📚 KS3 CCEA Science: Quick Reference Handbook of Formulas and Theorems | KS3 CCEA 科学：公式定理速查手册
This quick-reference guide brings together the essential formulas, equations and relationships you will encounter in KS3 CCEA Science. Use it to revise how quantities are linked, practise rearranging equations and learn the correct SI units. Each section presents a core formula, explains its meaning and gives helpful tips for calculations.
这本速查手册汇集了你在 KS3 CCEA 科学课程中会用到的重要公式、方程与定量关系。你可以用它来复习物理量之间的联系，练习公式变形，并记住正确的国际单位。每一节都会给出一个核心公式，解释其含义，并提供有助于计算的提示。
1. Speed, Distance and Time | 速度、距离和时间
e formula is written as: speed = distance ÷ time. In symbols, this is often written v = d / t, where d is distance and t is time. Speed is measured in metres per second (m/s), distance in metres (m) and time in seconds (s). You can also use kilometres per hour (km/h) if distance is in kilometres and time in hours.
平均速度等于通过的总距离除以所用的总时间。公式为：速度 = 距离 ÷ 时间。通常用符号表示为 v = d / t，其中 d 代表距离，t 代表时间。速度的单位是米每秒 (m/s)，距离的单位是米 (m)，时间的单位是秒 (s)。如果距离用千米、时间用小时，也可以使用千米每小时 (km/h)。
distance ÷ speed. Always make sure the units match before you start a calculation.
要求距离，可对公式变形：距离 = 速度 × 时间。要求时间：时间 = 距离 ÷ 速度。计算前要确保所有单位匹配。
2. Acceleration and Force (Newton's Second Law) | 加速度和力（牛顿第二定律）
changes. It is calculated using: acceleration = change in velocity ÷ time taken, or a = (v - u) / t, where u is the initial velocity, v is the final velocity and t is time. Acceleration is measured in metres per second squared (m/s²).
加速度是速度变化的快慢。它的计算公式是：加速度 = 速度变化量 ÷ 时间，即 a = (v - u) / t，其中 u 是初速度，v 是末速度，t 是时间。加速度的单位是米每二次方秒 (m/s²)。
An unbalanced force causes an object to accelerate. The size of the acceleration depends on the mass of the object and the size of the force, expressed by F = m × a. Force is measured in newtons (N), mass in kilograms (kg) and acceleration in m/s². One newton is the force needed to accelerate a 1 kg mass by 1 m/s².
不平衡的力会使物体加速。加速度的大小取决于物体的质量和力的大小，用公式 F = m × a 表示。力的单位是牛顿 (N)，质量的单位是千克 (kg)，加速度的单位是 m/s²。1 牛顿就是使 1 kg 的物体产生 1 m/s² 加速度所需的力。
3. Weight and Mass | 重量和质量
Weight is the force of gravity acting on an object's mass. It is not the same as mass. The relationship is: weight = mass × gravitational field strength, or W = m × g. Weight is measured in newtons (N), mass in kilograms (kg) and g in newtons per kilogram (N/kg). On Earth, g is approximately 9.8 N/kg, but often rounded to 10 N/kg for KS3 calculations.
重量是作用在物体质量上的重力。它与质量不同。二者的关系为：重量 = 质量 × 重力场强度，即 W = m × g。重量的单位是牛顿 (N)，质量的单位是千克 (kg)，g 的单位是牛顿每千克 (N/kg)。在地球表面，g 大约为 9.8 N/kg，但在 KS3 计算中常取 10 N/kg。
Mass is a measure of the amount of matter in an object and stays the same everywhere. Weight changes depending on the gravitational field strength – for example, you would weigh less on the Moon because its gravitational field is weaker.
质量是物体所含物质的多少，在任何地方都保持不变。重量则会随重力场强度变化——例如，在月球上你的重量会变轻，因为那里的重力场较弱。
4. Pressure in Solids and Fluids | 固体和流体中的压力
Pressure is a measure of how concentrated a force is over an area. The formula for pressure on a surface is: pressure = force ÷ area, or P = F / A a), where 1 Pa = 1 N/m²;. Force is in newtons (N) and area in square metres (m²).
