📚 Year 9 Cambridge Science: Formula & Theorem Quick Reference Handbook | 9年级剑桥科学公式定理速查手册
This handbook compiles all the essential formulas, laws and theorems from the Year 9 Cambridge Science course. It covers physics, chemistry and biology, providing a one‑stop revision tool for quick referencing and exam preparation.
本手册汇集了 9 年级剑桥科学课程中所有重要的公式、定律和定理，涵盖物理、化学和生物，提供一站式的快速查阅和备考工具。
1. Speed, Distance and Time | 速度、路程和时间
Speed is a measure of how quickly an object moves. It is calculated by dividing the total distance travelled by the time taken.
速度是衡量物体运动快慢的物理量，由物体通过的路程除以所用的时间计算得出。
The average speed formula is: speed = distance / time.
平均速度的公式为：速度 = 路程 ÷ 时间。
v = d / t
SI unit of speed is metre per second (m/s). When distance is measured in metres and time in seconds, speed will be in m/s.
速度的国际单位是米 / 秒（m/s）。当路程以米、时间以秒为单位时，速度的单位就是 m/s。
The formula can be rearranged: distance = speed × time, and time = distance / speed.
公式可以变形为：路程 = 速度 × 时间，时间 = 路程 ÷ 速度。
2. Acceleration and Motion Graphs | 加速度与运动图像
Acceleration is the rate of change of velocity. It describes how quickly an object speeds up, slows down or changes direction.
加速度是速度变化的快慢，描述物体加速、减速或改变方向的快慢程度。
Acceleration is calculated using the change in velocity divided by the time taken for that change.
加速度由速度的变化量除以发生变化所用的时间求得。
a = (v – u) / t or a = Δv / t
where v is final velocity, u is initial velocity and Δv is the change in velocity. The unit is m/s².
其中 v 为末速度，u 为初速度，Δv 为速度的变化量。加速度的单位是 m/s²。
On a speed‑time graph, acceleration is shown by the gradient of the line. A steeper slope means a greater acceleration.
在速度－时间图像中，加速度由直线的斜率表示。斜率越大，加速度越大。
The area under a speed‑time graph represents the distance travelled.
速度－时间图像下方的面积代表物体运动的路程。
3. Forces, Mass and Newton's Laws | 力、质量与牛顿定律
A force is a push or pull that can change an object's motion. Forces are measured in newtons (N).
力是能够改变物体运动状态的推或拉，单位是牛顿（N）。
Newton's First Law (Law of Inertia) states that an object remains at rest or moves at a constant velocity unless acted on by a resultant force.
牛顿第一定律（惯性定律）指出，物体在不受外力作用时将保持静止或匀速直线运动状态。
Newton's Second Law relates resultant force, mass and acceleration.
牛顿第二定律建立了合力、质量和加速度之间的关系：合力 = 质量 × 加速度。
F = m × a
If mass is in kg and acceleration in m/s², the force is in N.
如果质量以 kg、加速度以 m/s² 为单位，则力的单位是 N。
Newton's Third Law states that for every action force there is an equal and opposite reaction force.
牛顿第三定律指出，每一个作用力都有一个大小相等、方向相反的反作用力。
The weight of an object is the gravitational force acting on its mass and is calculated by:
物体的重量是作用在其质量上的重力，由下式求得：
W = m × g
On Earth, g is approximately 9.8 N/kg (often rounded to 10 N/kg). Weight is measured in newtons.
在地球表面，g 约为 9.8 N/kg（常近似为 10 N/kg），重量以牛顿为单位。
4. Density and Pressure | 密度与压强
Density measures how much mass is packed into a given volume. It is a characteristic property of materials.
密度衡量单位体积内所含物质的质量，是物质的一种特征性质。
ρ = m / V
where ρ (rho) is density, m is mass and V is volume. The SI unit is kg/m³, but g/cm³ is also commonly used.
其中 ρ 表示密度，m 为质量，V 为体积。国际单位是 kg/m³，也常用 g/cm³。
Pressure is the force acting per unit area. It explains why sharp objects cut more easily and the functioning of hydraulic systems.
压强是单位面积上受到的压力，可以解释为什么尖锐物体容易切割以及液压系统的工作原理。
P = F / A
pascals (Pa), where 1 Pa = 1 N/m². A larger area reduces the pressure for the same force.
压强的单位是帕斯卡（Pa），1 Pa = 1 N/m²。当力相同时，受力面积越大，压强越小。
5. Work, Energy and Power | 功、能量与功率
Work is done when a force moves an object. Energy is the capacity to do work. Both are measured in joules (J).
力使物体移动时做功。能量是做功的能力，功和能量的单位都是焦耳（J）。
Work done by a constant force is:
恒力做的功为：
W = F × d
where d is the distance moved in the direction of the force.
其中 d 是物体沿力的方向移动的距离。
Kinetic energy is the energy an object possesses due to its motion.
动能是物体由于运动而具有的能量。
KE = ½ m v²
Gravitational potential energy is the energy stored in an object because of its height above the ground.
重力势能是物体因被举高而储存的能量。
GPE = m g h
where h is the height above a reference level.
其中 h 是物体相对于参考水平面的高度。
Power is the rate of doing work or transferring energy.
功率是做功或能量转化的快慢。
P = W / t or P = E / t
The unit of power is the watt (W), where 1 W = 1 J/s.
功率的单位是瓦特（W），1 W = 1 J/s。
Efficiency tells us how well energy is converted into useful forms.
