📚 Year 11 CCEA Science: Quick Reference Formula & Theorem Handbook | Year 11 CCEA 科学：公式定理速查手册
This handbook is designed to give Year 11 CCEA Science students a rapid overview of the essential formulae, equations and key principles required for success in the double award or single award science examinations. Covering physics, chemistry and biology, it presents each relationship in a clear, standard notation, together with the units and the typical contexts in which it is applied. Use it as a daily revision card, a pre‑exam checklist or a structure for self‑testing – the bilingual format helps you nail both the English terminology and the conceptual understanding behind each equation.
本手册专为 Year 11 CCEA 科学课程的学生编写，旨在快速梳理双奖或单奖考试中不可或缺的公式、方程和核心定理。手册涵盖物理、化学和生物三个学科，以清晰的符号体系呈现每一个等量关系，同时注明单位及常见应用情境。你可以把它当作每日复习卡片、考前清单或自测提纲——中英双语的设计不仅能帮你掌握英文术语，更能加深对每个公式背后概念的理解。
1. Motion, Forces and Newton's Laws | 运动、力与牛顿定律
Speed is the rate of change of distance, and velocity is the rate of change of displacement in a given direction.
速率是距离随时间的变化率，速度则是给定方向上位移随时间的变化率。
average speed = total distance ÷ time taken (v = d/t) – unit: m/s
平均速率 = 总距离 ÷ 所用时间 (v = d/t) – 单位：m/s
acceleration = change in velocity ÷ time taken (a = Δv / t) – unit: m/s²
加速度 = 速度变化量 ÷ 所用时间 (a = Δv / t) – 单位：m/s²
final velocity of a uniformly accelerating object: v = u + at, where u is initial velocity
匀加速直线运动的末速度：v = u + at，其中 u 为初速度
distance travelled under uniform acceleration: s = ut + ½at²
匀加速运动的位移：s = ut + ½at²
Newton's second law: resultant force = mass × acceleration (F = ma) – unit: newton (N) or kg·m/s²
牛顿第二定律：合力 = 质量 × 加速度 (F = ma) – 单位：牛 (N) 或 kg·m/s²
weight = mass × gravitational field strength (W = mg) – on Earth g ≈ 9.8 N/kg, often rounded to 10 N/kg
重量 = 质量 × 重力场强 (W = mg) – 地球上 g ≈ 9.8 N/kg，常取 10 N/kg
stopping distance = thinking distance + braking distance
停车距离 = 思维反应距离 + 制动距离
momentum = mass × velocity (p = mv) – unit: kg·m/s
动量 = 质量 × 速度 (p = mv) – 单位：kg·m/s
fore collision = total momentum after collision, provided no external resultant force acts
动量守恒：若无外合力作用，碰撞前的总动量 = 碰撞后的总动量
2. Energy, Work and Power | 能量、功与功率
Energy is measured in joules (J) and can be stored in different forms; work is done when a force moves an object through a distance.
能量以焦耳 (J) 为单位，能以多种形式储存；力使物体位移时做“功”。
work done = force × distance moved in the direction of the force (W = F × d) – unit: J
做功 = 力 × 沿力方向移动的距离 (W = F × d) – 单位：J
gravitational potential energy: GPE = mass × g × height (Ep = mgh) – unit: J
重力势能：GPE = 质量 × g × 高度 (Ep = mgh) – 单位：J
kinetic energy: KE = ½ × mass × speed² (Ek = ½mv²) – unit: J
动能：KE = ½ × 质量 × 速度² (Ek = ½mv²) – 单位：J
elastic potential energy: Ee = ½ × spring constant × extension² (Ee = ½kx²) – extension in metres
弹性势能：Ee = ½ × 弹性常数 × 伸长量² (Ee = ½kx²) – 伸长量单位 m
power = work done ÷ time taken = energy transferred ÷ time (P = W/t) – unit: watt (W) or J/s
功率 = 做功 ÷ 时间 = 转移的能量 ÷ 时间 (P = W/t) – 单位：瓦特 (W) 或 J/s
efficiency = useful output energy transfer ÷ total input energy transfer (× 100% for percentage)
效率 = 有用输出能量 ÷ 总输入能量 (乘 100% 得百分数)
wasted energy = total input energy – useful output energy; energy is always dissipated to the thermal store of the surroundings
浪费的能量 = 总输入能量 – 有用输出能量；能量总是向周围环境的热储库耗散
conservation of energy: energy cannot be created or destroyed, only transferred, stored or dissipated
能量守恒：能量不能被创造或消灭，只能被转移、储存或耗散
3. Electricity: Charge, Current, Resistance and Power | 电学：电荷、电流、电阻与电功率
Electric circuits obey a set of measurable relationships; knowing the correct equation to use for series or parallel circuits is key.
