📚 Formula & Theorems Quick Reference Handbook | 公式定理速查手册
This quick-reference guide covers the essential formulas and key principles you will encounter in Year 9 Cambridge Science. Each section pairs a clear English explanation with a Chinese translation, followed by worked examples and practical applications to help you master the content efficiently. Use it for revision, homework assistance, or last-minute test preparation.
本速查手册涵盖 Year 9 剑桥科学中所有核心公式和重要原理。每个板块先提供清晰的英文解释，再给出对应的中文翻译，并配有简单例题和实际应用，帮助你高效掌握课程内容。适用于复习、作业辅导或考前冲刺。
1. Speed, Distance and Time | 速度、距离与时间
The relationship between speed, distance and time is one of the most fundamental in physics. Speed tells you how fast an object is moving.
速度、距离和时间之间的关系是物理学中最基础的关系之一。速度表示物体运动的快慢。
v = d / t
where v is speed (m/s), d is distance (m) and t is time (s). You can rearrange this to find distance: d = v × t, or time: t = d / v.
式中 v 为速度（米/秒），d 为距离（米），t 为时间（秒）。变形可得距离公式 d = v × t 或时间公式 t = d / v。
A cyclist travels 150 m in 30 seconds. Their speed is v = 150 ÷ 30 = 5 m/s.
一名自行车骑手在 30 秒内前进了 150 米，速度为 150 ÷ 30 = 5 米/秒。
2. Density | 密度
Density describes how much mass is packed into a given volume. Objects with tightly packed particles have high densities.
密度描述了一定体积内所含质量的多少。粒子排列紧密的物体密度较大。
ρ = m / V
where ρ (rho) is density (kg/m³ or g/cm³), m is mass (kg or g) and V is volume (m³ or cm³). Rearranged forms: m = ρ × V and V = m / ρ.
ρ 为密度（千克/立方米或克/立方厘米），m 为质量（千克或克），V 为体积（立方米或立方厘米）。变形公式：m = ρ × V 和 V = m / ρ。
metal has a mass of 500 g and a volume of 100 cm³. Its density is ρ = 500 ÷ 100 = 5 g/cm³.
一块金属的质量为 500 克，体积为 100 立方厘米，密度为 500 ÷ 100 = 5 克/立方厘米。
3. Pressure | 压强
Pressure measures how much force is applied over a certain area. A sharp knife exerts high pressure because its area is small.
压强衡量单位面积上所受压力的大小。锋利的刀因为面积小而产生较大的压强。
p = F / A
where p is pressure (Pa or N/m²), F is force (N) and A is area (m²). This shows pressure increases with force and decreases with larger area.
p 为压强（帕斯卡或牛顿/平方米），F 为力（牛顿），A 为面积（平方米）。可见力越大、面积越小，压强越大。
force of 200 N acts on an area of 0.5 m², producing a pressure of p = 200 ÷ 0.5 = 400 Pa.
200 牛的力作用在 0.5 平方米的面积上，压强为 200 ÷ 0.5 = 400 帕斯卡。
4. Moments | 力矩
A moment is the turning effect of a force around a pivot. It depends on both the size of the force and the perpendicular distance from the pivot.
力矩是力使物体绕支点转动的效应，取决于力的大小和力到支点的垂直距离。
M = F × d
M stands for moment (N m), F is the force (N) and d is the perpendicular distance from the pivot (m). For an object in equilibrium, total clockwise moments equal total anticlockwise moments.
M 为力矩（牛·米），F 为力（牛），d 为支点到力的作用线的垂直距离（米）。物体平衡时，顺时针力矩之和等于逆时针力矩之和。
3 N m. To balance a 5 N force applied at 0.4 m on the other side, you need 8 N at 0.25 m.
用 10 牛的力在距门铰链 0.3 米处推门，力矩为 3 牛·米。若另一侧有 5 牛的力作用在 0.4 米处，要平衡则需在 0.25 米处施加 8 牛的力。
5. Work, Energy and Power | 功、能与功率
Work is done when a force moves an object through a distance in the direction of the force. Energy is the ability to do work, and power is the rate at which work is done.
