📚 Year 11 CIE Science: Quick Reference Formula & Theorem Handbook | Year 11 CIE 科学：公式定理速查手册
This handbook gathers the essential formulas, equations, and theorems you need for Year 11 CIE Science. It covers core topics from physics, chemistry, and biology – perfect for revision, quick checks, and building confidence before your examination. The content is aligned with the CIE Coordinated Sciences and Combined Science syllabuses, focusing on the most frequently assessed relationships and principles.
本手册汇总了 Year 11 CIE 科学课程必备的核心公式、方程和定理，涵盖物理、化学和生物的关键主题，非常适合考前复习、快速查阅和巩固信心。内容紧扣 CIE 综合科学和组合科学大纲，聚焦最常考查的关系和原理。
1. Physics: Kinematics | 物理：运动学
Kinematics describes motion without considering its causes. The following equations apply to motion with uniform acceleration.
运动学描述物体的运动，不涉及引起运动的原因。以下方程适用于匀加速直线运动。
The final velocity v is related to initial velocity u, acceleration a, and time t.
末速度 v 与初速度 u、加速度 a 和时间 t 之间的关系。
v = u + a t
Displacement s can be calculated using initial velocity, time, and acceleration.
位移 s 可以通过初速度、时间和加速度计算。
s = u t + ½ a t²
The average speed is total distance travelled divided by total time taken.
平均速度等于总路程除以总时间。
average speed = total distance / total time
2. Physics: Forces and Motion | 物理：力与运动
Newton's second law relates net force, mass, and acceleration. Weight is the gravitational force on an object.
牛顿第二定律将合力、质量和加速度联系起来。重量是作用在物体上的引力。
The net force F acting on a body equals its mass m multiplied by acceleration a.
作用在物体上的合力 F 等于质量 m 乘以加速度 a。
F = m a
eight W is the product of mass and gravitational field strength g (on Earth g ≈ 9.8 N/kg).
重量 W 等于质量与引力场强度 g 的乘积（地球上 g ≈ 9.8 N/kg）。
W = m g
Momentum p is given by mass × velocity. In a closed system, total momentum is conserved.
动量 p 等于质量乘以速度。在封闭系统中，总动量守恒。
p = m v
3. Physics: Energy, Work and Power | 物理：能量、功与功率
Energy cannot be created or destroyed, only transferred. Work is done when a force moves an object.
能量不能凭空产生或消失，只能转移。力使物体移动时做功。
Work done W equals force F multiplied by distance d moved in the direction of the force.
做功 W 等于力 F 与沿力方向移动的距离 d 的乘积。
W = F d
Kinetic energy KE depends on mass and speed; gravitational potential energy GPE depends on mass, height, and g.
动能 KE 取决于质量和速度；重力势能 GPE 取决于质量、高度和 g。
KE = ½ m v²
GPE = m g h
Power P is the rate of doing work or transferring energy.
功率 P 是做功或能量转移的速率。
P = W / t
Efficiency is the ratio of useful energy output to total energy input, often expressed as a percentage.
效率是有用能量输出与总能量输入的比率，常用百分数表示。
efficiency = (useful output / total input) × 100%
4. Physics: Pressure and Density | 物理：压强与密度
Pressure is the force acting per unit area. Fluids exert pressure due to their weight.
压强是单位面积上所受的力。流体由于自身重量而产生压强。
Pressure p equals force F divided by area A.
压强 p 等于力 F 除以面积 A。
p = F / A
In a liquid, pressure increases with depth h and depends on the liquid density ρ and g.
在液体中，压强随深度 h 增加，并与液体密度 ρ 和 g 有关。
p = h ρ g
Density ρ is mass per unit volume.
密度 ρ 是单位体积的质量。
ρ = m / V
5. Physics: Electricity | 物理：电学
Ohm's law, electric power, and energy transfer are fundamental in circuit analysis.
欧姆定律、电功率和电能转移是电路分析的基础。
For an ohmic conductor at constant temperature, voltage V equals current I times resistance R.
对恒温下的欧姆导体，电压 V 等于电流 I 乘以电阻 R。
V = I R
Electrical power P can be calculated using current and voltage.
电功率 P 可用电流和电压计算。
P = I V
Energy transferred E in a circuit is power multiplied by time.
电路中的电能转移 E 等于功率乘以时间。
E = I V t
For resistors in series, total resistance is the sum; in parallel, the reciprocal sum applies.
电阻串联时，总电阻为各电阻之和；并联时，总电阻的倒数等于各电阻倒数之和。
Rtotal = R₁ + R₂ + ... (series)
1/Rtotal = 1/R₁ + 1/R₂ + ... (parallel)
6. Physics: Waves | 物理：波
Wave speed depends on frequency and wavelength. Refraction follows Snell's law.
波速取决于频率和波长。折射遵循斯涅尔定律。
The wave equation links speed v, frequency f, and wavelength λ.
波速方程将波速 v、频率 f 和波长 λ 联系起来。
v = f λ
Refractive index n is the ratio of sin of angle of incidence i to sin of angle of refraction r.
