📚 Year 8 OCR Science: Formula & Theorem Quick Reference Handbook | Year 8 OCR 科学：公式定理速查手册
This quick reference handbook collects all the essential formulas, equations and important principles you will meet in the Year 8 OCR Science course. Keep it handy when revising, solving problems or preparing for assessments. Each topic is presented in a clear pair of English and Chinese explanations so you can master both the concepts and the scientific vocabulary.
这份速查手册汇集了 Year 8 OCR 科学课程中所有必须掌握的公式、方程和重要原理。复习、解题或备考时随时翻阅都很方便。每个主题都配有清晰的中英文对照讲解，帮助你同时掌握概念与科学术语。
1. Speed, Distance and Time | 速度、距离和时间
Speed describes how quickly an object covers a distance. The formula is: v = s / t, where v represents speed (metres per second, m/s), s stands for distance (metres, m) and t is time (seconds, s).
速度描述物体移动的快慢。公式为：v = s / t，其中 v 表示速度（米/秒，m/s），s 代表距离（米，m），t 代表时间（秒，s）。
You can rearrange the equation to find distance or time: distance = speed × time (s = v × t) and time = distance ÷ speed (t = s / v). Always ensure units match before substituting values.
你可以通过变形求出距离或时间：距离 = 速度 × 时间（s = v × t），时间 = 距离 ÷ 速度（t = s / v）。代入数值前务必确保单位一致。
In everyday life we often use kilometres per hour (km/h). To convert m/s to km/h, multiply by 3.6; to convert km/h to m/s, divide by 3.6.
日常生活中常用千米/时（km/h）。将 m/s 换算为 km/h 需要乘以 3.6，将 km/h 换算为 m/s 则需要除以 3.6。
2. Density, Mass and Volume | 密度、质量和体积
Density measures how much mass is packed into a given volume. The equation is: ρ = m / V, where ρ (rho) is density (kg/m³ or g/cm³), m is mass (kg or g) and V is volume (m³ or cm³).
密度衡量单位体积内所含质量的大小。公式为：ρ = m / V，其中 ρ 为密度（千克/立方米或克/立方厘米），m 为质量（千克或克），V 为体积（立方米或立方厘米）。
To find mass or volume, rearrange the formula: mass = density × volume (m = ρ × V), volume = mass ÷ density (V = m / ρ). Remember that 1 cm³ = 0.000001 m³ and 1 g/cm³ = 1000 kg/m³.
要求质量或体积时可对公式变形：质量 = 密度 × 体积（m = ρ × V），体积 = 质量 ÷ 密度（V = m / ρ）。注意 1 cm³ = 0.000001 m³，1 g/cm³ = 1000 kg/m³。
Objects with a density less than water (1 g/cm³) will float; those with greater density sink. Density is a characteristic property useful for identifying materials.
密度小于水（1 g/cm³）的物体会上浮，大于水的下沉。密度是物质的一种特性，常用于鉴别材料。
3. Pressure, Force and Area | 压强、力和面积
Pressure is the force applied per unit area. The formula is: P = F / A, where P is pressure (pascals, Pa or N/m²), F is force (newtons, N) and A is area over which the force acts (m²).
压强是单位面积上施加的力。公式为：P = F / A，其中 P 为压强（帕斯卡，Pa 或 N/m²），F 为力（牛顿，N），A 为受力面积（m²）。
A larger area reduces pressure for the same force (e.g. snowshoes spread weight). A smaller area increases pressure (e.g. a sharp knife cuts easily). This principle also explains the behaviour of fluids and pneumatic systems.
当力相同时，面积越大压强越小（如雪鞋分散体重）；面积越小压强越大（如锋利的刀更容易切割）。这一原理也可解释流体和气压系统的行为。
Fluid pressure acts equally in all directions and increases with depth. The pressure at a depth h in a liquid of density ρ is given by P = ρ g h, where g is gravitational field strength. At Year 8 level, this relationship is often explored qualitatively.
流体压强向各个方向均匀传递，并随深度增加而增大。密度为 ρ 的液体中深度 h 处的压强满足 P = ρ g h（g 为重力场强度）。在八年级阶段，通常定性认识这一关系。
4. Forces and Hooke’s Law | 力与胡克定律
When a spring is stretched, the extension is directly proportional to the applied force up to the elastic limit. This is Hooke’s Law: F = k e, where F is force (N), k is the spring constant (N/m) and e is extension (m).