电路遵循一系列可测量的关系；区分串联与并联电路时选对公式至关重要。
charge = current × time (Q = It) – unit: coulomb (C), where current I is in amperes (A), time t in seconds (s)
电荷量 = 电流 × 时间 (Q = It) – 单位：库仑 (C)，电流单位为安培 (A)，时间单位为秒 (s)
potential difference = current × resistance (V = IR) – Ohm's law for a fixed metal conductor at constant temperature
电压 = 电流 × 电阻 (V = IR) – 恒温下固定金属导体的欧姆定律
resistance = voltage ÷ current (R = V/I) – unit: ohm (Ω)
电阻 = 电压 ÷ 电流 (R = V/I) – 单位：欧姆 (Ω)
in a series circuit: total resistance Rtotal = R₁ + R₂ + R₃ + ... – current is the same everywhere; voltage splits across components
串联电路：总电阻 Rtotal = R₁ + R₂ + R₃ + … 各处电流相等；电压在各元件间分配
in a parallel circuit: 1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + ... – voltage is the same across each branch; current splits between branches
并联电路：1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + … 各支路两端电压相等；电流在支路间分割
electrical power: P = I × V (current × voltage), also P = I²R and P = V²/R – unit: watt (W)
电功率：P = I × V (电流 × 电压)，也可用 P = I²R 及 P = V²/R – 单位：瓦特 (W)
energy transferred in a circuit: E = P × t = I × V × t – unit: joule (J)
电路中转移的能量：E = P × t = I × V × t – 单位：焦耳 (J)
kilowatt‑ s used for domestic electricity: energy (kWh) = power (kW) × time (h); 1 kWh = 3.6 × 10⁶ J
家庭用电以千瓦时 (kWh) 为单位：能量 (kWh) = 功率 (kW) × 时间 (h)；1 kWh = 3.6 × 10⁶ J
4. Waves: Speed, Frequency and Wavelength | 波：波速、频率与波长
The wave equation links the physical properties of any periodic wave, from sound to electromagnetic radiation.
波动方程将任何周期波（从声波到电磁波）的物理属性联系在一起。
wave speed = frequency × wavelength (v = f λ) – unit: m/s
波速 = 频率 × 波长 (v = f λ) – 单位：m/s
frequency = 1 ÷ time period (f = 1/T) – unit: hertz (Hz), period T in seconds (s)
频率 = 1 ÷ 周期 (f = 1/T) – 单位：赫兹 (Hz)，周期 T 单位秒 (s)
refractive index n = speed of light in vacuum ÷ speed of light in medium (n = c/v)
折射率 n = 真空中光速 ÷ 介质中光速 (n = c/v)
for electromagnetic waves in a vacuum, v = c ≈ 3.00 × 10⁸ m/s
真空中电磁波的波速 v = c ≈ 3.00 × 10⁸ m/s
in a transverse wave, oscillations are perpendicular to the direction of energy transfer; in a longitudinal wave, they are parallel
横波中振动方向与能量传递方向垂直；纵波中两者平行
angle of incidence = angle of reflection (law of reflection)
入射角 = 反射角（反射定律）
Snell's law: n₁ sin θ₁ = n₂ sin θ₂, where θ₁ and θ₂ are measured from the normal
斯涅尔定律：n₁ sin θ₁ = n₂ sin θ₂，其中角度从法线量起
5. Radioactivity and Half-Life | 放射性与半衰期
Radioactive decay is a random process, but the half‑life provides a statistical measure of its speed.
放射性衰变是一个随机过程，但半衰期提供了衡量其快慢的统计指标。
activity is the number of decays per second, measured in becquerels (Bq)
放射性活度是每秒衰变次数，单位：贝克勒尔 (Bq)
half‑life is the time taken for the activity (or number of radioactive nuclei) to fall to half its initial value
半衰期是指活度（或放射性核的数量）降至初始值一半所需的时间
after n half‑lives, remaining fraction = (½)ⁿ
经过 n 个半衰期后，剩余比例 = (½)ⁿ
background radiation must be subtracted from measured count rate to obtain the corrected count rate
必须从测量计数率中扣除本底辐射，以得到修正计数率
umber (bottom): for alpha decay ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He; for beta decay ¹⁴₆C → ¹⁴₇N + ⁰₋₁e
核衰变方程中质量数（上标）和原子序数（下标）守恒：α 衰变 ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He；β 衰变 ¹⁴₆C → ¹⁴₇N + ⁰₋₁e
6. Chemical Quantities: The Mole | 化学计量：摩尔
The mole is the bridge between the laboratory scale (grams) and the atomic scale (formula units).
