📚 KS3 OCR Science Formula & Theorem Quick Reference Handbook | KS3 OCR 科学：公式定理速查手册
Whether you’re revising for a topic test or preparing for end-of-year assessments, having key science formulas and theorems at your fingertips makes all the difference. This handbook brings together the essential equations and principles from the KS3 OCR Science curriculum, covering physics, chemistry, and biology. Each entry is presented in a clear, student-friendly way, with examples of how and when to use it.
无论你是在为单元测验复习，还是准备学年评估，掌握关键的科学公式和定理都会大有帮助。这本速查手册汇集了 KS3 OCR 科学课程中物理、化学和生物的重要方程和原理。每个条目都以清晰、易于学生理解的方式呈现，并配有应用示例和使用时机说明。
1. Speed, Distance and Time | 速度、距离与时间
The relationship between speed, distance and time is one of the most fundamental in physics. The formula is: speed = distance ÷ time. You can rearrange it to find distance = speed × time, or time = distance ÷ speed. Always ensure the units match: for example, metres per second (m/s) for speed, metres for distance, and seconds for time.
速度、距离和时间之间的关系是物理学中最基本的关系之一。公式为：速度 = 距离 ÷ 时间。你可以变形得到 距离 = 速度 × 时间，或 时间 = 距离 ÷ 速度。一定要确保单位一致：例如，速度用米每秒（m/s），距离用米，时间用秒。
v = d / t
Where v = average speed, d = total distance travelled, t = total time taken. If a car travels 100 m in 5 s, its average speed is v = 100 ÷ 5 = 20 m/s.
其中 v = 平均速度，d = 总行驶距离，t = 总耗时。如果一辆汽车在 5 秒内行驶了 100 米，它的平均速度为 v = 100 ÷ 5 = 20 m/s。
2. Acceleration (for Higher Ability) | 加速度（高能力拓展）
Acceleration tells us how quickly the speed of an object changes. The formula is: acceleration = change in speed ÷ time taken. Some KS3 schemes touch on this concept to prepare for GCSE. Change in speed is final speed minus initial speed.
加速度描述物体速度变化的快慢。公式为：加速度 = 速度变化量 ÷ 所花时间。部分 KS3 教学计划会涉及此概念以便衔接 GCSE。速度变化量等于末速度减初速度。
a = (v – u) / t
Where a = acceleration, v = final speed, u = initial speed, t = time. If a cyclist speeds up from 2 m/s to 8 m/s in 3 s, a = (8 – 2) ÷ 3 = 2 m/s².
其中 a = 加速度，v = 末速度，u = 初速度，t = 时间。如果一名自行车手在 3 秒内从 2 m/s 加速到 8 m/s，则 a = (8 – 2) ÷ 3 = 2 m/s²。
3. Density | 密度
Density describes how much mass is packed into a given volume. It helps to identify materials and predict whether they will float or sink. The formula is: density = mass ÷ volume.
密度描述在给定体积内所含质量的大小。它有助于鉴别物质并预测其浮沉情况。公式为：密度 = 质量 ÷ 体积。
ρ = m / V
Where ρ (rho) = density, m = mass, V = volume. Common units are g/cm³ for solids and liquids, and kg/m³ for gases. Water has a density of 1 g/cm³; objects with density less than 1 g/cm³ float.
其中 ρ（rho）= 密度，m = 质量，V = 体积。固体和液体的常用单位是 g/cm³，气体用 kg/m³。水的密度为 1 g/cm³；密度小于 1 g/cm³ 的物体会漂浮。
4. Gas Pressure and the Particle Model | 气体压强与粒子模型
Pressure in gases is caused by particles colliding with the walls of their container. Although KS3 does not require a formal equation, the principle is key: increasing temperature makes particles move faster and hit harder and more often, raising pressure. If you squeeze a gas into a smaller volume (compression), pressure increases because particles hit the walls more frequently.
