📚 Year 8 Cambridge Science: Formula & Theorem Quick Reference Handbook | Year 8 剑桥科学：公式定理速查手册
This revision handbook is your one‑stop reference for all essential formulas, equations and key theorems covered in the Year 8 Cambridge Lower Secondary Science curriculum. Each entry is presented with a clear definition, the symbolic form and a worked‑example idea to help you apply it in tests and practicals. The guide is organised by topic – from motion and forces to chemistry calculations and biology magnification – so you can find exactly what you need in seconds.
本速查手册是Year 8剑桥初中科学课程所有核心公式、方程式和关键定理的一站式参考。每个条目都配有清晰的定义、符号形式和例题思路，帮助你在测试和实验中灵活运用。手册按主题编排——从运动与力、化学计算到生物放大率——让你能在几秒钟内找到所需内容。
1. Motion: Speed and Acceleration | 运动：速度与加速度
it only has magnitude. The formula is speed = distance ÷ time, often written as v = s / t.
速度是物体在单位时间内通过的距离。它是标量，只有大小。公式为速度 = 距离 ÷ 时间，通常写为 v = s / t。
l distance travelled by the total time taken: average speed = total distance ÷ total time.
当物体不以恒定速率运动时，平均速度很有用。它用总路程除以总时间来计算：平均速度 = 总距离 ÷ 总时间。
al velocity) ÷ time, or a = (v − u) / t, where u is the starting velocity and v is the final velocity.
加速度衡量物体速度变化的快慢，是矢量。公式为加速度 =（末速度 − 初速度）÷ 时间，即 a = (v − u) / t，其中 u 为初速度，v 为末速度。
When acceleration is zero, an object moves at constant velocity. A negative acceleration is often called deceleration or retardation.
加速度为零时，物体做匀速运动。负加速度通常称为减速。
2. Forces and Newton’s Laws | 力与牛顿定律
Newton’s First Law (law of inertia): An object remains at rest or moves with constant velocity unless acted on by a resultant external force.
牛顿第一定律（惯性定律）：物体保持静止或匀速直线运动状态，除非受到合外力的作用。
ass. The fundamental equation is F = m × a, where F is force in newtons (N), m is mass in kilograms (kg) and a is acceleration in metres per second squared (m/s²).
牛顿第二定律：物体的加速度与作用在它上面的合外力成正比，与它的质量成反比。基本方程为 F = m × a，其中 F 为力（牛顿，N），m 为质量（千克，kg），a 为加速度（米每二次方秒，m/s²）。
where g is the gravitational field strength (on Earth approximately 10 N/kg or 9.8 N/kg).
物体的重量是作用在它质量上的重力。公式为 W = m × g，其中 g 是引力场强（在地球表面约 10 N/kg 或 9.8 N/kg）。
Newton’s Third Law: Whenever two objects interact, they exert equal and opposite forces on each other. These are often called action–reaction pairs.
牛顿第三定律：两个物体相互作用时，彼此施加大小相等、方向相反的力。这通常称为作用力与反作用力对。
Friction is a force that opposes motion between two surfaces in contact. It can be reduced by lubrication or streamlining.
摩擦力是一种阻碍接触面之间相对运动的力。可通过润滑或流线型设计来减小。
3. Density and Pressure | 密度与压强
rmula is density = mass ÷ volume, or ρ = m / V. It is usually expressed in kg/m³ or g/cm³.
密度是单位体积的质量。公式为密度 = 质量 ÷ 体积，或 ρ = m / V。常用单位是 kg/m³ 或 g/cm³。
The density of water is 1 g/cm³ or 1000 kg/m³. An object floats if its density is less than that of the fluid; it sinks if its density is greater.
水的密度为 1 g/cm³ 或 1000 kg/m³。物体密度小于流体密度时上浮，大于时下沉。
force ÷ area, or p = F / A, with p in pascals (Pa) if force is in newtons and area in m².
压强是作用在单位面积上的力。公式为压强 = 力 ÷ 面积，即 p = F / A，若力用牛顿、面积用平方米，则压强单位为帕斯卡（Pa）。
ough this specific formula is often introduced in Year 9; Year 8 students should understand the concept qualitatively.
