📚 Year 9 WJEC Science: Formula and Theorem Quick Reference Handbook | Year 9 WJEC 科学：公式定理速查手册
This quick reference guide brings together the essential formulas, equations and theorems you will meet in Year 9 WJEC Science. From motion and forces to electricity, energy and the building blocks of chemistry and biology, having these key relationships at your fingertips will boost your confidence in homework, tests and practical work.
这本速查手册汇集了你在 Year 9 WJEC 科学课程中将遇到的核心公式、方程和定理。从运动和力，到电学、能量，再到化学与生物的基本模块，掌握这些关键关系能让你在作业、测验和实验操作中更加自信从容。
1. Speed, Distance and Time | 速度、距离和时间
The relationship between speed, distance and time is one of the first formulas you learn in physics. It tells us how fast an object is moving over a known distance and time interval.
速度、距离和时间的关系是你在物理课上学到的第一个公式之一，它描述了物体在已知距离和时间间隔内的运动快慢。
speed = distance ÷ time
速度 = 距离 ÷ 时间
In symbols, we usually write v = d ÷ t, where v is speed (or velocity), d is distance travelled and t is the time taken. The standard unit of speed is metres per second (m/s).
用符号通常写成 v = d ÷ t，其中 v 代表速度，d 为通过的距离，t 为所用时间。速度的标准单位是米每秒 (m/s)。
| Quantity | Symbol | Unit | Unit symbol |
| Speed / 速度 | v | metres per second | m/s |
| Distance / 距离 | d | metres | m |
| Time / 时间 | t | seconds | s |
Example: A cyclist travels 450 m in 30 s. Speed = 450 ÷ 30 = 15 m/s.
例题：一名自行车手在 30 秒内行驶 450 米。速度 = 450 ÷ 30 = 15 m/s。
2. Density and its Calculation | 密度及其计算
Density describes how much mass is packed into a certain volume. It helps us predict whether an object will float or sink and is crucial in material science.
密度描述单位体积内所含的质量，它帮助我们预测物体会上浮还是下沉，并在材料科学中至关重要。
density = mass ÷ volume
密度 = 质量 ÷ 体积
Using symbols: ρ = m ÷ V. The Greek letter ρ (rho) represents density. Mass m is in kilograms (kg) and volume V is in cubic metres (m³) to give density in kg/m³. For smaller samples, grams per cubic centimetre (g/cm³) is often used.
用符号表示为：ρ = m ÷ V。希腊字母 ρ 代表密度。质量 m 的单位为千克 (kg)，体积 V 的单位为立方米 (m³)，由此得到密度的单位为 kg/m³。对于较小的样品，常用克每立方厘米 (g/cm³)。
To find the volume of a regular solid, multiply length × width × height. For a liquid, use a measuring cylinder. The density of water is 1.0 g/cm³ or 1000 kg/m³.
规则固体的体积可用长 × 宽 × 高求得；液体的体积则用量筒测量。水的密度为 1.0 g/cm³ 或 1000 kg/m³。
3. Pressure in Solids | 固体压强
Pressure is the force acting per unit area when a solid object pushes on a surface. It explains why sharp objects cut more easily and why wide tyres are used on soft ground.
压强是固体作用于表面时单位面积上承受的力。它解释了为什么尖锐物体更容易切割，以及为什么在松软地面上要使用宽轮胎。
pressure = force ÷ area
压强 = 力 ÷ 受力面积
P = F ÷ A, with force F in newtons (N) and area A in square metres (m²). The resulting unit is the pascal (Pa), where 1 Pa = 1 N/m².
P = F ÷ A，其中力 F 的单位是牛顿 (N)，面积 A 的单位是平方米 (m²)。得出的压强单位为帕斯卡 (Pa)，1 Pa = 1 N/m²。
If the same force is spread over a larger area, the pressure decreases. This principle is applied in snowshoes and in the design of foundations.
若相同的力分散在更大的面积上，压强就会减小。这一原理应用于雪鞋和地基设计中。
4. Hooke’s Law | 胡克定律
When a spring or elastic object is stretched, the extension is directly proportional to the applied force, provided the elastic limit is not exceeded. This relationship is known as Hooke’s Law.
在未超过弹性限度的情况下，弹簧或弹性体被拉伸时，其伸长量与施加的力成正比。这一关系被称为胡克定律。
F = k × e
F = k × e
Here, F is the force in newtons, e is the extension in metres, and k is the spring constant in N/m. A stiffer spring has a larger k value.
