📚 Year 12 Edexcel Science: Quick Reference Handbook of Formulas and Theorems | Year 12 爱德思科学：公式定理速查手册
This handbook compiles the key formulas, theorems, and essential concepts from Year 12 (AS-level) Physics, Chemistry, and Biology for the Edexcel specification. Use it as a rapid revision tool to strengthen your understanding and boost exam confidence.
本手册汇编了 Year 12（AS 阶段）爱德思物理、化学和生物课程中的核心公式、定理和重要概念，可用作快速复习工具，帮助你巩固理解并提升应试信心。
1. Kinematics and Dynamics | 运动学与动力学
For objects moving with constant acceleration, the SUVAT equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).
对于匀加速直线运动，以下 SUVAT 方程关联位移 s、初速度 u、末速度 v、加速度 a 和时间 t。
| Equation | Missing variable |
| v = u + at | s |
| s = ½(u + v)t | a |
| s = ut + ½at² | v |
| v² = u² + 2as | t |
Newton' en simplified to F = ma for constant mass. Weight is W = mg, with g = 9.81 m s⁻² on Earth.
牛顿第二定律指出，物体所受合力等于其动量的变化率，常简化为 F = ma（质量恒定）。重量 W = mg，地球表面的 g = 9.81 m s⁻²。
tal momentum before = total momentum after) is vital for collision and explosion problems.
动量 p 定义为质量 × 速度，即 p = mv。冲量引起动量的改变：FΔt = Δp。动量守恒定律（碰撞前后总动量不变）是处理碰撞和爆炸问题的关键。
gravitational potential energy GPE = mgΔh. Power is the rate of doing work: P = W/t = Fv.
恒力做功：W = Fd cos θ，θ 为力与位移间的夹角。动能 KE = ½mv²，重力势能 GPE = mgΔh。功率为做功的速率：P = W/t = Fv。
2. Materials, Waves and Optics | 材料、波与光学
ng modulus E = stress / strain, representing stiffness of a material within elastic limit.
应力 = F / A（单位 Pa），应变 = ΔL / L₀（无单位），杨氏模量 E = 应力 / 应变，表示材料在弹性限度内的刚度。
speed, f is frequency and λ is wavelength. Wave intensity I is proportional to amplitude².
所有波都满足波动方程：v = f λ，其中 v 为波速，f 为频率，λ 为波长。波的强度 I 与振幅的平方成正比。
Refractive index n = c / v (where c = 3.00 × 10⁸ m s⁻¹). Snell' internal reflection, the critical angle c satisfies sin c = n₂ / n₁ (valid when n₁ > n₂).
折射率 n = c / v（c = 3.00 × 10⁸ m s⁻¹）。斯涅耳定律：n₁ sin θ₁ = n₂ sin θ₂。发生全内反射时，临界角 c 满足 sin c = n₂ / n₁（需 n₁ > n₂）。
u is object distance, v is image distance (real positive). Linear magnification m = v / u.
薄透镜公式：1/f = 1/u + 1/v，f 为焦距，u 为物距，v 为像距（实像取正值）。线放大率 m = v / u。
3. Electricity and Circuits | 电学与电路
Ohm' lates resistance to geometry: R = ρL / A, where L is length and A is cross-sectional area.
欧姆定律：V = IR，定义电阻 R，单位欧姆（Ω）。电阻率 ρ 将电阻与材料几何尺寸关联：R = ρL / A，L 为长度，A 为横截面积。
ectrical power can be expressed as P = IV = I²R = V² / R. Energy transferred E = Pt = IVt.
电功率表示为 P = IV = I²R = V² / R。传递的电能 E = Pt = IVt。
For resistors in series: Rtotal = R₁ + R₂ + … 1/R₁ + 1/R₂. Capacitors in parallel: Ctotal = C₁ + C₂; in series: 1/Ctotal = 1/C₁ + 1/C₂.
电阻串联：R总 = R₁ + R₂ + …；并联：1/R总 = 1/R₁ + 1/R₂。电容并联：C总 = C₁ + C₂；串联：1/C总 = 1/C₁ + 1/C₂。
The terminal pd V = ε - Ir. The potential divider formula: Vout = Vin × (R₂ / (R₁ + R₂)).
实际电源有电动势 ε 和内阻 r。路端电压 V = ε - Ir。电位器分压公式：Vout = Vin × (R₂ / (R₁ + R₂))。
4. Quantum Phenomena and Particle Physics | 量子现象与粒子物理
/ λ, where Planck constant h = 6.63 × 10⁻³⁴ J s. The electronvolt: 1 eV = 1.60 × 10⁻¹⁹ J.
光子能量：E = hf = hc / λ，普朗克常量 h = 6.63 × 10⁻³⁴ J s。电子伏特：1 eV = 1.60 × 10⁻¹⁹ J。
Einstein' ocurrent increases with intensity, while maximum kinetic energy depends only on frequency.
