📚 Year 11 Cambridge Science Formula & Theorem Quick Reference | 剑桥11年级科学公式定理速查手册
This handbook compiles the essential formulas and theorems for Year 11 Cambridge IGCSE Science, covering Physics, Chemistry, and Biology. Use it for last-minute revision and to reinforce core concepts before your exams.
本手册汇编了剑桥 IGCSE 11年级科学（物理、化学、生物）的核心公式与定理，适合考前快速复习和巩固关键知识点。
1. Motion and Forces | 运动与力
t, where s is distance (m) and t is time (s). Average speed = total distance / total time.
速度：v = s / t，s为距离（米），t为时间（秒）。平均速度 = 总路程 / 总时间。
initial velocity (m/s), v is final velocity, and t is time taken. Acceleration is the rate of change of velocity.
加速度：a = (v - u) / t，u为初速度（米/秒），v为末速度，t为时间。加速度是速度的变化率。
s = ut + ½at²; v² = u² + 2as; s = (u + v)t / 2. These apply when acceleration is constant.
匀加速运动方程：v = u + at；s = ut + ½at²；v² = u² + 2as；s = (u + v)t / 2。这些公式适用于加速度恒定的情况。
Newton' nt force (N), m is mass (kg), a is acceleration (m/s²). This links force, mass and motion.
牛顿第二定律：F = ma，F为合力（牛顿），m为质量（千克），a为加速度。此公式揭示了力、质量和运动的关系。
g is gravitational field strength (about 9.8 N/kg on Earth). Weight is a force, not mass.
重量：W = mg，g为引力场强度（地球上约为 9.8 牛/千克）。重量是一种力，与质量不同。
(kg/m³), m is mass, V is volume. Used when identifying substances or calculating buoyancy.
密度：ρ = m / V，ρ为密度（千克/米³），m为质量，V为体积。常用于鉴别物质或计算浮力。
Hooke' t (N/m), x is extension from natural length. Valid only up to the limit of proportionality.
胡克定律：F = kx，k为弹簧常数（牛/米），x为超出自然长度的形变量。仅在弹性限度内成立。
ciple of moments: sum of clockwise moments = sum of anticlockwise moments for equilibrium.
力矩：M = Fd，d为到支点的垂直距离（米）。力矩平衡原理：顺时针力矩之和等于逆时针力矩之和时，系统处于平衡状态。
essure: p = ρgh, where h is depth, ρ is liquid density, g is gravitational field strength.
压强：p = F / A。液体压强：p = ρgh，h为深度，ρ为液体密度，g为引力场强度。
2. Energy, Work and Power | 能量、功与功率
here m is mass (kg) and v is speed (m/s). This is the energy possessed by a moving object.
动能：Eₖ = ½mv²，m为质量（千克），v为速率（米/秒）。这是运动物体所具有的能量。
height above a reference level. This energy depends on position in a gravitational field.
重力势能：Eₚ = mgh，h为相对于参考水平面的高度。该能量取决于物体在引力场中的位置。
= Fd, when force and displacement are parallel. Unit is joule (J). Work transfers energy.
做功：W = Fd，当力与位移平行时。单位为焦耳（J）。做功过程伴随着能量转移。
Power: P = W / t = E / t, the rate of doing work or transferring energy. Unit is watt (W).
功率：P = W / t = E / t，即做功或能量转移的速率。单位为瓦特（W）。
Efficiency: η = (useful energy output / total energy input) × 100%. No device is 100% efficient due to energy dissipation as heat.
效率：η =（有用输出能量 / 总输入能量）× 100%。由于能量会以热等形式耗散，没有设备的效率为100%。
Conservation of energy: energy cannot be created or destroyed, only transferred or transformed. This principle underpins all energy equations.
能量守恒：能量无法被创造或毁灭，只能被转移或转化。这一原理是所有能量公式的基础。
3. Electricity | 电学
e I is current (A), Q is charge (C), t is time (s). Current is the rate of flow of charge.
电流：I = Q / t，I为电流（安培），Q为电荷量（库伦），t为时间（秒）。电流就是电荷流动的速率。
Q, where V is voltage (V), W is energy transferred (J), Q is charge. Also called voltage.
电压：V = W / Q，V为电势差（伏特），W为转移的能量（焦耳），Q为电荷量。也称为电压。
Resistance: R = V / I, from Ohm's law. For an ohmic conductor, R is constant at constant temperature. Unit: ohm (Ω).
电阻：R = V / I，源自欧姆定律。对于欧姆导体，温度不变时电阻恒定。单位为欧姆（Ω）。
Resistors in series: Rtotal = R₁ + R₂ + ...
串联电阻：R总 = R₁ + R₂ + ...
Resistors in parallel: 1 / Rtotal = 1 / R₁ + 1 / R₂ ...
并联电阻：1 / R总 = 1 / R₁ + 1 / R₂ ...
Electrical power: P = IV = I²R = V² / R. The energy transferred E = Pt = IVt.
电功率：P = IV = I²R = V² / R。消耗的电能E = Pt = IVt。
ns, where Vp, Vs are primary and secondary voltages, np, ns are coil turn numbers. For 100% efficiency: Vp Ip = Vs Is.
变压器：Vp / Vs = np / ns，Vp, Vs为原副线圈电压，np, ns为匝数。对于理想变压器，Vp Ip = Vs Is。
4. Waves and Optics | 波与光学
d: v = fλ, where f is frequency (Hz), λ is wavelength (m). This applies to all wave types.
波速：v = fλ，f为频率（赫兹），λ为波长（米）。该公式适用于所有波。
of refraction. Also n = c / v, where c is speed of light in vacuum, v is speed in medium.
