📚 Year 11 CIE Science: Formula & Theorem Quick Reference Handbook | 公式定理速查手册
Welcome to your essential quick-reference guide for CIE Year 11 Science. This handbook compiles the core formulas and theorems across Physics, Chemistry and Biology, helping you revise efficiently for your examinations.
欢迎使用这本关键的 CIE 11 年级科学速查手册。本手册汇编了物理、化学和生物的核心公式与定理，帮助你高效复习备考。
1. Motion and Forces | 运动与力
Average speed is defined as the total distance travelled divided by the total time taken. It is a scalar quantity.
v = s / t
平均速度定义为总路程除以总时间，是一个标量。
v = s / t
Acceleration is the rate of change of velocity. It can be calculated from the change in velocity over the time interval.
a = (v - u) / t
加速度是速度的变化率，可以用速度变化量除以时间计算。
a = (v - u) / t
When acceleration is constant, the final velocity v is related to initial velocity u, acceleration a and time t.
v = u + a t
当加速度恒定时，末速度 v 与初速度 u、加速度 a 和时间 t 的关系如下。
v = u + a t
Displacement s under uniform acceleration can be found from the initial velocity, time and acceleration.
s = u t + ½ a t²
匀加速直线运动的位移 s 可由初速度、时间和加速度求得。
s = u t + ½ a t²
The relationship between final velocity, initial velocity, acceleration and displacement without time.
v² = u² + 2 a s
末速度、初速度、加速度和位移之间不涉及时间的关系式。
v² = u² + 2 a s
Newton' s equal to the rate of change of its momentum. For constant mass, it simplifies to F = ma.
F = m a
牛顿第二定律指出，物体所受合力等于其动量变化率。质量不变时简化为 F = ma。
F = m a
The weight of an object is the gravitational force acting on its mass.
W = m g
物体的重量是作用在其质量上的重力。
W = m g
Density is mass per unit volume.
ρ = m / V
密度是单位体积的质量。
ρ = m / V
Pressure is defined as force acting per unit area.
P = F / A
压强定义为作用在单位面积上的力。
P = F / A
2. Energy, Work and Power | 能量、功与功率
Kinetic energy is the energy an object possesses due to its motion.
Eₖ = ½ m v²
动能是物体由于运动而具有的能量。
Eₖ = ½ m v²
Gravitational potential energy gained by an object when lifted in a gravitational field.
Eₚ = m g h
物体在重力场中被举高时所获得的重力势能。
Eₚ = m g h
Work done is the product of force and the distance moved in the direction of the force.
W = F d
功等于力与物体在力的方向上移动距离的乘积。
W = F d
Power is the rate at which work is done or energy is transferred.
P = W / t or P = E / t
功率是做功或能量转移的速率。
P = W / t 或 P = E / t
Efficiency is the ratio of useful output energy to total input energy, often expressed as a percentage.
Efficiency = (Useful output / Total input) × 100%
效率是有用输出能量与总输入能量之比，通常用百分数表示。
效率 = (有用输出 / 总输入) × 100%
The thermal energy change when a substance is heated depends on mass, specific heat capacity and temperature change.
ΔE = m c Δθ
物质受热时的热能变化取决于质量、比热容和温度变化。
ΔE = m c Δθ
3. Waves and Optics | 波与光学
The wave speed is the product of frequency and wavelength.
v = f λ
波速等于频率与波长的乘积。
v = f λ
Frequency is the reciprocal of the period.
f = 1 / T
频率是周期的倒数。
f = 1 / T
The law of reflection: the angle of incidence equals the angle of reflection, measured from the normal.
反射定律：入射角等于反射角，均从法线量起。
Snell' of the two media. For a boundary between vacuum (or air) and a medium, n = sin i / sin r.
n = sin i / sin r
斯涅尔定律联系了入射角、折射角与两种介质的折射率。对于真空（或空气）与介质界面，n = sin i / sin r。
n = sin i / sin r
When light travels from a denser to a less dense medium, the critical angle c is the angle of incidence for which the angle of refraction is 90°.
sin c = 1 / n
当光从光密介质射向光疏介质时，临界角 c 是使折射角为 90° 的入射角。
sin c = 1 / n
The magnification produced by a lens is the ratio of image height to object height, and also equals the ratio of image distance to object distance.
M = hᵢ / hₒ = v / u
透镜的放大率等于像高与物高之比，也等于像距与物距之比。
M = hᵢ / hₒ = v / u
4. Electricity and Magnetism | 电学与磁学
Electric current is the rate of flow of charge.
I = Q / t or Q = I t
电流是电荷流动的速率。
I = Q / t 或 Q = I t
Ohm's law states that the potential difference across a conductor is directly proportional to the current through it, provided temperature remains constant.
V = I R
欧姆定律表明，在温度不变时，导体两端的电势差与通过它的电流成正比。
V = I R
Electrical power is the product of current and potential difference.
P = I V
电功率是电流与电势差的乘积。
P = I V
The energy transferred by an electrical component depends on power and time, or on charge and voltage.
E = I V t or E = Q V
用电器转化的电能取决于功率和时间，或电荷与电压。
E = I V t 或 E = Q V
For resistors connected in series, the total resistance is the sum of individual resistances.
Rₜₒₜₐₗ = R₁ + R₂ + ...
串联电阻的总电阻等于各电阻之和。
Rₜₒₜₐₗ = R₁ + R₂ + ...
For resistors in parallel, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances.
1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + ...
并联电阻的总电阻的倒数等于各电阻倒数之和。
1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + ...
For an ideal transformer, the ratio of the voltages across the primary and secondary coils equals the ratio of the number of turns.
Vₚ / Vₛ = Nₚ / Nₛ
对于理想变压器，初级与次级线圈的电压之比等于其匝数之比。
Vₚ / Vₛ = Nₚ / Nₛ
Assuming 100% efficiency, the input power equals the output power for a transformer.
Vₚ Iₚ = Vₛ Iₛ
假设效率为 100%，变压器的输入功率等于输出功率。
Vₚ Iₚ = Vₛ Iₛ
5. Stoichiometry and the Mole | 化学计量与摩尔
unit of amount of substance. One mole contains 6.02 × 10²³ particles (Avogadro constant).
摩尔是物质的量的单位。1 摩尔含有 6.02 × 10²³ 个微粒（阿伏伽德罗常数）。
The number of moles n can be found from mass m and molar mass M.
n = m / M
摩尔数 n 可由质量 m 和摩尔质量 M 求得。
n = m / M
At room temperature and pressure (r.t.p.), one mole of any gas occupies 24 dm³.
V (dm³) = n × 24
在室温和常压下，1 摩尔任何气体的体积为 24 dm³。
V (dm³) = n × 24
Concentration of a solution is the amount of solute per unit volume, usually mol/dm³.
c = n / V
溶液的浓度是单位体积内溶质的量，通常用 mol/dm³ 表示。