液体内部压强随深度增加而增大，并向各个方向等大地作用。深度 h、密度 ρ 处的压强为 p = ρ × g × h，该公式通常在Year 9引入，但Year 8学生应能定性理解这一概念。
Gas pressure is caused by particles colliding with the walls of their container. Increasing the temperature or decreasing the volume raises gas pressure.
气体压强由粒子与容器壁碰撞产生。升高温度或减小体积都会使气压增大。
4. Energy, Work and Power | 能量、功和功率
distance moved in the direction of the force, or W = F × d. It is measured in joules (J).
当一个力使物体沿力的方向移动时，力做了功。功 = 力 × 在力的方向上移动的距离，即 W = F × d，单位是焦耳 (J)。
e energy an object has due to its motion. KE = ½ × m × v², where m is mass and v is speed.
动能（KE）是物体由于运动而具有的能量。公式为 KE = ½ × m × v²，其中 m 为质量，v 为速度。
because of its height above the ground. GPE = m × g × h, where h is the change in height.
重力势能（GPE）是物体因离地高度而储存的能量。公式为 GPE = m × g × h，其中 h 是高度的变化量。
rred. Power = work done ÷ time, or P = W / t. The unit is the watt (W), where 1 W = 1 J/s.
功率是做功或能量转换的速率。功率 = 功 ÷ 时间，即 P = W / t，单位是瓦特 (W)，1 W = 1 J/s。
converted to useful output. Efficiency = (useful output energy ÷ total input energy) × 100%. No machine can be 100% efficient because of friction and heat loss.
效率衡量输入能量转化为有用输出的比例。效率 =（有用的输出能量 ÷ 总输入能量）× 100%。由于摩擦和热损失，没有机器能达到 100% 的效率。
5. Electricity: Ohm’s Law, Power and Energy | 电学：欧姆定律、功率和电能
rrent × resistance, V = I × R. Here V is in volts (V), I in amperes (A) and R in ohms (Ω).
欧姆定律描述了恒温下电路中电压、电流和电阻的关系：电压 = 电流 × 电阻，即 V = I × R。V 的单位是伏特 (V)，I 为安培 (A)，R 为欧姆 (Ω)。
In series circuits, current is the same everywhere, and the total resistance is the sum of individual resistances: Rtotal = R₁ + R₂ + … e voltage across each branch is the same, and total current is the sum of branch currents.
在串联电路中，电流处处相等，总电阻为各电阻之和：R总 = R₁ + R₂ + … 。在并联电路中，各支路电压相等，总电流为各支路电流之和。
transferred. P = V × I. Using Ohm’s law, alternative forms are P = I² × R and P = V² / R.
电功率是电能转移的速率。P = V × I。结合欧姆定律，可变形为 P = I² × R 和 P = V² / R。
culated by energy = power × time, or E = P × t. It is often measured in joules or kilowatt‑hours (kWh).
传递的电能可通过能量 = 功率 × 时间计算，即 E = P × t。常用单位为焦耳或千瓦时 (kWh)。
Conductors have low resistance and allow current to flow easily; insulators have very high resistance. Resistance in wires depends on material, length, cross‑sectional area and temperature.
导体的电阻低，电流容易通过；绝缘体电阻极高。导线的电阻取决于材料、长度、横截面积和温度。
6. Waves: Speed, Frequency and Wavelength | 波：波速、频率和波长
wave speed (m/s), f is frequency in hertz (Hz) and λ (lambda) is wavelength in metres (m).
波速是波每秒传播的距离。通用波动方程为 v = f × λ，其中 v 为波速（m/s），f 为频率（Hz），λ（lambda）为波长（m）。
r of complete waves passing a point per second. It is the reciprocal of period: f = 1 / T.
频率是每秒通过某点的完整波数目。它是周期的倒数：f = 1 / T。
emperature. For light and all electromagnetic waves, the speed in a vacuum is 3 × 10⁸ m/s.
对于声波，室温下在空气中的速度约为 340 m/s。对于光和所有电磁波，真空中的速度为 3 × 10⁸ m/s。
When waves travel from one medium to another, their speed and wavelength may change, but frequency remains constant. Refraction can be explained by this change in speed.
