📚 Year 11 CAIE Science: Quick Formula & Theorem Handbook | Year 11 CAIE 科学：公式定理速查手册
This handbook provides a concise collection of essential formulas, equations, and scientific principles for CAIE Year 11 Science students. Covering physics, chemistry, and biology, each entry is presented in a bilingual format to support revision and exam preparation. Use this guide to quickly refresh core concepts and improve problem‑solving speed.
本手册为 CAIE Year 11 科学课程的学生整理了必备的公式、方程式和科学原理，涵盖物理、化学和生物。每条内容均以中英双语呈现，助力复习与备考。通过本速查手册，你可以快速回顾核心概念，提升解题速度。
1. Speed, Distance, and Time | 速度、距离与时间
The relationship between speed, distance, and time is fundamental in motion studies. Average speed is calculated by dividing total distance travelled by the time taken.
速度、距离和时间的关系是运动学的基础。平均速度等于总路程除以所用时间。
v = s / t
v = s ÷ t
Where v = average speed (m/s), s = distance (m), t = time (s). Rearrangements give s = v × t and t = s / v.
其中 v = 平均速度（米/秒），s = 距离（米），t = 时间（秒）。变形可得 s = v × t 和 t = s ÷ v。
2. Acceleration | 加速度
Acceleration measures how quickly velocity changes. It is the rate of change of velocity. A negative acceleration indicates deceleration.
加速度表示速度变化的快慢，是速度的变化率。负加速度表示减速。
a = (v – u) / t
a = (v – u) ÷ t
, v = final velocity (m/s), u = initial velocity (m/s), t = time (s). The SI unit is m/s².
其中 a = 加速度（米/秒²），v = 末速度（米/秒），u = 初速度（米/秒），t = 时间（秒）。国际单位是 m/s²。
3. Newton's Second Law | 牛顿第二定律
Newton’s second law relates the net force acting on an object to its mass and acceleration. The direction of acceleration is the same as the net force.
牛顿第二定律描述了物体所受合力与其质量和加速度的关系。加速度方向与合力方向相同。
F = m a
F = m × a
s²). This equation is used to calculate force, mass, or acceleration in dynamics problems.
其中 F = 合力（牛顿），m = 质量（千克），a = 加速度（米/秒²）。该方程常用于动力学问题中计算力、质量或加速度。
4. Weight and Gravitational Field Strength | 重力与引力场强
bject. It depends on mass and the gravitational field strength, g. On Earth, g ≈ 9.8 N/kg.
重力是作用在物体上的引力，取决于质量和引力场强 g。地球上 g ≈ 9.8 N/kg。
W = m g
W = m × g
ight (N), m = mass (kg), g = gravitational field strength (N/kg). Weight differs from mass – mass is constant, weight varies with g.
其中 W = 重力（牛顿），m = 质量（千克），g = 引力场强（N/kg）。重量与质量不同——质量恒定，重量随 g 变化。
5. Kinetic Energy | 动能
Kinetic energy is the energy an object possesses due to its motion. It depends on mass and the square of speed. Doubling the speed quadruples the kinetic energy.
动能是物体因运动而具有的能量，与质量和速度的平方成正比。速度加倍，动能变为四倍。
KE = ½ m v²
KE = ½ × m × v²
mass (kg), v = speed (m/s). This formula is essential in conservation of energy problems.
其中 KE = 动能（焦耳），m = 质量（千克），v = 速度（米/秒）。该公式在能量守恒问题中至关重要。
6. Gravitational Potential Energy | 重力势能
Gravitational potential energy (GPE) is stored energy due to an object’s position in a gravitational field. It increases with height above a reference level.
重力势能是物体因在引力场中的位置而储存的能量，随高度增加而增大。
GPE = m g h
GPE = m × g × h
g), h = height (m). Often used alongside kinetic energy in mechanical energy conservation.
其中 GPE 单位为焦耳（J），m = 质量（千克），g = 引力场强（N/kg），h = 高度（米）。常与动能一起用于机械能守恒问题。
7. Density | 密度
Density is the mass per unit volume of a material. It is a characteristic property that identifies substances. Units are commonly g/cm³ or kg/m³.
密度是物质单位体积的质量，是一种用于识别物质的特性。常用单位为 g/cm³ 或 kg/m³。
ρ = m / V
ρ = m ÷ V
uids and regular solids, volume can be calculated; for irregular solids, use displacement.
其中 ρ = 密度（千克/米³），m = 质量（千克），V = 体积（米³）。液体的体积可由量筒读出，规则固体用公式计算，不规则固体可用排水法测量。
8. Ohm's Law | 欧姆定律
Ohm’s law states that the current through a resistor is directly proportional to the potential difference across it, provided temperature remains constant.
欧姆定律指出，在温度不变的情况下，通过电阻器的电流与其两端的电势差成正比。
V = I R
V = I × R
Where V = voltage (V), I = current (A), R = resistance (Ω). Rearranged forms: I = V / R and R = V / I. Many components are non-ohmic, e.g. diodes.
其中 V = 电压（伏特），I = 电流（安培），R = 电阻（欧姆）。变形公式：I = V ÷ R 和 R = V ÷ I。许多元件是非欧姆的，例如二极管。
9. Electrical Power and Energy | 电功率与电能
common forms are used: P = IV and P = I²R. Energy transferred is power multiplied by time.
