📚 AS OCR Science: Formula and Theorem Quick Reference Handbook | AS OCR 科学：公式定理速查手册
Welcome to your essential quick-reference guide for AS OCR Science. This handbook brings together the most important formulae, laws, and key theorems from physics, chemistry, and biology in one accessible place. Whether you are revising for end-of-topic tests or preparing for your final AS examinations, use this resource to check your recall, deepen your understanding, and avoid common mistakes.
欢迎使用这份 AS OCR 科学必备速查手册。本手册将物理、化学和生物中最重要的公式、定律和关键定理汇集于一处，方便查阅。无论你是在为单元测验复习，还是为最终的 AS 考试做准备，都可以利用这个资源来检查记忆、加深理解并避免常见错误。
1. Kinematics Equations | 运动学方程
For motion in a straight line with constant acceleration, the SUVAT equations relate displacement s, initial velocity u, final velocity v, acceleration a, and time t. These are fundamental to solving linear motion problems.
在匀加速直线运动中，SUVAT 方程联系了位移 s、初速度 u、末速度 v、加速度 a 和时间 t。它们是解决直线运动问题的基础。
v = u + at
This equation gives the final velocity after accelerating for time t.
该方程给出加速 t 时间后的末速度。
s = ½(u + v)t
Displacement equals average velocity multiplied by time.
位移等于平均速度乘以时间。
s = ut + ½at²
Use this when time is known but final velocity is not.
当已知时间而未知末速度时，使用这个公式。
v² = u² + 2as
This form is useful when time is not given.
当未给出时间时，该形式很有用。
Remember to choose a positive direction and assign signs consistently to vector quantities.
记得选定一个正方向，并一致地为矢量赋予符号。
2. Newton’s Laws and Forces | 牛顿定律与力
Newton’s three laws of motion form the basis of classical mechanics. The second law is particularly important for solving force, mass, and acceleration problems.
牛顿三大运动定律构成了经典力学的基础。第二定律对于解决力、质量和加速度问题尤为重要。
F = ma
The net force F acting on an object is equal to the product of its mass m and acceleration a. This vector equation must be applied in each independent direction.
作用在物体上的合力 F 等于其质量 m 与加速度 a 的乘积。此矢量方程需在每一个独立的方向上应用。
W = mg
Weight W is the force due to gravity: mass multiplied by gravitational field strength g.
重力 W 是由引力引起的力：质量乘以重力场强度 g。
The coefficient of friction μ relates the frictional force Ff to the normal reaction N:
摩擦系数 μ 将摩擦力 Ff 与法向反作用力 N 联系起来：
Ff ≤ μN
Equilibrium problems often require resolving forces into components. For an angle θ to the horizontal:
平衡问题通常需要将力分解为分量。对于与水平方向成 θ 角：
Fx = F cos θ, Fy = F sin θ
3. Energy, Work and Power | 能量、功和功率
Energy is a conserved quantity that can be transformed between different forms. Understanding work and power is essential for analysing mechanical systems.
能量是一种守恒量，可以在不同形式之间转化。理解功和功率对于分析机械系统至关重要。
Work done W by a constant force F moving an object through displacement s in the direction of the force:
恒力 F 使物体沿力的方向发生位移 s 所做的功 W：
W = F s
If the force is at an angle θ to the displacement, use W = F s cos θ.
若力与位移成 θ 角，则使用 W = F s cos θ。
Kinetic energy Ek of an object with mass m and speed v:
质量为 m、速度为 v 的物体的动能 Ek：
Ek = ½mv²
Change in gravitational potential energy ΔEp when an object is raised by a height Δh:
物体被抬高 Δh 高度时重力势能的变化 ΔEp：
ΔEp = mgΔh
Power P is the rate of doing work or transferring energy:
功率 P 是做功或传递能量的速率：
P = W / t and P = E / t
Efficiency of a system is useful output energy divided by total input energy, often expressed as a percentage.
系统的效率是有用输出能量除以总输入能量，通常以百分数表示。
4. Waves and Optics | 波与光学
Wave properties can be described by the wave equation. The behaviour of light at boundaries and through slits is governed by well-defined relationships.
波的性质可用波方程描述。光在边界和通过狭缝的行为受明确的关系支配。
v = f λ
Wave speed v is the product of frequency f and wavelength λ. This applies to all waves.
