📚 GCSE CCEA Science: Formula Summary Handbook | GCSE CCEA 科学：公式汇总手册
Welcome to your ultimate formula handbook for GCSE CCEA Science (Double Award). This guide gathers every essential equation you will encounter across Physics, Chemistry and Biology topics, from motion and energy to mole calculations and magnification. Using the correct formula in the right units is half the battle – here you can revise each relationship, practice its application, and build confidence for your exams. The English explanation is followed immediately by a Chinese version, ensuring bilingual learners can master the content effortlessly.
欢迎使用 GCSE CCEA 科学（双奖）终极公式手册。本指南汇集了物理、化学和生物各主题中你会遇到的所有关键方程，从运动、能量到摩尔计算和放大率。使用正确的公式和单位是成功的一半——你可以在此复习每一个关系式，练习应用，建立考试信心。每个知识点都先提供英文解释，紧接着是中文对照，确保双语学习者轻松掌握内容。
1. Equations of Motion | 运动方程
These equations apply only when acceleration is constant. Always identify the known quantities and choose the equation that contains the unknown you need. The standard symbols are: u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement.
这些方程仅适用于加速度恒定的情况。始终找出已知量，然后选择包含所求未知量的方程。标准符号为：u = 初速度，v = 末速度，a = 加速度，t = 时间，s = 位移。
v = u + at
s = ut + ½at²
v² = u² + 2as
Use v = u + at when time is involved and displacement is not needed. The equation s = ut + ½at² gives displacement when initial velocity, time and acceleration are known. If final velocity and displacement are connected but time is missing, v² = u² + 2as is the best choice.
当涉及时间而不需要位移时，使用 v = u + at。方程 s = ut + ½at² 在已知初速度、时间和加速度时给出位移。如果末速度与位移相关而缺少时间，v² = u² + 2as 是最佳选择。
Remember to work in SI units: velocity in m/s, acceleration in m/s², time in s, displacement in m.
记住使用国际单位制：速度以 m/s 为单位，加速度以 m/s² 为单位，时间以 s 为单位，位移以 m 为单位。
2. Forces and Newton’s Second Law | 力与牛顿第二定律
The resultant force acting on an object determines its acceleration. The relationship is at the heart of mechanics.
作用在物体上的合力决定其加速度。这个关系是力学的核心。
F = m × a
where F is resultant force in newtons (N), m is mass in kilograms (kg), and a is acceleration in metres per second squared (m/s²).
其中 F 是合力，单位为牛顿 (N)；m 是质量，单位为千克 (kg)；a 是加速度，单位为米每二次方秒 (m/s²)。
Always resolve all forces acting on the body to find the net unbalanced force before applying the equation. If the resultant force is zero, the object either remains at rest or continues to move with constant velocity (Newton’s First Law).
在应用公式前，务必先分析作用在物体上的所有力，找出净不平衡力。如果合力为零，物体要么保持静止，要么以恒定速度继续运动（牛顿第一定律）。
Weight is a specific force calculated using gravitational field strength g (≈ 10 N/kg on Earth, or 9.8 N/kg in more precise work): W = m × g.
重力是一种特殊的力，用重力场强度 g 计算（地球表面约为 10 N/kg，精密计算中取 9.8 N/kg）：W = m × g。
3. Energy, Work and Power | 能量、功与功率
Energy is transferred when work is done or when heat flows. The principle of conservation of energy is fundamental: energy cannot be created or destroyed, only transferred, stored or dissipated.
当做功或热传递时，能量会发生转移。能量守恒定律是根本：能量不能凭空产生或消灭，只能转移、储存或耗散。
Work done (J) = Force (N) × distance moved in the direction of the force (m)
W = F × s
The joule (J) is the unit of energy and work. When a force of 1 N moves an object 1 m, 1 J of work is done.
焦耳 (J) 是能量和功的单位。1 N 的力使物体沿力的方向移动 1 m，就做了 1 J 的功。
Kinetic energy and gravitational potential energy are two key forms in mechanics.
Kinetic Energy: Eₖ = ½mv²
Gravitational Potential Energy: Eₚ = mgh
where m is mass (kg), v is speed (m/s), g is gravitational field strength (N/kg) and h is height above a reference level (m).
其中 m 为质量 (kg)，v 为速度 (m/s)，g 为重力场强度 (N/kg)，h 为参考高度 (m)。
Power is the rate of energy transfer or the rate of doing work.
Power (W) = Work done (J) / time (s) or P = E / t
The unit watt (W) is equivalent to one joule per second.
功率是能量转移或做功的速率。单位瓦特 (W) 相当于每秒 1 焦耳。
Efficiency can be expressed as a decimal or percentage:
Efficiency = Useful output energy / Total input energy
Often multiplied by 100 to give a percentage. No device is 100% efficient because some energy is always dissipated, usually as heat.
通常乘以 100 表示为百分比。没有设备能达到 100% 的效率，因为总有一部分能量耗散，通常以热的形式散失。
4. Specific Heat Capacity and Specific Latent Heat | 比热容与比潜热
When a substance is heated, its temperature rise depends on its mass and specific heat capacity. No change of state occurs in this calculation.