当波从一种介质进入另一种介质时，其速度和波长可能改变，但频率保持不变。速度的改变可以解释折射现象。
Transverse waves (e.g. light, water waves) have oscillations perpendicular to the direction of energy transfer; longitudinal waves (e.g. sound) have oscillations parallel to the direction of energy transfer.
横波（如光波、水波）的振动方向与能量传播方向垂直；纵波（如声波）的振动方向与能量传播方向平行。
7. Moments and Levers | 力矩与杠杆
orce × perpendicular distance from the pivot, or M = F × d. Moments are measured in newton‑metres (N m).
力矩是力的转动效应。计算公式为力矩 = 力 × 到支点的垂直距离，即 M = F × d。力矩单位为牛顿·米 (N m)。
The principle of moments states that for a system in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments: Σ Fc × dc = Σ Fa × da.
力矩原理指出，处于转动平衡的系统，顺时针力矩之和等于逆时针力矩之和：Σ Fc × dc = Σ Fa × da。
Levers are simple machines that use a pivot to multiply the force applied. In a first‑class lever the pivot is between effort and load; in a second‑class lever the load is between pivot and effort; in a third‑class lever the effort is between pivot and load.
杠杆是利用支点放大作用力的简单机械。第一类杠杆支点在力和负载之间；第二类杠杆负载在支点和力之间；第三类杠杆力在支点和负载之间。
Gears and pulley systems also work on the principle of moments to change speed, direction or force magnitude. A larger gear produces more moment but turns slower.
齿轮和滑轮系统也利用力矩原理来改变速度、方向或力的大小。较大的齿轮产生更大的力矩，但转动更慢。
8. Chemical Calculations: Relative Mass and Conservation | 化学计算：相对质量与守恒
The relative atomic mass (Ar) of an element is the average mass of its atoms compared to 1/12th the mass of a carbon‑12 atom. It has no units.
元素的相对原子质量（Ar）是其原子的平均质量与碳‑12 原子质量的 1/12 之比，没有单位。
The relative molecular mass (Mr) is the sum of the relative atomic masses of all atoms in a molecule. For example, Mr of water (H₂O) = 2×1 + 16 = 18.
相对分子质量（Mr）是分子中所有原子的相对原子质量之和。例如，水（H₂O）的 Mr = 2×1 + 16 = 18。
The law of conservation of mass states that in a chemical reaction, the total mass of reactants equals the total mass of products. Atoms are neither created nor destroyed, only rearranged.
质量守恒定律指出，在化学反应中，反应物的总质量等于生成物的总质量。原子既不会创生也不会毁灭，只是重新组合。
Percentage by mass of an element in a compound = (total Ar of the element ÷ Mr of the compound) × 100%. This helps determine the composition of ores and fertilisers.
化合物中某元素的质量百分比 =（该元素的总 Ar ÷ 化合物的 Mr）× 100%。这有助于确定矿石和肥料的组成。
Balancing chemical equations ensures the numbers of each type of atom are equal on both sides. Coefficients are placed in front of formulas; subscripts must remain unchanged.
配平化学方程式能确保每种原子的数目在两边相等。系数写在化学式前面，下标不可改变。
9. Biology Calculations: Magnification | 生物计算：放大率
ze ÷ actual size, or M = I / A. Both image size and actual size must be in the same units.
放大率是图像比实物放大的倍数。公式为放大率 = 图像大小 ÷ 实际大小，即 M = I / A。图像大小和实际大小必须使用相同单位。
= image size ÷ magnification. Remember to convert units (e.g. millimetres to micrometres).
要从显微照片求实际大小，改写公式：实际大小 = 图像大小 ÷ 放大率。记得换算单位（如毫米转微米）。
and the objective lens magnification: total magnification = eyepiece mag × objective mag.
复合显微镜的总放大率是目镜放大率与物镜放大率的乘积：总放大率 = 目镜放大率 × 物镜放大率。
Estimating cell size often involves using a stage micrometer or counting the number of cells along the field of view. The field of view diameter can be measured with a ruler under low power.
估算细胞大小常需使用镜台测微计或计算沿视野排列的细胞数目。低倍镜下可用直尺测量视野直径。
10. Key Chemical Equations and Reactions | 重要化学方程式和反应
e presence of light and chlorophyll. The balanced symbol equation: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂.
