📚 Year 7 CIE Science: Formula & Theorem Quick Reference | Year 7 CIE 科学：公式定理速查手册
Building a strong foundation in science means becoming comfortable with the key formulas and theorems that describe how the world works. This quick reference collects the most important equations and principles you will meet in Year 7 CIE Science. Each section gives you the formula in words and symbols, explains what it means, and shows you how to use it in simple calculations. Keep this handbook handy when you revise for tests or work through practice questions.
在科学中打好坚实的基础，意味着要熟悉描述世界运行方式的关键公式和定理。这份速查手册汇集了你在 Year 7 CIE 科学课程中会遇到的最重要的方程式和原理。每一节都会用文字和符号给出公式，解释其含义，并展示如何在简单计算中使用它。在你复习考试或做练习题时，请将这本手册放在手边。
1. Speed Formula | 速度公式
Speed tells you how fast an object is moving. It is the distance travelled in a certain amount of time. The formula that links speed, distance and time is one of the most useful in physics.
速度告诉你一个物体运动得有多快。它是在一定时间内通过的距离。将速度、距离和时间联系起来的公式是物理学中最有用的公式之一。
Speed = Distance ÷ Time
In symbols, we write this as:
用符号表示为：
v = s / t
Here v stands for speed, s stands for distance and t stands for time. Speed is measured in metres per second (m/s) when distance is in metres (m) and time is in seconds (s). You can also use kilometres per hour (km/h) for longer journeys.
这里 v 代表速度，s 代表距离，t 代表时间。当距离以米（m）为单位、时间以秒（s）为单位时，速度的单位是米每秒（m/s）。对于较长的行程，你也可以使用千米每小时（km/h）。
You can rearrange the formula into a triangle to find distance or time:
你可以将公式重新排列成一个三角形，来求出距离或时间：
Distance = Speed × Time
距离 = 速度 × 时间
Time = Distance ÷ Speed
时间 = 距离 ÷ 速度
Example: A cyclist travels 150 metres in 25 seconds. Speed = 150 ÷ 25 = 6 m/s.
例题：一名自行车手在25秒内行驶了150米。速度 = 150 ÷ 25 = 6 m/s。
2. Density Formula | 密度公式
Density is a measure of how much mass is packed into a certain volume. Different materials have different densities; this is why a piece of wood floats on water but a metal key sinks.
密度是衡量一定体积内含有多少质量的量度。不同的材料具有不同的密度；这就是为什么一块木头会浮在水面上而一把金属钥匙会沉下去。
Density = Mass ÷ Volume
The symbolic formula is:
符号公式为：
ρ = m / V
ρ (the Greek letter rho) stands for density, m for mass and V for volume. Common units are grams per cubic centimetre (g/cm³) for solids and liquids, and kilograms per cubic metre (kg/m³) for larger quantities. 1 g/cm³ equals 1000 kg/m³.
ρ（希腊字母 rho）代表密度，m 代表质量，V 代表体积。常见的单位有固体和液体采用的克每立方厘米（g/cm³），以及较大数量时采用的千克每立方米（kg/m³）。1 g/cm³ 等于 1000 kg/m³。
To find mass or volume you can rearrange:
要计算质量或体积，可重新排列：
Mass = Density × Volume
质量 = 密度 × 体积
Volume = Mass ÷ Density
体积 = 质量 ÷ 密度
: A brick of mass 2400 g has a volume of 1200 cm³. Its density is 2400 ÷ 1200 = 2.0 g/cm³.
例题：一块质量为2400克的砖，体积为1200立方厘米。它的密度是 2400 ÷ 1200 = 2.0 g/cm³。
3. Pressure Formula | 压强公式
Pressure describes how concentrated a force is over an area. A sharp knife cuts easily because the force is applied over a very small area, producing a high pressure.
