 1.15 hours.
有效数字、过程分与作图规范
计算题的答案写到 2 到 3 位有效数字就够，同一题里前后保持一致，题目给了位数就按题目写。评分方案给的不只是最终数字，公式、代入过程、单位各有分值，所以草稿上不能只留一个答案。中间步骤不要提前修约，把圆周率这类常数的完整值留在计算器里，最后一步再处理位数。反过来看，一道 4 分的题目如果单位写错，即使数字对，通常也只剩方法分。很多学生以为数字对了就没事，实际阅卷时单位、方向、正负号都是单独的给分点。图像题用直尺画直线、坐标点用小叉标注、曲线要平滑，坐标轴一定要写清物理量与单位。
Answers should be given to 2 or 3 significant figures and kept consistent within a question; if the question specifies a number, follow it. Marks are awarded for the relationship, the substitution and the unit as well as the final value, so a bare answer on the page forfeits method marks, and rounding must wait until the last step. Units, direction and sign are separate marking points, and graph questions demand a ruler for straight lines, crosses for plotted points, a smooth curve and axes labelled with both quantity and unit.
速度时间图的斜率与面积：运动学三式怎么选
距离-时间图的斜率是速度，速度-时间图的斜率是加速度、曲线下的面积是位移，这三句话能处理力学部分几乎所有图像题。平均速度等于总位移除以总时间，往返运动最容易在这里出错：跑出 100 米再走回 100 米，平均速度是 0，平均速率不是 0。匀加速的三个关系式都在公式手册里，选式子之前先写下已知量、未知量和方向约定。举一组数：小车从静止以 2.0 m/s^2 加速 5.0 s，末速度 v = u + at = 10 m/s，位移 s = ut + at^2/2 = 25 m。题干里出现 constant speed 往往意味着加速度为零，受力图上合力也是零。距离-时间图上两条线相交表示两个物体处在同一位置，不表示速度相同。
A distance-time graph gives speed from the gradient, while a velocity-time graph gives acceleration from the gradient and displacement from the area underneath. Average velocity is total displacement divided by total time, which is why running 100 m out and walking 100 m back gives an average velocity of zero but a non-zero average speed; list the knowns, the unknown and the sign convention before choosing one of the three equations of uniform acceleration. A trolley accelerating from rest at 2.0 m/s^2 for 5.0 s reaches 10 m/s and travels 25 m, and the phrase constant speed normally signals zero acceleration and zero resultant force.
力矩、压强与受力分析
力矩等于力乘上到支点的垂直距离，平衡条件是顺时针力矩总和等于逆时针力矩总和。压强 p = F/A，单位是 N/m^2 也就是 Pa，受力面积越小压强越大，钉子尖端和滑雪板宽窄的差别就在这个反比关系上。液体内部的压强随深度增加，同一深度朝各个方向的压强相同，这一点常和气体压强放在一起比较。受力题先画自由体受力图，把重力 W = mg 单独标出来，再判断哪些力互相抵消。很多学生以为质量大的一定先落地，真空里不同质量的球同时落地，只有空气阻力明显时结果才不同。一根 2.0 m 的均匀杆在距支点 0.50 m 处受 30 N 的力，支点另一侧 1.5 m 处需要约 10 N 才能平衡。
A moment is a force multiplied by the perpendicular distance from the pivot, and equilibrium means the clockwise moments add up to the same total as the anticlockwise ones. Pressure is force per unit area in N/m^2 or Pa, so a smaller contact area produces a larger pressure, which is the whole story behind a sharp nail and a wide ski; pressure in a liquid rises with depth and acts equally in all directions at a given depth. A 30 N force 0.50 m from the pivot of a uniform 2.0 m rod needs about 10 N at 1.5 m on the other side to balance it.
串并联规律与 I-V 特性曲线
串联电路电流处处相同、电压按电阻分配；并联电路电压相同、电流之和等于总电流。欧姆定律 V = IR 只对温度稳定的金属导体成立，灯丝灯泡的 I-V 曲线在电流增大时会弯，二极管只有正向电压超过约 0.6 V 才导通。测 I-V 特性时用可变电阻改变电流，电压表并联在元件两端，电流表串联进主回路，读数要连续记五六组。两盏 6 V 的小灯泡并联在 6 V 电源上都能正常发光，改成串联每盏只有 3 V，亮度明显下降。很多学生以为并联会分走电流所以更暗，实际并联的每个支路都拿到完整的电源电压。并联总电阻用倒数相加来求，两个 4 ohm 并联是 2 ohm，这个结果可以当作快速检查。
In series the current is the same everywhere and the voltage divides between components, while in parallel the voltage is the same across each branch and the currents add up. Ohm's law only holds for a metallic conductor at constant temperature, which is why a filament lamp curves as the current rises and a diode starts conducting above roughly 0.6 V in the forward direction; record five or six readings when plotting an I-V characteristic, with the voltmeter in parallel and the ammeter in series. Two 6 V lamps in parallel both light normally from a 6 V supply, whereas in series each gets only 3 V.