爱因斯坦光电方程：hf = φ + ½mv²max，φ 为金属的逸出功。阈频率 f₀ 满足 φ = hf₀。光电流随光强增大，而最大动能只取决于频率。
th of a particle: λ = h / p, where p = mv is momentum. This explains electron diffraction.
实物粒子的德布罗意波长：λ = h / p，p = mv 为动量，该式可解释电子衍射现象。
are conserved. Proton = uud, neutron = udd. The weak interaction can change quark flavour.
在粒子相互作用中，电荷、重子数和轻子数守恒。质子由 uud 夸克组成，中子由 udd 组成。弱相互作用可以改变夸克味。
5. Quantitative Chemistry and the Mole | 定量化学与摩尔
TP (room temperature and pressure, Edexcel assumes 24.0 dm³ mol⁻¹): n = V (in dm³) / 24.0.
摩尔连接质量、体积和粒子数。物质的量 n = m / M，m 为质量，M 为摩尔质量（g mol⁻¹）。在室温常压（RTP，爱德思取 24.0 dm³ mol⁻¹）下，气体 n = V (dm³) / 24.0。
), often obtained by titration. Standard solutions require precise mass or volume measurements.
浓度 c = n / V（单位 mol dm⁻³），常通过滴定法获得。配制标准溶液需精确称量或体积量取。
T is absolute temperature (K), and R = 8.31 J K⁻¹ mol⁻¹. (Note: units must be consistent.)
理想气体方程：pV = nRT，p 为压强（Pa），V 为体积（m³），T 为绝对温度（K），R = 8.31 J K⁻¹ mol⁻¹。使用时单位必须一致。
Percentage yield = (actual yield / theoretical yield) × 100%. Atom economy = (molar mass of desired product / total molar mass of all reactants) × 100%. These measure reaction efficiency.
产率百分比 =（实际产量 / 理论产量）× 100%。原子经济性 =（目标产物的摩尔质量 / 所有反应物摩尔质量之和）× 100%，两者共同衡量反应效率。
rmula = n × empirical formula, where n = relative molecular mass / empirical formula mass.
实验式给出原子最简整数比；分子式 = n × 实验式，其中 n = 相对分子质量 / 实验式质量。
6. Energetics and Bond Enthalpies | 能量学与键焓
thalpy change ΔH = -q / n (negative for exothermic, positive for endothermic, assuming heat absorbed by surroundings).
溶液吸收或释放的热量：q = mcΔT，m 为质量，c 为比热容（水常取 4.18 J g⁻¹ K⁻¹），ΔT 为温度变化。焓变 ΔH = -q / n（放热为负，吸热为正，假设热量由环境吸收）。
Hess' . Using standard formation enthalpies: ΔH°reaction = Σ ΔH°f(products) - Σ ΔH°f(reactants).
赫斯定律指出，反应的总焓变与途径无关。利用标准生成焓计算：ΔH°反应 = Σ ΔH°f(产物) - Σ ΔH°f(反应物)。
bond enthalpies of bonds broken) - Σ (bond enthalpies of bonds formed). This average method works best for gaseous reactions.
键焓近似计算：ΔH ≈ Σ（断裂键的键焓）- Σ（形成键的键焓）。这种平均值方法最适合气态反应。
7. Introduction to Organic Chemistry | 有机化学入门
hydes (-CHO), ketones (C=O between carbons), carboxylic acids (-COOH), esters (-COO-), amines (-NH₂), amides (-CONH₂), nitriles (-C≡N).
官能团定义同系物：烷烃（C-C 单键）、烯烃（C=C 双键）、卤代烷（-X）、醇（-OH）、醛（-CHO）、酮（碳间 C=O）、羧酸（-COOH）、酯（-COO-）、胺（-NH₂）、酰胺（-CONH₂）、腈（-C≡N）。
alkanes with halogens under UV), oxidation (alcohol → aldehyde → carboxylic acid), elimination (alcohol → alkene), condensation (esterification, amide formation), hydrolysis.
应识别的反应类型：加成（烯→烷/醇），亲电加成（烯烃与 HX 或 Br₂），自由基取代（烷烃与卤素在紫外线下），氧化（醇→醛→羧酸），消除（醇→烯），缩合（酯化、酰胺化），水解。
Structural isomers share the same molecular formula but differ in carbon skeleton or functional group. Stereoisomers (E/Z) arise from restricted rotation around double bonds or ring structures.
结构异构体分子式相同，但碳链或官能团连接方式不同。立体异构体（E/Z）由双键或环状结构限制旋转而产生。
8. Biological Molecules | 生物分子
Monomers join by condensation reactions (releasing water) and polymers are broken by hydrolysis. Key monosaccharides: α-glucose and β-glucose (C₆H₁₂O₆). Disaccharides include maltose (glucose + glucose, α-1,4 glycosidic bond), sucrose (glucose + fructose), lactose (glucose + galactose).
