📚 Year 11 OCR Science: Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This handbook brings together the essential formulas, theorems, and scientific laws you need for Year 11 OCR Science. Each section presents key equations with practical examples, helping you to memorise and apply them confidently across Physics, Chemistry, and Biology. Use this as your go‑to revision companion before exams.
这本手册汇集了 Year 11 OCR 科学所需的核心公式、定理和科学定律。每个部分都提供关键方程及实用示例，帮助你在物理、化学和生物中自信地记忆与应用。把它当作考前复习的随身伴侣吧。
1. Forces and Motion | 力与运动
In OCR Physics, motion is described by a set of equations that link velocity, acceleration, time, and displacement. These are known as the SUVAT equations, derived from uniform acceleration.
在 OCR 物理中，运动由一组联系速度、加速度、时间和位移的方程描述，这些方程称为 SUVAT 方程，由匀加速运动推导而来。
Average speed = total distance ÷ total time. The equation is v = s / t, where v is speed, s is distance, and t is time.
平均速度 = 总路程 ÷ 总时间。公式为 v = s / t，其中 v 为速度，s 为路程，t 为时间。
Acceleration = change in velocity ÷ time taken. a = (v − u) / t, where u is initial velocity and v is final velocity.
加速度 = 速度变化量 ÷ 所用时间。a = (v − u) / t，其中 u 为初速度，v 为末速度。
Final velocity, initial velocity, acceleration, and displacement are related by v² = u² + 2 a s.
末速度、初速度、加速度和位移之间的关系为 v² = u² + 2 a s。
Newton's second law: resultant force = mass × acceleration. F = m a, with force in newtons (N), mass in kg, acceleration in m/s².
牛顿第二定律：合力 = 质量 × 加速度。F = m a，力的单位为牛顿 (N)，质量单位为 kg，加速度单位为 m/s²。
ervation of momentum states that total momentum before a collision equals total momentum after, provided no external force acts.
动量 p = m v。动量守恒定律表明，在没有外力作用时，碰撞前的总动量等于碰撞后的总动量。
p = m v
2. Energy Equations | 能量方程
Energy can be stored in various ways and transferred between stores. The following equations are fundamental for work, kinetic energy, gravitational potential energy, and power.
能量可以多种形式储存并在不同储存之间转移。下列方程是功、动能、重力势能和功率的基础。
Work done = force × distance moved in the direction of the force. W = F d. Energy transferred is measured in joules (J).
做功 = 力 × 在力的方向上移动的距离。W = F d。转移的能量以焦耳 (J) 为单位。
Kinetic energy depends on mass and speed: Eₖ = ½ m v². Doubling speed quadruples kinetic energy.
动能取决于质量和速度：Eₖ = ½ m v²。速度翻倍会使动能变为原来的四倍。
Gravitational potential energy gained when lifting an object: Eₚ = m g h. g is gravitational field strength, 9.8 N/kg on Earth (often rounded to 10 N/kg in OCR questions).
物体被举高时获得的重力势能：Eₚ = m g h。g 为重力场强度，地球上取 9.8 N/kg（OCR 试题中常近似为 10 N/kg）。
Power is the rate of energy transfer: P = E / t or P = W / t. Unit: watt (W), 1 W = 1 J/s.
功率是能量转移的速率：P = E / t 或 P = W / t。单位：瓦特 (W)，1 W = 1 J/s。
ul output energy transfer ÷ total input energy transfer. Can be expressed as a percentage.
效率 = 有用输出能量转移 ÷ 总输入能量转移。可用百分数表示。
Eₖ = ½ m v² ; Eₚ = m g h ; P = W / t
3. Electricity | 电学
Electrical circuits follow a set of relationships linking charge, current, potential difference, resistance, and power. These are essential for both circuit calculations and domestic electricity.
电路遵循一套联系电荷、电流、电位差、电阻和功率的关系式。这些对电路计算和家庭用电都至关重要。
Charge moved = current × time. Q = I t, where Q is in coulombs (C), I in amperes (A), t in seconds (s).
移动的电荷量 = 电流 × 时间。Q = I t，其中 Q 的单位为库仑 (C)，I 为安培 (A)，t 为秒 (s)。
Ohm's law: potential difference = current × resistance. V = I R, with V in volts (V) and R in ohms (Ω).
欧姆定律：电位差 = 电流 × 电阻。V = I R，V 的单位为伏特 (V)，R 为欧姆 (Ω)。
Electrical power: P = I V and P = I² R. Energy transferred is given by E = I V t.
电功率：P = I V 和 P = I² R。转移的电能由 E = I V t 给出。
In series circuits, current is the same everywhere, total resistance is the sum of individual resistances: Rₜₒₜ = R₁ + R₂ + ...