气体的压强是由粒子与容器壁碰撞引起的。尽管 KS3 不要求掌握正式方程，但有一条关键原理：升高温度使粒子运动更快，碰撞更剧烈且更频繁，从而提高压强。如果将气体压缩到更小的体积（压缩），压强会因粒子更频繁地撞击容器壁而增大。
The qualitative relationship: for a fixed mass of gas at constant temperature, pressure is inversely proportional to volume. This is known as Boyle’s Law in later years, but KS3 uses ‘squashing’ and ‘expanding’ ideas.
定性关系为：对于一定质量、温度不变的气体，压强与体积成反比。这在更高年级称为波义耳定律，但 KS3 中使用“压缩”和“膨胀”的概念。
5. Moments (Turning Forces) | 力矩（转动效应）
A moment is the turning effect of a force. It depends on the size of the force and the perpendicular distance from the pivot to the line of action of the force. This is key for levers, seesaws, and spanners.
力矩是力产生的转动效应。它取决于力的大小以及从支点到力作用线的垂直距离。这对于杠杆、跷跷板和扳手来说非常关键。
M = F × d
Where M = moment (in newton-metres, Nm), F = force (in newtons, N), d = perpendicular distance from pivot (in metres, m). To balance a seesaw, the total clockwise moment must equal the total anticlockwise moment.
其中 M = 力矩（单位牛顿·米，N·m），F = 力（单位牛顿，N），d = 到支点的垂直距离（单位米，m）。要使跷跷板平衡，顺时针力矩之和必须等于逆时针力矩之和。
6. Pressure on Solids | 固体压强
Pressure on a solid surface is the force applied per unit area. Sharp objects exert high pressure because the area is small. This explains why knives cut well and why snowshoes prevent sinking in snow.
固体表面受到的压强是单位面积上施加的力。尖锐物体因面积小而产生高压强。这解释了为什么刀能够轻松切割，以及为什么雪鞋能防止人陷入雪中。
P = F / A
Where P = pressure (in pascals, Pa or N/m²), F = force (N), A = area (m²). A force of 50 N applied over an area of 0.1 m² gives a pressure of 50 ÷ 0.1 = 500 Pa.
其中 P = 压强（单位帕斯卡，Pa 或 N/m²），F = 力（N），A = 面积（m²）。在 0.1 m² 的面积上施加 50 N 的力，产生的压强为 50 ÷ 0.1 = 500 Pa。
7. Current, Voltage and Resistance | 电流、电压与电阻
In electrical circuits, current is the flow of charge, voltage is the ‘push’ driving the current, and resistance opposes the flow. Ohm’s Law links these three quantities for a metallic conductor at constant temperature.
在电路中，电流是电荷的流动，电压是推动电流的“推力”，电阻则阻碍电流。欧姆定律将金属导体在恒温下的这三个物理量联系起来。
V = I × R
Where V = voltage or potential difference (volts, V), I = current (amps, A), R = resistance (ohms, Ω). For example, if a lamp has a resistance of 6 Ω and a current of 0.5 A flows through it, the voltage across it is V = 0.5 × 6 = 3 V.
其中 V = 电压或电势差（伏特，V），I = 电流（安培，A），R = 电阻（欧姆，Ω）。例如，若一个灯泡的电阻为 6 Ω，流过它的电流为 0.5 A，则其两端的电压为 V = 0.5 × 6 = 3 V。
8. Energy and Power | 能量与功率
Energy is the ability to do work, and power is the rate at which energy is transferred. These concepts underpin many topics, from food energy to electrical appliances. The formulas connect joules, watts, and time.
能量是做功的本领，功率是能量传递的速率。这些概念支撑着从食物能量到电器功率的众多主题。这些公式将焦耳、瓦特和时间关联起来。
E = P × t
Where E = energy transferred (joules, J), P = power (watts, W), t = time (seconds, s). Also, for electrical power: P = V × I (power = voltage × current). A 40 W lamp left on for 60 s transfers E = 40 × 60 = 2400 J of energy.
