Year 7 CIE Science: Quick Reference Handbook of Formulas and Theorems | Year 7 CIE 科学：公式定理速查手册

📚 Year 7 CIE Science: Quick Reference Handbook of Formulas and Theorems | Year 7 CIE 科学：公式定理速查手册

This handbook collects the essential formulas and theorems you will meet in Year 7 CIE Science. Use it to review key relationships in physics, chemistry and biology, check units and practise applying each rule to example problems. The bilingual layout helps you learn the terminology in both English and Chinese, building confidence for class tests and checkpoint assessments.

本手册汇集了 Year 7 CIE 科学课程中你必须掌握的核心公式与定理。你可以用它复习物理、化学和生物中的关键关系，检查单位并练习把每一条规则应用到例题中。中英对照的编排能够帮助你同时熟悉英文和中文的科学术语，为课堂测验和 checkpoint 评估打下信心。

1. Speed, Distance and Time | 速度、距离与时间

The relationship between speed, distance and time is one of the first quantitative formulas you will use. It tells you how fast an object is moving on average.

速度、距离和时间之间的关系是你最早会使用到的定量公式之一。它告诉我们一个物体运动的平均快慢。

average speed = total distance ÷ total time

平均速度 = 总距离 ÷ 总时间

Symbol / 符号	Quantity / 物理量	SI unit / 国际单位	Other common units / 常用其他单位
v or s	speed / 速度	m/s	km/h, mph
d	distance / 距离	m	km, cm
t	time / 时间	s	min, h

Always check that units match before calculating. If distance is in km and time in h, speed will be in km/h.

在计算前要确保单位一致。如果距离用 km，时间用 h，那么速度的单位就是 km/h。

2. Density, Mass and Volume | 密度、质量与体积

Density describes how much mass is packed into a certain volume. It is a property of the material and can be used to identify substances.

密度描述单位体积内所含质量的大小。它是材料本身的一种属性，可以用来鉴别物质。

density = mass ÷ volume

密度 = 质量 ÷ 体积

Symbol / 符号	Quantity / 物理量	SI unit / 国际单位
ρ (rho)	density / 密度	kg/m³ or g/cm³
m	mass / 质量	kg or g
V	volume / 体积	m³ or cm³

For regular solids, volume can be calculated from length × width × height. For liquids, use a measuring cylinder. Remember: 1 cm³ = 1 mL.

对于规则固体，体积可以用长 × 宽 × 高计算。测量液体体积时使用量筒。请记住：1 cm³ = 1 mL。

3. Pressure, Force and Area | 压强、力与面积

Pressure is a measure of how concentrated a force is. A large force spread over a large area produces low pressure, whereas the same force on a small area gives high pressure.

压强表示力的集中程度。一个很大的力分布在很大面积上会产生较小的压强，而相同的力作用在很小的面积上则会产生很大的压强。

pressure = force ÷ area

压强 = 力 ÷ 面积

Symbol / 符号	Quantity / 物理量	SI unit / 国际单位
P	pressure / 压强	Pa (N/m²)
F	force / 力	N
A	area / 面积	m²

High-heeled shoes exert more pressure on the ground than flat shoes because the heel has a very small area. This principle explains why sharp knives cut better than blunt ones.

高跟鞋对地面的压强比平底鞋更大，因为鞋跟的面积非常小。这个原理也解释了为什么锋利的刀具比钝的刀具更容易切割。

4. Work, Force and Distance | 功、力与距离

In science, work is done when a force moves an object. If there is no movement, no work is done, even if a large force is applied.

在科学中，当一个力使物体移动时，我们就说力做了功。如果没有发生移动，即使施加了很大的力，也没有做功。

work done = force × distance moved in the direction of the force

做功 = 力 × 在力的方向上移动的距离

Symbol / 符号	Quantity / 物理量	SI unit / 国际单位
W	work / 功	J (joule)
F	force / 力	N
d	distance / 距离	m

1 joule is the work done when a force of 1 newton moves an object 1 metre. Lifting a 1 kg book onto a 1 m high shelf does about 10 J of work (taking g ≈ 10 N/kg).

1 焦耳表示 1 牛顿的力使物体移动 1 米所做的功。将一本 1 kg 的书提起放到 1 米高的书架上大约做功 10 J（取 g ≈ 10 N/kg）。

5. Hooke’s Law | 胡克定律

Hooke’s Law describes how a spring stretches when a force is applied. It applies as long as the spring is not stretched beyond its elastic limit.

胡克定律描述了弹簧在受力时的伸长规律。只要弹簧的伸长没有超过它的弹性限度，这个定律就成立。

F = k × x

Here F is the force applied (N), x is the extension (m) – the extra length the spring gains – and k is the spring constant (N/m). A stiff spring has a large k value.

式中 F 为施加的力（N），x 为伸长量（m）——即弹簧增加的长度，k 为弹簧常数（N/m）。较硬的弹簧 k 值较大。

Symbol / 符号	Meaning / 含义	Unit / 单位
F	applied force / 作用力	N
k	spring constant / 弹簧常数	N/m
x	extension / 伸长量	m

If you hang a 2 N weight on a spring and it stretches by 5 cm (0.05 m), the spring constant is k = F ÷ x = 2 N ÷ 0.05 m = 40 N/m. You can predict that doubling the force will double the extension.

