📚 Year 7 CAIE Science: Formula & Theorem Quick Reference Handbook | 七年级 CAIE 科学：公式定理速查手册
This quick reference handbook gathers the essential formulas and theorems you will meet in Year 7 CAIE Science. It covers topics from physics, chemistry and biology – speed, density, pressure, energy, electricity, forces, moments, matter, cell theory, photosynthesis and basic chemical word equations. Keep these fundamentals close; they are the building blocks for every investigation and exam question you will face.
这本速查手册汇总了你在七年级 CAIE 科学课中会遇到的所有核心公式和定理，涵盖物理、化学和生物三大领域——速度、密度、压强、能量、电流、力、力矩、物质状态、细胞学说、光合作用以及基本的化学文字方程式。把这些基础内容记在心里，它们是你攻克每一次探究活动和每一道考题的基石。
1. Speed, Distance and Time | 速度、距离和时间
Speed tells you how fast something is moving. The formula links distance travelled to the time taken. In Year 7 you will use average speed, measured in metres per second (m/s) or kilometres per hour (km/h).
速度告诉你物体运动的快慢。这个公式将移动的距离与所用时间联系起来。七年级阶段主要使用平均速度，单位是米每秒（m/s）或千米每小时（km/h）。
Speed = Distance ÷ Time
速度 = 距离 ÷ 时间
You can rearrange the triangle to find distance (distance = speed × time) or time (time = distance ÷ speed). Always check that units match – if speed is in m/s, distance must be in metres and time in seconds.
你可以通过公式变形求距离（距离 = 速度 × 时间）或求时间（时间 = 距离 ÷ 速度）。一定要检查单位是否统一——如果速度的单位是 m/s，那么距离必须是米，时间必须是秒。
2. Density | 密度
Density is the mass of a substance packed into a unit volume. It explains why some objects float and others sink. The SI unit is kilograms per cubic metre (kg/m³), but in the lab you will often use grams per cubic centimetre (g/cm³).
密度是单位体积内所含物质的质量。它解释了为什么有些物体会浮起来而有些会沉下去。国际单位是千克每立方米（kg/m³），但在实验室中常用克每立方厘米（g/cm³）。
Density = Mass ÷ Volume
密度 = 质量 ÷ 体积
To find mass: mass = density × volume. To find volume: volume = mass ÷ density. Remember that 1 g/cm³ = 1000 kg/m³. Water has a density of 1 g/cm³; objects with density less than 1 g/cm³ float in water.
求质量：质量 = 密度 × 体积。求体积：体积 = 质量 ÷ 密度。记住 1 g/cm³ = 1000 kg/m³。水的密度是 1 g/cm³；密度小于 1 g/cm³ 的物体会浮在水面上。
3. Pressure | 压强
Pressure measures how concentrated a force is over an area. A small force on a tiny area can create a large pressure, while a large force spread out reduces pressure. The unit of pressure is the pascal (Pa), where 1 Pa = 1 N/m².
压强衡量力在面积上的集中程度。很小的力作用在极小的面积上会产生很大的压强，而很大的力分散开来则会减小压强。压强的单位是帕斯卡（Pa），1 Pa = 1 N/m²。
Pressure = Force ÷ Area
压强 = 力 ÷ 面积
From this, force = pressure × area and area = force ÷ pressure. Everyday examples include sharp knives (small area, high pressure) and snow shoes (large area, low pressure).
由此可得，力 = 压强 × 面积，面积 = 力 ÷ 压强。生活中的例子有锋利的刀刃（面积小、压强大）和雪地鞋（面积大、压强小）。
4. Work, Energy and Power | 功、能和功率
Whenever a force moves an object, work is done. Energy is the ability to do work, and power tells you the rate at which work is done. These concepts are central to understanding machines and living systems.
只要力使物体移动，就做了功。能量是做功的本领，而功率表示做功的快慢。这些概念对于理解机器和生命系统至关重要。
Work Done = Force × Distance moved in the direction of the force
做功 = 力 × 沿力方向移动的距离
Power = Work ÷ Time
功率 = 功 ÷ 时间
Work is measured in joules (J), force in newtons (N) and distance in metres (m). Power is measured in watts (W); 1 W = 1 J/s. Energy can be stored in many forms – kinetic, potential, thermal, chemical – but the total energy in a closed system is always conserved.