串联电路中电流处处相等，总电阻等于各电阻之和：Rₜₒₜ = R₁ + R₂ + ...
In parallel circuits, the total current is split among branches, and the total resistance is found using 1/Rₜₒₜ = 1/R₁ + 1/R₂ + ...
并联电路中总电流在各支路中分配，总电阻由 1/Rₜₒₜ = 1/R₁ + 1/R₂ + ... 计算。
V = I R ; P = I V ; E = I V t
4. Waves | 波动
Wave behaviour is described by the properties of amplitude, wavelength, frequency, and wave speed. The wave equation is a cornerstone for both sound and electromagnetic waves.
波的行为由振幅、波长、频率和波速等属性描述。波动方程是声波和电磁波的核心。
Wave speed = frequency × wavelength. v = f λ, where v is in m/s, f in hertz (Hz), λ in metres (m).
波速 = 频率 × 波长。v = f λ，v 的单位为 m/s，f 为赫兹 (Hz)，λ 为米 (m)。
Period T is the time for one complete wave cycle: T = 1 / f. Measured in seconds.
周期 T 是完成一次完整波动所需的时间：T = 1 / f。单位为秒。
the law: angle of incidence = angle of reflection. This is measured from the normal line.
反射遵循定律：入射角 = 反射角。角度从法线量起。
Refraction obeys Snell's law: n₁ sin θ₁ = n₂ sin θ₂ (higher tier only). Refractive index n = speed of light in vacuum / speed in medium.
折射遵循斯涅耳定律：n₁ sin θ₁ = n₂ sin θ₂（仅高阶段）。折射率 n = 真空中的光速 / 介质中的光速。
For electromagnetic waves, all travel at the same speed in a vacuum: c = 3.0 × 10⁸ m/s.
电磁波在真空中传播速度相同：c = 3.0 × 10⁸ m/s。
v = f λ ; T = 1 / f
5. Quantitative Chemistry – Moles | 定量化学 — 摩尔
The mole concept is central to chemical calculations. It links mass, relative formula mass, and number of particles through Avogadro's constant.
摩尔概念是化学计算的核心。它通过阿伏伽德罗常数将质量、相对式量和微粒数联系起来。
Number of moles = mass ÷ relative formula mass. n = m / Mᵣ, where m is in grams and Mᵣ is the relative formula mass (g/mol).
摩尔数 = 质量 ÷ 相对式量。n = m / Mᵣ，其中 m 以克为单位，Mᵣ 为相对式量 (g/mol)。
ubstance contains 6.02 × 10²³ particles (Avogadro constant). Number of particles = n × Nₐ.
1 摩尔任何物质含有 6.02 × 10²³ 个微粒（阿伏伽德罗常数）。微粒数 = n × Nₐ。
Reacting masses can be calculated from balanced equations: find moles of known substance, use mole ratio to determine moles of unknown, then convert to mass.
根据化学方程式可计算反应质量：先求已知物质的摩尔数，利用摩尔比求出未知物质的摩尔数，再换算为质量。
t ÷ theoretical mass) × 100. This compares what was actually made to the maximum possible.
产率 = （实际产物质量 ÷ 理论产量）× 100。这用于比较实际产量与最大可能产量。
m of Mᵣ of all products) × 100. Higher atom economy indicates a more sustainable reaction.
原子经济性 = （所需产物的 Mᵣ ÷ 所有产物 Mᵣ 之和）× 100。原子经济性越高，反应越可持续。
n = m / Mᵣ ; N = n × 6.02×10²³
6. Titrations and Concentration | 滴定与浓度
Titration calculations allow chemists to find the concentration of an unknown solution. The key expression links moles, concentration, and volume.
滴定计算使化学家能求出未知溶液的浓度。核心表达式将摩尔、浓度和体积联系起来。
Concentration in mol/dm³: c = n / V, where V is volume in dm³. Often the volume is given in cm³, so convert by dividing by 1000.
浓度 (mol/dm³)：c = n / V，V 为体积，单位 dm³。题目常以 cm³ 给出体积，需除以 1000 进行换算。
e point follow the mole ratio from the balanced equation. For a 1:1 reaction, c₁V₁ = c₂V₂.
滴定中，等当点时酸和碱的摩尔数遵循配平方程式的摩尔比。对于 1:1 反应，有 c₁V₁ = c₂V₂。
Concentration in g/dm³: mass concentration = mass (g) / volume (dm³). This is linked to mol/dm³ by mass conc = c × Mᵣ.
质量浓度 (g/dm³)：质量浓度 = 质量 (g) / 体积 (dm³)。与 mol/dm³ 的关系为：质量浓度 = c × Mᵣ。
To prepare a standard solution, accurately weigh the solid, dissolve in water, and make up to a known volume in a volumetric flask.