压力是衡量力在面积上集中程度的物理量。作用在表面上的压力公式为：压力 = 力 ÷ 面积，即 P = F / A。压力的单位是帕斯卡 (Pa)，1 Pa = 1 N/m²;。力用牛顿 (N)，面积用平方米 (m²)。
A larger area reduces pressure, while a smaller area increases pressure for the same force. This is why sharp knives cut more easily and why caterpillar tracks stop heavy vehicles sinking into mud.
相同的力下，面积越大压强越小，面积越小压强越大。这就是锋利的刀更容易切割、以及履带能防止重型车辆陷入泥地的原因。
5. Density | 密度
Density tells us how much mass is packed into a certain volume. The formula is: density = mass ÷ volume, or using the Greek letter rho: ρ = m / V. Density is commonly measured in kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³). Remember that 1 g/cm³ equals 1000 kg/m³.
密度表示单位体积内所含质量的多少。公式为：密度 = 质量 ÷ 体积，或用希腊字母 rho 表示：ρ = m / V。密度的常用单位是千克每立方米 (kg/m³) 或克每立方厘米 (g/cm³)。注意 1 g/cm³ 等于 1000 kg/m³。
You can use the density formula to identify materials, predict whether an object will float (if its density is less than that of the fluid), and calculate mass or volume when the other two quantities are known.
你可以用密度公式鉴别材料，预测物体的浮沉（密度小于流体密度时会浮起），以及在已知两个物理量时求出质量或体积。
6. Hooke's Law | 胡克定律
Hooke's Law describes the extension of a spring when a force is applied, up to its limit of proportionality. It states: force = spring constant × extension, or F = k × e. Here, F is the force in newtons (N), k is the spring constant in newtons per metre (N/m) and e is the extension in metres (m).
胡克定律描述了在弹性限度内弹簧的伸长量与外力的关系。其内容为：力 = 弹簧常数 × 伸长量，即 F = k × e。式中 F 是力 (N)，k 是弹簧常数 (N/m)，e 是伸长量 (m)。
If you stretch a spring too far, it will exceed its elastic limit and no longer obey Hooke's Law – it becomes permanently deformed. A graph of force against extension is a straight line through the origin only while the spring obeys the law.
如果过度拉伸弹簧，就会超过它的弹性极限，弹簧就不再遵循胡克定律，并产生永久形变。只有当弹簧遵循该定律时，力 – 伸长量的图线才是通过原点的直线。
7. Moments and Levers | 力矩和杠杆
A moment is the turning effect of a force. It is calculated using: moment = force × perpendicular distance from the pivot, or M = F × d. Moment is measured in newton metres (N m), force in newtons (N) and distance in metres (m). The distance must be the perpendicular distance from the line of action of the force to the pivot.
力矩是力的转动效果，计算公式为：力矩 = 力 × 支点到力作用线的垂直距离，即 M = F × d。力矩的单位是牛顿米 (N m)，力用牛顿 (N)，距离用米 (m)。距离必须是支点到力作用线的垂直距离。
For a lever or see-saw to be balanced, the total clockwise moment must equal the total anticlockwise moment. This is the principle of moments: F&sb1; × d&sb1; = F&sb2; × d&sb2; for two forces. You can use this to find unknown forces or distances.
杠杆或跷跷板要平衡，顺时针力矩的总和必须等于逆时针力矩的总和。这就是力矩原理：对于两个力的情况，有 F&sb1; × d&sb1; = F&sb2; × d&sb2;。你可以利用该原理求解未知的力或距离。
8. Work Done and Power | 做功和功率
Work is done when a force moves an object. The amount of work is given by: work done = force × distance moved in the direction of the force, or W = F × s. Work is measured in joules (J), force in newtons (N) and distance in metres (m). One joule is the work done when a force of 1 N moves an object 1 m in the direction of the force.
当一个力使物体移动时，力就做了功。功的大小计算公式为：做的功 = 力 × 沿力方向移动的距离，即 W = F × s。功的单位是焦耳 (J)，力用牛顿 (N)，距离用米 (m)。1 焦耳就是 1 N 的力使物体沿力的方向移动 1 m 所做的功。
Power is the rate at which work is done or energy is transferred. The formula is: power = work done ÷ time taken, or P = W / t watts (W), where 1 W = 1 J/s. A more powerful appliance transfers more energy each second.
