📚 Year 7 Cambridge Science: Quick Reference Formula & Theorem Handbook | 剑桥7年级科学：公式定理速查手册
Welcome to your quick-reference guide for the essential formulas and theorems you will encounter in Year 7 Cambridge Science. This handbook covers key equations from physics, chemistry, and biology in a clear bilingual format, helping you build a strong foundation for scientific calculations and conceptual understanding. Use it to revise, practise, and check your knowledge as you progress through the course.
欢迎使用这本为剑桥7年级科学课程准备的核心公式与定理速查手册。手册以清晰的双语形式呈现物理、化学和生物中的重要方程式，帮助你为科学计算和概念理解打下坚实基础。你可以用它来复习、练习，并在学习过程中随时核对知识。
1. Speed Formula | 速度公式
Speed is a measure of how fast an object moves. It is calculated by dividing the distance travelled by the time taken. The formula is:
speed = distance ÷ time (v = s / t)
速度是衡量物体运动快慢的物理量。它等于运动距离除以所用时间。公式为：
速度 = 距离 ÷ 时间 (v = s / t)
The standard unit of speed is metres per second (m/s), but kilometres per hour (km/h) is also commonly used. Always make sure units are consistent when using the formula. If distance is in metres and time in seconds, speed will be in m/s.
速度的标准单位是米每秒（m/s），千米每小时（km/h）也常用。使用公式时务必保证单位一致。如果距离用米，时间用秒，速度就是 m/s。
A car travels 200 metres in 10 seconds. Its speed is 200 ÷ 10 = 20 m/s. This simple triangle relationship (s = v × t) can be rearranged to find distance or time.
一辆汽车10秒行驶了200米，速度就是200 ÷ 10 = 20 m/s。这个简单的三角关系（s = v × t）可以变形用于求距离或时间。
- v = s / t (speed from distance and time)
- s = v × t (distance from speed and time)
- t = s / v (time from distance and speed)
- v = s / t（已知距离和时间求速度）
- s = v × t（已知速度和时间求距离）
- t = s / v（已知距离和速度求时间）
2. Density Formula | 密度公式
Density tells us how much mass is packed into a certain volume. It is a property of materials and helps identify substances. The formula is:
density = mass ÷ volume (ρ = m / V)
密度表示单位体积内含有多少质量，是物质的一种特性，可用于鉴别物质。公式为：
密度 = 质量 ÷ 体积 (ρ = m / V)
The Greek letter rho (ρ) is often used to denote density. Mass is typically in grams (g) or kilograms (kg), volume in cubic centimetres (cm³) or cubic metres (m³). Common units of density are g/cm³ or kg/m³. For example, water has a density of about 1 g/cm³.
希腊字母 ρ 常用来代表密度。质量通常用克（g）或千克（kg），体积用立方厘米（cm³）或立方米（m³）。密度的常用单位是 g/cm³ 或 kg/m³。例如，水的密度大约是 1 g/cm³。
An iron block has a mass of 780 g and a volume of 100 cm³. Its density is 780 ÷ 100 = 7.8 g/cm³. Objects with lower density than water float, while denser objects sink.
一块铁质量780克，体积100立方厘米，它的密度是780 ÷ 100 = 7.8 g/cm³。密度小于水的物体会浮起，大于水的则会下沉。
3. Force and Acceleration (Newton’s Second Law) | 力与加速度（牛顿第二定律）
When an unbalanced force acts on an object, it causes the object to accelerate. The relationship between force, mass and acceleration is described by Newton’s second law:
force = mass × acceleration (F = m × a)
当不平衡的力作用在物体上时，物体会产生加速度。力、质量和加速度之间的关系由牛顿第二定律描述：
力 = 质量 × 加速度 (F = m × a)
Force is measured in newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²). One newton is the force needed to accelerate a 1 kg mass by 1 m/s². This law is fundamental in understanding motion and is often tested alongside balanced and unbalanced forces.
力的单位是牛顿（N），质量用千克（kg），加速度用米每二次方秒（m/s²）。1牛顿是使1千克物体产生1 m/s² 加速度所需的力。这一定律是理解运动的基础，常与平衡和不平衡力一起考查。
A trolley of mass 2 kg is pushed with a force of 8 N. Its acceleration is a = F / m = 8 ÷ 2 = 4 m/s². The equation can be rearranged to m = F / a or a = F / m.
