📚 GCSE AQA Science: Formula Summary Handbook | GCSE AQA 科学：公式汇总手册
Mastering the essential formulae is a key step to success in GCSE AQA Science – whether you are studying Combined Science: Trilogy or the separate Physics, Chemistry and Biology courses. This handbook brings together all the critical quantitative relationships you need to memorise and apply confidently in your examinations. Each equation is presented clearly with its standard symbols, units and a brief note on how it is used in typical exam questions.
掌握核心公式是攻克 GCSE AQA 科学的关键一步——无论你学习的是 Combined Science: Trilogy 还是单独的物理、化学、生物课程。本手册汇集了所有你需要熟记并能自信应用于考试的关键数量关系。每个方程都清晰给出标准符号、单位，并简要说明在典型考题中的使用方法。
1. Speed and Acceleration | 速度与加速度
Speed describes how fast an object is moving. For motion at a constant speed, the relationship between distance, speed and time is straightforward. When an object changes its velocity, acceleration is introduced, linking the change in velocity to the time taken.
速度描述物体运动的快慢。对于匀速运动，距离、速度和时间之间的关系很简单。当物体速度发生变化时，就引入了加速度，它把速度的变化与所用时间联系起来。
s = v t
distance travelled (s) = speed (v) × time (t). s in metres (m), v in metres per second (m/s), t in seconds (s). This equation is used when speed is constant.
行驶距离 (s) = 速度 (v) × 时间 (t)。s 单位为米 (m)，v 单位为米每秒 (m/s)，t 单位为秒 (s)。该方程用于匀速运动。
a = Δv / t
acceleration (a) = change in velocity (Δv) ÷ time taken (t). a in metres per second squared (m/s²), Δv in m/s, t in s. Remember Δv = final velocity – initial velocity (v – u).
加速度 (a) = 速度变化量 (Δv) ÷ 所用时间 (t)。a 单位为米每二次方秒 (m/s²)，Δv 单位为 m/s，t 单位为 s。记住 Δv = 末速度 – 初速度 (v – u)。
2. Forces and Newton’s Laws | 力与牛顿定律
Newton’s second law links force, mass and acceleration, while weight is a special force caused by gravity. Momentum introduces the concept of ‘quantity of motion’ and is conserved in collisions and explosions when no external forces act.
牛顿第二定律将力、质量和加速度联系起来，而重量是由引力引起的一种特殊的力。动量则引入了“运动量”的概念，当没有外力作用时，它在碰撞和爆炸中守恒。
F = m a
resultant force (F) = mass (m) × acceleration (a). F in newtons (N), m in kilograms (kg), a in m/s². Often used with free-body diagrams.
合力 (F) = 质量 (m) × 加速度 (a)。F 单位为牛顿 (N)，m 单位为千克 (kg)，a 单位为 m/s²。常与受力分析图一起使用。
W = m g
weight (W) = mass (m) × gravitational field strength (g). W in N, m in kg, g on Earth ≈ 9.8 N/kg (often rounded to 10 N/kg in exams).
重量 (W) = 质量 (m) × 重力场强度 (g)。W 单位为 N，m 单位为 kg，地球上 g ≈ 9.8 N/kg（考试中常取 10 N/kg）。
p = m v
momentum (p) = mass (m) × velocity (v). p in kilogram metres per second (kg m/s). Conservation of momentum: total momentum before = total momentum after.
动量 (p) = 质量 (m) × 速度 (v)。p 单位为千克米每秒 (kg m/s)。动量守恒：碰撞前的总动量 = 碰撞后的总动量。
3. Work, Energy and Power | 功、能量与功率
Energy can be stored, transferred and used to do work. Understanding kinetic energy, gravitational potential energy and the concept of power is vital for solving energy problems, as is calculating efficiency to assess how well energy is converted.
能量可以被储存、转移并用来做功。理解动能、重力势能以及功率的概念对于解决能量问题至关重要，计算效率以评估能量转换的有效性也同样重要。
W = F s
work done (W) = force (F) × distance (s) moved in the direction of the force. W in joules (J), F in N, s in m. Work done is equal to energy transferred.
做功 (W) = 力 (F) × 沿力方向移动的距离 (s)。W 单位为焦耳 (J)，F 单位为 N，s 单位为 m。做功等于转移的能量。
Eₖ = ½ m v²
kinetic energy (Eₖ) = 0.5 × mass (m) × (speed)² (v²). Eₖ in J, m in kg, v in m/s. Used for moving objects.