当力使物体沿力的方向移动一段距离时，便做了功。能量是做功的能力，而功率是做功的快慢。
W = F × d
Work W is 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.
功 W 的单位是焦耳（J），力 F 的单位是牛（N），距离 d 的单位是米（m）。1 焦耳就是 1 牛的力使物体移动 1 米所做的功。
P = W / t
Power P asured in watts (W). If 500 J of work is done in 10 seconds, the power is 500 ÷ 10 = 50 W.
功率 P 的单位是瓦特（W）。若 10 秒内做了 500 焦耳的功，功率为 500 ÷ 10 = 50 瓦。
6. Ohm's Law | 欧姆定律
Ohm's Law links the current flowing through a conductor, the voltage across it and its resistance. It applies to many components at constant temperature.
欧姆定律描述通过导体的电流、导体两端的电压和电阻之间的关系，适用于恒定温度下的许多元件。
V = I × R
V is voltage (V), I is current (A), and R is resistance (Ω). You can also write I = V / R or R = V / I. The resistance of a wire increases with length and decreases with cross-sectional area.
V 为电压（伏特），I 为电流（安培），R 为电阻（欧姆，符号 Ω）。也可写作 I = V / R 或 R = V / I。导线的电阻随长度增加而增大，随横截面积增大而减小。
Ω has a current of 0.5 A flowing through it. The voltage across it is V = 0.5 × 12 = 6 V.
一个电阻为 12 Ω 的灯泡，流过 0.5 安培的电流，两端电压为 0.5 × 12 = 6 伏特。
7. Weight and Mass | 重量与质量
Mass is the amount of matter in an object and is measured in kilograms (kg). Weight is the gravitational force on that mass and varies with the gravitational field strength.
质量是物体所含物质的多少，单位是千克（kg）。重量是该质量所受的重力，随引力场强度而变化。
W = m × g
Weight W is in newtons (N), mass m in kilograms (kg), and g vitational field strength. On Earth, g ≈ 10 N/kg (or 9.8 N/kg). On the Moon, g ≈ 1.6 N/kg.
重量 W 的单位是牛（N），质量 m 的单位是千克（kg），g 为引力场强度。地球上 g ≈ 10 N/kg（或 9.8 N/kg），月球上 g ≈ 1.6 N/kg。
Her weight on Earth is 70 × 10 = 700 N, but on the Moon it would be only 70 × 1.6 ≈ 112 N.
一位宇航员质量为 70 千克，地球上重 70 × 10 = 700 牛，而在月球上仅为 70 × 1.6 ≈ 112 牛。
8. Chemical Equations and Relative Formula Mass | 化学方程式与相对式量
Chemical equations use symbols to show the reactants, products and their relative amounts. The total mass of reactants always equals the total mass of products.
化学方程式用符号表示反应物、生成物及其相对数量。反应物的总质量始终等于生成物的总质量。
The relative formula mass (Mr) of a compound is the sum of the relative atomic masses (Ar) of all atoms in its formula. For water H₂O: Ar of H = 1, O = 16, so Mr = (2 × 1) + 16 = 18.
化合物的相对式量（Mr）是其化学式中所有原子的相对原子质量（Ar）之和。例如水 H₂O：H 的 Ar = 1，O = 16，故 Mr = (2 × 1) + 16 = 18。
ions ensures the same number of each type of atom on both sides. Example: 2H₂ + O₂ → 2H₂O.
配平方程式使得两边每种原子的数目相等。例如：2H₂ + O₂ → 2H₂O。
9. The Law of Conservation of Mass | 质量守恒定律
In a chemical reaction, atoms are neither created nor destroyed. They are simply rearranged to form new substances, so mass is conserved.