功的单位是焦耳（J），力是牛顿（N），距离是米（m）。功率的单位是瓦特（W）；1 W = 1 J/s。能量可以以多种形式储存——动能、势能、热能、化学能——但在封闭系统中总能量总是守恒的。
5. Current, Voltage and Resistance | 电流、电压和电阻
Electric circuits obey a simple relationship known as Ohm’s Law. Current is the flow of electric charge, voltage is the push driving the current, and resistance opposes the flow.
电路遵循一个简单的关系，即欧姆定律。电流是电荷的流动，电压是驱动电流的压力，而电阻阻碍电流的流动。
Voltage = Current × Resistance
电压 = 电流 × 电阻
Or, in symbols: V = I × R. Voltage is measured in volts (V), current in amperes (A) and resistance in ohms (Ω). You can also write current = voltage ÷ resistance and resistance = voltage ÷ current. In a series circuit, current is the same everywhere but voltage divides; in a parallel circuit, voltage is the same across branches but current divides.
或者用符号表示：V = I × R。电压的单位是伏特（V），电流是安培（A），电阻是欧姆（Ω）。也可以写作 电流 = 电压 ÷ 电阻，电阻 = 电压 ÷ 电流。串联电路中电流处处相等但电压分配；并联电路中各支路电压相等但电流分配。
6. Force, Mass and Acceleration | 力、质量和加速度
Newton’s Second Law of Motion describes how a resultant force changes the motion of an object. In Year 7 you will begin to use this idea with simple calculations, often treating acceleration as a change in speed over time.
牛顿第二运动定律描述合力如何改变物体的运动状态。七年级时，你将开始用简单的计算来应用这个概念，通常将加速度视为速度随时间的变化。
Force = Mass × Acceleration
力 = 质量 × 加速度
Force is measured in newtons (N), mass in kilograms (kg) and acceleration in metres per second squared (m/s²). For a given force, a larger mass results in a smaller acceleration. This is why a heavy truck needs a much bigger engine to accelerate like a car.
力的单位是牛顿（N），质量是千克（kg），加速度是米每二次方秒（m/s²）。在力一定的情况下，质量越大加速度越小。这就是为什么重型卡车需要比小汽车大得多的发动机才能获得同样的加速度。
7. Moments | 力矩
A moment is the turning effect of a force about a pivot. Understanding moments helps explain how levers, see-saws and spanners work. The principle of moments states that for an object in equilibrium, the total clockwise moment equals the total anticlockwise moment.
力矩是力绕支点产生的转动效果。理解力矩有助于解释杠杆、跷跷板和扳手的工作原理。力矩原理指出，当物体平衡时，顺时针力矩之和等于逆时针力矩之和。
Moment = Force × Perpendicular distance from pivot
力矩 = 力 × 支点到力作用线的垂直距离
Moment is measured in newton metres (N m). To increase a moment, you can either increase the force or apply it further from the pivot. A door handle is placed far from the hinges to make the door easier to open.
力矩的单位是牛顿米（N m）。要增大力矩，可以增大作用力，或者让它离支点更远。门把手安装在远离铰链的位置，就是为了让开门更省力。
8. States of Matter and Changes of State | 物质的状态及其变化
While not a formula, the particle model is a fundamental theorem in Year 7 science. Matter exists as solid, liquid or gas, and changes state when heated or cooled. These changes occur at fixed melting and boiling points for a pure substance.
虽然这不是一个公式，但粒子模型是七年级科学中的一项基本理论。物质以固态、液态或气态存在，并在加热或冷却时改变状态。对于纯净物，这些变化在固定的熔点和沸点发生。
The key changes are: melting (solid → liquid), freezing (liquid → solid), boiling/evaporation (liquid → gas), condensation (gas → liquid), sublimation (solid → gas directly). During a state change, temperature stays constant even though energy is being transferred – this energy is used to overcome inter-particle forces, not to raise temperature.