电功率、电能与保险丝的选择
电功率 P = VI，所以电流 I = P/V；家用电 230 V 的 2.0 kW 电水壶电流约 8.7 A，这就是它要配 13 A 插头的原因。电能 E = Pt，功率用瓦、时间用秒时得到焦耳，功率用千瓦、时间用小时时得到的就是 kWh，也就是电表上读到的数字。一台 1.5 kW 的取暖器工作 4 小时消耗 6 kWh，最后再用题目给的单价换算成费用。电线过热由电流过大引起，短路的危险也来自电流骤增，而不是电压本身升高。保险丝和开关都要接在火线上，故障时才能把带电部分断开。充电器的能量题里输入一定大于输出，差值变成热量散失掉。
Electrical power is P = VI, so a 2.0 kW kettle on a 230 V supply draws about 8.7 A and needs a 13 A plug rather than a 3 A fuse. Energy transferred is E = Pt, measured in joules when power is in watts and time in seconds, or in kWh when power is in kilowatts and time in hours, which is exactly what the meter records; a 1.5 kW heater left on for 4 hours uses 6 kWh before the unit price is applied. Fuses and switches belong in the live wire so that a fault disconnects the part of the circuit that is at mains potential.
波速、折射与临界角
波速 v = fλ，频率由波源决定、跨过界面不变，波长随介质改变。光从空气进入玻璃速度下降、波长变短、折射角小于入射角，反过来从光密射向光疏并超过临界角时就发生全反射。临界角只由两侧介质的折射率决定，玻璃对空气约 42 度，光纤靠这个角度把光锁在纤芯里。折射图里的法线垂直于界面，所有角度一律从法线量，不是从界面量。很多学生以为全反射在任何角度都会发生，不到临界角时只有部分光反射，大部分还是折射出去了。水波从深水进入浅水速度变小、波长变短、频率不变，同一列波的波峰间隔会挤得更密。
Wave speed is v = f times lambda, and frequency is fixed by the source while wavelength changes with the medium. Light slows down on entering glass, so the wavelength shortens and the angle of refraction is smaller than the angle of incidence; travelling the other way from a denser medium, total internal reflection begins once the angle exceeds the critical angle, about 42 degrees for glass into air, which is how light is trapped inside an optical fibre. Angles are always measured from the normal, and below the critical angle only part of the light is reflected.
比热容、能量守恒与效率
比热容公式 E = mcΔT 里的比热容，指的是让 1 kg 物质升温 1 摄氏度需要的能量，水的 4200 J/kg°C 在题目中都会给出。200 g 水从 20 摄氏度升到 60 摄氏度需要 E = 0.200 x 4200 x 40 = 33600 J，这里质量必须先换成 0.200 kg。效率等于有用能量除以总输入能量再乘 100%，没有机器能做到 100%，热量散失、摩擦与声音都会带走一部分。桑基图的箭头宽度按能量比例画，读完图先找有用能的去向，再算效率。很多学生以为温度高的物体含有的热量一定多，热量是能量转移的量，只能对某个过程说吸收或放出了多少热量。
Specific heat capacity is the energy needed to raise 1 kg of a substance by 1 degree Celsius, and 4200 J/kg°C for water is always given in the question. Heating 200 g of water from 20 to 60 degrees takes 0.200 x 4200 x 40 = 33600 J, so the mass must be converted into kilograms first; efficiency is useful output divided by total input, and nothing reaches 100% because heat, friction and sound carry energy away. In a Sankey diagram the arrow widths are proportional to the energy transferred, so identify the useful output before calculating.
密度、气压与气体分子运动
密度 ρ = m/V，单位是 kg/m^3；一块 540 g 的石头体积 200 cm^3，密度就是 2.7 g/cm^3，换成 SI 单位是 2700 kg/m^3。气压由气体分子撞击容器壁产生，温度升高分子运动更快、压强增大，温度不变时体积压缩到一半，压强大约翻倍。沸点随外界气压改变，高山上气压低，水在 90 摄氏度左右就沸腾；压力锅里气压高，水要 120 摄氏度才沸。绝对零度是 -273 摄氏度，在那里气体分子动能降到最低，不可能更低。很多学生以为水结冰后体积变小，水是少数固态密度小于液态的物质，冰浮在水面上就是这个原因。
Density is mass divided by volume, so a 540 g stone with a volume of 200 cm^3 has a density of 2.7 g/cm^3, or 2700 kg/m^3 in SI units. Gas pressure comes from molecules striking the walls: heating speeds them up and raises the pressure, while halving the volume at constant temperature roughly doubles it, and boiling point follows the surrounding pressure, which is why water boils near 90 degrees Celsius on a mountain and near 120 degrees in a pressure cooker. Absolute zero sits at -273 degrees Celsius, and water is unusual in that its solid form is less dense than its liquid form.