动能 (Eₖ) = 0.5 × 质量 (m) × 速度的平方 (v²)。Eₖ 单位为 J，m 单位为 kg，v 单位为 m/s。用于运动的物体。
Eₚ = m g h
gravitational potential energy (Eₚ) = mass (m) × gravitational field strength (g) × height (h). Eₚ in J, m in kg, g in N/kg, h in m.
重力势能 (Eₚ) = 质量 (m) × 重力场强度 (g) × 高度 (h)。Eₚ 单位为 J，m 单位为 kg，g 单位为 N/kg，h 单位为 m。
P = E / t
power (P) = energy transferred (E) ÷ time (t). P in watts (W), E in J, t in s. Alternatively, P = W / t (work done over time).
功率 (P) = 转移的能量 (E) ÷ 时间 (t)。P 单位为瓦特 (W)，E 单位为 J，t 单位为 s。也可用 P = W / t（一段时间内做功的功率）。
efficiency = useful output energy transfer / total input energy transfer
Efficiency can be given as a decimal or percentage. It may also be calculated as useful power output / total power input. No unit, and always ≤ 1 (or 100%).
效率可以表示为小数或百分数。也可用有效输出功率 / 总输入功率来计算。效率无单位，且始终 ≤ 1（或 100%）。
4. Forces and Elasticity | 力与弹性
When a spring is stretched or compressed, the extension is proportional to the applied force up to the limit of proportionality. This relationship is known as Hooke’s law, and it allows us to calculate the force required or the spring constant of a material.
当弹簧被拉伸或压缩时，在比例极限内，伸长量与施加的力成正比。这一关系被称为胡克定律，它可以帮助我们计算所需的力或材料的劲度系数。
F = k e
force (F) = spring constant (k) × extension (e). F in N, k in newtons per metre (N/m), e in m. The extension is the difference between the stretched length and the original length.
力 (F) = 劲度系数 (k) × 伸长量 (e)。F 单位为 N，k 单位为牛每米 (N/m)，e 单位为 m。伸长量是拉伸后的长度与原长之差。
5. Moments, Levers and Pressure | 力矩、杠杆与压强
A moment is the turning effect of a force about a pivot. Moments can be used to calculate equilibrium in levers and gears. Pressure is a measure of how concentrated a force is on a surface, and it applies to solids, liquids and gases.
力矩是力绕支点产生的转动效应。力矩可用于计算杠杆和齿轮的平衡。压强是力在表面上集中程度的量度，适用于固体、液体和气体。
M = F d
moment of a force (M) = force (F) × perpendicular distance (d) from the pivot. M in newton metres (Nm), F in N, d in m. For equilibrium, total clockwise moments = total anticlockwise moments.
力矩 (M) = 力 (F) × 从支点到力作用线的垂直距离 (d)。M 单位为牛米 (Nm)，F 单位为 N，d 单位为 m。平衡时，总顺时针力矩 = 总逆时针力矩。
p = F / A
pressure (p) = force normal to a surface (F) ÷ area (A). p in pascals (Pa), F in N, A in square metres (m²). 1 Pa = 1 N/m². This formula is also used for fluid pressure calculations (where pressure is transmitted equally in all directions).
压强 (p) = 垂直于表面的力 (F) ÷ 面积 (A)。p 单位为帕斯卡 (Pa)，F 单位为 N，A 单位为平方米 (m²)。1 Pa = 1 N/m²。该公式也用于流体压强计算（压强在所有方向均匀传递）。
6. Electricity | 电学
Electric circuits obey a small set of fundamental equations linking charge, current, potential difference, resistance and power. These relationships are indispensable for analysing series and parallel circuits, choosing fuses and calculating the energy transferred by domestic appliances.
电路遵循一小套基本方程，将电荷、电流、电势差、电阻和功率联系起来。这些关系对于分析串联和并联电路、选择熔断器以及计算家用电器的能量转移不可或缺。
Q = I t
charge flow (Q) = current (I) × time (t). Q in coulombs (C), I in amperes (A), t in s. This equation is used when you need to find the total charge passing a point.
