📚 Formula & Theorem Quick Reference Guide for Year 11 AQA Science | Year 11 AQA 科学：公式定理速查手册
This quick reference guide gathers all the essential formulas and key theorems you need to master for the Year 11 AQA GCSE Science examinations, covering Physics, Chemistry, and Biology. Whether you are taking Combined Science: Trilogy or the separate sciences, having these equations at your fingertips will boost your confidence and speed when tackling calculation questions. Each equation is presented with clear symbols and units, and we indicate where memorisation is required versus those provided on the exam equation sheet.
本速查手册汇集了 Year 11 AQA GCSE 科学考试中必须掌握的所有核心公式与关键定理，涵盖物理、化学和生物。无论你学习的是组合科学：三部曲还是单独科学，熟记这些公式都能提升你应对计算题的信心与速度。每个公式都配有清晰的符号与单位，并且我们标注了哪些需要记忆，哪些会在考试提供的公式表中给出。
1. Motion Equations | 运动公式
Understanding motion is fundamental in AQA Physics. You need to recall and apply equations for speed, acceleration, and uniform motion. The average speed equation is especially tested and must be memorised.
理解运动是 AQA 物理的基础。你需要记忆并应用速度、加速度和匀速运动的方程。平均速度公式是考试重点，必须牢记。
v = s ÷ t
v = speed (m/s), s = distance (m), t = time (s) — must be memorised.
v = 速度（米/秒），s = 距离（米），t = 时间（秒）——必须记忆。
a = (v − u) ÷ t
= acceleration (m/s²), v = final velocity (m/s), u = initial velocity (m/s), t = time (s) — provided on the equation sheet for Combined Science, but memorisation is useful.
a = 加速度（米/秒²），v = 末速度（米/秒），u = 初速度（米/秒），t = 时间（秒）——组合科学的公式表中会提供，但记忆有益。
v² − u² = 2 a s
Applies for uniform acceleration; given on the separate physics equation sheet.
适用于匀加速运动；在单独物理试卷的公式表中提供。
2. Forces & Newton's Laws | 力与牛顿定律
Newton' ackbone of many mechanics problems. You must be confident with F=ma, weight, and momentum.
牛顿第二定律及相关力的方程是许多力学问题的核心。你必须熟练运用 F=ma、重力公式和动量公式。
F = m × a
Resultant force (N) = mass (kg) × acceleration (m/s²) — essential, must be memorised.
合力（牛） = 质量（千克） × 加速度（米/秒²）——关键公式，必须记忆。
W = m × g
Weight (N) = mass (kg) × gravitational field strength (N/kg); g ≈ 9.8 N/kg on Earth — memorise.
重量（牛） = 质量（千克） × 重力场强度（牛/千克）；地球表面 g ≈ 9.8 N/kg——需记忆。
p = m × v
m/s) = mass (kg) × velocity (m/s); higher-tier and separate sciences only, given on sheet.
动量（千克·米/秒） = 质量（千克） × 速度（米/秒）；仅高等级和单独科学涉及，公式表提供。
F = k × e
Force applied to a spring (N) = spring constant (N/m) × extension (m) — given on sheet.
施加在弹簧上的力（牛） = 弹簧常数（牛/米） × 伸长量（米）——公式表提供。
3. Energy & Power | 能量与功率
Energy calculations form a significant part of AQA Physics papers. You must know equations for kinetic energy, gravitational potential energy, power, and efficiency. Many of these are provided, but check your specification.
能量计算在 AQA 物理试卷中占据很大比重。你需要掌握动能、重力势能、功率和效率的公式。许多公式会在试卷中给出，但需核对考纲要求。
Eₖ = ½ m v²
Kinetic energy (J) = ½ × mass (kg) × (speed)² (m/s) — given on equation sheet for Combined Science; memorisation recommended.
动能（焦） = ½ × 质量（千克） × 速度²（米/秒）——组合科学公式表提供；推荐记忆。
Eₚ = m g h
Gravitational potential energy (J) = mass (kg) × g (N/kg) × height (m) — given on sheet; g = 9.8 N/kg.
重力势能（焦） = 质量（千克） × g（牛/千克） × 高度（米）——公式表提供；g = 9.8 N/kg。
P = E ÷ t
Power (W) = energy transferred (J) ÷ time (s); also P = W ÷ t for work done — provided.
功率（瓦） = 传递的能量（焦） ÷ 时间（秒）；也有 P = 做功 ÷ 时间——公式表提供。
Efficiency = (useful output energy ÷ total input energy) × 100%
Efficiency can also be expressed as useful power output ÷ total power input — must be memorised.
