📚 Year 9 CAIE Science Quick-Reference Formula and Theorem Handbook | Year 9 CAIE 科学：公式定理速查手册
Welcome to your essential quick-reference handbook for Year 9 CAIE Science. This guide brings together the most important formulas, laws and equations you will encounter in physics, chemistry and biology. It is designed to help you revise efficiently and apply the right relationship in calculations and explanations. Each section covers a key topic, pairing a clear statement of the rule or equation with the units you will need to use.
欢迎使用这份 Year 9 CAIE 科学速查手册。手册汇集了物理、化学和生物学科中最重要的公式、定律和方程式，帮助你高效复习，在计算和解释中准确运用。每个小节围绕一个核心主题，清晰陈述规律或等式，并附上你需要掌握的单位与说明。
1. Speed and Velocity | 速度与速率
Speed describes how fast an object is moving. It is a scalar quantity, meaning it has magnitude only. The average speed of an object can be found by dividing the total distance travelled by the time taken.
速度描述物体运动的快慢。它是标量，只有大小。物体的平均速度等于移动的总距离除以所用的时间。
v = d / t
where v is speed (metres per second, m/s), d is distance (metres, m), and t is time (seconds, s). Velocity is a vector quantity that includes direction, but in many early calculations the same formula is used for speed.
其中 v 是速度（米/秒），d 是距离（米），t 是时间（秒）。速率是包含方向的矢量，但在许多初级计算中速度公式同样适用。
When rearranging the formula, distance can be found by d = v × t, and time by t = d / v. Always remember to convert units, for example changing kilometres to metres and hours to seconds, before substituting numbers.
公式变形后，距离 d = v × t，时间 t = d / v。代入数值前务必统一单位，例如将公里转换为米，小时转换为秒。
2. Acceleration | 加速度
Acceleration measures how quickly an object changes its velocity. It can be positive (speeding up) or negative (slowing down, often called deceleration).
加速度衡量物体速度变化的快慢，可以是正值（加速）或负值（减速，常称减速度）。
a = (v − u) / t
where a is acceleration (metres per second squared, m/s²), v is final velocity (m/s), u is initial velocity (m/s), and t is the time taken (s). The change in velocity is v − u.
其中 a 是加速度（米/秒²），v 是末速度（m/s），u 是初速度（m/s），t 是时间（s）。速度的变化量为 v − u。
This formula comes from Newton’s laws of motion. If an object moves with constant acceleration, you can also find the distance travelled using more advanced equations, but in Year 9 you will mainly use a = (v − u)/t to link velocity changes with time.
该公式源自牛顿运动定律。如果物体做匀加速运动，还可以用更复杂的方程求出位移，但在 Year 9 你主要用 a = (v − u)/t 建立速度变化与时间的关系。
3. Density | 密度
Density is the mass of a substance per unit volume. It explains why some objects float while others sink and is a characteristic property of materials.
密度是单位体积内物质的质量，解释了为什么有些物体会浮起而另一些会下沉，也是材料的一种特征属性。
ρ = m / V
where ρ (the Greek letter rho) represents density (kilograms per metre cubed, kg/m³, or grams per centimetre cubed, g/cm³), m is mass (kg or g), and V is volume (m³ or cm³).
其中 ρ（希腊字母 rho）表示密度（千克/米³ 或 克/厘米³），m 是质量（千克或克），V 是体积（米³ 或 厘米³）。
For regular solids, volume is found by measuring dimensions (e.g. length × width × height). For irregular solids, you can use a displacement can to measure the volume of water pushed out. The density of water is approximately 1 g/cm³ or 1000 kg/m³.
对于规则固体，体积可通过测量尺寸（如长×宽×高）得到。对于不规则固体，可以用排水法测量排出的水的体积。水的密度约为 1 g/cm³ 或 1000 kg/m³。
4. Pressure in Solids and Fluids | 固体与流体的压强
Pressure is the force acting perpendicularly per unit area. In solids, the formula is simple; in liquids and gases, pressure is transmitted equally in all directions, which is the basis of hydraulic systems.
压强是垂直作用在单位面积上的力。在固体中公式简单；在液体和气体中，压强向各个方向等大小传递，这是液压系统的基础。
p = F / A
where p is pressure (pascals, Pa, or N/m²), F is the force in newtons (N), and A is the area in square metres (m²). A larger area reduces the pressure for the same force, which is why camels have wide feet and sharp knives have small cutting edges.
其中 p 是压强（帕斯卡，Pa，或 N/m²），F 是力（牛顿，N），A 是面积（平方米，m²）。同样作用力下，面积越大压强越小，因此骆驼的脚掌宽大，而锋利的刀具刃口面积很小。
In a hydraulic system, Pascal’s principle states that pressure applied to an enclosed fluid is transmitted undiminished. This gives the relation F₁/A₁ = F₂/A₂, which allows a small input force to lift a heavy load by using different piston areas.