单体通过缩合反应连接（脱去水），聚合物通过水解断裂。关键单糖：α- 和 β- 葡萄糖（C₆H₁₂O₆）。二糖包含麦芽糖（葡萄糖+葡萄糖，α-1,4 糖苷键）、蔗糖（葡萄糖+果糖）、乳糖（葡萄糖+半乳糖）。
Polysaccharides: starch (amylose and amylopectin, plant energy store), glycogen (animal storage, highly branched), cellulose (β-1,4 glycosidic bonds, plant cell walls – long straight chains with hydrogen bonds).
多糖：淀粉（直链淀粉与支链淀粉，植物储能）、糖原（动物储能，高度支化）、纤维素（β-1,4 糖苷键，植物细胞壁，长直链间形成氢键）。
Triglycerides consist of one glycerol molecule ester-linked to three fatty acid chains. Phospholipids have two fatty acids and a phosphate group, forming the bilayer basis of cell membranes.
甘油三酯由一个甘油分子与三条脂肪酸链通过酯键连接而成。磷脂含有两条脂肪酸和一个磷酸基团，构成细胞膜脂双层的基础。
Proteins are polymers of amino acids. General amino acid structure: H₂N–CHR– ding (ionic, disulfide, hydrophobic interactions, H-bonds); quaternary = multiple polypeptide chains.
蛋白质是氨基酸的聚合物。氨基酸通式：H₂N–CHR–COOH。肽键在氨基酸间形成。一级结构为序列；二级结构为 α-螺旋/β-折叠（氢键维系）；三级结构为三维折叠（离子键、二硫键、疏水作用、氢键等）；四级结构为多条多肽链的组合。
Nucleotides consist of a phosphate group, a pentose sugar (ribose/deoxyribose), and a nitrogenous base. DNA double helix has complementary base pairing A-T and G-C, held by hydrogen bonds. RNA contains uracil instead of thymine and is single-stranded.
核苷酸由磷酸基团、五碳糖（核糖/脱氧核糖）和含氮碱基组成。DNA 双螺旋中 A 与 T、G 与 C 通过氢键互补配对。RNA 含尿嘧啶代替胸腺嘧啶，通常为单链。
9. Cell Membranes and Transport | 细胞膜与物质运输
The fluid mosaic model describes membranes as a phospholipid bilayer with embedded proteins (channel and carrier), cholesterol (regulating fluidity), and glycoproteins/glycolipids (cell recognition).
流动镶嵌模型将膜描绘为磷脂双分子层，其中散布着蛋白质（通道蛋白和载体蛋白）、胆固醇（调节流动性），以及糖蛋白/糖脂（细胞识别）。
Diffusion is net movement of particles from high to low concentration, described by Fick's law: rate of diffusion ∝ (surface area × concentration difference) / thickness of exchange surface.
扩散是粒子从高浓度区间向低浓度区的净移动，符合菲克定律：扩散速率 ∝ （表面积 × 浓度差）/ 交换面厚度。
water ψ = 0; solutions have negative ψ. ψ = ψs (solute potential) + ψp (pressure potential).
渗透是水通过部分通透膜的扩散，从高水势（ψ）移向低水势。纯水 ψ = 0；溶液水势为负值。水势 ψ = ψs（溶质势）+ ψp（压力势）。
Active transport uses ATP to move substances against their concentration gradient via specific carrier proteins. Co-transport couples the movement of one substance (e.g. glucose) with the downhill movement of Na⁺ ions.
主动运输利用 ATP，通过特定的载体蛋白将物质逆浓度梯度转运。协同转运将一种物质的移动（如葡萄糖）与 Na⁺ 离子的顺梯度移动相偶联。
10. Enzymes and Metabolism | 酶与代谢
Enzymes are biological catalysts that lower activation energy, speeding up reactions without being used up. The induced-fit model states that the active site changes shape slightly to bind substrate, forming enzyme-substrate complexes.
酶是生物催化剂，能降低活化能，从而加快反应且自身不被消耗。诱导契合模型认为，酶的活性中心发生轻微形变以结合底物，形成酶-底物复合体。
Rate of enzyme-catalysed reactions increases with temperature up to an optimum; beyond this, denaturation occurs as hydrogen bonds break. pH also affects rate by altering ionic interactions at the active site.
酶促反应速率随温度升高而增加直至最适温度；超过最适温度则酶变性，氢键断裂。pH 值通过改变活性中心的离子相互作用来影响反应速率。
As substrate concentration increases, rate rises until all active sites are saturated, reaching Vmax. The Michaelis-Menten equation models this, though AS focuses on qualitative understanding of Vmax and competitive/non-competitive inhibition.
随底物浓度增加，反应速率升高，直至所有活性位点饱和，达到最大速率 Vmax。米氏方程对此进行了模型化，但 AS 阶段主要定性理解 Vmax 和竞争性/非竞争性抑制的作用。
Competitive inhibitors resemble the substrate and bind to the active site; their effect can be overcome by increasing substrate concentration. Non-competitive inhibitors bind elsewhere, altering enzyme shape and reducing Vmax.
竞争性抑制剂与底物结构相似
Published by TutorHao | Year 12 Science Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图