配制标准溶液时，准确称取固体，溶于水后转移至容量瓶中定容。
Common indicators and their colour changes are not formula-based but are essential for practical work (e.g., methyl orange: red in acid, yellow in alkali).
常用指示剂及其颜色变化虽非公式，却是实验操作的基础（如甲基橙：酸性中呈红色，碱性中呈黄色）。
c = n / V ; c₁V₁ = c₂V₂ (for 1:1 ratios)
7. Gas Volumes | 气体体积
At room temperature and pressure (RTP), one mole of any gas occupies 24 dm³. This makes it straightforward to link gas volume to moles in chemical reactions.
在室温和常压 (RTP) 下，1 摩尔任何气体占据 24 dm³ 的体积。这使得在化学反应中将气体体积与摩尔数关联起来非常简单。
Volume of gas at RTP: volume (dm³) = number of moles × 24. This holds for reactions involving gases only.
RTP 下气体体积：体积 (dm³) = 摩尔数 × 24。此关系适用于涉及气体的反应。
ert between cm³ and dm³, remember 1 dm³ = 1000 cm³. Always check the unit in the question.
在 cm³ 与 dm³ 之间转换时，记住 1 dm³ = 1000 cm³。一定要检查题目中的单位。
Combining the mole formula and gas volume, volume = (mass / Mᵣ) × 24 gives a direct route from mass to gas volume.
结合摩尔公式和气体体积公式，体积 = (质量 / Mᵣ) × 24 可直接从质量求得气体体积。
In reactions producing gases, you can compare volumes directly using the mole ratios from the balanced equation, as volume is proportional to moles.
在产生气体的反应中，可直接利用配平方程式中的摩尔比来比较体积，因为体积与摩尔数成正比。
RTP (20 °C, 1 atm). If conditions change, the ideal gas equation PV = nRT would be used (A‑level content).
该关系仅在 RTP（20 °C，1 atm）下成立。若条件改变，需使用理想气体方程 PV = nRT（属于 A‑level 内容）。
Volume (dm³) = n × 24 ; Volume = (m / Mᵣ) × 24
8. Biology – Magnification | 生物 — 放大倍数
In microscopy, magnification describes how much larger an image appears compared to the actual specimen. The formula is simple yet examiners frequently test it by asking to convert units.
在显微镜使用中，放大倍数描述了图像相比实际标本放大了多少。公式虽然简单，但考官常通过单位换算来考查。
Magnification = image size ÷ actual size. M = I / A. Both image and actual size must be in the same units.
放大倍数 = 图像大小 ÷ 实际大小。M = I / A。图像大小和实际大小必须使用相同单位。
Rearrange to find actual size: A = I / M. This is common when a scale bar is given on a micrograph.
整理可得实际大小：A = I / M。当显微照片给出比例尺时，常用此式计算。
1 mm = 1000 µm; 1 µ e same unit before calculating. Writing all values in micrometres often prevents mistakes.
1 mm = 1000 µm；1 µm = 1000 nm。务必先统一单位再计算。将所有数值写成以微米为单位可避免出错。
agnification of a microscope = eyepiece lens magnification × objective lens magnification.
显微镜的总放大倍数 = 目镜放大倍数 × 物镜放大倍数。
When drawing biological diagrams, the drawing magnification should match your calculation; a clear scale is essential.
绘制生物图时，绘图放大倍数应与计算一致；清晰的标尺必不可少。
M = I / A ; A = I / M
9. Biology – Photosynthesis and Respiration | 生物 — 光合作用与呼吸作用
While there is no single 'equation' to recall for respiration in formula terms, the word and symbol summaries are vital. Photosynthesis and respiration are reverse processes that drive ecosystems.
尽管呼吸作用没有单一的“公式”式方程，但其文字概括和符号式总结至关重要。光合作用与呼吸作用是一对相反的过程，驱动着生态系统。
tion: carbon dioxide + water → glucose + oxygen, in the presence of light and chlorophyll.
光合作用的文字表达式：二氧化碳 + 水 → 葡萄糖 + 氧气，需要光和叶绿素。
Balanced symbol equation for photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂.
光合作用的平衡符号方程式：6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂。
tion word equation: glucose + oxygen → carbon dioxide + water (+ energy). Symbol equation: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O.
有氧呼吸的文字表达式：葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）。符号方程式：C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O。
ose → lactic acid. In yeast and plants: glucose → ethanol + carbon dioxide (fermentation).
动物体内的无氧呼吸：葡萄糖 → 乳酸。酵母和植物中：葡萄糖 → 乙醇 + 二氧化碳（发酵）。
Oxygen debt refers to the extra oxygen needed after exercise to oxidise lactic acid. Related concept: EPOC (excess post‑exercise oxygen consumption).