在液压系统中，帕斯卡原理指出，施加在密闭流体上的压强会大小不变地传递。由此得出 F₁/A₁ = F₂/A₂，利用不同的活塞面积就可以用小力举起重物。
5. Force, Mass and Acceleration | 力、质量与加速度
Newton’s second law of motion explains how the motion of an object changes when a resultant force acts on it. The acceleration is directly proportional to the force and inversely proportional to the mass.
牛顿第二运动定律说明，有合力作用时物体的运动如何改变。加速度与合力成正比，与质量成反比。
F = m × a
where F is the resultant force (newtons, N), m is the mass (kilograms, kg), and a is the acceleration (m/s²). One newton is the force needed to accelerate a 1 kg mass by 1 m/s².
其中 F 是合力（牛顿），m 是质量（千克），a 是加速度（m/s²）。1 牛顿就是使 1 kg 物体产生 1 m/s² 加速度所需的力。
This formula can be rearranged to a = F / m and m = F / a. When forces are balanced, the resultant force is zero and the object remains at rest or moves at constant velocity. When forces are unbalanced, the object accelerates in the direction of the resultant force.
公式可变形为 a = F / m 和 m = F / a。当力平衡时，合力为零，物体保持静止或匀速运动；力不平衡时，物体沿合力方向加速。
6. Moments (The Turning Effect) | 力矩（转动效应）
A moment is the turning effect of a force around a pivot. It depends on the size of the force and the perpendicular distance from the pivot to the line of action of the force.
力矩是力绕支点产生的转动效应，取决于力的大小以及从支点到力作用线的垂直距离。
M = F × d
where M is the moment (newton metres, Nm), F is the force (N), and d is the perpendicular distance from the pivot (m). To increase the turning effect, you can increase the force or use a longer lever.
其中 M 是力矩（牛顿·米，Nm），F 是力（N），d 是支点到力作用线的垂直距离（m）。要增大转动效果，可以增大作用力或使用更长的杠杆。
When a seesaw or beam is balanced, the total clockwise moments equal the total anticlockwise moments. This is the principle of moments and can be written as F₁ × d₁ = F₂ × d₂, which is extremely useful for calculations involving levers and equilibrium.
当跷跷板或横梁平衡时，顺时针力矩之和等于逆时针力矩之和。这就是力矩原理，可写作 F₁ × d₁ = F₂ × d₂，在杠杆与平衡计算中非常有用。
7. Work, Energy and Power | 功、能与功率
Work is done when a force moves an object in the direction of the force. Energy is transferred when work is done, and power is the rate at which work is done or energy is transferred.
一个力使物体沿力的方向移动时就说它做了功。做功的同时发生能量转移，功率则是做功或转移能量的快慢。
W = F × d
Work (W) is measured in joules (J), force (F) in newtons (N), and distance (d) 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.
功（W）的单位是焦耳（J），力（F）是牛顿，距离（d）是米。1 焦耳就是 1 牛顿的力使物体沿力的方向移动 1 米所做的功。
P = W / t
Power (P) is measured in watts (W), where 1 W = 1 J/s. The same formula can be written as P = E / t when referring to energy transferred.
功率（P）的单位是瓦特（W），1 W = 1 J/s。涉及能量转移时公式也可写作 P = E / t。
8. Gravitational Potential and Kinetic Energy | 重力势能与动能
Energy can be stored in different ways. Two of the most important stores in mechanics are gravitational potential energy (GPE) and kinetic energy (KE).
能量能以不同形式储存。力学中最重要的两种储能形式是重力势能（GPE）和动能（KE）。
GPE = m × g × h
m is mass (kg), g is the gravitational field strength (on Earth approximately 9.8 m/s², often rounded to 10 m/s²), and h is the height above a reference level (m). GPE increases when an object is lifted.
m 是质量（kg），g 是引力场强度（地球表面约为 9.8 m/s²，常取 10 m/s² 进行估算），h 是相对基准面的高度（m）。物体被举高时重力势能增加。
KE = ½ × m × v²
KE is kinetic energy (J), m is mass (kg), and v is speed (m/s). Notice that doubling the speed quadruples the kinetic energy, because v is squared.
KE 是动能（J），m 是质量（kg），v 是速率（m/s）。注意速率加倍会使动能增至原来的四倍，因为 v 被平方了。
In many situations, GPE is converted to KE and vice versa, assuming no energy is transferred to the surroundings as heat.
在许多情况下，如果没有能量以热的形式散失到环境中，重力势能会转化为动能，反之亦然。
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