摩尔是连接实验室尺度（克）与原子尺度（化学式单元）的桥梁。
number of moles = mass (g) ÷ molar mass (g/mol): n = m / M
摩尔数 = 质量 (g) ÷ 摩尔质量 (g/mol)：n = m / M
concentration (mol/dm³) = number of moles ÷ volume (dm³): c = n / V
浓度 (mol/dm³) = 摩尔数 ÷ 体积 (dm³)：c = n / V
mass (g) = moles × molar mass; also mass = concentration × volume × molar mass
质量 (g) = 摩尔数 × 摩尔质量；亦可写作 质量 = 浓度 × 体积 × 摩尔质量
for gases at room temperature and pressure (RTP), 1 mole of any gas occupies 24 dm³; at standard temperature and pressure (STP, 0 °C, 1 atm) the molar volume is 22.4 dm³. CCEA normally uses 24 dm³ at 20 °C and 1 atm.
在室温常压 (RTP) 下，1 摩尔任何气体的体积为 24 dm³；CCEA 通常使用 20 °C、1 atm 下的 24 dm³。
volume of gas (dm³) = moles × 24 (at RTP)
气体体积 (dm³) = 摩尔数 × 24（在 RTP 下）
number of particles = moles × Avogadro's number (6.02 × 10²³ mol⁻¹)
粒子数 = 摩尔数 × 阿伏伽德罗常数 (6.02 × 10²³ mol⁻¹)
using balanced equations, the molar ratio of reactants and products is given by the coefficients
根据配平的化学方程式，反应物与生成物的摩尔比由系数给出
7. Rates of Reaction | 反应速率
The rate of a chemical reaction can be measured by the speed at which a reactant is used up or a product is formed.
化学反应的速率可通过反应物消耗或生成物形成的快慢来衡量。
mean rate of reaction = change in quantity of reactant or product ÷ time taken
平均反应速率 = 反应物或生成物量的变化 ÷ 所用时间
units can be g/s (for mass loss), cm³/s (for volume of gas produced) or mol/dm³/s when monitoring concentration
单位可为 g/s（质量减少）、cm³/s（产生气体的体积）或 mol/dm³/s（监测浓度变化时）
collision theory: particles must collide with sufficient energy (activation energy) and the correct orientation for a reaction to occur
碰撞理论：粒子必须发生碰撞，且能量大于等于活化能、取向正确，反应才会发生
rates increase with higher concentration, pressure (gases), surface area (solids) and temperature, because these factors increase the frequency of successful collisions
增大浓度、压强（气体）、固体表面积和温度都能提高速率，因为这些因素增加了有效碰撞的频率
a catalyst provides an alternative reaction pathway with a lower activation energy; it is chemically unchanged at the end of the reaction
催化剂提供活化能较低的另一反应途径，反应结束时催化剂化学性质不变
8. Acids, Bases and Titrations | 酸、碱与滴定
Stoichiometric calculations are essential for working out the concentration of an unknown solution from a titration.
化学计量计算对于通过滴定求算未知溶液浓度至关重要。
ic, pH 7 = neutral, pH greater than 7 = alkaline. A change of one pH unit represents a ten‑fold change in H⁺ concentration.
pH 标度：pH ＜ 7 为酸性，pH = 7 为中性，pH ＞ 7 为碱性。pH 每变化 1 个单位，H⁺ 浓度变化 10 倍。
tion reaction: acid + base → salt + water; the ionic equation is H⁺(aq) + OH⁻(aq) → H₂O(l)
中和反应：酸 + 碱 → 盐 + 水；离子方程式为 H⁺(aq) + OH⁻(aq) → H₂O(l)
in mol/dm³ and V is volume in dm³ (or use consistent units, e.g., cm³ if the ratio is 1:1)
一元酸与一元碱按 1:1 反应时的滴定公式：M₁V₁ = M₂V₂，M 为浓度 (mol/dm³)，V 为体积 (dm³)（若比例 1:1，可直接使用 cm³，单位一致即可）
equation ratio to find moles of alkali, then calculate its concentration = moles ÷ volume
通用方法：酸的摩尔数 = 酸的浓度 × 体积；由配平方程式的系数比求出碱的摩尔数，再计算碱的浓度 = 摩尔数 ÷ 体积
for reactions producing a gas or precipitate: mass of product can be calculated from the limiting reactant using moles and molar mass
对于产生气体或沉淀的反应：可通过限制反应物的摩尔数和摩尔质量计算产物的质量
9. Bond Energies and Energy Change | 键能与能量变化
Every chemical reaction involves bond breaking (endothermic) and bond making (exothermic); the overall enthalpy change tells us whether the reaction is exothermic or endothermic.
