Year 10 CIE Science: Formula & Theorem Quick Reference Handbook | Year 10 CIE 科学：公式定理速查手册

📚 Year 10 CIE Science: Formula & Theorem Quick Reference Handbook | Year 10 CIE 科学：公式定理速查手册

This quick reference handbook brings together the essential formulae, theorems and key equations you will meet in the Year 10 CIE Science curriculum, spanning Physics, Chemistry and Biology. Use it for rapid revision, homework support and exam preparation.

本速查手册汇集了 Year 10 CIE 科学课程中涉及的重要公式、定理和关键方程式，涵盖物理、化学和生物学科，供快速复习、作业辅助和备考使用。

Before you begin, note the conventions used throughout: all symbols are written in standard Unicode form, units follow the SI system unless stated otherwise, and every equation is followed by the quantity it calculates. When a question gives data in non-SI units, convert first, then substitute.

开始阅读前请注意全文的书写约定：所有符号均采用标准 Unicode 形式，除特别说明外单位一律使用国际单位制，每个公式后都说明了它所求解的物理量或化学量。若题目给出的数据不是国际单位，应先换算、再代入计算。

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1. Kinematics and Forces | 运动学与力

Average speed (v) is the total distance travelled (s) divided by the total time taken (t). Because it is a scalar quantity, no direction is required.

平均速度 (v) 等于总路程 (s) 除以总时间 (t)。由于它是标量，不需要写出方向。

v = s / t

Acceleration (a) is the change in velocity (v − u) divided by the time taken (t), where u is the initial velocity and v is the final velocity. The unit is metres per second squared (m/s²).

加速度 (a) 等于速度变化量 (v − u) 除以所用时间 (t)，其中 u 为初速度，v 为末速度。其单位是米每二次方秒 (m/s²)。

a = (v − u) / t

For motion with uniform acceleration, the squared-velocity equation links displacement, velocity and acceleration without involving time.

在匀加速直线运动中，速度平方公式把位移、速度与加速度联系起来，而不涉及时间。

v² = u² + 2as

Newton's second law states that the resultant force (F) acting on an object equals its mass (m) multiplied by its acceleration (a). One newton is the force that gives a 1 kg mass an acceleration of 1 m/s².

牛顿第二定律指出，作用在物体上的合力 (F) 等于其质量 (m) 乘以加速度 (a)。1 牛顿就是使 1 千克物体产生 1 m/s² 加速度的力。

F = m × a

acting on a mass (m), equal to mass times gravitational field strength (g). Near the Earth's surface g ≈ 9.8 N/kg, often rounded to 10 N/kg in CIE questions.

重量 (W) 是作用在质量 (m) 上的重力，等于质量乘以引力场强度 (g)。在地球表面附近 g ≈ 9.8 N/kg，CIE 题目中常取 10 N/kg。

W = m × g

Momentum (p) is the product of mass (m) and velocity (v). In an isolated system, total momentum before a collision equals total momentum after it.

动量 (p) 是质量 (m) 与速度 (v) 的乘积。在孤立系统中，碰撞前的总动量等于碰撞后的总动量。

p = m × v

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

ass (m) per unit volume (V). It is measured in kg/m³ or g/cm³, where 1 g/cm³ = 1000 kg/m³.

密度 (ρ) 是单位体积 (V) 内所含的质量 (m)。单位为 kg/m³ 或 g/cm³，其中 1 g/cm³ = 1000 kg/m³。

ρ = m / V

Pressure (p) is force (F) acting normally per unit area (A). A smaller area produces a larger pressure for the same force.

压强 (p) 是垂直作用在单位面积 (A) 上的力 (F)。在力相同的情况下，受力面积越小，压强越大。

p = F / A

The moment of a force (M) equals the force (F) multiplied by the perpendicular distance (d) from the pivot. A body is balanced when clockwise moments equal anticlockwise moments.

力矩 (M) 等于力 (F) 乘以从支点到力的作用线的垂直距离 (d)。当顺时针力矩等于逆时针力矩时，物体处于平衡状态。

M = F × d

Hooke's law states that the extension (x) of a spring is directly proportional to the applied force (F), provided the elastic limit is not exceeded.

胡克定律指出：在不超过弹性限度时，弹簧的伸长量 (x) 与所受拉力 (F) 成正比。

F = k × x

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2. Energy, Work and Power | 能量、功与功率

irection of the force is given by W = F × d. The unit is the joule (J), where 1 J = 1 N·m.

恒力 (F) 沿力的方向移动物体距离 (d) 所做的功 (W) 由 W = F × d 给出。其单位是焦耳 (J)，1 J = 1 N·m。

W = F × d

Kinetic energy (Eₖ) is the energy possessed by a moving object and depends on its mass (m) and speed (v). Doubling the speed quadruples the kinetic energy.

