📚 Year 13 CCEA Science: Formula & Theorem Quick Reference Handbook | Year 13 CCEA 科学：公式定理速查手册
This comprehensive quick‑reference handbook covers the essential formulas, theorems and definitions required for Year 13 CCEA AS Physics, Chemistry and Biology. Each section is structured to provide paired English and Chinese explanations, helping you to locate key content rapidly during revision or while tackling past‑paper problems. Use the clear tables, bullet points and centred equations to master the mathematical and conceptual backbone of the CCEA Science specifications.
这本综合性的速查手册涵盖了 Year 13 CCEA AS 物理、化学和生物所需的核心公式、定理与定义。每个小节都采用中英对照的形式，便于你在复习或刷题时快速定位关键内容。借助清晰的表格、要点列表和居中排版的方程式，你能轻松掌握 CCEA 科学大纲背后的数学与概念支柱。
1. Mechanics: Kinematics & Dynamics | 力学：运动学与动力学
The equations of motion apply to objects moving with constant acceleration along a straight line. They link initial velocity u, final velocity v, acceleration a, displacement s and time t. Newton's three laws form the foundation of classical dynamics.
运动学方程适用于沿直线做匀加速运动的物体。它们将初速度 u、末速度 v、加速度 a、位移 s 和时间 t 联系在一起。牛顿三定律构成了经典动力学的基础。
v = u + at s = ut + ½at² v² = u² + 2as
F = ma W = mg
- Momentum p = mv mentum before collision = total momentum after collision, provided no external forces act. | 动量 p = mv；动量守恒定律：若无外力作用，碰撞前总动量 = 碰撞后总动量。
- Impulse F∆t = ∆(mv); area under a force–time graph. | 冲量 F∆t = ∆(mv)；力–时间图下的面积。
2. Mechanics: Work, Energy & Power | 力学：功、能量与功率
The work–energy theorem states that the net work done on an object equals its change in kinetic energy. Gravitational potential energy and elastic potential energy are both forms of stored mechanical energy.
功能原理指出，合力对物体做的功等于其动能的变化量。重力势能和弹性势能都是储存的机械能形式。
W = Fs cos θ K.E. = ½mv² ΔK.E. = Wnet
G.P.E. = mgh E.P.E. = ½k(Δx)²
Power is the rate of doing work or transferring energy. Efficiency compares useful output to total input. | 功率是做功或传递能量的速率。效率用于比较有用输出与总输入。
P = W / t = Fv Efficiency = (useful power output) / (total power input) × 100%
3. Waves: Properties & The Wave Equation | 波动：性质与波动方程
All waves transfer energy without net transfer of matter. The wave equation relates speed v, frequency f and wavelength λ. Phase difference and path difference are crucial when describing interference and standing waves.
所有波传递能量而不净传递物质。波动方程联系了波速 v、频率 f 和波长 λ。相位差和波程差在描述干涉和驻波时至关重要。
v = fλ T = 1/f
- Refractive index n = c / v = sin i / sin r (Snell's law). Critical angle: sin C = 1/n (when light travels from denser to less dense medium). | 折射率 n = c / v = sin i / sin r（斯涅尔定律）。临界角：sin C = 1/n（光从光密介质射向光疏介质时）。
- Double‑slit fringe spacing: Δy = λD / d, where d is slit separation, D is distance to screen. | 双缝条纹间距：Δy = λD / d，其中 d 为缝间距，D 为屏距。
- Diffraction grating: nλ = d sin θ for n‑th order maximum. | 衍射光栅：第 n 级明纹满足 nλ = d sin θ。
4. Electricity: Circuits, Resistance & EMF | 电学：电路、电阻与电动势
Ohm's law defines resistance as the ratio of potential difference to current for an ohmic conductor at constant temperature. Kirchhoff's laws govern current and voltage in complex circuits.
欧姆定律定义了在恒定温度下，欧姆导体的电阻等于电势差与电流之比。基尔霍夫定律支配复杂电路中的电流与电压。
V = IR P = IV = I²R = V²/R
- Resistors in series: Rtotal = R₁ + R₂ + .... In parallel: 1/Rtotal = 1/R₁ + 1/R₂ + .... | 电阻串联：Rₜₒₜₐₗ = R₁ + R₂ + …。并联：1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + …。
- EMF (ε) and internal resistance (r): ε = I(R + r) and terminal p.d. V = ε − Ir. | 电动势 (ε) 与内阻 (r)：ε = I(R + r)，路端电压 V = ε − Ir。
- Potential divider: Vout = Vin × (R₂ / (R₁ + R₂)). | 分压器：Vₒᵤₜ = Vₗₙ × (R₂ / (R₁ + R₂))。
5. Physics: Thermal Physics & Gases | 物理：热学与气体
The kinetic theory of gases links macroscopic properties (pressure, volume, temperature) to microscopic behaviour of particles. The ideal gas equation and the Boltzmann constant are central to this topic.