电荷量 (Q) = 电流 (I) × 时间 (t)。Q 单位为库仑 (C)，I 单位为安培 (A)，t 单位为 s。当需要求通过某点的总电荷时使用该方程。
V = I R
potential difference (V) = current (I) × resistance (R). V in volts (V), I in A, R in ohms (Ω). This is Ohm’s law for a resistor at constant temperature.
电势差 (V) = 电流 (I) × 电阻 (R)。V 单位为伏特 (V)，I 单位为 A，R 单位为欧姆 (Ω)。这是恒定温度下电阻器的欧姆定律。
P = V I
power (P) = potential difference (V) × current (I). P in W, V in V, I in A. This is the general formula for electrical power.
功率 (P) = 电势差 (V) × 电流 (I)。P 单位为 W，V 单位为 V，I 单位为 A。这是电功率的通用公式。
P = I² R
power (P) = (current)² (I²) × resistance (R). P in W, I in A, R in Ω. Useful when current and resistance are known.
功率 (P) = 电流的平方 (I²) × 电阻 (R)。P 单位为 W，I 单位为 A，R 单位为 Ω。当已知电流和电阻时很方便。
E = P t
energy transferred (E) = power (P) × time (t). E in J, P in W, t in s. Also written as E = I t V (using Q = I t and E = Q V).
转移的能量 (E) = 功率 (P) × 时间 (t)。E 单位为 J，P 单位为 W，t 单位为 s。也可写作 E = I t V（利用 Q = I t 和 E = Q V）。
E = Q V
energy transferred (E) = charge flow (Q) × potential difference (V). E in J, Q in C, V in V. This relates the energy per unit charge to the potential difference.
转移的能量 (E) = 电荷量 (Q) × 电势差 (V)。E 单位为 J，Q 单位为 C，V 单位为 V。它将单位电荷的能量与电势差联系起来。
7. Waves | 波
All waves – whether transverse or longitudinal – obey the wave equation, linking wave speed, frequency and wavelength. This relationship is used extensively in ray diagrams, electromagnetic spectrum calculations and sound wave problems.
所有的波——无论是横波还是纵波——都遵从波动方程，该方程将波速、频率和波长联系在一起。这一关系广泛应用于光线图、电磁波谱计算和声波问题。
v = f λ
wave speed (v) = frequency (f) × wavelength (λ). v in m/s, f in hertz (Hz), λ in m. In the same medium, wave speed is constant for a given type of wave.
波速 (v) = 频率 (f) × 波长 (λ)。v 单位为 m/s，f 单位为赫兹 (Hz)，λ 单位为 m。在同一介质中，给定类型的波其波速是恒定的。
8. Density and the Particle Model | 密度与粒子模型
Density links the mass of a substance to its volume and is a characteristic physical property. It is used to identify materials, explain whether objects float or sink, and to perform calculations involving changes of state and the particle model.
密度将物质的质量与其体积联系起来，是一种特征的物理性质。它用于鉴别材料、解释物体的浮沉，并进行涉及状态变化和粒子模型的计算。
ρ = m / V
density (ρ) = mass (m) ÷ volume (V). ρ in kilograms per cubic metre (kg/m³), m in kg, V in m³. In the lab, density can be measured in g/cm³ (1 g/cm³ = 1000 kg/m³).
密度 (ρ) = 质量 (m) ÷ 体积 (V)。ρ 单位为千克每立方米 (kg/m³)，m 单位为 kg，V 单位为 m³。实验中密度也可用 g/cm³ 表示（1 g/cm³ = 1000 kg/m³）。
9. Quantitative Chemistry – The Mole | 定量化学——摩尔
The mole concept is central to all quantitative chemistry: it bridges the gap between the atomic scale and the laboratory scale. You must be confident converting between mass, moles and relative formula mass, and using the Avogadro constant where required.
摩尔概念是所有定量化学的核心：它搭建了原子尺度与实验室尺度之间的桥梁。你必须能熟练地在质量、摩尔和相对式量之间进行转换，并在需要时使用阿伏伽德罗常数。
n = m / Mᵣ
amount of substance (n, in mol) = mass (m, in g) ÷ relative formula mass (Mᵣ, in g/mol). Sometimes Mᵣ is called molar mass. Always check your units carefully.
物质的量 (n，单位 mol) = 质量 (m，单位 g) ÷ 相对式量 (Mᵣ，单位 g/mol)。Mᵣ 有时也称为摩尔质量。务必仔细检查单位。
Number of particles = n × Nₐ
where Nₐ is the Avogadro constant, 6.02 × 10²³ mol⁻¹. This link is used to calculate the number of atoms, ions or molecules in a sample.
