📚 IGCSE CCEA Science: Calculation Practice | IGCSE CCEA 科学：计算题专项训练
Calculations form the backbone of IGCSE CCEA Science, turning qualitative ideas into quantitative predictions. Whether you are studying Physics, Chemistry or Biology, the ability to select the right formula, substitute values correctly and interpret units is essential. This article provides a structured practice guide covering the most common calculation types, with step-by-step reasoning and bilingual explanations to reinforce your understanding.
计算是 IGCSE CCEA 科学的支柱，它将定性概念转化为定量预测。无论你学习物理、化学还是生物，选择正确的公式、正确代入数值并解读单位的能力都至关重要。本文提供了一份结构化的练习指南，涵盖最常见的计算类型，并配有逐步推理和双语解释来巩固你的理解。
1. Units and Conversions | 单位与换算
Always start by checking that all quantities are expressed in SI units or consistent unit systems. The base units you will most often use are metre (m) for length, kilogram (kg) for mass and second (s) for time.
始终先检查所有物理量是否用 SI 单位或一致的单位系统表示。你最常用的基本单位是长度单位米 (m)、质量单位千克 (kg) 和时间单位秒 (s)。
Memorise the common prefixes: kilo (k) means 1000, centi (c) means 0.01 and milli (m) means 0.001. For example, 1 km = 1000 m, 1 cm = 0.01 m and 1 g = 0.001 kg.
记住常见的前缀：千 (k) 表示 1000，厘 (c) 表示 0.01，毫 (m) 表示 0.001。例如，1 km = 1000 m，1 cm = 0.01 m，1 g = 0.001 kg。
When converting speed from km/h to m/s, multiply the value by 1000 (to turn km into m) and divide by 3600 (to turn hours into seconds). The factor simplifies to 5/18. Therefore, 72 km/h = 72 × (5/18) = 20 m/s.
将速度从 km/h 转换为 m/s 时，将数值乘以 1000（将 km 转为 m）再除以 3600（将小时转为秒）。换算因子简化为 5/18。因此，72 km/h = 72 × (5/18) = 20 m/s。
Always show your working clearly, writing down the conversion factor first. Never skip steps when dealing with unit changes, as this is a frequent source of error.
始终清晰地展示你的计算过程，先写下转换因子。在处理单位变更时切勿跳过步骤，因为这是常见的错误来源。
2. Speed, Distance and Time | 速度、距离与时间
The relationship between speed, distance and time is given by the formula v = d / t, where v is speed, d is distance and t is time. You can rearrange this to d = v × t or t = d / v.
速度、距离与时间之间的关系由公式 v = d / t 给出，其中 v 是速度，d 是距离，t 是时间。你可以将其变形为 d = v × t 或 t = d / v。
v = d / t
For example, a car travels 150 m in 5 seconds. Its speed is v = 150 / 5 = 30 m/s. Always include the correct unit; leaving it out loses marks.
例如，一辆汽车在 5 秒内行驶了 150 m。它的速度为 v = 150 / 5 = 30 m/s。始终带上正确的单位；遗漏单位会扣分。
If a runner keeps a steady speed of 8 m/s for 25 seconds, the distance covered is d = 8 × 25 = 200 m. When using the formula, ensure the units for time match – if time is given in minutes, convert it to seconds first.
如果一名跑步者以 8 m/s 的恒定速度跑了 25 秒，那么跑过的距离是 d = 8 × 25 = 200 m。使用公式时，确保时间单位匹配——如果给出的是分钟，要先转换为秒。
In many IGCSE questions you will be asked to calculate average speed for a journey with different stages. Add total distance and total time, then apply v = total d / total t.
在许多 IGCSE 试题中，你会被要求计算包含不同阶段的路程的平均速度。将总距离和总时间相加，然后应用 v = 总 d / 总 t。
3. Density | 密度
Density (ρ) is defined as mass per unit volume: ρ = m / V, where m is mass and V is volume. Common units are kg/m³ and g/cm³.
