IGCSE Edexcel Science: Calculation Questions Masterclass | IGCSE Edexcel 科学：计算题专项训练

📚 IGCSE Edexcel Science: Calculation Questions Masterclass | IGCSE Edexcel 科学：计算题专项训练

Calculation questions are a core component of the IGCSE Edexcel Science exams, spanning Physics, Chemistry and sometimes Biology. This guide provides targeted practice strategies, key equations, worked examples and common pitfalls to help you master the numerical skills required for top marks.

计算题是IGCSE Edexcel科学考试的核心组成部分，涵盖物理、化学，有时也包括生物。本指南提供针对性的练习策略、关键公式、范例解析和常见错误分析，帮助您掌握取得高分所需的数字运算技能。

1. Speed, Distance and Time | 速度、距离和时间

The relationship between speed, distance and time is fundamental. You must be able to rearrange the formula and convert units confidently.

速度、距离和时间的关系是基础。你必须能够自信地进行公式变形和单位换算。

v = s / t

s = v × t | t = s / v

Common units are metres per second (m/s), kilometres per hour (km/h) and seconds (s). For objects moving at constant speed, this equation applies directly; for average speed, use total distance and total time.

常见单位是米每秒 (m/s)、千米每小时 (km/h) 和秒 (s)。对于匀速运动的物体，直接应用此方程；对于平均速度，使用总距离和总时间。

Always convert minutes to seconds (×60) and hours to seconds (×3600) unless the question specifies otherwise.
除非题目另有规定，始终将分钟转换为秒 (×60)，将小时转换为秒 (×3600)。
To convert km/h to m/s: divide by 3.6. For m/s to km/h: multiply by 3.6.
将 km/h 转换为 m/s：除以 3.6。将 m/s 转换为 km/h：乘以 3.6。

2. Acceleration | 加速度

Acceleration is the rate of change of velocity. You must be able to calculate it from a velocity–time graph or using the change in velocity.

加速度是速度的变化率。你必须能够通过速度-时间图或速度变化量来计算加速度。

a = (v − u) / t

Where v is final velocity, u is initial velocity and t is time taken. Acceleration can be positive (speeding up) or negative (slowing down, sometimes called deceleration).

其中 v 是末速度，u 是初速度，t 是所用时间。加速度可以是正值（加速）或负值（减速，有时称为减速度）。

On a velocity–time graph, acceleration is the gradient. A straight sloping line means constant acceleration, while a curve indicates changing acceleration.

在速度-时间图中，加速度是斜率。一条倾斜的直线表示匀加速度，而曲线表示加速度在变化。

Unit: m/s² (metres per second squared). If time is in seconds and velocity in m/s, acceleration will be in m/s².
单位：m/s²（米每二次方秒）。如果时间以秒为单位，速度以 m/s 为单位，加速度的单位则为 m/s²。

3. Force, Mass and Acceleration (Newton’s Second Law) | 力、质量与加速度（牛顿第二定律）

Newton’s Second Law links resultant force, mass and acceleration. Mastering this equation is essential for dynamics problems.

牛顿第二定律将合力、质量和加速度联系起来。掌握这一方程对于动力学问题至关重要。

F = m × a

Resultant force (F) in newtons (N), mass (m) in kilograms (kg), acceleration (a) in m/s². The force must be the net (unbalanced) force acting on the object.

合力 (F) 以牛顿 (N) 为单位，质量 (m) 以千克 (kg) 为单位，加速度 (a) 以 m/s² 为单位。该力必须是作用在物体上的净（非平衡）力。

If mass is given in grams, convert to kg (÷1000).
如果质量以克为单位给出，请转换为千克 (÷1000)。
This equation can be rearranged: m = F / a, a = F / m.
可以对该方程进行变形：m = F / a，a = F / m。

In combination with other forces, always subtract opposing forces first to find the resultant force before applying F = m × a.

在结合其他力时，务必先减去相反的力以求得合力，然后再应用 F = m × a。

4. Weight, Mass and Gravitational Field Strength | 重量、质量与重力场强度

Weight is the force due to gravity acting on a mass. It should not be confused with mass itself.

重量是由于重力作用在质量上的力。不应将其与质量本身混淆。

W = m × g

Weight (W) in newtons (N), mass (m) in kilograms (kg), gravitational field strength (g) in N/kg. On Earth, g is approximately 9.8 N/kg, but exam questions often use 10 N/kg for simplicity.

重量 (W) 以牛顿 (N) 为单位，质量 (m) 以千克 (kg) 为单位，重力场强度 (g) 以 N/kg 为单位。在地球上，g 大约为 9.8 N/kg，但考试题常为简便而使用 10 N/kg。

Mass is constant everywhere; weight changes with the gravitational field strength. For example, an astronaut’s mass remains the same on the Moon, but their weight is about 1/6 of that on Earth because g is lower.

质量在任何地方都是恒定的；重量会随重力场强度而变化。例如，航天员在月球上的质量保持不变，但其重量大约是地球上的 1/6，因为 g 较低。

5. Density | 密度

Density relates the mass of a substance to its volume. You need to be able to determine density for regular solids, liquids, and irregular objects.