一个质量为2千克的小车受到8牛推力，它的加速度 a = F / m = 8 ÷ 2 = 4 m/s²。该方程可变形为 m = F / a 或 a = F / m。
4. Pressure Formula | 压强公式
Pressure is the amount of force applied per unit area. A sharp knife cuts better because the small area gives high pressure for the same force. The formula is:
pressure = force ÷ area (P = F / A)
压强是单位面积上所受的力。锋利的刀更容易切割，因为在相同的力下，较小的面积会产生较大的压强。公式为：
压强 = 力 ÷ 面积 (P = F / A)
Pressure is measured in pascals (Pa) when force is in newtons and area in square metres (m²). 1 Pa = 1 N/m². In everyday contexts, we often talk about pressure in N/cm² or even in atmospheres. The larger the area over which a force spreads, the lower the pressure.
当力用牛顿、面积用平方米（m²）时，压强的单位是帕斯卡（Pa）。1 Pa = 1 N/m²。在日常情景中，我们也用 N/cm² 甚至大气压。力分布的面积越大，压强越小。
A block weighing 40 N rests on a surface with an area of 0.5 m². Pressure = 40 ÷ 0.5 = 80 Pa. Snowshoes work by increasing the contact area, reducing pressure so you do not sink into the snow.
一块重40牛的物体放在0.5平方米的表面上，压强 = 40 ÷ 0.5 = 80 Pa。雪鞋通过增大接触面积来减小压强，使人不会陷入雪中。
5. Energy Transfers & Conservation | 能量转换与守恒
Energy cannot be created or destroyed; it is only transferred or transformed from one form to another. This principle is known as the law of conservation of energy. In Year 7 science, you learn about different energy stores: kinetic, thermal, chemical, gravitational potential, elastic, nuclear, and electrostatic.
能量既不能被创造也不能被消灭，它只能从一种形式转移或转化为另一种形式。这一原理称为能量守恒定律。在7年级科学中，你会接触到不同的能量储存：动能、热能、化学能、引力势能、弹性势能、核能和静电势能。
For calculations involving gravitational potential energy (GPE) and kinetic energy (KE), the formulas are introduced at a basic level. GPE gained by an object lifted upwards is given by:
ΔEp = m × g × h (change in GPE = mass × gravitational field strength × height)
涉及引力势能（GPE）和动能（KE）的计算会以基础形式引入。物体被举起时增加的引力势能公式为：
ΔEp = m × g × h（引力势能变化 = 质量 × 重力场强度 × 高度）
On Earth, g ≈ 10 N/kg (or 9.8 N/kg for more precision). So if a 2 kg book is lifted 1.5 m, ΔEp = 2 × 10 × 1.5 = 30 J. Kinetic energy depends on mass and speed: KE = ½ m v². However, in Year 7, the emphasis is often on qualitative understanding and simple calculations.
在地球上，g ≈ 10 N/kg（或更精确的 9.8 N/kg）。因此，把一本2千克的书举高1.5米，ΔEp = 2 × 10 × 1.5 = 30 J。动能取决于质量和速度：KE = ½ m v²。不过在7年级，重点通常是定性理解和简单计算。
6. Ohm’s Law (Basic) | 欧姆定律（基础）
Ohm’s law describes the relationship between voltage, current and resistance in an electrical circuit. It is one of the most important laws in electricity at this level. The formula is:
voltage = current × resistance (V = I × R)
欧姆定律描述了电路中电压、电流和电阻之间的关系。这是本阶段电学中最重要的定律之一。公式为：
电压 = 电流 × 电阻 (V = I × R)
Voltage (V) is measured in volts (V), current (I) in amps (A), and resistance (R) in ohms (Ω). If you know any two of these values, you can calculate the third. For a fixed resistor at constant temperature, the current is directly proportional to the voltage across it.
电压（V）的单位是伏特（V），电流（I）的单位是安培（A），电阻（R）的单位是欧姆（Ω）。只要知道其中任意两个量，就能计算出第三个。对于温度恒定的固定电阻，其两端的电压与通过它的电流成正比。
A lamp has a resistance of 24 Ω and a current of 0.5 A flows through it. The voltage across the lamp is V = 0.5 × 24 = 12 V. Understanding Ohm’s law is essential for building and analysing simple series circuits.