效率告诉我们能量转化为有用形式的比例。
Efficiency = (Useful output energy / Total input energy) × 100%
Efficiency has no units and is often expressed as a percentage.
效率没有单位，通常用百分数表示。
6. Electricity: Ohm's Law and Electrical Power | 电学：欧姆定律与电功率
Current (I) is the rate of flow of electric charge. Voltage (V) is the energy transferred per unit charge. Resistance (R) measures how much a component opposes the flow of current.
电流（I）是电荷流动的快慢，电压（V）是每单位电荷转移的能量，电阻（R）表示元件对电流阻碍作用的大小。
Ohm's Law states that the current through a conductor is directly proportional to the voltage across it, provided temperature remains constant.
欧姆定律指出，在温度不变的条件下，通过导体的电流与其两端电压成正比。
V = I × R
where V is in volts (V), I in amperes (A) and R in ohms (Ω).
其中 V 的单位是伏特（V），I 的单位是安培（A），R 的单位是欧姆（Ω）。
The electrical power transferred in a circuit can be calculated by:
电路中的电功率可由下式计算：
P = I × V
For resistors connected in series, the total resistance is the sum of the individual resistances.
电阻串联时，总电阻等于各电阻之和。
Rtotal = R₁ + R₂ + R₃ + ...
For resistors connected in parallel, the reciprocal of the total resistance equals the sum of the reciprocals of each resistance.
电阻并联时，总电阻的倒数等于各电阻倒数之和。
1 / Rtotal = 1 / R₁ + 1 / R₂ + 1 / R₃ + ...
7. Wave Equation | 波的公式
Waves transfer energy without transferring matter. The key properties of a wave are its speed, frequency and wavelength.
波传递能量而不传递物质。波的主要特性包括波速、频率和波长。
The wave speed equation relates these three quantities:
波速方程将这三者联系起来：
v = f × λ
where v is wave speed in m/s, f is frequency in hertz (Hz) and λ (lambda) is wavelength in metres.
其中 v 为波速（m/s），f 为频率（Hz），λ（lambda）为波长（m）。
This equation applies to all types of waves, including sound, light and water waves.
该方程适用于所有类型的波，包括声波、光波和水波。
Frequency is the number of complete waves passing a point per second. The period (T) is the time for one complete wave, and f = 1 / T.
频率是每秒通过某点的完整波的数量。周期（T）是完成一次振动的时间，且 f = 1 / T。
8. Moments and Levers | 力矩与杠杆
The moment of a force measures its turning effect about a pivot. It depends on the size of the force and its perpendicular distance from the pivot.
力矩衡量力使物体绕支点转动的效应，取决于力的大小以及力到支点的垂直距离。
M = F × d
where M is the moment in newton‑metres (Nm), F is the force in newtons and d is the perpendicular distance in metres.
其中 M 为力矩（N·m），F 为力（N），d 为垂直距离（m）。
The principle of moments states that for an object in equilibrium, the sum of the clockwise moments equals the sum of the anticlockwise moments.
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。
Levers are simple machines that use the principle of moments to make work easier by increasing the distance from the pivot.
杠杆是利用力矩原理的简单机械，通过增加力臂来省力。
9. Chemical Reactions and Conservation of Mass | 化学反应与质量守恒
In a chemical reaction, atoms are rearranged to form new substances. The Law of Conservation of Mass states that the total mass of the reactants equals the total mass of the products.
在化学反应中，原子重新组合形成新的物质。质量守恒定律指出，反应物的总质量等于生成物的总质量。
A word equation shows the names of reactants and products.
文字方程式用名称表示反应物和生成物。
sodium + water → sodium hydroxide + hydrogen
A balanced symbol equation uses chemical formulae and shows the relative numbers of atoms.
配平的符号方程式用化学式表示，并体现原子的相对数目。
2Na + 2H₂O → 2NaOH + H₂
State symbols are often added: (s) solid, (l) liquid, (g) gas and (aq) aqueous solution.
通常需要标注状态符号：(s) 固体，(l) 液体，(g) 气体，(aq) 水溶液。
Balancing equations ensures the number of atoms for each element is the same on both sides, satisfying the conservation of mass.
配平化学方程式意味着反应前后每种元素的原子数目相等，从而满足质量守恒。
10. Biology Equations: Photosynthesis and Respiration | 生物学方程：光合作用与呼吸作用
Photosynthesis is the process by which green plants use light energy to convert carbon dioxide and water into glucose and oxygen.
光合作用是绿色植物利用光能将二氧化碳和水转化为葡萄糖和氧气的过程。
carbon dioxide + water → glucose + oxygen
The balanced chemical equation is:
配平的化学方程式为：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
This reaction occurs in chloroplasts and requires chlorophyll and light energy.
该反应发生在叶绿体中，需要叶绿素和光能。
Aerobic respiration releases energy from glucose using oxygen.
有氧呼吸利用氧气从葡萄糖中释放能量。
glucose + oxygen → carbon dioxide + water (+ energy)
It takes place in the mitochondria of cells.
该过程发生在细胞的线粒体内。
Anaerobic respiration in animals produces lactic acid when oxygen is scarce.
动物在缺氧时的无氧呼吸产生乳酸。
glucose → lactic acid (+ energy)
In yeast and some plants, anaerobic respiration produces ethanol and carbon dioxide (fermentation).
酵母和某些植物的无氧呼吸产生乙醇和二氧化碳（发酵）。
glucose → ethanol + carbon dioxide (+ energy)
11. Units and Conversions | 单位与换算
Using standard SI units is essential in science. The base units are metre (m) for
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