每一个化学反应都包含断键（吸热）和成键（放热）；总的焓变表明反应是放热还是吸热。
bond energy is the energy required to break one mole of a particular covalent bond, measured in kJ/mol
键能指断裂 1 摩尔某种共价键所需的能量，单位为 kJ/mol
overall energy change = sum of bond energies of bonds broken – sum of bond energies of bonds formed
总的能量变化 = 断裂的所有键的键能总和 – 形成的所有键的键能总和
exothermic reactions release energy to the surroundings (temperature rises, ΔH negative); endothermic reactions absorb energy (temperature falls, ΔH positive)
放热反应向周围释放能量（温度升高，ΔH 为负）；吸热反应吸收能量（温度降低，ΔH 为正）
activation energy is the minimum energy colliding particles must have for a reaction to occur; it is represented on an energy profile diagram
活化能是碰撞粒子必须具有的最低能量，反映在能量变化曲线图中
10. Biology – Microscopy and Magnification | 生物学 – 显微镜与放大倍数
Understanding scale in biology relies on the magnification equation, which links image size, actual size and the magnification of the instrument.
理解生物学中的尺度离不开放大倍数公式，它连接了图像大小、实际大小与仪器放大倍数。
magnification = size of image ÷ size of real object (M = I/A)
放大倍数 = 图像大小 ÷ 实际物体大小 (M = I/A)
both image size and actual size must be in the same unit; common conversions: 1 mm = 1000 µm, 1 µm = 1000 nm
图像大小和实际大小须使用相同单位；常用换算：1 mm = 1000 µm，1 µm = 1000 nm
rearrange to find actual size: A = I / M
变形求实际大小：A = I / M
magnification of a microscope = eyepiece lens magnification × objective lens magnification
显微镜总放大倍数 = 目镜放大倍数 × 物镜放大倍数
11. Biology – Body Mass Index and Energy in Food | 生物学 – 体重指数与食物能量
Quantitative human biology includes BMI calculations and the determination of energy content in foods.
定量人体生物学包括体重指数 (BMI) 的计算以及食物中能量含量的测定。
BMI = mass (kg) ÷ (height (m))²
BMI = 体重 (kg) ÷ 身高 (m)²
BMI categories: below 18.5 underweight, 18.5–24.9 healthy weight, 25–29.9 overweight, 30 and above obese
BMI 分类：＜18.5 过轻，18.5–24.9 正常体重，25–29.9 超重，≥30 肥胖
d burnt × 1000) for a calorimetry experiment; 4.2 J is the specific heat capacity of water
食物样品能量含量 (kJ/g) = (水的质量 × 4.2 J/g/°C × 温升) ÷ (燃烧的食物质量 × 1000) 适用于量热实验；4.2 J 是水的比热容
basal metabolic rate (BMR) estimates vary with age, gender and mass, but the general idea is that energy intake minus energy expended determines weight change.
基础代谢率 (BMR) 估算随年龄、性别和体重而异，但总体概念是能量摄入减去能量消耗决定体重变化。
12. Biology – Ecosystems and Energy Transfer | 生物学 – 生态系统与能量传递
The efficiency of energy transfer between trophic levels limits the length of food chains and the biomass available at each level.
营养级之间能量传递的效率限制了食物链的长度和每一级的生物量。
iomass transfer = (biomass in higher trophic level ÷ biomass in lower trophic level) × 100%
生物量传递效率 = (较高营养级的生物量 ÷ 较低营养级的生物量) × 100%
efficiency of energy transfer can be calculated similarly using energy values (kJ per m² per year)
能量传递效率可类似地用能量值 (kJ/m²/年) 计算
around 10% of the energy is typically transferred from one trophic level to the next; the rest is lost as heat through respiration, as waste, or in uneaten parts
通常约 10% 的能量从一个营养级传递到下一营养级；其余能量通过呼吸以热的形式散失、成为废物或未被食用
pyramids of biomass and pyramids of energy can both be used to represent feeding relationships; pyramids of energy are always upright
生物量金字塔和能量金字塔均可表示取食关系；能量金字塔总是正立的
nergy and chlorophyll needed); the balanced symbol equation is 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
光合作用文字方程式：二氧化碳 + 水 → 葡萄糖 + 氧气（需要光能和叶绿素）；配平的符号方程式为 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
glucose + oxygen → carbon dioxide + water (+ energy released); C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
有氧呼吸：葡萄糖 + 氧气 → 二氧化碳 + 水（+ 释放的能量）；C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
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