密度将物质的质量与其体积联系起来。你需要能够测量规则固体、液体和不规则物体的密度。

ρ = m / V

Density (ρ, the Greek letter rho) in kg/m³ or g/cm³, mass (m) in kg or g, volume (V) in m³ or cm³. Note: 1 g/cm³ = 1000 kg/m³.

密度 (ρ，希腊字母 rho) 以 kg/m³ 或 g/cm³ 为单位，质量 (m) 以 kg 或 g 为单位，体积 (V) 以 m³ 或 cm³ 为单位。注意：1 g/cm³ = 1000 kg/m³。

For a regular solid, calculate volume from dimensions (e.g. length × width × height).
对于规则固体，根据尺寸计算体积（例如长 × 宽 × 高）。
For an irregular solid, measure volume by displacement of water using a measuring cylinder.
对于不规则固体，使用量筒通过排水法测量体积。

If an object’s density is less than that of the fluid it is placed in, it will float.

如果物体的密度小于其所处流体的密度，它就会漂浮。

6. Work Done and Energy Transferred | 做功与能量转移

Work is done when a force moves an object. It represents the energy transferred by a force.

当一个力使物体移动时，就做了功。它表示通过力传递的能量。

W = F × d

Work done (W) in joules (J), force (F) in newtons (N), distance moved in the direction of the force (d) in metres (m).

做功 (W) 以焦耳 (J) 为单位，力 (F) 以牛顿 (N) 为单位，沿力的方向移动的距离 (d) 以米 (m) 为单位。

Gravitational potential energy gained by an object lifted upwards is also calculated with a similar idea:

物体被举高时所增加的重力势能也用类似的思路计算：

ΔEₚ = m × g × Δh

Change in gravitational potential energy (ΔEₚ) in J, mass in kg, g in N/kg, change in height (Δh) in m.

重力势能的变化量 (ΔEₚ) 以 J 为单位，质量以 kg 为单位，g 以 N/kg 为单位，高度变化量 (Δh) 以 m 为单位。

Kinetic energy is calculated using:

动能的计算公式为：

KE = ½ × m × v²

Kinetic energy in J, mass in kg, velocity in m/s.

动能以 J 为单位，质量以 kg 为单位，速度以 m/s 为单位。

7. Power and Efficiency | 功率与效率

Power is the rate of energy transfer or the rate of doing work. Efficiency describes how well energy is converted to useful output.

功率是能量转换的速率或做功的速率。效率描述了能量转化为有用输出的程度。

P = E / t or P = W / t

Power (P) in watts (W), energy transferred or work done (E or W) in J, time (t) in s.

功率 (P) 以瓦特 (W) 为单位，转移的能量或做的功 (E 或 W) 以 J 为单位，时间 (t) 以 s 为单位。

Efficiency can be expressed as a decimal or percentage:

效率可以表示为小数或百分比：

Efficiency = Useful output energy / Total input energy

No machine is 100% efficient due to energy dissipated as heat, sound, etc. In calculations, you may also use power instead of energy.

由于能量会以热、声等形式耗散，没有机器是 100% 效率的。在计算中，你也可以使用功率代替能量。

8. The Mole and Molar Mass | 摩尔与摩尔质量

The mole is the unit for amount of substance. Most chemical calculations begin with converting masses to moles.

摩尔是物质数量的单位。大多数化学计算始于将质量转换为摩尔。

n = m / M

Number of moles (n) in mol, mass (m) in grams (g), molar mass (M) in g/mol. Molar mass is the relative atomic mass (Aᵣ) or relative formula mass (Mᵣ) expressed in grams per mole.

摩尔数 (n) 以 mol 为单位，质量 (m) 以克 (g) 为单位，摩尔质量 (M) 以 g/mol 为单位。摩尔质量是以克每摩尔表示的相对原子质量 (Aᵣ) 或相对式量 (Mᵣ)。

For elements, use Aᵣ from the Periodic Table. For compounds, add together the Aᵣ values of all atoms in the formula.
对于单质，使用元素周期表中的 Aᵣ。对于化合物，将化学式中所有原子的 Aᵣ 值相加。
Example: M of H₂O = (2 × 1) + 16 = 18 g/mol.
例如：H₂O 的 M = (2 × 1) + 16 = 18 g/mol。

Once moles are known, you can use the mole ratio from a balanced equation to find the moles of another substance.

一旦知道摩尔数，您就可以利用配平方程式中的摩尔比，求出另一种物质的摩尔数。

9. Concentration of Solutions | 溶液浓度

Concentration measures how much solute is dissolved in a given volume of solvent. Calculations often involve converting between mass, moles and concentration.

浓度衡量的是在给定体积的溶剂中溶解了多少溶质。计算通常涉及在质量、摩尔和浓度之间进行转换。

c = n / V and n = c × V

Concentration (c) in mol/dm³, amount (n) in mol, volume (V) in dm³. Note that 1 dm³ = 1000 cm³, so convert cm³ to dm³ by dividing by 1000.