气体动理论将宏观性质（压强、体积、温度）与粒子的微观行为联系起来。理想气体状态方程和玻尔兹曼常数是这一部分的核心。
pV = nRT pV = NkT k = R / NA
pV = ⅓ N m (crms)² Average K.E. per molecule = ³⁄₂ kT
Specific heat capacity and specific latent heat are required for energy calculations during heating and phase changes. | 在加热和相变能量计算中需要用到比热容和比潜热。
Q = mcΔθ Q = ml
6. Physical Chemistry: Quantitative & Energetics | 物理化学：定量化学与能量学
Stoichiometric calculations rely on the mole concept. The molar volume of a gas at room temperature and pressure (RTP) is taken as 24 dm³ mol⁻¹ (or an appropriate value given in the exam). Enthalpy changes are measured using calorimetry and Hess's law.
化学计量计算建立在物质的量概念上。常温常压 (RTP) 下气体的摩尔体积取 24 dm³ mol⁻¹（或试题给定值）。焓变通过量热法和赫斯定律来测定。
n = m / M n = V / Vm Concentration = n / V (mol dm⁻³)
q = mcΔT ΔH = − q / n
Hess's law: the total enthalpy change for a reaction is independent of the route taken. It allows the use of enthalpy cycles. | 赫斯定律：反应的总焓变与途径无关。可利用焓变循环进行计算。
| Standard enthalpy of formation (ΔHf°) | 标准生成焓 | ΔH = ΣΔHf°(products) − ΣΔHf°(reactants) |
| Standard enthalpy of combustion (ΔHc°) | 标准燃烧焓 | ΔH = ΣΔHc°(reactants) − ΣΔHc°(products) |
7. Chemical Equilibria & Acids‑Bases | 化学平衡与酸碱
The equilibrium constant Kc expresses the ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficients, at equilibrium. For gaseous systems, Kp uses partial pressures.
平衡常数 Kc 表示平衡时产物浓度与反应物浓度的比值，各自升以其化学计量系数为幂。对气体体系，Kp 采用分压。
aA + bB ⇌ cC + dD Kc = [C]ᶜ[D]ᵈ / ([A]ᵃ[B]ᵇ)
Le Chatelier's principle predicts the direction of shift when a system at equilibrium is subjected to a change in concentration, pressure or temperature. | 勒夏特列原理可预测平衡体系在浓度、压强或温度改变时的移动方向。
For acids and bases, pH is a logarithmic measure of hydrogen ion concentration. The ionic product of water Kw is temperature dependent. | 对酸碱而言，pH 是氢离子浓度的对数度量。水的离子积 Kw 随温度变化。
pH = −log₁₀[H⁺] [H⁺] = 10⁻ᵖᴴ pOH = −log₁₀[OH⁻] pH + pOH = 14 (at 25 °C)
Kₐ = [H⁺][A⁻] / [HA] Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ (at 25 °C)
8. Organic Chemistry: Key Formulae & Mechanisms | 有机化学：关键公式与机理
Organic reactions are best understood through their functional groups, reaction conditions and mechanisms. General molecular formulae for homologous series are essential for systematic naming.
理解有机反应的最好方式是通过其官能团、反应条件和机理。同系物的通式对系统命名至关重要。
- Alkanes: CₙH₂ₙ₊₂ Alkenes: CₙH₂ₙ Alcohols: CₙH₂ₙ₊₁OH | 烷烃、烯烃、醇
- Halogenoalkanes: CₙH₂ₙ₊₁X Carboxylic acids: CₙH₂ₙO₂ | 卤代烷、羧酸
- Percentage yield = (actual yield / theoretical yield) × 100% tom economy = (molar mass of desired product / sum of molar masses of all reactants) × 100% | 产率与原子经济性
Structural isomerism and stereoisomerism (E‑Z, optical) are explained using Cahn‑Ingold‑Prelog rules and chiral centres. | 结构异构和立体异构（E‑Z 异构、旋光异构）用 Cahn‑Ingold‑Prelog 规则和手性中心解释。
9. Biology: Cell Structure & Biological Molecules | 生物学：细胞结构与生物分子
The magnification formula and the relationship between actual size, image size and magnification are fundamental in microscopy. The surface area to volume ratio explains limits on cell size and adaptations for transport.