压强描述的是力在一个面积上的集中程度。锋利的刀切东西很容易，因为力施加在一个非常小的面积上，产生了很大的压强。
Pressure = Force ÷ Area
The symbolic form is:
符号形式为：
P = F / A
P stands for pressure, F for force and A for area. The SI unit of pressure is the pascal (Pa), where 1 Pa is equal to 1 newton per square metre (N/m²). Larger forces or smaller areas lead to higher pressure.
P 代表压强，F 代表力，A 代表面积。压强的国际单位是帕斯卡（Pa），1 Pa 等于 1 牛顿每平方米（N/m²）。较大的力或较小的面积会导致较高的压强。
You can find force or area using these rearrangements:
你可以用以下变形求出力或面积：
Force = Pressure × Area
力 = 压强 × 面积
Area = Force ÷ Pressure
面积 = 力 ÷ 压强
Example: A force of 500 N acts on an area of 0.25 m². Pressure = 500 ÷ 0.25 = 2000 Pa.
例题：一个500 N的力作用在0.25 m²的面积上。压强 = 500 ÷ 0.25 = 2000 Pa。
4. Work and Energy | 功与能量
When a force moves an object, work is done. Work is a way of transferring energy from one store to another. The amount of work done is calculated using this formula.
当一个力使物体移动时，就做了功。功是将能量从一个储存库转移到另一个储存库的一种方式。所做的功的量用以下公式计算。
Work Done = Force × Distance moved in the direction of the force
In symbols:
符号表示为：
W = F × d
W represents work done, F is the force applied and d is the displacement in the direction of the force. 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.
W 代表做的功，F 是施加的力，d 是沿力方向的位移。功的单位是焦耳（J），力的单位是牛顿（N），距离的单位是米（m）。当1 N的力使物体移动1 m时，所做的功就是1焦耳。
ushes a trolley with a force of 30 N over a distance of 10 m. Work done = 30 × 10 = 300 J.
例题：一个人用30 N的力推一辆手推车，移动了10 m的距离。所做的功 = 30 × 10 = 300 J。
The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. In any process, the total energy at the start equals the total energy at the end.
能量守恒定律指出，能量不能被创造或消灭，只能被转移或转化。在任何过程中，起始的总能量等于结束时的总能量。
5. Moments (Turning Effect) | 力矩（转动效应）
A moment is the turning effect of a force about a pivot. It depends on the size of the force and how far it is applied from the pivot.
力矩是力绕一个枢轴的转动效应。它取决于力的大小以及力离枢轴的距离。
Moment = Force × Perpendicular distance from pivot
Symbolically:
符号表示为：
M = F × d
M is the moment, F is the force and d is the perpendicular distance from the pivot to the line of action of the force. The unit for moment is newton-metre (Nm).
M 是力矩，F 是力，d 是从枢轴到力的作用线的垂直距离。力矩的单位是牛顿·米（Nm）。
When an object is balanced, the sum of the clockwise moments equals the sum of the anticlockwise moments about the pivot. This is known as the principle of moments.
当一个物体平衡时，顺时针方向的总力矩等于逆时针方向的总力矩。这被称为力矩原理。
The distance can be found using: 20 N × 0.5 m = 10 N × d, so d = (20 × 0.5) ÷ 10 = 1.0 m.
例题：一个20 N的重物放置在跷跷板左侧距枢轴0.5 m处。要使其平衡，必须在右侧放置一个10 N的重物。根据 20 N × 0.5 m = 10 N × d，可得 d = (20 × 0.5) ÷ 10 = 1.0 m。
6. Microscopy Magnification | 显微镜放大倍数
When you use a light microscope to observe cells, the image you see is magnified by two lenses: the eyepiece lens and the objective lens. The total magnification can be calculated easily.
当你使用光学显微镜观察细胞时，你看到的图像被两个透镜放大：目镜和物镜。总放大倍数可以很容易地计算出来。
Total Magnification = Eyepiece Magnification × Objective Magnification
ears 400 times larger than its actual size. This formula applies to all compound light microscopes.