浓度 (c) 以 mol/dm³ 为单位，物质的量 (n) 以 mol 为单位，体积 (V) 以 dm³ 为单位。注意 1 dm³ = 1000 cm³，因此将 cm³ 转换为 dm³ 需除以 1000。

If concentration is given in g/dm³, you can still use the mass–concentration formula:

如果浓度以 g/dm³ 给出，你仍然可以使用质量-浓度公式：

Concentration (g/dm³) = mass (g) / volume (dm³)

To link the two, use: concentration (mol/dm³) = concentration (g/dm³) / M.
要将两者联系起来，可使用：浓度 (mol/dm³) = 浓度 (g/dm³) / M。

10. Titration Calculations | 滴定计算

Titration is a method to determine an unknown concentration by reacting it with a standard solution. The key is to use the mole ratio from the balanced equation.

滴定是一种通过与标准溶液反应来测定未知浓度的方法。关键在于利用配平方程式中的摩尔比。

Steps:

步骤：

Calculate the moles of the known substance using its concentration and volume (in dm³).
利用已知物质的浓度和体积（以 dm³ 为单位）计算其摩尔数。
Use the balanced equation to find the moles of the unknown substance (mole ratio).
利用配平方程式求出未知物质的摩尔数（摩尔比）。
Calculate the unknown concentration: c = n / V (volume in dm³ of unknown solution used).
计算未知浓度：c = n / V（所用未知溶液的体积，以 dm³ 为单位）。

For example, if sulfuric acid (H₂SO₄) reacts with sodium hydroxide (NaOH) in a 1:2 ratio, then moles of NaOH = 2 × moles of H₂SO₄.

例如，如果硫酸 (H₂SO₄) 与氢氧化钠 (NaOH) 以 1:2 的比例反应，则 NaOH 的摩尔数 = 2 × H₂SO₄ 的摩尔数。

Always check the stoichiometric coefficients. Common errors include forgetting to divide or multiply by the ratio correctly.

请始终核对化学计量系数。常见错误包括忘记正确除以或乘以该比例。

11. Rates of Reaction | 反应速率

The rate of a chemical reaction can be calculated by measuring the change in amount of reactant or product over time.

化学反应的速率可以通过测量反应物或产物的量随时间的变化来计算。

Mean rate = Δquantity / Δtime

Quantity could be mass lost (in g) if a gas is evolved, or volume of gas produced (cm³), or concentration change. Time is usually in seconds (s).

该量可以是逸出气体的质量损失（以 g 计）、产生气体的体积 (cm³) 或浓度变化。时间通常以秒 (s) 为单位。

From a graph of quantity against time:

从数量-时间图来看：

The steeper the gradient, the faster the rate at that point.
斜率越陡，该点的速率越快。
To find the rate at a specific time, draw a tangent and calculate its gradient.
要找出某一特定时刻的速率，可以画一条切线并计算其斜率。

Units of rate depend on what is being measured: g/s, cm³/s, mol/dm³/s, etc.

速率的单位取决于所测量的量：g/s、cm³/s、mol/dm³/s 等。

12. Energy Changes and Calorimetry | 能量变化与量热法

When a reaction transfers energy as heat, you can calculate the heat energy change using the specific heat capacity equation.

当反应以热的形式传递能量时，你可以使用比热容方程计算热能变化。

Q = m × c × ΔT

Heat energy (Q) in joules (J), mass of the substance being heated (m) in g, specific heat capacity (c) in J/g°C (or J/kg°C if mass in kg), temperature change (ΔT) in °C.

热能 (Q) 以焦耳 (J) 为单位，被加热物质的质量 (m) 以 g 为单位，比热容 (c) 以 J/g°C 为单位（若质量以 kg 为单位则为 J/kg°C），温度变化 (ΔT) 以 °C 为单位。

For water, c = 4.2 J/g°C (4200 J/kg°C). This value is often provided. To find the enthalpy change per mole, divide Q by the number of moles of fuel or limiting reactant.

对于水，c = 4.2 J/g°C (4200 J/kg°C)。这个值通常会被给出。要计算每摩尔的焓变，可将 Q 除以燃料或限制反应物的摩尔数。

Remember to use the mass of water or solution that is being heated, not the mass of the fuel burnt.
记住要使用被加热的水或溶液的质量，而不是燃烧的燃料的质量。
If the temperature increases, Q is positive (exothermic). If temperature decreases, Q is negative (endothermic).
如果温度升高，Q 为正（放热反应）。如果温度降低，Q 为负（吸热反应）。

Practising these core calculations repeatedly will build speed and accuracy, giving you a solid foundation for the IGCSE Edexcel Science exams.

反复练习这些核心计算将提高速度和准确性，为您的 IGCSE Edexcel 科学考试打下坚实基础。

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IGCSE Edexcel Science: Calculation Questions Masterclass | IGCSE Edexcel 科学：计算题专项训练