📚 CAIE Year 10 Science: Essential Formulas and Theorems Quick Reference Guide | CAIE Year 10 科学：必背公式定理速查手册
Welcome to your fast‑reference companion for Year 10 CAIE Science. This guide gathers the essential formulas, laws and theorems from physics, chemistry and biology that you must recall confidently for your examinations. Each entry is paired in English and Chinese to help you build bilingual fluency while mastering the scientific principles. Use it for quick revision, self‑testing and bridging any gaps in your knowledge.
欢迎使用 Year 10 CAIE 科学速查手册。本手册汇集了物理、化学和生物中必须熟练掌握的核心公式、定律和定理，每一组均以中英双语呈现，帮助你巩固学科知识的同时建立双语思维。可用于快速复习、自我检测和查漏补缺。
1. Physics: Speed, Velocity and Acceleration | 物理：速度与加速度
The speed of an object is the distance moved per unit time: v = d / t. Velocity is speed in a given direction.
物体的速率是单位时间内移动的距离：v = d / t。速度则是具有方向的速率。
Acceleration is the rate of change of velocity. When an object accelerates uniformly from initial velocity u to final velocity v in time t, the acceleration is a = (v – u) / t.
加速度是速度的变化率。若物体在时间 t 内从初速度 u 匀加速到末速度 v，则加速度为 a = (v – u) / t。
The final velocity, initial velocity, acceleration and distance travelled s are linked by v² = u² + 2 a s.
末速度、初速度、加速度和移动距离 s 之间的关系为 v² = u² + 2 a s。
2. Physics: Newton's Laws of Motion | 物理：牛顿运动定律
Newton's First Law states that an object remains at rest or moves with constant velocity unless acted on by a resultant force.
牛顿第一定律指出，除非受到合外力作用，否则物体将保持静止或匀速直线运动状态。
Newton's Second Law relates resultant force F, mass m and acceleration a: F = m a. The unit of force is the newton (N).
牛顿第二定律将合外力 F、质量 m 和加速度 a 联系起来：F = m a。力的单位是牛顿 (N)。
Newton's Third Law states that if body A exerts a force on body B, then body B exerts an equal and opposite force on body A.
牛顿第三定律指出，若物体 A 对物体 B 施加一个力，则物体 B 同时对物体 A 施加一个大小相等、方向相反的力。
3. Physics: Momentum and Impulse | 物理：动量与冲量
Momentum p is the product of mass and velocity: p = m v. It is a vector quantity measured in kg m/s.
动量 p 是质量与速度的乘积：p = m v。动量是矢量，单位为 kg·m/s。
In a closed system with no external forces, total momentum before an event equals total momentum after: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
在没有外力的封闭系统中，事件前的总动量等于事件后的总动量：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。
Impulse equals the change in momentum: F Δt = Δp = m v – m u.
冲量等于动量的变化量：F Δt = Δp = m v – m u。
4. Physics: Work, Energy and Power | 物理：功、能量与功率
Work done W by a constant force F moving an object distance d in the direction of the force is W = F d. The unit is the joule (J).
恒力 F 使物体沿力的方向移动距离 d 做的功为 W = F d。单位是焦耳 (J)。
Kinetic energy Eₖ = ½ m v². Gravitational potential energy Eₚ = m g h.
动能 Eₖ = ½ m v²。重力势能 Eₚ = m g h。
Power P is the rate of doing work: P = W / t, measured in watts (W).
功率 P 是做功的速率：P = W / t，单位是瓦特 (W)。
Principle of conservation of energy: energy cannot be created or destroyed, only transferred, stored or dissipated.
能量守恒定律：能量既不会凭空产生也不会凭空消失，只会转移、储存或耗散。
5. Physics: Electrical Quantities and Ohm's Law | 物理：电学量与欧姆定律
Electric current I is the charge flowing per second: I = Q / t, where Q is charge in coulombs (C).
电流 I 是单位时间内通过的电荷量：I = Q / t，其中 Q 的单位是库仑 (C)。
Ohm's law relates voltage V, current I and resistance R: V = I R.
欧姆定律给出电压 V、电流 I 和电阻 R 的关系：V = I R。
Electrical power: P = V I. Energy transferred: E = V I t.
电功率：P = V I。能量转化：E = V I t。
6. Physics: Wave Equation | 物理：波动方程
Wave speed v, frequency f and wavelength λ are linked: v = f λ. Frequency is measured in hertz (Hz).
波速 v、频率 f 和波长 λ 的关系为：v = f λ。频率的单位是赫兹 (Hz)。
The period T is the time for one complete wave to pass a point: T = 1 / f.