波速 v 是频率 f 与波长 λ 的乘积。适用于所有波。
For refraction, Snell’s law relates angles of incidence and refraction to the refractive indices of the two media:
对于折射，斯涅尔定律将入射角和折射角与两种介质的折射率联系起来：
n₁ sin θ₁ = n₂ sin θ₂
Critical angle θc for total internal reflection occurs when sin θ₂ = 1:
当 sin θ₂ = 1 时，发生全反射的临界角 θc 为：
sin θc = n₂ / n₁ (where n₁ > n₂)
The double-slit interference fringe spacing Δy is given by:
双缝干涉的条纹间距 Δy 由下式给出：
Δy = λ D / d
where D is the distance from slits to screen and d is the slit separation.
其中 D 是狭缝到屏幕的距离，d 是狭缝间距。
5. Electricity and Circuits | 电学与电路
Electric circuits are analysed using concepts of current, voltage, and resistance. Key formulae include Ohm’s law and power dissipation.
电路分析运用电流、电压和电阻的概念。关键公式包括欧姆定律和功率消耗。
V = I R
Ohm’s law: potential difference V across a resistor equals current I multiplied by resistance R, assuming constant temperature.
欧姆定律：在恒定温度下，电阻两端的电势差 V 等于电流 I 乘以电阻 R。
Charge Q transferred by a steady current I in time t:
恒定电流 I 在时间 t 内转移的电荷量 Q：
Q = I t
Electrical power P can be expressed in three equivalent forms:
电功率 P 可用三种等价形式表示：
P = V I, P = I² R, P = V² / R
Energy transferred E by a component:
元件传递的能量 E：
E = V I t
Resistance of a wire depends on its resistivity ρ, length L, and cross-sectional area A:
导线的电阻取决于其电阻率 ρ、长度 L 和横截面积 A：
R = ρ L / A
6. Chemical Quantities and the Mole | 化学计量与摩尔
The mole is the central unit for quantifying chemical substances. Calculations involving mass, volume, and concentration are essential across all topics.
摩尔是量化化学物质的中心单位。涉及质量、体积和浓度的计算贯穿所有主题。
n = m / M
Amount of substance n (in mol) equals mass m divided by molar mass M.
物质的量 n（以 mol 为单位）等于质量 m 除以摩尔质量 M。
For gases at room temperature and pressure (RTP: 20 °C, 1 atm), molar volume Vm ≈ 24 dm³/mol:
对于在常温常压（RTP：20 °C，1 atm）下的气体，摩尔体积 Vm ≈ 24 dm³/mol：
V = n × 24 (in dm³)
Concentration c of a solution:
溶液的浓度 c：
c = n / V (with V in dm³)
Percentage yield and atom economy are used to assess reaction efficiency.
产率和原子利用率用于评估反应效率。
% yield = (actual mass / theoretical mass) × 100
% atom economy = (molar mass of desired product / total molar mass of reactants) × 100
7. Acids, Bases and pH | 酸碱与 pH
The behaviour of acids and bases is described by proton transfer and dissociation constants. pH provides a measure of hydrogen ion concentration.
酸和碱的行为通过质子转移和离解常数来描述。pH 提供了氢离子浓度的量度。
pH = −log₁₀[H⁺]
This logarithmic scale means a change of one pH unit represents a tenfold change in [H⁺].
这种对数标度意味着 pH 值每变化 1 个单位，[H⁺] 就变化十倍。
The ionic product of water Kw at 25 °C:
25 °C 时水的离子积 Kw：
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ (in mol² dm⁻⁶)
For a weak acid HA, the acid dissociation constant Ka quantifies the equilibrium:
对于弱酸 HA，酸离解常数 Ka 量化了平衡：
Ka = [H⁺][A⁻] / [HA]
In a buffer solution, the Henderson–Hasselbalch equation helps calculate pH:
在缓冲溶液中，亨德森-哈塞尔巴尔赫方程有助于计算 pH：
pH = pKa + log₁₀([A⁻]/[HA])
8. Organic Chemistry Key Concepts | 有机化学关键概念
Organic chemistry in AS focuses on nomenclature, functional groups, and reaction mechanisms. Understanding general formulae of homologous series is crucial.
AS 有机化学的重点在于命名、官能团和反应机理。理解同系列的通式至关重要。
-
Alkanes: CnH2n+2
烷烃：CnH2n+2
-
Alkenes: CnH2n
烯烃：CnH2n
-
Alcohols: CnH2n+1OH
醇：CnH2n+1OH
-
Carboxylic acids: CnH2n+1COOH
羧酸：CnH2n+1COOH
Addition polymerisation of alkenes can be represented as:
烯烃的加成聚合可表示为：
n(CH₂=CH₂) → −(CH₂−CH₂)−n
Key mechanisms: electrophilic addition of HX or halogens to alkenes, and nucleophilic substitution for halogenoalkanes.