其中 F 为力（牛顿），e 为伸长量（米），k 为弹簧常数（N/m）。弹簧越硬，k 值越大。
The extension e is calculated as the new length minus the original length. Hooke’s Law is used in force meters and suspension systems.
伸长量 e 的计算方法为拉伸后长度减去原长。胡克定律被广泛应用于弹簧秤和悬挂系统中。
5. Gravitational Potential Energy | 重力势能
Any object lifted against Earth’s gravity stores gravitational potential energy (GPE). The amount depends on the object’s mass, the gravitational field strength and the height gained.
任何克服地球重力被抬升的物体都会储存重力势能。其大小取决于物体的质量、引力场强度和提升的高度。
GPE = m × g × h
重力势能 = m × g × h
Mass m is in kilograms, g is the gravitational field strength (≈ 10 N/kg on Earth), and h is the vertical height in metres. The energy is measured in joules (J).
质量 m 单位为千克，g 为引力场强度（地球表面约 10 N/kg），h 为垂直高度（米）。能量单位为焦耳 (J)。
Lifting a 2 kg book onto a 1.5 m shelf stores 2 × 10 × 1.5 = 30 J of gravitational potential energy.
将一本 2 千克的书抬升至 1.5 米高的书架上，可储存 2 × 10 × 1.5 = 30 J 的重力势能。
6. Kinetic Energy | 动能
All moving objects possess kinetic energy. The faster an object moves and the greater its mass, the more kinetic energy it carries.
所有运动的物体都具有动能。物体运动得越快、质量越大，携带的动能就越多。
KE = ½ × m × v²
动能 = ½ × m × v²
Here, m is mass in kg and v is speed in m/s. The factor ½ indicates that doubling the speed quadruples the kinetic energy, which is why braking distances increase rapidly with speed.
其中 m 为质量（kg），v 为速度（m/s）。系数 ½ 表明速度加倍会使动能变为原来的四倍，这就是为什么制动距离随速度急剧增加。
For a 1000 kg car moving at 10 m/s, KE = ½ × 1000 × 10² = 50 000 J.
一辆 1000 kg 的汽车以 10 m/s 行驶时，动能 = ½ × 1000 × 10² = 50 000 J。
7. Ohm’s Law | 欧姆定律
Ohm’s Law describes the relationship between voltage, current and resistance in an electrical circuit. It is a fundamental rule for understanding how circuits behave.
欧姆定律描述了电路中电压、电流和电阻之间的关系，是理解电路行为的基础规律。
V = I × R
V = I × R
Voltage V is in volts (V), current I is in amperes (A) and resistance R is in ohms (Ω). This relationship holds for ohmic conductors at constant temperature.
电压 V 的单位为伏特 (V)，电流 I 为安培 (A)，电阻 R 为欧姆 (Ω)。对于恒定温度下的欧姆导体，这一关系成立。
If a component has a resistance of 20 Ω and a current of 0.5 A flows through it, the potential difference across it is 20 × 0.5 = 10 V.
若某元件的电阻为 20 Ω，通过它的电流为 0.5 A，则其两端的电压为 20 × 0.5 = 10 V。
8. Electrical Power and Energy | 电功率与电能
Power is the rate at which energy is transferred. In electrical circuits, power can be calculated from current and voltage, and the total energy used can be found from power and time.
功率是能量传递的速率。在电路中，功率可由电流和电压计算得出，而消耗的总电能可由功率和时间求出。
P = I × V
P = I × V
E = P × t or E = I × V × t
E = P × t 或 E = I × V × t
Power P is in watts (W), energy E is in joules (J) and time t is in seconds (s). A 60 W lamp left on for 120 s transfers 60 × 120 = 7200 J of electrical energy into light and heat.
功率 P 的单位为瓦特 (W)，能量 E 为焦耳 (J)，时间 t 为秒 (s)。一盏 60 W 的灯点亮 120 秒，会将 7200 J 的电能转化为光能和热能。
9. Efficiency of Energy Transfers | 能量转换效率
No energy transfer is perfect. Efficiency tells us what fraction of the input energy is converted into useful output energy or power.