例如，如果目镜放大10倍，物镜放大40倍，那么总放大倍数就是 10 × 40 = 400倍。标本显示的大小是实际尺寸的400倍。这个公式适用于所有复式光学显微镜。
agnification. But in Year 7, you will most often be asked to find the total magnification.
要计算在显微镜下观察到的物体的实际尺寸，你可以重新排列关系：实际尺寸 = 图像尺寸 ÷ 放大倍数。但在 Year 7，你最常被问到的是求出总放大倍数。
7. Photosynthesis Word and Symbol Equation | 光合作用的文字方程式与符号方程式
Photosynthesis is the process by which green plants make their own food using light energy. The raw materials are carbon dioxide and water, and the products are glucose and oxygen. This reaction only happens in the presence of light and chlorophyll.
光合作用是绿色植物利用光能制造自己食物的过程。原料是二氧化碳和水，产物是葡萄糖和氧气。这个反应只有在光和叶绿素存在的条件下才能发生。
The word equation is:
文字方程式为：
Carbon dioxide + Water → Glucose + Oxygen
The light and chlorophyll are written above the arrow as conditions, not as reactants.
光和叶绿素作为条件写在箭头之上，而不是反应物。
The balanced chemical equation (which you will begin to use) is:
配平的化学方程式（你将开始使用）为：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
This shows that six molecules of carbon dioxide react with six molecules of water to produce one molecule of glucose and six molecules of oxygen. The subscript numbers ₂ and ₆ tell you how many atoms of each element are in the molecule.
这表明6个二氧化碳分子与6个水分子反应，生成1个葡萄糖分子和6个氧分子。下标数字₂和₆告诉你每个分子中有多少个该元素的原子。
8. Aerobic Respiration Equation | 有氧呼吸方程式
Respiration is the process that releases energy from glucose in all living cells. Aerobic respiration uses oxygen to break down glucose and releases a relatively large amount of energy.
呼吸作用是所有活细胞从葡萄糖中释放能量的过程。有氧呼吸利用氧气分解葡萄糖，并释放出相对大量的能量。
The word equation is:
文字方程式为：
Glucose + Oxygen → Carbon dioxide + Water (+ energy)
The energy released is not a chemical substance, so it is often placed in brackets or written alongside the arrow.
释放的能量不是化学物质，因此常常放入括号中或写于箭头旁边。
The balanced chemical equation is:
配平的化学方程式为：
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
Comparing this with the photosynthesis equation shows that respiration is almost the reverse of photosynthesis. Respiration uses the glucose and oxygen produced in photosynthesis, and returns carbon dioxide and water to the atmosphere.
将此与光合作用方程式进行比较，可以看出呼吸作用几乎是光合作用的逆过程。呼吸作用利用光合作用产生的葡萄糖和氧气，并将二氧化碳和水返回大气。
9. Conservation of Mass in Reactions | 化学反应中的质量守恒
During a chemical reaction, atoms are not created or destroyed; they are only rearranged. This principle is called the law of conservation of mass.
在化学反应过程中，原子不会被创造或消灭；它们只是重新排列。这个原理叫做质量守恒定律。
Total mass of reactants = Total mass of products
This means if you could measure the mass of all the substances before and after a reaction in a closed system, the total mass would stay exactly the same. For example, if you burn magnesium ribbon in a crucible with a lid, the mass of the magnesium oxide produced equals the mass of magnesium plus the mass of oxygen that reacted.
这意味着如果你能在一个封闭系统中测量反应前后所有物质的质量，总质量将保持完全不变。例如，如果你在带盖的坩埚中燃烧镁条，生成的氧化镁的质量等于镁的质量加上参与反应的氧气的质量。
In a reaction that appears to lose mass, such as a carbonate reacting with an acid, the loss is due to a gas escaping. When the gas is collected and its mass added, the total mass remains constant. This law helps chemists balance equations and predict how much product will form.
在一个看似质量减少的反应中，例如碳酸盐与酸的反应，质量的减少是由于气体逸出。当收集气体并加上其质量时，总质量保持不变。这条定律帮助化学家配平方程式并预测将生成多少产物。
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