化学反应中，原子既不会凭空产生也不会凭空消失，只是重新组合形成新物质，因此质量守恒。
If 24 g of magnesium reacts exactly with 16 g of oxygen, the magnesium oxide produced will have a mass of 40 g. This is true whether the reaction happens in a sealed or open container, though gas exchange may make it appear otherwise.
若 24 克镁恰好与 16 克氧气反应，生成的氧化镁质量为 40 克。无论反应在密封容器还是开放容器中进行，总质量守恒，但若有气体逸出或进入，表观质量可能变化。
Precipitation reactions and neutralisation reactions are common examples where you can measure total mass before and after to verify the law.
沉淀反应和中和反应是常见的实例，可以通过测量反应前后的总质量来验证该定律。
10. Photosynthesis and Respiration Word Equations | 光合作用与呼吸作用的文字方程式
Photosynthesis is the process by which green plants make glucose using light energy. The overall word equation summarises the reactants and products.
光合作用是绿色植物利用光能制造葡萄糖的过程，总文字方程式概括了反应物和生成物。
carbon dioxide + water → glucose + oxygen
This reaction takes place in chloroplasts and requires light energy. The glucose can be converted into starch for storage.
该反应在叶绿体中进行，需要光能。生成的葡萄糖可转化为淀粉储存起来。
Aerobic respiration releases energy from glucose in living cells. Its word equation is:
有氧呼吸在活细胞中从葡萄糖释放能量，其文字方程式为：
glucose + oxygen → carbon dioxide + water (+ energy)
Respiration occurs continuously in all living cells to supply energy for life processes. Photosynthesis and respiration are complementary processes in the carbon cycle.
所有活细胞时刻都在进行呼吸作用，为生命活动提供能量。光合作用和呼吸作用是碳循环中互补的两个过程。
11. Genetic Inheritance: Punnett Squares and Ratios | 遗传：庞纳特方格与比例
Inherited characteristics are determined by genes. A Punnett square helps predict the probability of offspring inheriting particular combinations of alleles.
遗传特征由基因决定。庞纳特方格可预测后代继承特定等位基因组合的概率。
parents are heterozygous (Tt) for the tall trait. T = dominant tall, t = recessive short.
考虑一个单基因杂交：双亲均为高茎性状的杂合子（Tt）。T 为显性高茎，t 为隐性矮茎。
| T | t | |
| T | TT | Tt |
| t | Tt | tt |
The genotypic ratio is 1 TT : 2 Tt : 1 tt. The phenotypic ratio is 3 tall : 1 short.
基因型比例为 1 TT : 2 Tt : 1 tt，表现型比例为 3 高茎 : 1 矮茎。
Co-dominance and sex-linked inheritance follow similar principles but produce different ratios. Punnett squares always assume random fertilisation.
共显性和伴性遗传遵循相似原理，但会呈现不同比例。庞纳特方格始终假设随机受精。
12. Hooke's Law | 胡克定律
Hooke's Law describes the behaviour of springs and elastic objects. It states that the extension of a spring is directly proportional to the force applied, provided the elastic limit is not exceeded.
胡克定律描述弹簧等弹性物体的行为：在弹性限度内，弹簧的伸长量与所受外力成正比。
F = k × x
F is the force applied (N), k is the spring constant (N/m), and x is the extension (m). A stiffer spring has a larger k value. The graph of force against extension is a straight line through the origin up to the limit of proportionality.
F 为施加的力（牛），k 为弹簧常数（牛/米），x 为伸长量（米）。弹簧越硬，k 值越大。在比例极限范围内，力-伸长图是一条过原点的直线。
n k = F/x = 10 ÷ 0.05 = 200 N/m. Beyond the elastic limit, the spring deforms permanently.
若弹簧在 10 牛的力作用下伸长 0.05 米，则 k = 10 ÷ 0.05 = 200 牛/米。超过弹性限度后，弹簧会发生永久变形。
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