若在弹簧上悬挂 2 N 的重物，弹簧伸长了 5 cm（0.05 m），则弹簧常数为 k = F ÷ x = 2 N ÷ 0.05 m = 40 N/m。你可以预测，力增大为两倍时，伸长量也会变为两倍。

6. Moments and Levers | 力矩与杠杆

A moment is the turning effect of a force. It helps us understand how levers and seesaws work.

力矩是力的转动效应，它能帮助我们理解杠杆和跷跷板是如何工作的。

moment = force × perpendicular distance from pivot

力矩 = 力 × 支点到力作用线的垂直距离

Symbol / 符号	Quantity / 物理量	Unit / 单位
M	moment / 力矩	N m
F	force / 力	N
d	perpendicular distance / 垂直距离	m

The principle of moments states that for an object to be balanced, the total clockwise moment must equal the total anticlockwise moment about the same pivot.

力矩平衡原理指出，一个物体要保持平衡，以同一支点计算时，顺时针方向的力矩总和必须等于逆时针方向的力矩总和。

Example: A 30 N child sits 2 m from the centre of a seesaw. On the other side a 40 N child must sit at a distance d such that 40 N × d = 30 N × 2 m, giving d = 1.5 m.

举例：一个 30 N 的孩子坐在离跷跷板中心 2 m 处，另一边一个 40 N 的孩子需要坐在距离 d 处，使得 40 N × d = 30 N × 2 m，解得 d = 1.5 m。

7. Ohm’s Law (Basic Electricity) | 欧姆定律（基础电学）

Ohm’s Law links the voltage, current and resistance in a circuit. It is a fundamental rule for understanding how electrical components behave.

欧姆定律把电路中的电压、电流和电阻联系起来。它是理解电路元件如何工作的基本规则。

V = I × R

电压 = 电流 × 电阻

Symbol / 符号	Quantity / 物理量	Unit / 单位
V	voltage (potential difference) / 电压	V (volt)
I	current / 电流	A (amp)
R	resistance / 电阻	Ω (ohm)

In Year 7, you will use this relationship in simple series circuits. If a lamp has a resistance of 10 Ω and the current through it is 0.3 A, the voltage across the lamp is V = 0.3 A × 10 Ω = 3 V.

在 Year 7，你会在简单的串联电路中使用这一关系。若一个灯泡的电阻为 10 Ω，通过它的电流为 0.3 A，那么灯泡两端的电压为 V = 0.3 A × 10 Ω = 3 V。

Remember: current is measured with an ammeter connected in series, and voltage is measured with a voltmeter connected in parallel. Always draw circuit diagrams with straight lines and correct symbols.

记住：电流要用串联在电路中的电流表测量，电压要用并联在电器两端的电压表测量。画电路图时要用直线和正确的电路符号。

8. Law of Conservation of Mass | 质量守恒定律

In a chemical reaction, the total mass of the reactants always equals the total mass of the products. This is the law of conservation of mass. Atoms are not created or destroyed; they are simply rearranged.

在化学反应中，反应物的总质量总是等于生成物的总质量。这就是质量守恒定律。原子既不能被创造也不能被消灭，它们只是重新排列了。

Experiment tip: When burning magnesium in air, the ash (magnesium oxide) appears heavier than the original ribbon because oxygen from the air has combined with the magnesium. If you seal the container, the total mass stays the same.

实验提示：镁条在空气中燃烧时，灰烬（氧化镁）的质量看起来比原来的镁条更重，这是因为空气中的氧气与镁发生了化合。如果你在密封容器中进行实验，总质量保持不变。

Word equation example: magnesium + oxygen → magnesium oxide

文字方程式示例：镁 + 氧气 → 氧化镁

Any precipitation reaction also demonstrates this law: when you mix two clear solutions and a solid forms, the total mass of the mixture before and after is unchanged.

任何沉淀反应也都能证明这一定律：当你混合两种透明溶液并有固体生成时，混合前后的总质量不会改变。

9. Photosynthesis and Respiration (Word Equations) | 光合作用与呼吸作用（文字方程式）

While not numerical formulas, these two life processes are written as ‘word equations’ that you must know and balance symbol equations when you study chemistry later.

虽然这两个生命过程不是数值公式，但它们以”文字方程式”的形式来表达，这是你必须掌握的内容，等以后学习化学时还要配平符号方程式。

Photosynthesis:

carbon dioxide + water → glucose + oxygen

光合作用:

二氧化碳 + 水 → 葡萄糖 + 氧气

This process takes place in the chloroplasts of plant cells, using light energy. The glucose produced can be used for energy or stored as starch.

这个过程在植物细胞的叶绿体中进行，需要光能。产生的葡萄糖可以用于提供能量，也可以转化为淀粉储存起来。

Aerobic respiration:

glucose + oxygen → carbon dioxide + water

有氧呼吸:

葡萄糖 + 氧气 → 二氧化碳 + 水

All living cells carry out respiration to release energy. Notice that aerobic respiration is essentially the reverse of photosynthesis in terms of substances, but the energy transfer is completely different.

