📚 Year 9 CIE Science: Formula and Theorem Quick Reference Handbook | Year 9 CIE 科学：公式定理速查手册
Welcome to your essential quick reference handbook for Year 9 CIE Science. This resource brings together the most important formulas, theorems, and key equations from physics, chemistry, and biology. Use it to reinforce your understanding, build confidence, and prepare effectively for assessments.
欢迎使用你的 Year 9 CIE 科学必备速查手册。本手册汇集了物理、化学和生物中最重要的公式、定理和关键方程式。用它来巩固理解、建立信心，并为考试做好高效准备。
1. Speed and Velocity | 速率与速度
Speed tells you how fast an object is moving, without regard to direction. It is calculated as distance travelled divided by time: s = d / t. The standard unit of speed is metres per second (m/s). Speed is a scalar quantity — it has magnitude only. In contrast, velocity is the speed in a particular direction, making it a vector quantity.
速率表示物体运动的快慢，不考虑方向。它由移动的距离除以时间计算：s = d / t。速率的国际单位是米每秒 (m/s)。速率是标量——只有大小。相反，速度是特定方向上的速率，因此是矢量。
2. Acceleration | 加速度
Acceleration measures how quickly velocity changes. The formula is a = (v − u) / t, where v is final velocity (m/s), u is initial velocity (m/s), and t is time (s). Acceleration is measured in metres per second squared (m/s2). A negative acceleration indicates deceleration or slowing down.
加速度衡量速度变化的快慢。公式为 a = (v − u) / t，其中 v 是末速度 (m/s)，u 是初速度 (m/s)，t 是时间 (s)。加速度的单位是米每二次方秒 (m/s2)。负加速度表示减速。
3. Density | 密度
Density describes how much mass is packed into a given volume. The formula is ρ = m / V, with m representing mass (kg or g) and V representing volume (m3 or cm3). The SI unit is kilograms per cubic metre (kg/m3), but grams per cubic centimetre (g/cm3) is also commonly used. Remember: 1 g/cm3 = 1000 kg/m3.
密度描述单位体积内所含质量的大小。公式为 ρ = m / V，其中 m 代表质量 (kg 或 g)，V 代表体积 (m3 或 cm3)。国际单位是千克每立方米 (kg/m3)，但克每立方厘米 (g/cm3) 也常用。记住：1 g/cm3 = 1000 kg/m3。
4. Force and Weight | 力与重量
Newton's Second Law of Motion states that the net force acting on an object is equal to its mass multiplied by its acceleration: F = m a. Force is measured in newtons (N). Weight is a specific force caused by gravity: W = m g, where g is the gravitational field strength (on Earth, approximately 9.8 m/s2 or roughly 10 m/s2). Do not confuse mass (amount of matter, kg) with weight (gravitational force, N).
牛顿第二运动定律指出，作用在物体上的合力等于质量乘以加速度：F = m a。力的单位是牛顿 (N)。重量是由引力产生的一种特定的力：W = m g，其中 g 是引力场强 (地球上约 9.8 m/s2 或大约 10 m/s2)。切勿混淆质量 (物质的量，单位 kg) 和重量 (引力，单位 N)。
5. Pressure | 压强
Pressure is the force applied per unit area. The formula is P = F / A, where F is force (N) and A is area (m2). The unit of pressure is the pascal (Pa); 1 Pa = 1 N/m2. In liquids, pressure also depends on depth and density: P = h ρ g, where h is the depth (m), ρ is the liquid's density (kg/m3), and g is the gravitational field strength. This shows that liquid pressure increases with depth.
压强是单位面积上所受的力。公式为 P = F / A，其中 F 是力 (N)，A 是面积 (m2)。压强的单位是帕斯卡 (Pa)；1 Pa = 1 N/m2。在液体中，压强还跟深度和密度有关：P = h ρ g，其中 h 是深度 (m)，ρ 是液体密度 (kg/m3)，g 是引力场强。这表明液体压强随深度增加而增大。
6. Work, Energy and Power | 功、能与功率
Work is done when a force moves an object. W = F d, with work in joules (J) when force is in newtons and distance in metres. Gravitational potential energy (Ep) is stored energy due to position: Ep = m g h. Kinetic energy (Ek) is the energy of motion: Ek = ½ m v2. Power is the rate of doing work or transferring energy: P = W / t or P = E / t, measured in watts (W; 1 W = 1 J/s).