关键变化有：熔化（固态 → 液态）、凝固（液态 → 固态）、沸腾/蒸发（液态 → 气态）、冷凝（气态 → 液态）、升华（固态直接变为气态）。在状态变化期间，即使能量在传递，温度也保持不变——这部分能量用于克服粒子间作用力，而不是提升温度。
9. Cell Theory | 细胞学说
Cell theory is the foundation of biology. It states: all living organisms are made of one or more cells; the cell is the basic unit of life; and all cells arise from pre-existing cells. In Year 7 you will learn to identify plant and animal cells and their organelles.
细胞学说是生物学的基础。它指出：所有生物都由一个或多个细胞组成；细胞是生命的基本单位；所有细胞都来自已有的细胞。在七年级，你将学会识别植物细胞和动物细胞以及它们的细胞器。
Key organelles include: nucleus (controls the cell, contains DNA), cytoplasm (site of chemical reactions), cell membrane (controls entry and exit of substances), mitochondria (release energy through respiration), and in plant cells only: cell wall (provides support), chloroplasts (absorb light for photosynthesis) and a large permanent vacuole (contains cell sap).
重要的细胞器包括：细胞核（控制细胞，含 DNA）、细胞质（化学反应场所）、细胞膜（控制物质进出）、线粒体（通过呼吸作用释放能量）。仅在植物细胞中：细胞壁（提供支持）、叶绿体（吸收光进行光合作用）和中央大液泡（含细胞液）。
10. Photosynthesis | 光合作用
Photosynthesis is the process by which green plants make their own food using light energy. It can be summarised as a word equation, a concept you will use frequently in Year 7.
光合作用是绿色植物利用光能制造自身养料的过程。它可以用一个文字方程式来概括，你会在七年级的学习中频繁用到。
Carbon dioxide + Water → Glucose + Oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
This reaction takes place in the chloroplasts, requires chlorophyll to capture light energy, and only occurs during daylight. The glucose produced is used for respiration, stored as starch, or turned into other substances like cellulose for cell walls.
这个反应发生在叶绿体中，需要叶绿素来捕获光能，并且只在有光照时发生。生成的葡萄糖用于呼吸作用，转化为淀粉储存，或者转化为其他物质，比如构成细胞壁的纤维素。
11. Word Equations for Simple Chemical Reactions | 简单化学反应的文字方程式
In Year 7 chemistry, you represent chemical reactions using word equations. These show the reactants (what you start with) and the products (what you end with), linked by an arrow that means ‘reacts to form’. No formulas are needed yet – words are enough.
在七年级化学中，你用文字方程式来表示化学反应。方程式中包括反应物（起始物质）和生成物（终了物质），中间用箭头连接，箭头表示“反应生成”。此时还不必写化学式，文字就足够了。
Examples: Methane + Oxygen → Carbon dioxide + Water (combustion); Magnesium + Oxygen → Magnesium oxide (oxidation); Hydrochloric acid + Sodium hydroxide → Sodium chloride + Water (neutralisation).
例如：甲烷 + 氧气 → 二氧化碳 + 水（燃烧）；镁 + 氧气 → 氧化镁（氧化）；盐酸 + 氢氧化钠 → 氯化钠 + 水（中和）。
12. The Law of Conservation of Mass | 质量守恒定律
During any chemical reaction, the total mass of the reactants always equals the total mass of the products. Atoms are rearranged, but none are created or destroyed. This theorem is crucial when you balance equations later, and it underpins every chemical calculation.
在任何化学反应中，反应物的总质量总是等于生成物的总质量。原子重新排列，但既不会凭空产生也不会凭空消失。这个定律是日后配平方程式和所有化学计算的基础。
For example, if 12 g of carbon reacts with 32 g of oxygen to produce carbon dioxide, the carbon dioxide formed will have a mass of exactly 44 g. In all experiments you design, you must consider that apparent mass changes are due to gases entering or leaving the reaction container.
例如，如果 12 g 碳与 32 g 氧气反应生成二氧化碳，那么生成的二氧化碳的质量恰好是 44 g。在你设计的任何实验中，都必须考虑到表观质量的变化往往是因为气体进入或离开了反应容器。
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