所有活细胞都进行呼吸作用来释放能量。请注意，从物质角度看，有氧呼吸基本上是光合作用的逆过程，但它们的能量转化截然不同。

10. Energy Conservation and Transfers | 能量守恒与转移

The law of conservation of energy tells us that energy cannot be created or destroyed, only transferred from one form to another. The total energy before a change is always equal to the total energy after the change.

能量守恒定律告诉我们，能量既不能被创造也不能被消灭，只能从一种形式转化为另一种形式。变化前的总能量总是等于变化后的总能量。

Forms of energy you will meet: kinetic (movement), thermal (heat), light, sound, electrical, chemical potential, elastic potential and gravitational potential. In any energy transfer, some energy is almost always ‘wasted’ as thermal energy that spreads out into the surroundings.

你会遇到的各种能量形式有：动能（运动）、热能、光能、声能、电能、化学势能、弹性势能和重力势能。在任何能量转移过程中，几乎总有一部分能量以热能的形式”浪费”掉，散失到周围环境中。

For a falling object, gravitational potential energy (GPE) is converted into kinetic energy. While a formal formula for GPE (mass × g × height) is often introduced in Year 8, Year 7 students can describe the transfer qualitatively: the higher an object, the more GPE it stores.

就下落的物体而言，重力势能转化为动能。虽然重力势能的具体公式（质量 × g × 高度）通常要到 Year 8 才正式引入，Year 7 的学生可以定性描述这种转移：物体位置越高，储存的重力势能就越多。

Energy chains are a useful way to show transfers, e.g. for a battery-powered torch: chemical energy in battery → electrical energy in wires → light energy + thermal energy from the bulb.

能量链是一种展示能量转移的实用方法，例如，对于电池供电的手电筒：电池中的化学能 → 导线中的电能 → 灯泡发出的光能 + 热能。

11. Particle Theory and States of Matter | 粒子理论与物质状态

Particle theory is not a formula, but it is a fundamental model that explains the properties of solids, liquids and gases. It provides the underlying reason for density, pressure and changes of state.

粒子理论不是一个公式，但它是一个用来解释固体、液体和气体性质的基本模型。它为密度、压强以及状态变化提供了根本原因。

In solids, particles are tightly packed in a regular pattern, vibrating in fixed positions.

固体中，粒子紧密排列成规则结构，在固定位置振动。
In liquids, particles are close together but can slide past each other, taking the shape of the container.

液体中，粒子彼此靠近但能相互滑动，因而形状随容器改变。
In gases, particles are far apart, moving rapidly in all directions and have negligible attractive forces between them.

气体中，粒子相隔很远，向各个方向快速运动，粒子间吸引力极小。

When a substance is heated, its particles gain kinetic energy. This can cause a change of state: melting (solid to liquid), boiling/evaporation (liquid to gas). Temperature remains constant during a change of state because the energy is used to break inter-particle bonds rather than raise temperature.

物质受热时，粒子获得动能。这可能导致状态改变：熔化（由固体变液体）、沸腾/蒸发（由液体变气体）。在状态变化过程中，温度保持不变，因为能量被用来破坏粒子间的结合，而不是使温度升高。

The kinetic theory also links to gas pressure: gas particles collide with the walls of their container; each collision exerts a tiny force. Summed over millions of collisions, this creates measurable pressure.

运动理论也与气体压强有关：气体粒子与容器壁碰撞，每一次碰撞都施加微小的力。数百万次碰撞的累积效果就产生了可以测量的压强。

12. Investigations and Key Practical Equations | 探究与关键实验公式

In CIE Checkpoint Science, you will be asked to calculate averages, plot graphs and interpret results. You need to recall the formula for calculating a mean (average).

在 CIE Checkpoint 科学考试中，你会被要求计算平均值、画图并解释实验结果。你需要记住计算平均值（平均数）的公式。

mean = sum of all measurements ÷ number of measurements

平均值 = 所有测量值之和 ÷ 测量次数

Another skill is calculating the rate of a reaction or process, which is often expressed as ‘change in quantity ÷ time’. For example, the rate of gas production can be measured as volume of gas produced per minute (cm³/min).

另一项技能是计算反应或过程的速率，通常表示为”变化量 ÷ 时间”。例如，产生气体的速率可以表示为每分钟生成的气体体积（cm³/min）。

Table of common practical formulas:

常见实验公式表：

Formula / 公式	Example / 示例
mean = total ÷ count	(8+9+7) ÷ 3 = 8
rate = amount changed ÷ time	30 cm³ ÷ 5 min = 6 cm³/min
% change = (final – start) ÷ start × 100	(12 – 10) ÷ 10 × 100 = 20%

Always repeat readings and calculate a mean to improve reliability. Anomalous results that do not fit the pattern should be identified and excluded from the mean.

要始终重复测量并计算平均值以提高可靠性。不符合整体趋势的异常结果应被找出，并在计算平均值时舍去。

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Year 7 CIE Science: Quick Reference Handbook of Formulas and Theorems | Year 7 CIE 科学：公式定理速查手册