其中 Nₐ 为阿伏伽德罗常数，6.02 × 10²³ mol⁻¹。这一关系用于计算样品中的原子、离子或分子数目。
10. Concentration, Titrations and Gas Volumes | 浓度、滴定与气体体积
Concentration expresses how much solute is dissolved in a given volume of solution. Titration calculations rely on the concept of moles reacting in stoichiometric ratios, while the molar gas volume at room temperature and pressure simplifies calculations for gases produced in reactions.
浓度表示在一定体积的溶液中溶解了多少溶质。滴定计算依赖摩尔按化学计量比反应的概念，而在室温和常压下气体的摩尔体积可简化反应生成气体的计算。
c = n / V
concentration (c) = amount of solute (n) ÷ volume of solution (V). c in mol/dm³, n in mol, V in dm³. Remember 1 dm³ = 1000 cm³; you must convert cm³ to dm³ by dividing by 1000.
浓度 (c) = 溶质的物质的量 (n) ÷ 溶液体积 (V)。c 单位为 mol/dm³，n 单位为 mol，V 单位为 dm³。记住 1 dm³ = 1000 cm³；必须将 cm³ 除以 1000 换算为 dm³。
Volume of gas (dm³) = n × 24 (at RTP)
At room temperature and pressure (RTP), 1 mol of any gas occupies 24 dm³. This is used to convert between moles of gas and the volume it occupies, e.g. in reacting mass calculations.
在室温和常压 (RTP) 下，1 mol 任何气体占据 24 dm³。用于在气体的摩尔数与其所占体积之间进行转换，例如在计算反应质量时。
11. Yield, Atom Economy and Percentage Composition | 产率、原子经济性与元素百分含量
Chemists need to evaluate how efficient a reaction is. Percentage yield measures the success of actually obtaining the product, while atom economy shows how much of the starting material ends up in the desired product. Percentage by mass helps determine the composition of compounds.
化学家需要评估反应的效率。产率衡量实际获得产品的成功程度，而原子经济性显示有多少起始原料进入了目标产物。元素质量百分数有助于确定化合物的组成。
Percentage yield = (actual yield / theoretical yield) × 100%
The actual yield is the mass or moles of product collected in the experiment. The theoretical yield is the maximum amount predicted by stoichiometry.
实际产率是实验中收集到的产物的质量或摩尔数。理论产率是根据化学计量比预测的最大量。
Atom economy = (Mᵣ of desired product / sum of Mᵣ of all reactants) × 100%
Atom economy is a measure of green chemistry; higher values mean fewer waste atoms. The calculation uses relative formula masses of the balanced equation.
原子经济性是绿色化学的一个量度；数值越高意味着废弃原子越少。计算使用配平方程中各物质的相对式量。
Percentage by mass of an element = (total mass of element in compound / Mᵣ of compound) × 100%
For example, in H₂O, % oxygen = (16 / 18) × 100%. Used to determine empirical formulae and to analyse the purity of samples.
例如，在 H₂O 中，氧的质量百分数 = (16 / 18) × 100%。用于确定经验式和分析样品纯度。
12. Rates of Reaction and Biology Magnification | 反应速率与生物放大率
Rates of reaction can be monitored by measuring the speed at which a reactant is used up or a product is formed. In Biology, magnification relates the size of an image to the actual size of the specimen – a simple but essential skill for microscopy.
反应速率可以通过测量反应物被消耗或产物生成的速度来监测。在生物学中，放大率将图像的大小与标本的实际大小联系起来——这是显微镜操作中一项简单但必要的技能。
Mean rate of reaction = quantity of reactant used or product formed / time taken
This can be measured in g/s, cm³/s or mol/s. The rate can be determined from the gradient of a graph of volume of gas against time, or mass lost against time.
这可以用 g/s、cm³/s 或 mol/s 来量度。反应速率可以通过气体体积-时间图或质量损失-时间图的斜率求得。
Magnification = image size / actual size
Used in cell biology. Make sure both measurements are in the same unit (usually mm or µm). Rearranging allows you to find actual size = image size / magnification.
用于细胞生物学。确保两个测量值单位相同（通常是 mm 或 µm）。公式变形后可求实际大小 = 图像大小 / 放大率。
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