关键机理：卤化氢或卤素与烯烃的亲电加成，以及卤代烷的亲核取代。
9. Cell Biology and Microscopy | 细胞生物学与显微镜
Cell theory states that all living organisms are composed of cells, the basic unit of life. Microscopy allows us to visualise and measure these structures.
细胞学说指出所有生物体都由细胞组成，细胞是生命的基本单位。显微镜使我们能够观察并测量这些结构。
Magnification = size of image / size of real object
This formula is used when drawing scale bars or interpreting micrographs.
在绘制比例尺或解读显微照片时使用此公式。
For magnification calculations, ensure consistent units. Convert all lengths to the same unit (e.g., µm or mm) before calculating.
进行放大倍率计算时，要确保单位一致。在计算前将所有长度转换为相同单位（如 µm 或 mm）。
Be familiar with the key differences between light and electron microscopes: resolution, magnification, and sample preparation.
熟悉光学显微镜与电子显微镜的主要区别：分辨率、放大倍数和样品制备。
The formula for the number of cells after n divisions, starting from 1 cell:
从 1 个细胞开始，经过 n 次分裂后的细胞数公式：
N = 2ⁿ
10. Genetics and Hardy-Weinberg | 遗传学与哈代-温伯格平衡
The Hardy–Weinberg principle provides a mathematical framework for studying allele frequencies in a population that is not evolving. It is a core concept in AS biology.
哈代-温伯格原理为研究非进化种群中的等位基因频率提供了一个数学框架。这是 AS 生物学的核心概念。
p + q = 1
Here p and q represent the frequencies of the two alleles of a gene. This equation simply states that the total allele frequency equals 1.
这里 p 和 q 代表一个基因的两个等位基因的频率。该方程仅表明总等位基因频率等于 1。
p² + 2pq + q² = 1
This equation gives the expected genotype frequencies: homozygous dominant (p²), heterozygous (2pq), and homozygous recessive (q²). Use it to predict carrier frequencies or the percentage of a population with a recessive condition.
该方程给出了预期的基因型频率：纯合显性 (p²)、杂合 (2pq) 和纯合隐性 (q²)。可使用它来预测携带者频率或种群中患有隐性遗传病的百分比。
Assumptions of the Hardy–Weinberg equilibrium: no mutation, random mating, no natural selection, large population size, and no gene flow. Understanding these helps identify when real populations might be evolving.
哈代-温伯格平衡的假设条件：无突变、随机交配、无自然选择、大种群规模、无基因流动。理解这些有助于判断真实种群何时可能正在进化。
11. Photosynthesis and Energy | 光合作用与能量
Photosynthesis is the process by which plants convert light energy into chemical energy. While deep biochemistry is explored in A2, AS requires understanding the overall equation and limiting factors.
光合作用是植物将光能转化为化学能的过程。尽管 A2 会深入探讨生物化学，但 AS 要求掌握总反应方程式和限制因素。
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
This balanced equation summarises photosynthesis. Light energy is absorbed by chlorophyll and used to synthesise glucose.
这个平衡方程式概括了光合作用。光能被叶绿素吸收并用于合成葡萄糖。
The rate of photosynthesis can be investigated by measuring oxygen production. Key limiting factors are light intensity, carbon dioxide concentration, and temperature.
光合作用速率可通过测量氧气产量来研究。关键限制因素是光照强度、二氧化碳浓度和温度。
For energy transfer, recall that respiration provides ATP. Although less formula-focused, you may use simple ratios:
关于能量传递，请记住呼吸作用提供 ATP。尽管公式较少，但你可能用到简单的比率：
Respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy (ATP)
12. Data Handling and Significant Figures | 数据处理与有效数字
Accurate recording and processing of experimental data are essential skills. You must handle significant figures, uncertainties, and basic statistical measures confidently.
准确记录和处理实验数据是必备技能。你必须自信地处理有效数字、不确定度和基本统计量。
For mean of repeated measurements: sum of values divided by number of values.
多次测量的平均值：数值之和除以数值的个数。
Percentage uncertainty of a measurement = (absolute uncertainty / measured value) × 100. When combining measurements, add absolute uncertainties for addition/subtraction, and add percentage uncertainties for multiplication/division.
测量的百分不确定度 = (绝对不确定度 / 测量值) × 100。当组合测量时，加减法用绝对不确定度相加，乘除法用百分不确定度相加。
Be consistent with significant figures: final answers should generally be given to the same number of significant figures as the least precise measurement used.
注意有效数字的一致性：最终答案通常应与所用最不精确的测量值的有效数字位数相同。
This quick reference is not exhaustive but covers the core formulae and theorems you will repeatedly use throughout your AS OCR Science course.
本速查手册虽非详尽无遗，但涵盖了你在 AS OCR 科学课程中反复使用的核心公式和定理。
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