能量转换不可能达到完美。效率告诉我们输入能量中有多大比例转化为有用的输出能量或功率。
efficiency = (useful output energy ÷ total input energy) × 100%
效率 = (有用输出能量 ÷ 输入总能量) × 100%
Efficiency can also be given as a decimal between 0 and 1. A higher efficiency means less energy is wasted, usually as thermal energy. Sankey diagrams can be used to visualise energy flows.
效率也可以用 0 到 1 之间的小数表示。效率越高意味着浪费的能量（通常以热能形式）越少。可用桑基图将能量流动可视化。
If an electric motor uses 100 J of electrical energy and does 70 J of useful mechanical work, its efficiency is (70 ÷ 100) × 100% = 70%.
如果一台电动机消耗 100 J 电能并完成 70 J 的有用机械功，其效率为 (70 ÷ 100) × 100% = 70%。
10. Relative Formula Mass (Mᵣ) | 相对式量
Relative formula mass (Mᵣ) is the sum of the relative atomic masses (Aᵣ) of all atoms shown in the chemical formula. It gives the mass of one formula unit on the atomic mass scale.
相对式量 (Mr) 是化学式中所有原子的相对原子质量 (Ar) 的总和，它给出了一个式单位在原子质量标度上的质量。
Mᵣ = Σ(Aᵣ of each atom in the formula)
Mᵣ = Σ(化学式中每个原子的 Aᵣ)
Example: for water H₂O, Aᵣ of H = 1, Aᵣ of O = 16, so Mᵣ = (2 × 1) + 16 = 18. For carbon dioxide CO₂, Mᵣ = 12 + (2 × 16) = 44. No units are written for relative mass.
例：水 H₂O 中 H 的 Ar = 1，O 的 Ar = 16，因此 Mr = (2 × 1) + 16 = 18。二氧化碳 CO₂ 的 Mr = 12 + (2 × 16) = 44。相对质量不书写单位。
11. Conservation of Mass in Reactions | 化学反应中的质量守恒
During a chemical reaction, atoms are rearranged but no atoms are created or destroyed. This means the total mass of all products equals the total mass of all reactants.
在化学反应过程中，原子重新排列，但没有原子被创造或消失。这意味着所有产物的总质量等于所有反应物的总质量。
total mass of reactants = total mass of products
反应物总质量 = 生成物总质量
If a reaction appears to lose mass, it is usually because a gas has escaped. In a closed system, the mass reading stays constant. This principle underpins all balanced chemical equations.
如果反应看上去质量减少了，通常是因为有气体逸出。在封闭系统中，质量读数保持不变。这一原理是所有配平化学方程式的基础。
For example, when 5.6 g of iron reacts exactly with 3.2 g of sulfur, the iron sulfide formed will have a mass of 5.6 + 3.2 = 8.8 g.
例如，5.6 g 铁与 3.2 g 硫恰好完全反应，生成的硫化铁质量为 5.6 + 3.2 = 8.8 g。
12. Magnification, Photosynthesis and Respiration | 放大倍率、光合作用与呼吸
Biology makes regular use of formulae for microscope work and of word equations to summarise the two most important life processes. These relationships are essential knowledge for Year 9.
生物学经常使用显微镜相关公式和文字方程式来概括两个最重要的生命过程。这些关系是 Year 9 的必备知识。
magnification = image size ÷ actual size
放大倍率 = 图像尺寸 ÷ 实际尺寸
If a microscope image of a cell measures 6 mm and the actual cell is 0.02 mm, the magnification is 6 ÷ 0.02 = 300 ×. Both sizes must be in the same unit.
若显微镜下细胞的图像尺寸为 6 mm，而实际细胞为 0.02 mm，则放大倍率为 6 ÷ 0.02 = 300 倍。两者单位必须统一。
Photosynthesis: carbon dioxide + water → glucose + oxygen
光合作用：二氧化碳 + 水 → 葡萄糖 + 氧气
This reaction takes place in the chloroplasts of green plants, using light energy. The glucose produced is used for energy, growth and storage.
该反应在绿色植物叶绿体中进行，利用光能。产生的葡萄糖用于能量供应、生长和储存。
Aerobic respiration: glucose + oxygen → carbon dioxide + water (+ energy)
有氧呼吸：葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）
Respiration occurs in the mitochondria of all living cells, releasing the energy stored in food. It is not the same as breathing in and out.
呼吸作用在所有活细胞的线粒体中进行，释放储存在食物中的能量。它与吸气和呼气是两回事。
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