动能 (Eₖ) 是运动物体所具有的能量，取决于质量 (m) 和速度 (v)。速度加倍，动能变为原来的四倍。

Eₖ = ½ × m × v²

Gravitational potential energy (Eₚ) is the energy stored when an object of mass (m) is raised through a height (h) in a gravitational field (g).

重力势能 (Eₚ) 是质量为 (m) 的物体在引力场 (g) 中被提升高度 (h) 时所储存的能量。

Eₚ = m × g × h

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The principle of conservation of energy states that energy cannot be created or destroyed, only transferred from one store to another. In a closed system, total energy remains constant.

能量守恒定律指出：能量既不会凭空产生，也不会凭空消失，只能从一种形式转移到另一种形式。在封闭系统中，总能量保持不变。

Efficiency compares the useful energy or power output with the total energy or power input, expressed as a percentage.

效率把有用的能量或功率输出与总能量或功率输入相比较，用百分数表示。

efficiency = (useful output / total input) × 100%

, equal to work done (W) divided by time (t). The unit is the watt (W), where 1 W = 1 J/s.

功率 (P) 是做功或能量转移的速率，等于所做的功 (W) 除以时间 (t)。单位为瓦特 (W)，1 W = 1 J/s。

P = W / t = E / t

When a force moves an object at constant velocity, power can also be calculated from force and speed.

当力使物体以恒定速度运动时，功率也可由力与速度求出。

P = F × v

The specific heat capacity (c) of a substance is the energy needed to raise the temperature of 1 kg of it by 1 °C. This gives the heating equation.

物质的比热容 (c) 是使 1 kg 该物质温度升高 1 °C 所需的能量，由此得到加热公式。

Q = m × c × ΔT

The specific latent heat (L) is the energy needed to change the state of 1 kg of a substance without changing its temperature.

比潜热 (L) 是在温度不变的情况下使 1 kg 物质发生状态变化所需的能量。

Q = m × L

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3. Thermal Physics and Gas Laws | 热学与气体定律

Temperature is a measure of the average kinetic energy of the particles in a substance, while heat is energy transferred because of a temperature difference. They are not the same thing.

温度是物质中粒子平均动能的量度，而热量是由于温度差而转移的能量，两者并不等同。

The absolute temperature scale starts at absolute zero. To convert degrees Celsius to kelvin, add 273.

绝对温标以绝对零度为起点。把摄氏度转换为开尔文时，需要加上 273。

T (K) = θ (°C) + 273

Boyle's law states that for a fixed mass of gas at constant temperature, pressure is inversely proportional to volume.

玻意耳定律指出：对于一定质量的气体，在温度不变时，压强与体积成反比。

p₁V₁ = p₂V₂

Charles's law states that for a fixed mass of gas at constant pressure, volume is directly proportional to absolute temperature.

查理定律指出：对于一定质量的气体，在压强不变时，体积与绝对温度成正比。

V₁ / T₁ = V₂ / T₂

The pressure law states that for a fixed mass of gas at constant volume, pressure is directly proportional to absolute temperature.

压强定律指出：对于一定质量的气体，在体积不变时，压强与绝对温度成正比。

p₁ / T₁ = p₂ / T₂

Combining the three gas laws gives the combined gas equation, valid for a fixed mass of gas when all three quantities change.

把三个气体定律合并起来就得到理想气体状态方程，适用于一定质量气体中三个量同时变化的情形。

p₁V₁ / T₁ = p₂V₂ / T₂

Heat is transferred by conduction, convection and radiation. Conduction occurs mainly in solids, convection requires a fluid, and radiation needs no medium at all.

热传递有三种方式：传导、对流和辐射。传导主要发生在固体中，对流需要流体，而辐射完全不需要介质。

Good absorbers of infrared radiation are also good emitters. Dull black surfaces absorb and emit best, while shiny silver surfaces reflect radiation.

良好的红外线吸收体同时也是良好的发射体。暗黑色表面吸收和发射能力最强，而光亮银白色表面则善于反射辐射。

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4. Waves, Sound and Light | 波、声与光

The wave equation links wave speed (v), frequency (f) and wavelength (λ). Frequency is measured in hertz (Hz) and wavelength in metres (m).

波速公式把波速 (v)、频率 (f) 和波长 (λ) 联系起来。频率的单位是赫兹 (Hz)，波长的单位是米 (m)。

v = f × λ

The period (T) of a wave is the time for one complete oscillation, which is the reciprocal of the frequency.

波的周期 (T) 是完成一次全振动所用的时间，它等于频率的倒数。

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