物质加热时，温度升高的程度取决于其质量和比热容。此计算中不发生物态变化。
Change in thermal energy (J) = mass (kg) × specific heat capacity (J/kg°C) × temperature change (°C)
ΔQ = m c Δθ
Specific heat capacity, c, is the energy needed to raise the temperature of 1 kg of a substance by 1 °C.
比热容 c 是使 1 kg 物质温度升高 1 °C 所需的能量。
During a change of state, the temperature remains constant even though energy is being supplied. The energy required to change state is given by the specific latent heat.
在物态变化过程中，即使提供能量，温度也保持恒定。改变物态所需的能量由比潜热给出。
Energy for change of state (J) = mass (kg) × specific latent heat (J/kg)
Q = m L
Use Lf for fusion (melting/freezing) and Lv for vaporisation (boiling/condensing). The symbol L may be given in data sheets.
使用 Lf 表示熔化/凝固（熔解潜热），Lv 表示汽化/液化（汽化潜热）。数据表上可能会给出符号 L。
5. Waves: Speed, Frequency and Wavelength | 波：波速、频率与波长
All waves obey the wave equation, linking wave speed, frequency and wavelength.
所有波都遵循波动方程，将波速、频率和波长联系起来。
wave speed (m/s) = frequency (Hz) × wavelength (m)
v = f λ
The period T of a wave is the time for one complete oscillation and is the inverse of frequency:
T = 1 / f
For electromagnetic waves, the speed in a vacuum is constant at 3.0 × 10⁸ m/s. Sound waves travel much slower and require a medium.
对于电磁波，真空中的波速恒为 3.0 × 10⁸ m/s。声波传播慢得多，且需要介质。
Make sure frequency is in hertz (Hz), wavelength in metres, and speed in m/s. When measuring waves from a diagram, check whether you are given a full wavelength or half-wavelength.
确保频率用赫兹 (Hz)，波长用米，波速用 m/s。通过图示测量波时，要确认给出的是一个完整波长还是半个波长。
6. Electricity: Current, Voltage and Resistance | 电学：电流、电压与电阻
The foundation of circuit calculations is Ohm’s law, which holds for many conductors at constant temperature.
电路计算的基础是欧姆定律，适用于许多恒温下的导体。
voltage (V) = current (A) × resistance (Ω)
V = I R
Charge and current are related through time:
charge (C) = current (A) × time (s)
Q = I t
In series circuits, current is the same everywhere, total resistance is the sum of individual resistances, and voltage is shared. In parallel circuits, voltage across each branch is the same, total current splits, and total resistance decreases as more branches are added.
串联电路中，各处电流相同，总电阻为各电阻之和，电压分配。并联电路中，各支路两端电压相同，总电流分流，增加支路则总电阻减小。
7. Electrical Power and Energy Transfer | 电功率与电能转移
Electrical power is the rate at which an appliance transfers energy. Three useful forms of the power equation are commonly used.
电功率是用电器转移能量的速率。三个常用的功率公式形式如下。
Power (W) = voltage (V) × current (A) P = V I
P = I² R and P = V² / R
Energy transferred by an electrical device is simply power multiplied by time:
Energy (J) = Power (W) × time (s) E = P t
Combining with Q = I t, we also have E = V I t and E = Q V.
结合 Q = I t，还可得到 E = V I t 和 E = Q V。
When calculating the cost of electricity, energy is often measured in kilowatt-hours (kW h). One kilowatt-hour is the energy used by a 1 kW device running for 1 hour.
计算电费时，电能通常以千瓦时 (kW h) 计量。1 千瓦时是 1 kW 的用电器工作 1 小时所消耗的能量。
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Cost = number of kW h × cost per kW h
费用 = 用电量 (kW h) × 每千瓦时价格
8. Density and Pressure | 密度与压强
Density relates mass and volume, and is a characteristic property of materials.
密度将质量与体积联系起来，是物质的一种特性。
density (kg/m³) = mass (kg) / volume (m³)
ρ = m / V
For irregular solids, volume can be found by displacement in a measuring cylinder. Ensure units are consistent: 1 g/cm³ = 1000 kg/m³.
对于不规则固体，可用量筒排水法测量体积。务必保持单位一致：1 g/cm³ = 1000 kg/m³。
Pressure on a surface is force per unit area.
pressure (Pa) = force (N) / area (m²)
p = F / A
The pascal (Pa) is equal to one newton per square metre. A larger area reduces pressure for a given force, which explains why snow shoes prevent sinking.
帕斯卡 (Pa) 等于每平方米 1 牛顿。给定力下，面积越大压强越小，这就解释了为什么雪鞋能防止下陷。
Fluid pressure at a depth is also important in some contexts:
p = ρ g h
where ρ is the density of the fluid, g is gravitational field strength and h is the depth.