一盏灯的电阻为24 Ω，通过的电流为0.5 A，灯两端的电压 V = 0.5 × 24 = 12 V。理解欧姆定律对于搭建和分析简单串联电路至关重要。
7. Balancing Chemical Equations | 化学方程式配平
In a chemical reaction, atoms are rearranged but the total number of each type of atom stays the same. This is the law of conservation of mass. Balanced symbol equations show the correct ratio of reactants and products. For example, the reaction of hydrogen with oxygen to form water:
2H₂ + O₂ → 2H₂O
在化学反应中，原子重新排列，但每种原子的总数保持不变，这就是质量守恒定律。配平的化学方程式表示反应物与生成物的正确比例。例如，氢气与氧气反应生成水：
2H₂ + O₂ → 2H₂O
When balancing equations, never change the chemical formulas themselves; only add coefficients in front. Start by counting atoms of each element on both sides of the arrow and adjust the coefficients to make them equal. State symbols (s), (l), (g) and (aq) indicate solid, liquid, gas, and aqueous solution.
配平方程式时，绝不能改变化学式本身，只能在前面添加系数。先数箭头两边每种元素的原子个数，再调整系数使之相等。状态符号 (s)、(l)、(g) 和 (aq) 分别表示固态、液态、气态和水溶液。
Example: magnesium + oxygen → magnesium oxide. Unbalanced: Mg + O₂ → MgO. Balanced: 2Mg + O₂ → 2MgO. Here, 2 Mg atoms and 2 O atoms appear on both sides. Practising simpler equations builds skills for more complex reactions later.
例如：镁 + 氧气 → 氧化镁。未配平：Mg + O₂ → MgO。配平后：2Mg + O₂ → 2MgO。此时两边各有2个镁原子和2个氧原子。先练习简单的方程式，为后续复杂反应打下基础。
8. Photosynthesis Equation | 光合作用方程式
Photosynthesis is the process by which green plants make their own food using light energy. The word equation and symbol equation summarise the reactants and products:
carbon dioxide + water → glucose + oxygen
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
光合作用是绿色植物利用光能制造自身食物的过程。文字方程式和化学方程式概括了反应物和生成物：
二氧化碳 + 水 → 葡萄糖 + 氧气
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
This reaction takes place in chloroplasts, which contain chlorophyll to absorb light energy. Photosynthesis is an endothermic reaction because it takes in energy from sunlight. The glucose produced is used by the plant for respiration, growth, and storage as starch.
该反应发生在叶绿体中，叶绿体含有吸收光能的叶绿素。光合作用是吸热反应，因为它从阳光中吸收能量。产生的葡萄糖被植物用于呼吸作用、生长，并以淀粉形式储存。
Testing a leaf for starch with iodine solution is a classic Year 7 experiment to prove that photosynthesis has occurred. The balanced equation shows that six molecules of carbon dioxide and six of water yield one glucose molecule and six of oxygen.
用碘液测试叶片中的淀粉是7年级的经典实验，用以证明光合作用确实发生。配平的方程式表明，六分子二氧化碳和六分子水生成一分子葡萄糖和六分子氧气。
9. Respiration Equation | 呼吸作用方程式
Respiration is a chemical reaction that releases energy from glucose in the cells of all living organisms. The word equation for aerobic respiration is:
glucose + oxygen → carbon dioxide + water (+ energy)
呼吸作用是所有生物细胞中从葡萄糖释放能量的化学反应。有氧呼吸的文字方程式为：
葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）
The symbol equation is essentially the reverse of photosynthesis:
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O (+ energy as ATP)
其化学方程式本质上是光合作用的逆反应：
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O（+ 以ATP形式存在的能量）
This reaction is exothermic, meaning it releases energy (often as heat). Respiration happens continuously in every living cell to fuel life processes like movement, growth, and repair. In Year 7, you also learn about anaerobic respiration, which occurs without oxygen and produces lactic acid in animals, or ethanol and carbon dioxide in yeast.
该反应是放热反应，即释放能量（通常表现为热量）。每个活细胞都在不断进行呼吸作用，为运动、生长和修复等生命过程提供能量。在7年级，你还会学习无氧呼吸，它发生在无氧条件下，动物体内产生乳酸，酵母则产生酒精和二氧化碳。
Comparing the photosynthesis and respiration equations helps highlight how plants recycle gases in ecosystems.
比较光合作用和呼吸作用的方程式，有助于理解植物如何在生态系统中循环气体。
10. Particle Theory of Matter | 物质粒子理论
The particle theory explains the properties of solids, liquids and gases in terms of tiny, moving particles. Key ideas include:
- All matter is made up of tiny particles (atoms, molecules or ions).
- Particles are constantly in motion – the higher the temperature, the faster they move.
- There are forces of attraction between particles. These forces are strongest in solids and weakest in gases.