密度（ρ）定义为单位体积的质量：ρ = m / V，其中 m 是质量，V 是体积。常见的单位有 kg/m³ 和 g/cm³。
A solid block has a mass of 600 g and a volume of 200 cm³. Its density is ρ = 600 / 200 = 3 g/cm³. In SI units this equals 3000 kg/m³ because 1 g/cm³ = 1000 kg/m³.
一个固体块质量为 600 g，体积为 200 cm³。它的密度为 ρ = 600 / 200 = 3 g/cm³。用 SI 单位表示即为 3000 kg/m³，因为 1 g/cm³ = 1000 kg/m³。
When using the formula, always verify that mass and volume are in compatible units. If mass is in kilograms and volume is in cubic metres, density will be in kg/m³. A common mistake is dividing grams by cm³ but wrongly stating the unit as kg/m³.
使用公式时，始终核实质量和体积是否使用了一致的单位。如果质量以千克为单位、体积以立方米为单位，那么密度的单位就是 kg/m³。一个常见错误是用克除以 cm³ 却错误地给出 kg/m³ 的单位。
To find the volume of an irregular object, you can use the displacement method. Subtracting the initial water volume from the final volume gives the object’s volume, which is then used in ρ = m / V.
要找出不规则物体的体积，可以使用排水法。用最终水的体积减去初始水的体积就得到物体的体积，然后代入 ρ = m / V 计算密度。
4. Newton’s Second Law: Force, Mass and Acceleration | 牛顿第二定律：力、质量与加速度
Newton’s second law states that the resultant force acting on an object is equal to its mass multiplied by its acceleration: F = m a. Force is measured in newtons (N), mass in kilograms (kg) and acceleration in metres per second squared (m/s²).
牛顿第二定律指出，作用在物体上的合力等于物体的质量乘以加速度：F = m a。力的单位是牛顿 (N)，质量的单位是千克 (kg)，加速度的单位是米每二次方秒 (m/s²)。
If a 3 kg trolley accelerates at 4 m/s², the resultant force is F = 3 × 4 = 12 N. Always remember that 1 N is equivalent to 1 kg m/s².
如果一个 3 kg 的小车以 4 m/s² 的加速度运动，那么合力为 F = 3 × 4 = 12 N。始终记住 1 N 等同于 1 kg m/s²。
Weight is a force caused by gravity: W = m g, where g is the gravitational field strength (on Earth, g ≈ 10 N/kg or more precisely 9.8 N/kg). A 5 kg object weighs W = 5 × 10 = 50 N.
重量是重力引起的力：W = m g，其中 g 是引力场强度（在地球上，g ≈ 10 N/kg 或更精确地 9.8 N/kg）。一个 5 kg 的物体重量为 W = 5 × 10 = 50 N。
In calculation questions, always identify whether ‘weight’ or ‘mass’ is given. Mass does not change with location, but weight does. Use the correct value of g as stated in the question.
在计算题中，始终辨别给出的是“重量”还是“质量”。质量不随地点而变，但重量会变。请使用题目中给出的 g 值。
5. Work and Energy | 功与能
Work is done whenever a force moves an object in the direction of the force. The formula is W = F × d, where W is work in joules (J), F is force in newtons (N) and d is distance moved in metres (m).
每当力使物体沿力的方向移动一段距离时，就做了功。公式为 W = F × d，其中 W 是功，单位为焦耳 (J)；F 是力，单位为牛顿 (N)；d 是移动的距离，单位为米 (m)。
For example, a person pushes a box with a constant force of 40 N over a distance of 5 m. The work done is W = 40 × 5 = 200 J. This work transfers energy to the box and the surroundings.