在弹性限度内，弹簧的伸长量与所施加的力成正比，这就是胡克定律：F = k e，其中 F 为力（N），k 为弹簧劲度系数（N/m），e 为伸长量（m）。
The spring constant k measures the stiffness of the spring: a stiffer spring has a larger k value. If a graph of force against extension is plotted, the gradient equals k.
弹簧劲度系数 k 反映弹簧的软硬程度：弹簧越硬，k 值越大。如果绘制力-伸长量图像，其斜率大小就是 k。
Beyond the elastic limit, the spring deforms permanently and Hooke’s Law no longer applies. Materials that obey Hooke’s Law are called elastic materials.
超过弹性极限后，弹簧会发生永久形变，胡克定律不再适用。遵循胡克定律的材料称为弹性材料。
5. Moments (Turning Forces) | 力矩（转动力）
A moment is the turning effect of a force. It depends on the size of the force and the perpendicular distance from the pivot. The formula is: M = F × d, where M is the moment (newton metres, N m), F is force (N) and d is the perpendicular distance from the pivot (m).
力矩是力产生的转动效果，它取决于力的大小以及力到支点的垂直距离。公式为：M = F × d，其中 M 为力矩（牛顿·米，N m），F 为力（N），d 为力到支点的垂直距离（m）。
For an object in rotational equilibrium, the total clockwise moment equals the total anticlockwise moment: ∑ clockwise moments = ∑ anticlockwise moments. This is the principle of moments and is used to solve problems with seesaws, levers and balances.
物体处于转动平衡时，顺时针方向的总力矩等于逆时针方向的总力矩：顺时针力矩之和 = 逆时针力矩之和。这就是力矩平衡原理，常用于解决跷跷板、杠杆和天平等问题。
Increasing the distance from the pivot reduces the force needed to produce the same turning effect, which is why spanners have long handles and doors have handles far from the hinges.
增大离支点的距离可以减小产生相同转动效果所需的力，这解释了为什么扳手有长手柄、门把手安装在远离铰链的位置。
6. Work Done and Power | 完成的功和功率
Work is done when a force moves an object in the direction of the force. The formula is: W = F × d, where W is work done (joules, J), F is force (N) and d is distance moved in the direction of the force (m). One joule equals one newton metre (1 J = 1 N m).
当一个力使物体沿力的方向移动时，力就对物体做了功。公式为：W = F × d，其中 W 为做功（焦耳，J），F 为力（N），d 为沿力方向移动的距离（m）。1 焦耳等于 1 牛顿·米（1 J = 1 N m）。
Power is the rate at which work is done or energy is transferred. The formula is: P = W / t or P = E / t, where P is power (watts, W, equal to J/s), W or E is work or energy (J) and t is time (s).
功率是做功或能量转移的快慢程度。公式为：P = W / t 或 P = E / t，其中 P 为功率（瓦特，W，等于 J/s），W 或 E 为功或能量（J），t 为时间（s）。
A machine that transfers more energy per second is more powerful. Understanding power helps us compare appliances, motors and even human performance in activities like climbing stairs or cycling.
每秒钟转移的能量越多，机器功率越大。理解功率可以帮助我们比较电器、发动机，甚至是爬楼梯、骑自行车时人体的运动表现。
7. Gravitational Potential Energy and Kinetic Energy | 重力势能和动能
When an object is lifted against gravity, it gains gravitational potential energy (GPE): ΔGPE = m g Δh, where m is mass (kg), g is gravitational field strength (9.8 N/kg on Earth, often rounded to 10 N/kg in Year 8 calculations) and Δh is the change in height (m).
物体被举高时会获得重力势能（GPE）：ΔGPE = m g Δh，其中 m 为质量（kg），g 为重力场强度（地球上约 9.8 N/kg，八年级计算中常取 10 N/kg），Δh 为高度变化（m）。
Kinetic energy is the energy an object possesses due to its motion: KE = ½ m v², where m is mass (kg) and v is speed (m/s). Notice the speed is squared, so doubling the speed quadruples the kinetic energy.
动能是物体因运动而具有的能量：KE = ½ m v²，其中 m 为质量（kg），v 为速度（m/s）。注意速度是平方项，因此速度加倍会使动能变为原来的四倍。
In many situations (without air resistance), GPE at the top of a drop is converted into KE at the bottom: m g h = ½ m v². Cancelling mass gives g h = ½ v², showing that the final speed depends only on the vertical height, not on mass.