电功率是电能传递的速率。常用形式有 P = IV 和 P = I²R。传递的电能等于功率乘以时间。
P = I V and P = I² R
P = I × V 以及 P = I² × R
Where P = power (W), I = current (A), V = voltage (V), R = resistance (Ω). Energy E = P t, with E in joules (J) or kilowatt-hours (kWh).
其中 P = 功率（瓦特），I = 电流（安培），V = 电压（伏特），R = 电阻（欧姆）。电能 E = P × t，单位是焦耳（J）或千瓦时（kWh）。
10. Wave Speed Equation | 波速公式
All waves obey the wave equation linking wave speed, frequency, and wavelength. This applies to sound, light, water waves, and waves on strings.
所有波都遵循波速公式，它将波速、频率和波长联系起来，适用于声波、光波、水波和弦上的波。
v = f λ
v = f × λ
cy (Hz), λ = wavelength (m). For electromagnetic waves in a vacuum, v = c ≈ 3.0 × 10⁸ m/s.
其中 v = 波速（米/秒），f = 频率（赫兹），λ = 波长（米）。真空中电磁波的波速 c ≈ 3.0 × 10⁸ m/s。
11. The Mole Concept (Chemistry) | 摩尔概念（化学）
× 10²³ particles. The mass of one mole of a substance is its molar mass in grams per mole.
摩尔是物质的量的单位。1 摩尔包含 6.02 × 10²³ 个粒子。1 摩尔物质的质量即其摩尔质量，单位为克/摩尔。
n = m / M and n = N / Nₐ
n = m ÷ M 及 n = N ÷ Nₐ
Avogadro constant (6.02 × 10²³ mol⁻¹). Group 1 and 7 elements are diatomic (e.g. Cl₂, O₂).
其中 n = 摩尔数（mol），m = 质量（克），M = 摩尔质量（g/mol），N = 粒子数，Nₐ = 阿伏伽德罗常数（6.02 × 10²³ mol⁻¹）。第 1 族和第 7 族元素多为双原子分子（如 Cl₂、O₂）。
12. Concentration of Solutions | 溶液浓度
Concentration expresses the amount of solute dissolved in a given volume of solution. Common units are mol/dm³ (molarity) or g/dm³.
浓度表示一定体积溶液中溶质的量，常用单位为 mol/dm³（摩尔浓度）或 g/dm³。
c = n / V and concentration (g/dm³) = mass (g) / volume (dm³)
c = n ÷ V 以及 浓度 (g/dm³) = 质量 (g) ÷ 体积 (dm³)
1000 cm³. For titration calculations, use moles of acid = moles of base at neutralisation.
其中 c = 浓度（mol/dm³），n = 摩尔数（mol），V = 体积（dm³）。1 dm³ = 1000 cm³。在滴定计算中，中和时酸的摩尔数等于碱的摩尔数。
13. Rate of Reaction | 反应速率
The rate of a chemical reaction can be measured by the change in amount of reactant or product per unit time. Two common formulas involve mass loss and gas volume.
化学反应速率可用单位时间内反应物或生成物量的变化来衡量。常见公式涉及质量损失和气体体积。
Rate = change in mass / time or Rate = change in volume of gas / time
速率 = 质量变化 ÷ 时间 或 速率 = 气体体积变化 ÷ 时间
Units can be g/s, cm³/s, or mol/s. Factors affecting rate include concentration, temperature, surface area, and catalysts. Collision theory explains these effects.
单位可以是 g/s、cm³/s 或 mol/s。影响速率的因素有浓度、温度、表面积和催化剂。碰撞理论解释了这些影响。
14. Photosynthesis Summary Equation | 光合作用总反应式
Photosynthesis is the process by which green plants produce glucose and oxygen from carbon dioxide and water, using light energy. A balanced word and symbol equation is a core requirement.
光合作用是绿色植物利用光能，由二氧化碳和水生成葡萄糖和氧气的过程。需要掌握配平的文字和符号方程式。
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Chlorophyll absorbs light energy, and the reaction takes place in chloroplasts. The rate is affected by light intensity, carbon dioxide concentration, and temperature.
叶绿素吸收光能，反应在叶绿体中进行。光合作用速率受光照强度、二氧化碳浓度和温度影响。
15. Magnification (Biology) | 放大倍数（生物）
an image to the actual size of the specimen. Correct unit conversion is vital: 1 mm = 1000 µm.
放大倍数是图像大小与标本实际大小的比值。正确的单位换算至关重要：1 mm = 1000 µm。
M = I / A
M = I ÷ A
agnification (no units), I = image size, A = actual size (same units as I). Alternatively, A = I / M. Use a graticule or scale bar for measurements.
其中 M = 放大倍数（无单位），I = 图像尺寸，A = 实际尺寸（与 I 单位相同）。也可用 A = I ÷ M。测量时可使用目镜测微尺或比例尺。
16. Chemical Bonding and Empirical Formulae | 化学键与经验式
Ionic bonds form between metals and non‑metals by electron transfer. Covalent bonds involve electron sharing between non‑metals. Empirical formula is the simplest whole‑number ratio of atoms in a compound.
离子键通过电子转移在金属和非金属之间形成。共价键是非金属原子间通过共用电子形成。经验式是化合物中各原子最简整数比。
To determine empirical formula from % composition: assume 100 g sample, convert masses to moles, divide by smallest number of moles. Example: a compound with 40% C, 6.7% H, 53.3% O gives CH₂O.
从百分组成求经验式的步骤：假设样品 100 g，将质量换算为摩尔数，除以最小摩尔数。例如：含 40% C、6.7% H、53.3% O 的化合物经验式为 CH₂O。
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