折射率 n 是入射角 i 的正弦与折射角 r 的正弦之比。
n = sin i / sin r
For total internal reflection, the critical angle c satisfies sin c = 1/n.
对于全内反射，临界角 c 满足 sin c = 1/n。
sin c = 1 / n
7. Chemistry: The Mole and Stoichiometry | 化学：摩尔与化学计量
The mole links the microscopic world of atoms to measurable quantities. Molar mass and molar volume are key.
摩尔将微观原子世界与可测量量联系起来。摩尔质量和摩尔体积是关键。
Amount of substance n (mol) equals mass m divided by molar mass M.
物质的量 n (mol) 等于质量 m 除以摩尔质量 M。
n = m / M
Concentration c of a solution is the amount of solute per unit volume (mol/dm³).
溶液的浓度 c 是单位体积内溶质的物质的量 (mol/dm³)。
c = n / V
At room temperature and pressure (rtp), one mole of any gas occupies 24 dm³.
在常温常压下 (rtp)，1 摩尔任何气体占据 24 dm³ 的体积。
Vgas = n × 24 dm³
8. Chemistry: Rate of Reaction and Equilibrium | 化学：反应速率与平衡
The rate of a reaction measures how quickly reactants are consumed or products are formed. Dynamic equilibrium is a reversible state where forward and backward rates are equal.
反应速率衡量反应物消耗或产物生成的快慢。动态平衡是一种可逆状态，此时正逆反应速率相等。
Average rate of reaction can be expressed as change in quantity over time.
平均反应速率可表示为单位时间内某种量的变化。
rate = Δ quantity / Δ time
Le Chatelier's principle states that if a system at equilibrium experiences a change in concentration, temperature, or pressure, the equilibrium shifts to counteract the imposed change.
勒夏特列原理指出，如果平衡体系经历浓度、温度或压强的变化，平衡将向减弱这种变化的方向移动。
Catalysts increase the rate of both forward and backward reactions by lowering activation energy, without affecting the position of equilibrium.
催化剂通过降低活化能同时增加正逆反应速率，但不影响平衡位置。
9. Chemistry: Acids, Bases and Salts | 化学：酸、碱与盐
Acids donate protons (H⁺) and bases accept them. Neutralisation forms a salt and water.
酸是质子 (H⁺) 的供体，碱是质子受体。中和反应生成盐和水。
The pH scale measures the concentration of hydrogen ions; it is logarithmic.
pH 值标度衡量氢离子浓度，是对数标度。
pH = -log[H⁺]
In a neutralisation reaction: acid + base → salt + water.
中和反应通式：酸 + 碱 → 盐 + 水。
HCl + NaOH → NaCl + H₂O
Metal carbonates react with acids to produce a salt, water, and carbon dioxide.
金属碳酸盐与酸反应生成盐、水和二氧化碳。
CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂
10. Chemistry: Electrolysis | 化学：电解
Electrolysis uses direct current to drive a non-spontaneous chemical reaction. Faraday's laws relate charge to mass deposited.
电解使用直流电驱动非自发化学反应。法拉第定律将电荷与沉积物质量联系起来。
The charge Q (coulombs) passed is current I (A) multiplied by time t (s).
通过的电量 Q (库仑) 等于电流 I (A) 乘以时间 t (s)。
Q = I t
The mass m of substance deposited or liberated at an electrode is given by:
在电极上沉积或释放的物质质量 m 可由下式给出：
m = (Q M) / (n F)
where M is molar mass, n is the number of electrons transferred per ion, and F is the Faraday constant (96 500 C/mol).
其中 M 为摩尔质量，n 为每个离子转移的电子数，F 为法拉第常数 (96 500 C/mol)。
11. Biology: Cells and Biomolecules | 生物：细胞与生物分子
Magnification helps visualise cell structures. Biochemical reactions sustain life.
放大有助于观察细胞结构。生物化学反应维持生命。
The total magnification of a light microscope is eyepiece lens magnification times objective lens magnification.
光学显微镜的总放大倍数是目镜放大倍数乘以物镜放大倍数。
total magnification = eyepiece magnification × objective magnification
Photosynthesis converts light energy into chemical energy in the form of glucose.
光合作用将光能转化为以葡萄糖形式储存的化学能。
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Aerobic respiration releases energy for cellular activities.
有氧呼吸为细胞活动释放能量。
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy
12. Biology: Genetics and Evolution | 生物：遗传与进化
Inheritance follows predictable patterns. Evolution by natural selection explains biodiversity.
遗传遵循可预测的模式。自然选择驱动的进化解释了生物多样性。
heterozygous parents (e.g., Tt × Tt) gives a phenotype ratio of 3:1 for a dominant trait.
杂合亲本 (如 Tt × Tt) 的单基因杂交产生的显性性状表型比为 3:1。
The probability of inheriting a particular allele can be calculated using a Punnett square.
可用庞纳特方格计算遗传特定等位基因的概率。
Natural selection acts on variation within a population; individuals best adapted to their environment are more likely to survive and reproduce, passing advantageous alleles to the next generation.
自然选择作用于种群内部的变异；最适应环境的个体更有可能生存和繁殖，将有利等位基因传递给下一代。
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