光合作用是绿色植物利用光能制造葡萄糖的过程。文字方程式：二氧化碳 + 水 → 葡萄糖 + 氧气，需要光与叶绿素。配平符号方程式：6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂。
oxygen → carbon dioxide + water (+ energy). Symbol equation: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O.
有氧呼吸在线粒体中进行，释放能量。文字方程式：葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）。符号方程式：C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O。
le, hydrochloric acid + magnesium → magnesium chloride + hydrogen: 2HCl + Mg → MgCl₂ + H₂.
酸与金属反应的通式：酸 + 金属 → 盐 + 氢气。例如，盐酸 + 镁 → 氯化镁 + 氢气：2HCl + Mg → MgCl₂ + H₂。
se to form a salt and water: acid + base → salt + water. Example: HCl + NaOH → NaCl + H₂O.
中和反应是酸与碱生成盐和水的反应：酸 + 碱 → 盐 + 水。例：HCl + NaOH → NaCl + H₂O。
id + carbonate → salt + water + carbon dioxide. Example: 2HCl + CaCO₃ → CaCl₂ + H₂O + CO₂.
碳酸盐与酸反应生成盐、水和二氧化碳：酸 + 碳酸盐 → 盐 + 水 + 二氧化碳。例：2HCl + CaCO₃ → CaCl₂ + H₂O + CO₂。
11. Important Principles in Physics | 物理重要原理
Archimedes’ principle: An object submerged in a fluid experiences an upthrust equal to the weight of the fluid it displaces. If the upthrust is greater than or equal to the object’s weight, it floats.
阿基米德原理：浸在流体中的物体受到向上的浮力，大小等于它排开的流体的重量。浮力大于或等于物体重量时，物体上浮。
he limit of proportionality. F = k × x, where k is the spring constant and x is extension.
胡克定律：对弹性材料而言，在比例极限内，伸长量与施加的力成正比。F = k × x，其中 k 为弹簧常数，x 为伸长量。
Pascal’s principle (qualitative): Pressure applied to an enclosed fluid is transmitted undiminished to all parts of the fluid and the walls of the container. This is the basis of hydraulic systems.
帕斯卡原理（定性）：施加在密闭流体上的压强，会大小不变地向流体各处和容器壁传递。这是液压系统的基础。
Bernoulli’s principle (simplified): Faster‑moving fluids exert lower pressure. This helps explain how aeroplane wings generate lift and why a spinning ball curves.
伯努利原理（简化）：流速越大的流体，压强越低。这解释了飞机机翼产生升力以及旋转球体的弧线运动。
The conservation of energy: Energy cannot be created or destroyed, only transferred or converted from one form to another. The total energy of an isolated system remains constant.
能量守恒：能量既不会创生也不会消灭，只能从一种形式转移或转化为另一种形式。孤立系统的总能量保持不变。
12. Quick Reference Formula Grid | 公式速查表
Below is a handy summary grid of the most used equations in Year 8 Science. Use it for last‑minute revision.
下面是Year 8科学中最常用公式的便捷汇总表，可用于考前冲刺。
| Quantity / 量 | Formula / 公式 | Units / 单位 |
|---|---|---|
| Speed / 速度 | v = s / t | m/s |
| Acceleration / 加速度 | a = (v − u) / t | m/s² |
| Force / 力 | F = m × a | N (newtons) |
| Weight / 重量 | W = m × g | N |
| Density / 密度 | ρ = m / V | kg/m³ or g/cm³ |
| Pressure / 压强 | p = F / A | Pa (N/m²) |
| Work / 功 | W = F × d | J (joules) |
| Kinetic energy / 动能 | KE = ½ m v² | J |
| Grav. potential energy / 重力势能 | GPE = m g h | J |
| Power / 功率 | P = W / t | W (watts) |
| Efficiency / 效率 | (Euseful / Einput) × 100% | % |
| Ohm’s Law / 欧姆定律 | V = I × R | V (volts), A, Ω |
| Electrical power / 电功率 | P = V × I | W |
| Wave speed / 波速 | v = f × λ | m/s |
| Moment / 力矩 | M = F × d (perpendicular) | N m |
| Hooke’s Law / 胡克定律 | F = k × x | N, N/m |
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