氧债指运动后需额外摄入氧气以氧化乳酸。相关概念：运动后过量氧耗 (EPOC)。
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ ; C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
10. Biology – Enzyme Activity and Health | 生物 — 酶活性与健康
Rates of enzyme‑controlled reactions are influenced by temperature, pH, and substrate concentration. Health indicators like BMI also rely on simple formulas.
酶控反应速率受温度、pH 和底物浓度的影响。像 BMI 这样的健康指标同样依赖简单公式。
e or product concentration / time. Often measured as 1/t when the time for a visible change is recorded.
反应速率 = 底物或产物浓度的变化 ÷ 时间。当记录可见变化所需时间时，常用 1/t 来计量。
Optimum temperature: enzymes work fastest at their optimum; above this, they denature and activity falls to zero.
最适温度：在各自的最适温度下酶活性最高；高于此温度酶会变性，活性降为零。
The lock‑and‑key model explains enzyme specificity. The activation energy is lowered, increasing reaction rate.
锁钥模型解释了酶的专一性。活化能降低，从而加快反应速率。
Body Mass Index (BMI) = mass (kg) / (height in m)². BMI = m / h². It is used to classify underweight, normal, overweight, and obese.
身体质量指数 (BMI) = 体重 (kg) / 身高 (m) 的平方。BMI = m / h²。用于划分体重不足、正常、超重和肥胖。
Waist‑to‑hip ratio is another health indicator, but the formula that is most tested is BMI.
腰臀比是另一健康指标，但最常考查的公式是 BMI。
Rate of reaction = 1 / t ; BMI = m / h²
11. Common Scientific Laws and Principles | 常见科学定律与原理
Several overarching laws and principles appear across topics. These are not always expressed as formulas but are fundamental to understanding and application.
有几条贯穿各专题的普遍定律和原理。它们并非总是以公式形式出现，但对理解和应用至关重要。
Conservation of energy: energy cannot be created or destroyed, only transferred between stores. This underpins all energy calculations.
能量守恒定律：能量不能被创造或消灭，只能在储存间转移。这是所有能量计算的基础。
Conservation of mass: in a chemical reaction, the total mass of products equals total mass of reactants. Used in balancing equations and calculating yields.
质量守恒定律：化学反应中，产物的总质量等于反应物的总质量。用于配平方程和计算产率。
Le Chatelier’s principle (higher tier): if a dynamic equilibrium is disturbed, the position of equilibrium shifts to counteract the change. Important for reversible reactions and the Haber process.
勒夏特列原理（高阶段）：若动态平衡受到扰动，平衡位置会移动以抵消该变化。对可逆反应和哈伯法很重要。
hysics): for a system in equilibrium, total clockwise moment = total anticlockwise moment. F₁ d₁ = F₂ d₂.
力矩原理（物理）：系统平衡时，顺时针力矩总和 = 逆时针力矩总和。F₁ d₁ = F₂ d₂。
Hooke’s law: extension of a spring is directly proportional to force applied, provided the limit of proportionality is not exceeded. F = k e.
胡克定律：弹簧的伸长量与施加的力成正比，前提是不超过比例极限。F = k e。
F = k e ; F₁ d₁ = F₂ d₂
12. Quick Reference Table of Units | 单位速查表
Correct use of SI units and their conversions is vital in calculations. The table below summarises the most common quantities and their units for OCR Science.
正确使用国际单位制及其换算对于计算至关重要。下表总结了 OCR 科学中最常见的量及其单位。
| Quantity 量 | Symbol 符号 | Unit 单位 | Common conversion 常用换算 |
| Mass 质量 | m | kg, g | 1 kg = 1000 g |
| Distance/Displacement 距离/位移 | d, s | m | 1 km = 1000 m |
| Time 时间 | t | s | 1 min = 60 s |
| Force 力 | F | N | — |
| Energy/Work 能量/功 | E, W | J | 1 kJ = 1000 J |
| Power 功率 | P | W | 1 kW = 1000 W |
| Charge 电荷 | Q | C | — |
| Potential difference 电位差 | V | V | — |
| Resistance 电阻 | R | Ω | — |
| Amount of substance 物质的量 | n | mol | — |
| Concentration 浓度 | c | mol/dm³ | 1 dm³ = 1000 cm³ |
| Gas volume 气体体积 | V | dm³ | 1 dm³ = 1000 cm³ |
ts. Use standard form for very large or very small numbers, e.g., 3.0 × 10⁸ not 300000000.
务必确保最终答案的单位与题目要求一致。对于极大或极小的数字请使用科学记数法，如 3.0 × 10⁸ 而非 300000000。
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