效率 =（有用输出能量 ÷ 总输入能量）× 100%——也可表示为有用输出功率 ÷ 总输入功率，必须记忆。
4. Electricity Equations | 电学公式
uations appear on the equation sheet, but core ones like V=IR must be recited confidently.
电路计算要求熟练掌握电荷、电势差、电阻和功率。部分公式在公式表上给出，但像 V=IR 这样的核心公式必须能够流畅写出。
Q = I × t
Charge (C) = current (A) × time (s) — provided on equation sheet.
电荷量（库） = 电流（安） × 时间（秒）——公式表提供。
V = I × R
Potential difference (V) = current (A) × resistance (Ω) — must be memorised.
电势差（伏） = 电流（安） × 电阻（欧）——必须记忆。
P = I × V
Power (W) = current (A) × potential difference (V) — provided.
功率（瓦） = 电流（安） × 电势差（伏）——公式表提供。
P = I² R
Power (W) = current² (A²) × resistance (Ω) — provided; useful when current is known.
功率（瓦） = 电流²（安²） × 电阻（欧）——公式表提供；已知电流时使用方便。
E = P × t and E = Q × V
Energy transferred (J) can be calculated from power × time or charge × voltage — both provided.
传递的能量（焦）可由功率 × 时间或电荷量 × 电压计算——公式表提供。
5. Wave Properties | 波的特性
Wave questions require rapid recall of the relationship between speed, frequency, and wavelength, as well as the link between period and frequency. These are straightforward but commonly tested.
波的考题要求快速回忆波速、频率和波长之间的关系，以及周期与频率的联系。这些公式简单，但考查频率高。
v = f × λ
Wave speed (m/s) = frequency (Hz) × wavelength (m) — must be memorised.
波速（米/秒） = 频率（赫兹） × 波长（米）——必须记忆。
T = 1 ÷ f
Period (s) = 1 ÷ frequency (Hz) — provided on equation sheet, but it is easy to recall.
周期（秒） = 1 ÷ 频率（赫兹）——公式表提供，但很容易记住。
6. Forces & Pressure | 力与压强
Pressure in solids and fluids appears in the Forces topic. Be ready to calculate pressure, and for higher-tier, the pressure due to a liquid column. The spring constant equation also fits here as a force–material relationship.
固体和流体中的压强出现在“力”单元。你需要会计算压强，高等级考生还要掌握液柱压强的计算。弹簧常数公式作为力–材料关系也可归入此节。
p = F ÷ A
Pressure (Pa) = force (N) ÷ area (m²) — provided on equation sheet; 1 Pa = 1 N/m².
压强（帕） = 力（牛） ÷ 面积（米²）——公式表提供；1 帕 = 1 牛/米²。
p = h × ρ × g
Pressure due to a liquid column (Pa) = height (m) × density (kg/m³) × g (N/kg) — separate sciences and higher-tier only; provided.
液柱产生的压强（帕） = 液柱高度（米） × 密度（千克/米³） × g（牛/千克）——仅单独科学和高等级涉及；公式表提供。
F = k × e
As seen in Forces, linking force and extension for elastic objects.
已在力部分出现，描述弹性体受力与伸长量关系。
7. Quantitative Chemistry: Moles & Mass | 定量化学：摩尔与质量
Chemistry calculations start with the mole concept. The equations linking mass, molar mass, and number of moles are the foundation of every titration and yield question. None of these are provided on the equation sheet — you must learn them thoroughly.
化学计算始于摩尔概念。连接质量、摩尔质量和摩尔数的方程是所有滴定和产率问题的基础。这些公式都不会在公式表中提供——你必须熟练掌握。
n = m ÷ Mᵣ
Number of moles (mol) = mass (g) ÷ relative formula mass (Mᵣ, g/mol) — must be memorised.
物质的量（摩尔） = 质量（克） ÷ 相对公式质量（Mᵣ，克/摩尔）——必须记忆。
Mᵣ = Σ (relative atomic masses)
The relative formula mass is the sum of the Aᵣ of all atoms in a formula unit — essential to calculate correctly.
相对公式质量是化学式中所有原子的相对原子质量（Aᵣ）之和——正确计算非常重要。
8. Concentration, Volume & Titration | 浓度、体积与滴定
When solutions are involved, concentration calculations become vital. In AQA Chemistry, you can express concentration in g/dm³ or in mol/dm³. Both forms require you to rearrange the formula flexibly.
涉及溶液时，浓度计算变得至关重要。在 AQA 化学中，浓度可以表示为克/分米³ 或摩尔/分米³。两种形式都需要你灵活变形公式。
c (g/dm³) = mass (g) ÷ volume (dm³)
Concentration in grams per cubic decimetre — must be memorised; 1 dm³ = 1000 cm³.