折射率：n = sin i / sin r，i为入射角，r为折射角。同样 n = c / v，c为真空中光速，v为介质中光速。
t travels from dense to less dense medium. For angles > c, total internal reflection occurs.
临界角：sin c = 1 / n，光从光密介质射向光疏介质时成立。入射角大于c时发生全内反射。
u, where v is image distance, u is object distance. No sign convention required at IGCSE.
放大率（透镜/面镜）：M = 像高 / 物高 = v / u，v为像距，u为物距。IGCSE 阶段通常不涉及符号规则。
5. Thermal Physics | 热物理
re Q is heat energy (J), m is mass (kg), c is specific heat capacity (J/kg°C), Δθ is temperature change.
比热容：Q = mcΔθ，Q为热量（焦耳），m为质量（千克），c为比热容，Δθ为温度变化。
s latent heat of fusion or vaporisation (J/kg). Temperature remains constant during the change of state.
比潜热：Q = mL，L为熔化潜热或汽化潜热（焦耳/千克）。在物态变化过程中温度不变。
Boyle' ure): p₁V₁ = p₂V₂. Pressure and volume are inversely proportional for a fixed mass of gas.
玻意耳定律（恒温）：p₁V₁ = p₂V₂。对于一定质量的气体，压强与体积成反比。
p₁ / T₁ = p₂ / T₂, where T is in kelvin. Pressure is proportional to absolute temperature.
压强定律（定容）：p₁ / T₁ = p₂ / T₂，T为开尔文温度。压强与绝对温度成正比。
Charles' aw (constant pressure): V₁ / T₁ = V₂ / T₂. Volume is proportional to absolute temperature.
查理定律（定压）：V₁ / T₁ = V₂ / T₂。体积与绝对温度成正比。
6. Quantitative Chemistry | 定量化学
Relative atomic mass Aᵣ and relative molecular mass Mᵣ: sum of relative atomic masses from the periodic table. Mᵣ has no unit.
相对原子质量Aᵣ与相对分子质量Mᵣ：为各原子相对原子质量之和，查阅周期表得到，Mᵣ无单位。
mount (mol), m is mass (g), M is molar mass (g/mol). This is the core conversion equation.
摩尔数：n = m / M，n为物质的量（摩尔），m为质量（克），M为摩尔质量（克/摩尔）。这是核心的换算公式。
solution in dm³. Unit: mol/dm³. Alternatively c = mass / V for mass concentration (g/dm³).
浓度：c = n / V，V为溶液体积（dm³）。单位是 mol/dm³。也可用 c = 质量 / V 表示质量浓度（g/dm³）。
P: 1 mol of any gas occupies 24 dm³ at room temperature and pressure (r.t.p.). V = n × 24.
标准状况气体体积：在常温常压下，1摩尔任何气体体积约为 24 dm³。V = n × 24。
Stoichiometry: use mole ratio from a balanced equation to calculate amounts of reactants and products. The ratio of coefficients equals the mole ratio.
化学计量法：根据配平化学方程式中的系数比（等于摩尔比）计算反应物和生成物的量。
7. Chemical Reactions and Energetics | 化学反应与能量
Exothermic reactions release energy to the surroundings, causing temperature rise; endothermic reactions absorb energy. Energy changes can be shown in energy profile diagrams.
放热反应向环境释放能量，温度升高；吸热反应从环境吸收能量。能量变化可在能量曲线图中体现。
cΔT is the heat absorbed or released by the solution (approximated), and n is moles of limiting reactant. Negative ΔH indicates exothermic.
焓变：ΔH = -Q / n，其中 Q = mcΔT 为溶液吸收或放出的热量（近似值），n为限制反应物的摩尔数。ΔH 为负表示放热。
utralisation: acid + base → salt + water, always exothermic. E.g. HCl + NaOH → NaCl + H₂O.
中和反应：酸 + 碱 → 盐 + 水，总是放热。例如 HCl + NaOH → NaCl + H₂O。
Redox: oxidation is loss of electrons, reduction is gain of electrons. OIL RIG: Oxidation Is Loss, Reduction Is Gain. Metals above hydrogen in reactivity series displace hydrogen from acids.
氧化还原：氧化是电子失去，还原是电子得到。助记 OIL RIG。金属活动性顺序中位于氢以上的金属可从酸中置换出氢。
Electrolysis: cations move to cathode (negative electrode) and gain electrons (reduction); anions move to anode and lose electrons (oxidation). Faraday’s constant is not required at IGCSE.
电解：阳离子移向阴极（负极）获得电子被还原；阴离子移向阳极失去电子被氧化。IGCSE 不要求法拉第常数定量计算。
8. Rates and Equilibrium | 速率与平衡
Rate of reaction: speed at which reactants are used up or products are formed. Measured by change in mass, volume of gas, or colour change per unit time.
反应速率：反应物消耗或生成物生成的快慢，可通过单位时间内质量变化、气体体积或颜色变化来测定。
Factors increasing rate: higher concentration, higher pressure (for gases), larger surface area, higher temperature, and use of a catalyst. Collision theory explains these effects.
加快反应速率的因素：提高浓度、增大压强（气体）、增大表面积、升高温度以及使用催化剂。碰撞理论可以解释这些影响。
Dynamic equilibrium: in a closed system, the forward and reverse reactions occur at equal rates, so concentrations remain constant. Le Chatelier’s principle states that the equilibrium shifts to oppose any imposed change.
动态平衡：封闭体系中正逆反应速率相等，各物质浓度不变。勒沙特列原理指出，平衡会向减弱外界改变的方向移动。
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