电磁感应、变压器与输电损耗
感应电动势的大小取决于磁通量变化的快慢：线圈匝数越多、磁场越强、磁铁插入越快，检流计指针偏转越大。变压器靠交流工作，理想情况下电压比等于匝数比，升压变压器副线圈匝数多、电压升高、电流降低。输电线上的损耗是 I^2 R，电流降一半损耗就降到四分之一，这就是高压输电的原因。变压器不能用在直流上，直流不产生变化的磁通量，副线圈里没有感应。很多学生以为升压能凭空增加功率，理想变压器进出功率相等，改变的只是电压与电流的组合。电动机与发电机是一对相反的过程：通电导线在磁场中受力是电动机，导线运动产生电流是发电机。
The size of an induced voltage depends on how fast the magnetic flux changes, so more turns, a stronger field and a faster-moving magnet all give a larger deflection. A transformer only works with alternating current, and in the ideal case the voltage ratio equals the turns ratio, so a step-up transformer has more turns on the secondary, a higher voltage and a lower current. Transmission losses follow I^2 R, which is why halving the current cuts the loss to a quarter and why the grid transmits at high voltage.
半衰期、三类辐射与核方程配平
放射性衰变是随机过程，单个原子何时衰变无法预测，大量原子的计数率按指数规律下降。半衰期是原子核数目减到一半所需的时间：880 Bq 的样品过两个半衰期剩 220 Bq，过三个半衰期剩 110 Bq。alpha 射线穿透力最弱、电离能力最强，beta 是高速电子，gamma 是电磁波，三者的穿透距离与屏蔽材料完全不同。本底辐射来自宇宙射线、建筑材料里的氡和食物中的钾，测量前必须先测本底计数率并从读数里减掉。很多学生以为半衰期过后原来的原子消失了，实际上它们衰变成了别的核素，质量数与电荷数按核方程守恒。配平核方程时先看质量数，alpha 衰变减 4，再看电荷数，alpha 衰变减 2。
Radioactive decay is random, so the fate of a single nucleus cannot be predicted even though the count rate from a large sample falls off predictably. Half-life is the time taken for the number of nuclei to halve, which takes a sample of 880 Bq down to 220 Bq after two half-lives and 110 Bq after three; alpha particles are the least penetrating and the most ionising, beta particles are fast electrons and gamma rays are electromagnetic waves, so their shielding needs differ completely. Background count rate, from cosmic rays, radon and potassium in food, must be measured and subtracted before any half-life calculation.
天体物理：恒星演化与红移
天体物理是 Edexcel IGCSE 物理（4PH1）独有的第八个主题，英国本土 GCSE 不考这一块，Paper 1 与 Paper 2 都可能出题。恒星的一生由质量决定：质量与太阳相仿的最后变成白矮星，质量大得多的以超新星爆发结束，留下的残骸可能是中子星甚至黑洞。黑体辐射的峰值波长随温度升高向短波方向移动，所以蓝白色恒星表面温度高于红色恒星，颜色反映的是温度而不是亮度。红移说明遥远星系正在远离我们，星系越远退行速度越大，这是大爆炸模型的观测证据之一。视差法用来测量较近恒星的距离，地球绕太阳运动使恒星在六个月后相对背景星发生微小位移，位移越大恒星越近。很多学生以为恒星颜色只是亮度的差别，实际亮度同时取决于表面温度与体积。
Astrophysics is the eighth topic unique to the Physics-only specification, and it can appear in either paper. A star's fate is set by its mass, with sun-like stars ending as white dwarfs and much heavier ones exploding as supernovae and leaving neutron stars or black holes; the peak wavelength of black-body radiation shifts towards shorter wavelengths as temperature rises, so blue-white stars are hotter than red ones and colour indicates temperature rather than brightness. Redshift shows that distant galaxies are receding, and the greater the distance the greater the recessional speed, which is one strand of evidence for the Big Bang model.
实验技能与答题口径：写清变量与命令词
4PH1 没有课程作业也没有单独的实验考试，实验技能全部放在笔试卷里考，所以画装置图、写变量与控制量都是可以练出来的分数。一份规范的实验设计要写清自变量、因变量和至少两个控制变量，还要写出读数方式与重复次数，比如测电阻的 I-V 特性时连续记五六组读数再取平均。命令词决定答法：describe 只要求写现象，explain 必须给出原因，calculate 要写公式与代入，suggest 通常允许合理的外推。常见的错误是把 explain 题答成描述题，两句话写完就停，分数自然上不去。错得最多的是表格与图像题里的单位与有效数字，数据表里同一列的单位只在表头写一次。很多学生以为画图题只是把点连起来，题目要的往往是趋势判断加一个具体数值。
There is no coursework and no separate practical examination, so experimental skills are assessed inside the written papers; a plan that names the independent variable, the dependent variable and at least two controlled variables, plus how readings are taken and repeated, collects those marks. Command words set the shape of the answer: describe asks for what happens, explain requires a cause, and calculate needs the relationship and the substitution written out. The most frequent losses are unit and significant-figure slips in tables and graphs, and turning an explain question into a one-line description.
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