功率是做功或能量转换的快慢。公式为：功率 = 做的功 ÷ 所用时间，即 P = W / t。功率的单位是瓦特 (W)，1 W = 1 J/s。功率越大的电器每秒转换的能量越多。
9. Electrical Formulas (Ohm's Law and Power) | 电学公式（欧姆定律和电功率）
Ohm's Law links voltage, current and resistance in a circuit at constant temperature: voltage = current × resistance, or V = I × R. Voltage is measured in volts (V), current in amperes (A) and resistance in ohms (Ω). This means that current is directly proportional to voltage if resistance stays the same.
欧姆定律描述了恒定温度下电路中电压、电流和电阻的关系：电压 = 电流 × 电阻，即 V = I × R。电压的单位是伏特 (V)，电流的单位是安培 (A)，电阻的单位是欧姆 (Ω)。这意味着在电阻不变时，电流与电压成正比。
Electrical power is the rate at which an appliance transfers electrical energy. Two useful forms of the power equation are: power = current × voltage (P = I × V) and, using Ohm's Law, P = I²; × R. Power is measured in watts (W). For example, a bulb drawing 0.5 A from a 10 V supply has a power of 5 W.
电功率是用电器转换电能的快慢。电功率的两个有用公式是：功率 = 电流 × 电压（P = I × V）以及结合欧姆定律得到的 P = I²; × R。功率的单位是瓦特 (W)。例如，一个在 10 V 电压下流过 0.5 A 的灯泡，其功率为 5 W。
10. Energy Efficiency | 能量效率
Efficiency measures how well a device converts input energy into useful output energy. The formula is: efficiency = (useful output energy ÷ total input energy) × 100% sed using power: efficiency = (useful power output ÷ total power input) × 100% s transferred to the thermal store of the surroundings, efficiency is always less than 100%.
效率衡量设备把输入能量转化为有用输出能量的有效程度。公式为：效率 = （有用输出能量 ÷ 总输入能量）× 100%。也可以用功率表示：效率 = （有用输出功率 ÷ 总输入功率）× 100%。由于总有部分能量转移到周围环境的内能中，效率始终低于100%。
but only 60 J is transferred to kinetic energy, its efficiency is 60/100 × 100 = 60%. The remaining 40 J is wasted, mostly as heat.
例如，一台电动机使用了 100 J 的电能，却只有 60 J 转化为动能，那么它的效率是 60/100 × 100 = 60%。剩下的 40 J 以热量等形式被浪费掉了。
11. Chemical and Biological Formulas | 化学和生物公式
In chemistry, mass is conserved during a reaction – the total mass of products equals the total mass of reactants. To calculate the relative formula mass (Mr) of a compound, add together the relative atomic masses (Ar) of all the atoms in the formula. For example, water H2O: Mr = (2 × 1) + 16 = 18. No unit is needed because it is a relative value.
在化学中，反应前后质量守恒——生成物的总质量等于反应物的总质量。要计算化合物的相对分子质量（Mr），只需把化学式中所有原子的相对原子质量（Ar）相加。例如水 H2O：Mr = (2 × 1) + 16 = 18。相对质量是一个比值，没有单位。
In biology, magnification is used to compare the size of an image seen through a microscope with the real size of the specimen. The formula is: magnification = image size ÷ actual size u can rearrange this to find actual size: actual size = image size ÷ magnification.
在生物学中，放大倍率用来比较显微镜下图像的尺寸和标本的真实尺寸。公式为：放大倍率 = 图像尺寸 ÷ 实际尺寸。两个尺寸必须使用相同的单位，通常是毫米 (mm) 或微米 (µm)。变形后可以求出实际尺寸：实际尺寸 = 图像尺寸 ÷ 放大倍率。
Another useful relationship in biology is the calculation of the total magnification of a microscope: total magnification = eyepiece lens magnification × objective lens magnification. For instance, a ×10 eyepiece and a ×40 objective give a total magnification of ×400.
生物学中另一个有用的关系是显微镜总放大倍率的计算：总放大倍率 = 目镜放大倍率 × 物镜放大倍率。例如，×10 的目镜和 ×40 的物镜带来 ×400 的总放大倍率。
Published by TutorHao | 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