- The spaces between particles are smallest in solids and largest in gases.
粒子理论用微小的运动粒子来解释固体、液体和气体的性质。其核心思想包括：
- 所有物质都由微小粒子（原子、分子或离子）构成。
- 粒子在永不停息地运动——温度越高，运动越快。
- 粒子间存在吸引力。这种力在固体中最强，在气体中最弱。
- 粒子之间的空隙在固体中最小，在气体中最大。
This theory is essential for understanding changes of state: melting, boiling, condensing, and freezing. When a solid is heated, particles gain energy and vibrate more vigorously until they can break free from fixed positions and move around – this is melting. Further heating gives them enough energy to overcome attractions and escape as a gas – boiling.
这个理论对理解状态变化至关重要：熔化、沸腾、冷凝和凝固。当固体受热，粒子获得能量并剧烈振动，直到能够挣脱固定位置自由移动——这就是熔化。继续加热给予它们足够能量来克服吸引力并逸出成为气体——这就是沸腾。
Diffusion, the movement of particles from a region of high concentration to low concentration, is also explained by particle theory and is faster in gases than in liquids due to larger spaces and faster movement.
扩散是指粒子从高浓度区域向低浓度区域的运动，同样可用粒子理论解释；气体中的扩散比液体中快，因为气体粒子间空隙更大且运动更快。
11. Key Units and Conversions | 关键单位与换算
Using the correct units is vital in any scientific calculation. Below is a table of common quantities, their symbols, and SI units used in Year 7:
在任何科学计算中，使用正确单位都至关重要。下表列出了7年级常见的物理量、符号和国际单位制单位：
| Quantity (量) | Symbol | Unit (单位) | Symbol |
|---|---|---|---|
| length (长度) | l, s, d | metre (米) | m |
| mass (质量) | m | kilogram (千克) | kg |
| time (时间) | t | second (秒) | s |
| temperature (温度) | T, θ | degree Celsius (摄氏度) | °C |
| force (力) | F | newton (牛顿) | N |
| energy (能量) | E | joule (焦耳) | J |
| voltage (电压) | V | volt (伏特) | V |
| current (电流) | I | ampere (安培) | A |
| resistance (电阻) | R | ohm (欧姆) | Ω |
Converting between unit prefixes is also important: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm. For mass: 1 kg = 1000 g, 1 g = 1000 mg. For volume: 1 m³ = 1000 dm³, 1 dm³ = 1000 cm³, and 1 litre = 1000 ml = 1000 cm³. These conversions often appear in density and speed calculations.
单位前缀之间的换算也很重要：1 千米 = 1000 米，1 米 = 100 厘米，1 厘米 = 10 毫米。质量：1 千克 = 1000 克，1 克 = 1000 毫克。体积：1 立方米 = 1000 立方分米，1 立方分米 = 1000 立方厘米，1 升 = 1000 毫升 = 1000 立方厘米。这些换算常在密度和速度计算中出现。
12. Summary Table of Formulas | 公式速查表
This final section compiles the most important formulas from the handbook into one convenient table for quick revision. Practise using these equations by substituting numbers and ensuring you can rearrange them as needed.
最后一节将本手册中最重要的公式汇编在一张表格里，方便快速复习。请通过代入数字和使用公式变形来练习，确保你能够灵活运用这些方程式。
| Topic (主题) | Formula (公式) | Variables (变量说明) |
|---|---|---|
| Speed (速度) | v = s / t | v: speed, s: distance, t: time |
| Density (密度) | ρ = m / V | ρ: density, m: mass, V: volume |
| Force (力) | F = m × a | F: force, m: mass, a: acceleration |
| Pressure (压强) | P = F / A | P: pressure, F: force, A: area |
| GPE change (引力势能变化) | ΔEp = m g h | m: mass, g: gravitational field strength, h: height |
| Ohm’s Law (欧姆定律) | V = I × R | V: voltage, I: current, R: resistance |
| Photosynthesis (光合作用) | 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ | carbon dioxide + water → glucose + oxygen |
| Aerobic Respiration (有氧呼吸) | C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O | glucose + oxygen → carbon dioxide + water |
Remember that while these equations provide a powerful toolkit, understanding the underlying concepts is just as important. Always check your units and ask yourself whether the answer makes sense in the real world.
请记住，尽管这些方程式提供了一个强大的工具箱，但理解背后的概念同样重要。始终检查你的单位，并问自己答案在现实世界中是否合理。
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