在许多情况下（忽略空气阻力），最高处的重力势能会完全转化为最低处的动能：m g h = ½ m v²。消去质量可得 g h = ½ v²，说明末速度只取决于高度，与质量无关。
8. Ohm’s Law and Resistance | 欧姆定律和电阻
Ohm’s Law describes the relationship between voltage, current and resistance in a conductor at constant temperature: V = I × R, where V is potential difference or voltage (volts, V), I is current (amperes, A) and R is resistance (ohms, Ω).
欧姆定律描述了恒定温度下导体两端电压、电流和电阻之间的关系：V = I × R，其中 V 为电势差或电压（伏特，V），I 为电流（安培，A），R 为电阻（欧姆，Ω）。
Resistance measures how much a component opposes the flow of current. Rearranging Ohm’s Law gives R = V / I and I = V / R. A greater resistance results in a smaller current for the same voltage.
电阻衡量元器件对电流的阻碍作用。对欧姆定律变形可得 R = V / I 和 I = V / R。在电压相同时，电阻越大，电流越小。
Components that obey Ohm’s Law produce a straight-line voltage–current graph passing through the origin. Filament bulbs and diodes do not follow Ohm’s Law because their resistance changes with temperature or current direction.
遵循欧姆定律的元器件，其电压–电流图像是一条过原点的直线。灯丝灯泡和二极管的电阻会随温度或电流方向改变，因此它们不遵循欧姆定律。
9. Wave Speed, Frequency and Wavelength | 波速、频率和波长
All waves obey the wave equation: v = f λ, where v is wave speed (m/s), f is frequency (hertz, Hz) and λ (lambda) is wavelength (m). Frequency is the number of complete waves passing a point per second.
所有波都遵循波动方程：v = f λ，其中 v 为波速（m/s），f 为频率（赫兹，Hz），λ 为波长（m）。频率是每秒经过某一点的完整波的数目。
When a wave passes from one medium to another, its speed and wavelength may change, but its frequency remains the same. For example, light slows down in glass, causing the wavelength to shorten and the ray to refract.
波从一种介质进入另一种介质时，波速和波长可能改变，但频率保持不变。例如，光在玻璃中速度变慢，导致波长缩短并发生折射。
For transverse waves (like light and water ripples), the vibrations are perpendicular to the direction of energy transfer. For longitudinal waves (like sound), the vibrations are parallel to the energy transfer direction.
横波（如光波和水波涟漪）的振动方向与能量传递方向垂直。纵波（如声波）的振动方向与能量传递方向平行。
10. Chemical Calculations: Ar, Mr and Conservation of Mass | 化学计算：相对原子质量、相对分子质量和质量守恒
The relative atomic mass (Ar) of an element compares the mass of one atom to 1/12 of a carbon‑12 atom. It has no units. You find Ar values on the Periodic Table (e.g. H = 1, C = 12, O = 16).
元素的相对原子质量（Ar）是该元素一个原子的质量与碳‑12 原子质量的 1/12 的比值，没有单位。Ar 数值可在周期表中查到（例如 H = 1，C = 12，O = 16）。
The relative formula mass (Mr) of a compound is the sum of the Ar values of all atoms in the chemical formula. For water, H₂O: Mr = (2 × 1) + 16 = 18. For carbon dioxide, CO₂: Mr = 12 + (2 × 16) = 44.
化合物的相对分子质量（Mr）是其化学式中所有原子 Ar 的总和。如水 H₂O：Mr = (2 × 1) + 16 = 18。二氧化碳 CO₂：Mr = 12 + (2 × 16) = 44。
Percentage composition by mass tells you how much of the total mass belongs to each element. The formula is: % element = (number of atoms of that element × Ar / Mr) × 100. For H₂O, % H = (2 × 1 / 18) × 100 ≈ 11.1 % and % O = (16 / 18) × 100 ≈ 88.9 %.
质量百分组成表示每种元素在化合物总质量中所占的比例。公式为：元素百分比 = (该元素的原子个数 × Ar / Mr) × 100。以水为例，氢的百分比 = (2 × 1 / 18) × 100 ≈ 11.1 %，氧的百分比 = (16 / 18) × 100 ≈ 88.9 %。
The law of conservation of mass states that the total mass of reactants equals the total mass of products in a chemical reaction. Atoms are rearranged, never created or destroyed, so mass stays constant.
质量守恒定律指出，化学反应中反应物的总质量等于生成物的总质量。原子只是重新排列，既不凭空产生也不会消失，因此质量保持不变。
11. Microscopy Magnification (Biology) | 显微镜放大倍数（生物）
Total magnification of a light microscope is calculated by
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