例如，一个人用 40 N 的恒力推动一个箱子移动了 5 m。所做的功为 W = 40 × 5 = 200 J。这些功将能量传递给箱子和周围环境。
It is crucial that the distance used is the distance moved in the direction of the force. If the force is applied vertically to lift an object, d is the vertical height gained, and the work done equals the gain in gravitational potential energy.
关键的是所使用的距离必须是沿力的方向移动的距离。如果施加垂直力来提升物体，d 就是上升的垂直高度，所做的功等于重力势能的增量。
When work is done against friction, energy is dissipated mainly as thermal energy. The formula still applies, but the useful energy transfer might be smaller.
当克服摩擦做功时，能量主要以热能的形式耗散。公式仍然适用，但有用的能量转移可能较小。
6. Kinetic and Gravitational Potential Energy | 动能和重力势能
Kinetic energy (KE) is the energy an object has due to its motion: KE = ½ m v², where m is mass in kg and v is speed in m/s. Gravitational potential energy (GPE) depends on height: GPE = m g h, with h in metres.
动能（KE）是物体因运动而具有的能量：KE = ½ m v²，其中 m 是质量（kg），v 是速度（m/s）。重力势能（GPE）取决于高度：GPE = m g h，h 的单位为米。
KE = ½ m v² GPE = m g h
A 2 kg ball moving at 5 m/s has KE = ½ × 2 × 5² = 25 J. The same ball raised to a height of 3 m gains GPE = 2 × 10 × 3 = 60 J (taking g = 10 N/kg).
一个 2 kg 的球以 5 m/s 运动，其动能为 KE = ½ × 2 × 5² = 25 J。若将同样的球举至 3 m 的高度，它获得的重力势能 GPE = 2 × 10 × 3 = 60 J（取 g = 10 N/kg）。
In many problems, energy is conserved: the decrease in one form equals the increase in another, assuming no energy lost to friction. For a falling object, m g h lost = ½ m v² gained, which can be rearranged to v = √(2gh).
在许多问题中，能量是守恒的：假设没有摩擦造成的能量损失，一种能量的减少等于另一种能量的增加。对于自由下落的物体，失去的 m g h = 获得的 ½ m v²，可变形为 v = √(2gh)。
Always square the speed first when using the KE formula. A common error is calculating ½ (m v)², which is incorrect. Use brackets carefully: ½ × m × (v)².
使用动能公式时，始终先计算速度的平方。一个常见的错误是计算 ½ (m v)²，这是不正确的。要小心使用括号：½ × m × (v)²。
7. Power and Efficiency | 功率与效率
Power is the rate at which work is done or energy is transferred: P = W / t or P = E / t. The unit of power is the watt (W), where 1 W = 1 J/s.
功率是做功或能量转移的速率：P = W / t 或 P = E / t。功率的单位是瓦特 (W)，1 W = 1 J/s。
An electric motor does 240 J of work in 12 seconds. Its power output is P = 240 / 12 = 20 W. If the motor receives 30 J of electrical energy each second, its efficiency must be assessed.
一台电动机在 12 秒内做了 240 J 的功。它的功率输出为 P = 240 / 12 = 20 W。如果电动机每秒接收 30 J 的电能，就需要评估它的效率。
Efficiency describes how much of the input energy is transferred into useful output. It is calculated using Efficiency = (useful energy output / total energy input) × 100%, and has no units.
效率描述了输入能量中有多少被转换为有用的输出能量。计算公式为 效率 = (有效输出能量 / 总输入能量) × 100%，并且没有单位。
In the motor example, if in 12 s the total electrical input is 12 × 30 = 360 J, the efficiency is (240 / 360) × 100% ≈ 66.7%. Efficiency is always between 0% and 100% for real machines.
在上述电动机的例子中，如果在 12 s 内总输入电能为 12 × 30 = 360 J，则效率为 (240 / 360) × 100% ≈ 66.7%。对于真实的机器，效率始终在 0% 到 100% 之间。
8. Moles and Molar Mass | 摩尔与摩尔质量
The mole
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