📚 GCSE Science: Formula Summary Handbook | GCSE 科学：公式汇总手册
Mastering the key formulas is essential for success in GCSE Science. This handbook brings together the most important equations from physics, with clear explanations, and units and worked examples so that you can memorise and apply them confidently in the exam. Each section states the formula, breaks down every symbol, and shows how the numbers fit together, and the final section bridges into the calculations you also need in chemistry and biology.
掌握关键公式是 GCSE 科学考试取得好成绩的基础。本手册汇总了物理学科最核心的方程式，并配有清晰的解释、单位和计算实例，帮助你牢固记忆、自信运用。每个小节都会给出公式、拆解每个符号的含义，并展示数值如何代入；最后一节还会延伸到化学与生物中同样需要掌握的计算。
1. How to Use This Handbook | 如何使用本手册
Before you memorise anything, find out what your exam board actually gives you. AQA, Edexcel and OCR all print some equations on the physics equation sheet, but a large number of the most frequently used formulas - including speed, acceleration and wave speed - must be recalled from memory. Knowing which is which saves you precious minutes and prevents panic.
在开始背诵之前，先弄清你的考试局究竟提供了哪些公式。AQA、Edexcel 和 OCR 都会在物理公式表中列出部分方程式，但很多最常用的公式——包括速度、加速度和波速——必须靠记忆。分清哪些是给出的、哪些要自己背，既省时间又能避免考场慌乱。
Units are the fastest way to check whether an answer is sensible. If a question gives the time in minutes or the distance in kilometres, convert before you substitute anything. Learn the standard prefixes and their powers of ten.
单位是判断答案是否合理最快的方法。如果题目给出的时间单位是分钟、距离单位是千米，代入前必须先换算。请记住常用词头及其十的幂次。
| Prefix | 词头 | Symbol | 符号 | Factor | 倍数 |
| giga | 吉 | G | × 10⁹ |
| mega | 兆 | M | × 10⁶ |
| kilo | 千 | k | × 10³ |
| centi | 厘 | c | × 10⁻² |
| milli | 毫 | m | × 10⁻³ |
| micro | 微 | µ | × 10⁻⁶ |
| nano | 纳 | n | × 10⁻⁹ |
Finally, work in a fixed order: write the formula, rearrange it with symbols, substitute the numbers, add the unit, then round to the significant figures asked for. Marks are awarded for the method as well as the answer, so never jump straight to a calculator.
最后，按固定顺序解题：写出公式 → 用符号变形 → 代入数值 → 补上单位 → 按题目要求取有效数字。评分时方法与答案同样给分，所以不要一上来就按计算器。
2. Speed, Distance and Time | 速度、距离和时间
The relationship between speed, distance and time is one of the most basic in physics. Average speed is the total distance travelled divided by the time taken.
速度、距离和时间的关系是物理学最基础的内容之一。平均速度等于通过的总距离除以所用的时间。
speed = distance ÷ time
v = s ÷ t
Speed (v) is measured in metres per second (m/s), distance (s) in metres (m) and time (t) in seconds (s). Always check that your units are consistent - if distance is given in kilometres and time in hours, convert to metres and seconds, or keep both in km and h and quote the answer in km/h.
速度 (v) 的单位是米每秒 (m/s)，距离 (s) 的单位为米 (m)，时间 (t) 的单位为秒 (s)。务必保持单位统一——如果距离以千米、时间以小时给出，需要转换为米和秒，或者两者都保留 km 和 h，答案写成 km/h。
ime, and time = distance ÷ speed. This triangle relationship is handy for problem-solving.
公式可以变形为另外两种常用形式：距离 = 速度 × 时间，以及时间 = 距离 ÷ 速度。这个三角关系对解题很有帮助。
= 300 m ÷ 25 s = 12 m/s. If you want that in km/h, multiply by 3.6: 12 × 3.6 = 43.2 km/h.
示例：一名自行车手在 25 秒内行驶了 300 米。平均速度 = 300 m ÷ 25 s = 12 m/s。若换算成 km/h，乘以 3.6，即 12 × 3.6 = 43.2 km/h。
Two exam traps are worth remembering. First, average speed is not the same as instantaneous speed: a car that speeds up and slows down has one average speed but many instantaneous values. Second, on a distance-time graph the gradient equals the speed, so a steeper line means a faster object and a flat line means it is stationary.
有两个易错点值得记住。第一，平均速度不等于瞬时速度：一辆忽快忽慢的汽车只有一个平均速度，却有无数个瞬时速度。第二，在距离—时间图像中，斜率就是速度，因此线越陡表示物体越快，水平线则表示物体静止。
3. Acceleration and the Equations of Motion | 加速度与运动方程
Acceleration tells us how quickly an object speeds up or slows down. It is defined as the change in velocity per unit time.
加速度表示物体加速或减速的快慢程度，定义为单位时间内速度的变化量。
acceleration = change in velocity ÷ time
a = Δv ÷ t
is in metres per second squared (m/s²), velocity in m/s and time in seconds. A negative acceleration means the object is decelerating - it is slowing down, not going backwards.
速度变化量 Δv 等于末速度 (v) 减去初速度 (u)，即 Δv = v − u。加速度 (a) 的单位是米每二次方秒 (m/s²)，速度单位是 m/s，时间单位是秒。加速度为负值表示物体在减速，而不是在倒退。
. Δv = 24 − 0 = 24 m/s, so a = 24 ÷ 8 = 3 m/s². Every second the car gains 3 m/s of speed.
示例：一辆汽车在 8 秒内从静止加速到 24 m/s。Δv = 24 − 0 = 24 m/s，因此 a = 24 ÷ 8 = 3 m/s²。也就是说，汽车每秒增加 3 m/s 的速度。
For uniform (constant) acceleration, four equations of motion link the five quantities u, v, a, s and t. They are sometimes called the SUVAT equations.
在匀加速（加速度恒定）的情况下，有四个运动方程把这五个量 u、v、a、s、t 联系起来，通常称为 SUVAT 方程。
v = u + at
s = (u + v) ÷ 2 × t
v² = u² + 2as
s = ut + ½at²
if a question mentions distance but not time, v² = u² + 2as is usually the quickest route.
挑选那个"包含已知三个量再加上所求量"的方程。例如，题目涉及距离但没有给出时间，用 v² = u² + 2as 通常最快。
+ 0.5 × 20 = 10 m/s. The distance travelled is s = (0 + 10) ÷ 2 × 20 = 100 m. Notice that
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