其中 E = 传递的能量（焦耳，J），P = 功率（瓦特，W），t = 时间（秒，s）。此外，电功率公式：P = V × I（功率 = 电压 × 电流）。一只 40 W 的灯泡亮 60 秒，传递的能量为 E = 40 × 60 = 2400 J。
9. Wave Speed Equation (for Higher Ability) | 波速方程（高能力拓展）
Waves transfer energy without transferring matter. The speed of a wave depends on its frequency and wavelength. This equation is introduced in some KS3 contexts, especially for water waves and sound waves on an oscilloscope.
波传递能量而不传递物质。波速取决于频率和波长。该方程在某些 KS3 教材中被引入，特别是用于水波和示波器上的声波。
v = f × λ
Where v = wave speed (m/s), f = frequency (hertz, Hz), λ = wavelength (metres, m). If a sound wave has frequency 440 Hz and wavelength 0.78 m, its speed is v = 440 × 0.78 ≈ 343 m/s (typical speed of sound).
其中 v = 波速（m/s），f = 频率（赫兹，Hz），λ = 波长（米，m）。若一个声波的频率为 440 Hz，波长为 0.78 m，则其速度为 v = 440 × 0.78 ≈ 343 m/s（典型的声速）。
10. Conservation of Mass in Reactions | 反应中的质量守恒定律
In chemical reactions, atoms are rearranged, not created or destroyed. Therefore, the total mass of the reactants equals the total mass of the products. This is the Law of Conservation of Mass. It is essential when balancing equations and calculating quantities.
在化学反应中，原子重新排列，不会被创造或毁灭。因此，反应物的总质量等于生成物的总质量。这就是质量守恒定律。在配平方程和计算用量时，这一定律至关重要。
For example, if 4 g of hydrogen reacts completely with 32 g of oxygen to form water, the mass of water produced will be exactly 36 g. This principle also explains why reactions in closed systems show no change in total mass.
例如，若 4 g 氢气与 32 g 氧气完全反应生成水，则生成水的质量恰好为 36 g。这一定律也解释了为何在密闭系统中反应时总质量保持不变。
11. Photosynthesis and Aerobic Respiration Word Equations | 光合作用与有氧呼吸的文字表达式
While these are not algebraic formulas, KS3 OCR expects students to recall the word equations for two fundamental life processes. Photosynthesis requires light, carbon dioxide, and water to produce glucose and oxygen.
虽然它们并非代数公式，但 KS3 OCR 要求学生会写出两个基本生命过程的文字表达式。光合作用需要光、二氧化碳和水，产生葡萄糖和氧气。
Carbon dioxide + Water → Glucose + Oxygen
(in the presence of light and chlorophyll)
二氧化碳 + 水 → 葡萄糖 + 氧气
（在光和叶绿体的参与下）
Aerobic respiration releases energy from glucose by reacting it with oxygen. The word equation is the reverse of photosynthesis in terms of chemicals, but occurs in all living cells all the time.
有氧呼吸通过让葡萄糖与氧反应来释放能量。就化学物质而言，其文字表达式是光合作用的逆过程，但它发生在所有活细胞中并且时刻进行。
Glucose + Oxygen → Carbon dioxide + Water
(releasing energy)
葡萄糖 + 氧气 → 二氧化碳 + 水
（释放能量）
12. Enzymes and the Lock-and-Key Model | 酶与锁钥模型
Enzymes are biological catalysts that speed up reactions without being used up. The lock-and-key model describes how each enzyme has an active site with a specific shape that fits only certain substrate molecules. If the enzyme becomes denatured (usually by high temperature or extreme pH), its shape changes and it cannot function.
酶是加快反应速度而自身不被消耗的生物催化剂。锁钥模型描述了每种酶都有一个特定形状的活性位点，只能与特定底物分子契合。如果酶变性（通常由高温或极端 pH 引起），其形状改变，就会失去功能。
Key points: the optimum temperature for most human enzymes is around 37 °C. Beyond this, the rate of reaction drops sharply. This theorem integrates well with practical investigations on factors affecting enzyme action.
关键要点：大多数人体酶的最适温度在 37 °C 左右。超过此温度，反应速率急剧下降。这一定理与探究影响酶活性因素的实验紧密结合。
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