周期 T 是一个完整波通过某点所需的时间：T = 1 / f。
7. Chemistry: Moles and Molar Calculations | 化学：摩尔与摩尔计算
The number of moles n of a substance can be found from its mass m and molar mass M: n = m / M.
物质的摩尔数 n 可由其质量 m 和摩尔质量 M 求得：n = m / M。
For gases at room temperature and pressure (rtp), one mole occupies 24 dm³: n = V (dm³) / 24.
在常温常压 (rtp) 下，1摩尔气体体积为 24 dm³：n = V (dm³) / 24。
Concentration of a solution c in mol/dm³: c = n / V, where V is the volume of solution in dm³.
溶液的摩尔浓度 c (mol/dm³)：c = n / V，其中 V 为溶液体积，单位 dm³。
8. Chemistry: Empirical and Molecular Formulae | 化学：实验式与分子式
Empirical formula shows the simplest whole‑number ratio of atoms in a compound. To find it, convert masses to moles, then divide by the smallest mole value.
实验式表示化合物中各原子最简整数比。求法：将各元素质量转换为摩尔数，再除以其中最小的摩尔数。
Molecular formula is a whole‑number multiple of the empirical formula: molecular formula = n × empirical formula, where n = relative molecular mass / empirical formula mass.
分子式是实验式的整数倍：分子式 = n × 实验式，其中 n = 相对分子质量 ÷ 实验式质量。
9. Chemistry: Rate of Reaction and Energy Changes | 化学：反应速率与能量变化
n = change in quantity of reactant or product / time taken. Common units are g/s or cm³/s.
平均反应速率 = 反应物或产物的变化量 ÷ 所用时间。常用单位为 g/s 或 cm³/s。
Exothermic reactions release thermal energy, making the surroundings hotter; endothermic reactions absorb energy, cooling the surroundings.
放热反应释放热能，使环境温度升高；吸热反应吸收能量，使环境温度降低。
Catalysts lower the activation energy and provide an alternative reaction pathway, but are not used up.
催化剂降低活化能，提供另一反应路径，但本身不参与净反应。
10. Biology: Photosynthesis and Respiration Equations | 生物：光合作用与呼吸作用方程
s is: carbon dioxide + water → glucose + oxygen, in the presence of light and chlorophyll.
光合作用的总文字方程式为：二氧化碳 + 水 → 葡萄糖 + 氧气，需要光和叶绿素。
The balanced chemical equation is: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂.
平衡化学方程式为：6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂。
n: glucose + oxygen → carbon dioxide + water (+ energy released). The balanced equation is C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O.
有氧呼吸：葡萄糖 + 氧气 → 二氧化碳 + 水 (+ 释放能量)。平衡方程式为 C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O。
Anaerobic respiration in muscles produces lactic acid; in yeast it produces ethanol and carbon dioxide.
肌肉中的无氧呼吸产生乳酸；酵母中的无氧呼吸产生乙醇和二氧化碳。
11. Biology: Genetic Principles and Monohybrid Crosses | 生物：遗传定律与单基因杂交
Mendel's law of segregation states that each individual carries two alleles for a gene, which separate during gamete formation so each gamete receives only one allele.
孟德尔分离定律指出，每个个体携带一对等位基因，在形成配子时彼此分离，每个配子只含其中一个等位基因。
In a monohybrid cross, the expected phenotypic ratios in the F₂ generation are typically 3:1 when both parents are heterozygous for a dominant‑recessive trait.
在单基因杂交中，若亲本均为显隐性性状的杂合子，F₂ 代的预期表型比通常为 3∶1。
Punnett squares can be used to predict genotype and phenotype ratios.
庞纳特方格可用于预测基因型和表型比例。
12. General Skills: Scientific Notation and Unit Conversions | 通用技能：科学记数法与单位换算
bers as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer. For example, 0.00340 = 3.40 × 10⁻³.
科学记数法将数字表示为 a × 10ⁿ 的形式，其中 1 ≤ a < 10，n 为整数。例如 0.00340 = 3.40 × 10⁻³。
Common SI prefixes: kilo (10³), centi (10⁻²), milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹).
常用国际单位词头：千 (10³)、厘 (10⁻²)、毫 (10⁻³)、微 (10⁻⁶)、纳 (10⁻⁹)。
rt to base units before substituting into formulas, e.g. cm → m, g → kg, °C → K (add 273).
代入公式前务必换算成基本单位，例如 cm → m，g → kg，°C → K（加 273）。
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