当力使物体移动一段距离时就做了功。W = F d，力以牛顿为单位、距离以米为单位时，功的单位为焦耳 (J)。重力势能 (Ep) 是由于位置而储存的能量：Ep = m g h。动能 (Ek) 是运动的能量：Ek = ½ m v2。功率是做功或传递能量的速率：P = W / t 或 P = E / t，单位是瓦特 (W；1 W = 1 J/s)。
7. Moments and Equilibrium | 力矩与平衡
The moment of a force about a pivot is the turning effect. It is calculated as M = F × d, where d is the perpendicular distance from the pivot to the line of action of the force. The unit is newton metre (N m). For an object to be in rotational equilibrium, the sum of clockwise moments must equal the sum of anticlockwise moments. This principle applies to levers and see-saws.
力对支点的力矩是转动效应。计算公式为 M = F × d，其中 d 是支点到力的作用线的垂直距离。单位是牛顿米 (N m)。若物体处于转动平衡，则顺时针力矩之和必定等于逆时针力矩之和。该原理适用于杠杆和跷跷板。
8. Ohm's Law | 欧姆定律
Ohm's Law describes the relationship between voltage, current and resistance in a metallic conductor at constant temperature: V = I R. V is potential difference in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω). If you know any two quantities, you can calculate the third.
欧姆定律描述了温度恒定时金属导体中电压、电流和电阻之间的关系：V = I R。其中 V 是电势差，单位伏特 (V)；I 是电流，单位安培 (A)；R 是电阻，单位欧姆 (Ω)。若已知任意两个量，即可求第三个量。
9. Electrical Power and Energy | 电功率与电能
Electrical power can be expressed in several forms: P = I V, P = I2 R, and P = V2 / R. Power is measured in watts (W). The electrical energy transferred is given by E = P t ules (J), but for larger quantities kilowatt-hours (kWh) may be used: 1 kWh = 3 600 000 J.
电功率可以用多种形式表达：P = I V、P = I2 R 和 P = V2 / R。功率的单位是瓦特 (W)。转换的电能由 E = P t 给出，其中 t 是以秒为单位的时间。能量通常以焦耳 (J) 计量，但对于较大的量可以用千瓦时 (kWh)：1 kWh = 3 600 000 J。
10. Series and Parallel Circuits | 串联与并联电路
In a series circuit, the total resistance is the sum of individual resistances: Rtotal = R1 + R2 + .... Current is the same everywhere, while the supply voltage is shared. In a parallel circuit, the total resistance is found using 1/Rtotal = 1/R1 + 1/R2 + .... Here, the voltage across each branch is the same, and the total current is the sum of the branch currents.
在串联电路中，总电阻为各电阻之和：R总 = R1 + R2 + ...。各处电流相等，而电源电压被分配。在并联电路中，总电阻通过 1/R总 = 1/R1 + 1/R2 + ... 计算。此时各支路两端电压相等，总电流等于各支路电流之和。
11. Conservation of Mass and Chemical Calculations | 质量守恒与化学计算
The law of conservation of mass states that the total mass of reactants equals the total mass of products in a chemical reaction. When using balanced equations, the mass ratio of substances can be found using relative atomic masses (Ar) and coefficients. For a reaction aA + bB → cC, the mass ratio of A to B is (a × Ar of A) : (b × Ar of B). This allows you to calculate unknown masses without using the mole concept at this stage.
质量守恒定律指出，化学反应中反应物的总质量等于生成物的总质量。利用配平后的方程式，可以通过相对原子质量 (Ar) 和化学计量数求出物质间的质量比。对于反应 aA + bB → cC，A 与 B 的质量比为 (a × A 的 Ar) : (b × B 的 Ar)。这样，你在现阶段无需使用摩尔概念就能计算未知质量。
12. Key Biological Equations | 重要生物方程式
Photosynthesis is the process by which plants make food using light energy. The word equation is: carbon dioxide + water → glucose + oxygen, with light and chlorophyll as essential conditions. The balanced chemical equation is 6CO2 + 6H2O → C6H12O6 + 6O2. Aerobic respiration releases energy from glucose: glucose + oxygen → carbon dioxide + water (+ energy). These two processes are fundamental to the cycling of carbon and oxygen on Earth.
光合作用是植物利用光能制造食物的过程。文字方程式为：二氧化碳 + 水 → 葡萄糖 + 氧气，光与叶绿素是必需条件。配平的化学方程式是 6CO2 + 6H2O → C6H12O6 + 6O2。有氧呼吸从葡萄糖中释放能量：葡萄糖 + 氧气 → 二氧化碳 + 水 (+ 能量)。这两个过程是地球上碳和氧循环的基础。
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