放大倍数公式以及实际大小、图像大小与放大率之间的关系是显微镜术的基础。表面积与体积比解释了细胞尺寸的限制及其在物质运输中的适应。
Magnification = Image size / Actual size SA:V ratio limits cell dimensions
Key biological molecules are polymers made from monomers. Condensation and hydrolysis reactions build and break these polymers. | 重要的生物分子是由单体构成的聚合物。缩合反应与水解反应分别构建和分解这些聚合物。
| Carbohydrates | Monosaccharides → disaccharides → polysaccharides. Glycosidic bonds. | 糖类：单糖→二糖→多糖，糖苷键。 |
| Proteins | Amino acids joined by peptide bonds; primary, secondary (α‑helix, β‑pleated sheet), tertiary and quaternary structure. | 蛋白质：氨基酸通过肽键连接；一、二、三、四级结构。 |
| Lipids | Triglycerides (glycerol + 3 fatty acids) joined by ester bonds. Phospholipids form bilayer membranes. | 脂类：甘油三酯（甘油+3脂肪酸），酯键。磷脂形成双分子层膜。 |
| Nucleic acids | DNA and RNA nucleotides linked by phosphodiester bonds. Semi‑conservative replication. | 核酸：DNA和RNA核苷酸通过磷酸二酯键连接。半保留复制。 |
10. Biology: Genetics & Populations | 生物学：遗传学与种群
Monohybrid and dihybrid crosses use Punnett squares to predict offspring genotypes and phenotypes. The Hardy–Weinberg principle provides a mathematical model for allele frequencies in a large, randomly mating population.
单因子和双因子杂交用旁氏棋盘格预测后代表现型和基因型。哈迪‑温伯格定律为大型随机交配种群中的等位基因频率提供了数学模型。
p + q = 1 p² + 2pq + q² = 1
- mptions: no mutation, no migration, large population, random mating, no natural selection. | p = 显性等位基因频率，q = 隐性等位基因频率。前提：无突变、无迁移、大种群、随机交配、无自然选择。
- Chi‑squared test: χ² = Σ (O − E)² / E, used to compare observed and expected frequencies and to test the goodness of fit. | 卡方检验：χ² = Σ (O − E)² / E，用于比较观测频率与期望频率并检验拟合优度。
- Allele frequency change over generations can be caused by natural selection, genetic drift and the founder effect. | 等位基因频率的逐代变化可由自然选择、遗传漂变和奠基者效应引起。
11. Data Handling & Mathematical Skills for Science | 科学数据处理与数学技能
Across all three sciences, students must be able to manipulate equations, convert units, construct and interpret graphs, and evaluate uncertainties. These cross‑curricular skills are tested in CCEA examination papers.
在三门科学课中，学生都必须具备变换方程、换算单位、构建和解读图表以及评估不确定性的能力。这些跨学科技能在 CCEA 试卷中均会考查。
Mean = Σx / n Range = max − min
- Percentage uncertainty = (absolute uncertainty / measured value) × 100%. Always quote uncertainties to 1 significant figure and match decimal places. | 百分数不确定度 = (绝对不确定度 / 测量值) × 100%。不确定度只保留一位有效数字并匹配小数位数。
- /Δx, area under the curve often represents a physical quantity (impulse, work done, etc.). | 图线：斜率 = Δy/Δx，曲线下面积常代表某个物理量（冲量、功等）。
- Logarithms: for exponential processes, plotting log (or ln) against time yields a straight line. Used in radioactive decay and bacterial growth. | 对数：对指数过程，以对数（或自然对数）对时间作图可得直线。用于放射性衰变和细菌生长。
12. Quick Reference Tables: Key Unit Conversions & Prefixes | 速查表：关键单位换算与词头
Fluent use of SI units and standard prefixes accelerates problem‑solving. The following table collects the most common conversions encountered at AS level.
熟练使用 SI 单位与标准词头能加快解题速度。下表汇集了 AS 阶段最常见的换算关系。
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| tera‑ | T | 10¹² | 1 THz = 10¹² Hz |
| giga‑ | G | 10⁹ | 1 Gm = 10⁹ m |
| mega‑ | M | 10⁶ | 1 MΩ = 10⁶ Ω |
| kilo‑ | k | 10³ | 1 kg = 10³ g |
| centi‑ | c | 10⁻² | 1 cm = 10⁻² m |
| milli‑ | m | 10⁻³ | 1 mA = 10⁻³ A |
| micro‑ | μ | 10⁻⁶ | 1 μm = 10⁻⁶ m |
| nano‑ | n | 10⁻⁹ | 1 nm = 10⁻⁹ m |
dm³ = 1 litre = 1000 cm³, 1 atm = 101 kPa, and temperature in kelvin (K) = θ/°C + 273.15. | 还需记住：1 dm³ = 1 升 = 1000 cm³，1 atm = 101 kPa，开尔文温度 (K) = θ/°C + 273.15。
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