其中 ρ 为流体密度，g 为重力场强度，h 为深度。
9. Chemistry: Moles, Mass and Molar Mass | 化学：摩尔、质量与摩尔质量
The mole is the unit for amount of substance. One mole contains 6.02 × 10²³ particles (Avogadro’s number). The link to measurable mass is through molar mass, which is the mass of one mole in grams.
摩尔是物质的量的单位。1 摩尔含有 6.02 × 10²³ 个粒子（阿伏伽德罗常数）。通过摩尔质量（1 摩尔物质的质量，以克计）与可测量的质量建立联系。
number of moles = mass (g) / molar mass (g/mol)
n = m / M
For elements, molar mass is the relative atomic mass Ar in grams; for compounds, it is the sum of the relative atomic masses of all atoms in the formula (relative formula mass Mr).
对于元素，摩尔质量是以克计的相对原子质量 Ar；对于化合物，是化学式中所有原子的相对原子质量之和（相对化学式质量 Mr）。
Example: Mr of H₂O = (2 × 1) + 16 = 18, so 18 g of water is 1 mole.
例如：H₂O 的 Mr = (2 × 1) + 16 = 18，因此 18 g 水为 1 摩尔。
When using equations to calculate reacting masses, always convert the given mass to moles, use the mole ratio from the balanced equation, and then convert back to mass for the target substance.
在利用方程式计算反应质量时，总是先将已知质量转换为物质的量，运用配平方程式的摩尔比，再将目标物质的物质的量转换回质量。
10. Chemistry: Concentration and Titration | 化学：浓度与滴定
Concentration describes the amount of solute dissolved in a given volume of solution. The most common units are mol/dm³ (moles per cubic decimetre) or g/dm³.
浓度描述溶解在一定体积溶液中的溶质的量。最常用的单位是 mol/dm³（摩尔每立方分米）或 g/dm³。
concentration (mol/dm³) = number of moles / volume (dm³)
c = n / V
Alternatively, concentration in g/dm³ = mass (g) / volume (dm³).
也可表示为质量浓度：g/dm³ = 质量 (g) / 体积 (dm³)。
Note: 1 dm³ = 1000 cm³. Volumes measured in cm³ must be divided by 1000 to convert to dm³.
注意：1 dm³ = 1000 cm³。以 cm³ 测量的体积必须除以 1000 转换为 dm³。
In a titration, the equation c₁V₁/c₂V₂ = n₁/n₂ (or simply nₐ = cₐVₐ) is used with the balanced equation to find an unknown concentration. The formula maVa / mbVb = a/b can be applied, but always check the mole ratio first.
在滴定中，结合配平的方程式使用 c₁V₁/c₂V₂ = n₁/n₂（或简写为 nₐ = cₐVₐ）来求算未知浓度。公式 mₐVₐ / mbVb = a / b 可以应用，但一定要先确认摩尔比。
11. Biology: Magnification and Size | 生物学：放大率与实际尺寸
In microscopy, magnification is the ratio between the size of an image and the true size of the specimen. This formula appears in the Practical Skills section and helps interpret drawings and micrographs.
在显微镜使用中，放大率是图像尺寸与标本真实尺寸之比。该公式出现在实验技能部分，有助于解读绘图和显微照片。
Magnification = image size / actual object size
M = I / A
Both image size and actual size must be in the same unit (e.g. millimetres, micrometres). A common rearrangement is: actual size = image size / magnification.
图像尺寸和实际尺寸必须使用相同单位（例如毫米、微米）。常用的变形公式为：实际尺寸 = 图像尺寸 / 放大率。
Remember the unit conversions: 1 mm = 1000 µm. When measuring a cell in a diagram, use a ruler to find the image length, then apply the formula. State your answer with the correct unit.
记住单位换算：1 mm = 1000 µm。测量示意图中的细胞时，用尺子量出图像长度，再代入公式。写出答案时记得标上正确单位。
12. Quick Reference: Essential Unit Conversions | 速查：关键单位换算
Using consistent units is vital for correct formula application. Keep this table of common conversions handy when practising numerical problems.
使用一致的单位对正确应用公式至关重要。在练习计算题时，将这份常用换算表放在手边。
| Quantity | Conversion |
| Time | 1 minute = 60 s; 1 hour = 3600 s |
| Length | 1 km = 1000 m; 1 cm = 0.01 m; 1 mm = 0.001 m |
| Mass | 1 tonne = 1000 kg; 1 g = 0.001 kg; 1 mg = 10⁻⁶ kg |
| Volume | 1 m³ = 1000 dm³; 1 dm³ = 1000 cm³; 1 litre = 1 dm³ = 1000 cm³ |
| Density | 1 g/cm³ = 1000 kg/m³ |
| Force | 1 N = 1 kg m/s² |
| Energy | 1 J = 1 N m; 1 kW h = 3.6 × 10⁶ J |
| Power | 1 W = 1 J/s; 1 kW = 1000 W |
Always check whether the data given in a question require conversion before substituting into a formula. Many errors come from mixed units like cm for length when the formula expects metres.
将数据代入公式前，务必检查是否需要转换单位。许多错误源于单位混用，例如公式要求以米为单位却使用了厘米。
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