浓度（克/分米³） = 质量（克） ÷ 体积（分米³）——必须记忆；1 分米³ = 1000 厘米³。
c (mol/dm³) = n (mol) ÷ V (dm³)
Molar concentration (mol/dm³) = number of moles ÷ volume in dm³ — must be memorised; often combined with the mole equation.
摩尔浓度（摩尔/分米³） = 物质的量（摩尔） ÷ 体积（分米³）——必须记忆；常与摩尔公式联用。
For titrations: nₐ / n₆ = (cₐ Vₐ) / (c₆ V₆) using the mole ratio from the balanced equation.
滴定计算中使用摩尔比：nₐ / n₆ = (cₐ Vₐ) / (c₆ V₆)，其中 a、b 代表酸和碱，摩尔比来自配平方程式。
9. Chemical Calculations: Yield & Atom Economy | 化学计算：产率与原子经济性
Yield and atom economy assess the efficiency of a chemical reaction. These percentages are not provided on the equation sheet, so you need to memorise the formulas and understand what each term means.
产率和原子经济性用于评估化学反应的效率。这些百分比的公式不在公式表上，需要记忆并理解各项的含义。
Percentage yield = (actual yield ÷ theoretical yield) × 100%
Actual yield comes from experiment; theoretical yield is calculated from stoichiometry — must be memorised.
实际产量来自实验数据；理论产量通过化学计量计算——必须记忆。
Atom economy = (Mᵣ of desired product ÷ Σ Mᵣ of all products) × 100%
Or use the total Mᵣ of reactants if the reaction yields a single desired product — must be memorised; high atom economy reduces waste.
若只生成一种目标产物，也可用反应物总 Mᵣ 计算——必须记忆；原子经济性高意味着废物少。
10. Energy Changes & Reaction Rates | 能量变化与反应速率
Thermochemistry and rates are quantitative topics where formulas tie experiment to theory. You need to be able to calculate the heat energy change in a reaction and the rate of reaction. Some equations are given, but you still must understand their application.
热化学和速率是定量研究的内容，公式将实验与理论联系起来。你需要能够计算反应的热能变化和反应速率。部分公式会提供，但你仍需理解其应用。
Q = m × c × ΔT
ty (J/g°C) × temperature change (°C); given on sheet, often used with water (c=4.2 J/g°C).
热能变化（焦） = 质量（克） × 比热容（焦/克·°C） × 温度变化（°C）；公式表提供，通常用水（c=4.2 J/g·°C）计算。
Rate of reaction = amount of reactant used ÷ time or amount of product formed ÷ time
Rate can be measured in g/s, cm³/s, or mol/s — must be memorised as a general formula.
速率可以以克/秒、厘米³/秒 或摩尔/秒 表示——作为通用公式必须记忆。
11. Biology: Magnification & Size | 生物：放大倍率与尺寸
In the Biology topics, the main calculation involves microscopy. You must be able to convert units (mm, µm, nm) and use the magnification equation accurately. This is one of the few equations you must learn by heart for Biology.
在生物学内容中，主要的计算与显微镜有关。你必须能够换算单位（毫米、微米、纳米）并准确使用放大倍率公式。这是生物学中少数必须背记的公式之一。
M = I ÷ A
Magnification = image size ÷ actual size — must be memorised; both sizes must be in the same unit.
放大倍率 = 图像大小 ÷ 实际大小——必须记忆；两个尺寸必须使用相同单位。
Common conversions: 1 cm = 10 mm = 10,000 µm; 1 µm = 1000 nm.
常用换算：1 厘米 = 10 毫米 = 10,000 微米；1 微米 = 1000 纳米。
12. Biology: Circulatory System & Rate Calculations | 生物：循环系统与速率计算
Physiology brings a few more quantitative relationships. You need to know cardiac output and may be asked to calculate heart rate or stroke volume. The idea of rate also appears when analysing enzyme activity or breathing rate, using the same general principle.
生理学中有几个其他的定量关系。你需要知道心输出量的计算，可能会要求计算心率或每搏输出量。速率的概念同样出现在分析酶活性或呼吸频率时，遵循相同的一般原则。
Cardiac output = heart rate × stroke volume
(cm³/min or L/min) = heart rate (beats/min) × stroke volume (cm³/beat); must be memorised.
心输出量（厘米³/分钟 或 升/分钟） = 心率（次/分钟） × 每搏输出量（厘米³/次）——必须记忆。
Rate = change in measurement ÷ time
Applied to breathing rate (breaths/min), enzyme activity (product formed/min), etc. — understand the pattern.
应用于呼吸频率（次/分钟）、酶活性（产物生成量/分钟）等——理解这一通式即可。
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