IGCSE Science: Calculation Practice | IGCSE 科学：计算题专项训练

📚 IGCSE Science: Calculation Practice | IGCSE 科学：计算题专项训练

Mastering calculation questions is essential for success in IGCSE Science exams. Whether you are studying Physics, Chemistry, or Co-ordinated Sciences, you will encounter numerical problems that test your ability to apply formulas, convert units, and interpret data. This guide provides focused practice on the most common types of calculations, with step-by-step examples and tips to build your confidence.

掌握计算题是在 IGCSE 科学考试中取得成功的关键。无论你学习物理、化学还是综合科学，都会遇到数值计算题，它们考验你运用公式、转换单位和解读数据的能力。本指南针对最常见的计算类型进行专项训练，提供分步示例和技巧，帮助你建立信心。

1. Unit Conversions and Standard Form | 单位换算与标准形式

Many calculation errors arise from incorrect units. Always convert quantities to SI base units before substituting into formulas. For very large or small numbers, use standard form (scientific notation), e.g. 0.005 m = 5 × 10⁻³ m. Practise prefix conversions: kilo- (10³), mega- (10⁶), milli- (10⁻³), micro- (10⁻⁶).

许多计算错误源于单位不正确。在代入公式之前，务必将物理量转换为国际基本单位。对于很大或很小的数字，使用标准形式（科学记数法），例如 0.005 m = 5 × 10⁻³ m。练习前缀换算：千 (10³)、兆 (10⁶)、毫 (10⁻³)、微 (10⁻⁶)。

Common conversion factors you must memorise:

• 1 km = 1000 m
• 1 m = 100 cm = 1000 mm
• 1 kg = 1000 g
• 1 minute = 60 s, 1 hour = 3600 s
• 1 m³ = 1 000 000 cm³
• 1 dm³ = 1000 cm³ = 1 litre

必须牢记的常见换算因子：

• 1 km = 1000 m
• 1 m = 100 cm = 1000 mm
• 1 kg = 1000 g
• 1 分钟 = 60 秒, 1 小时 = 3600 秒
• 1 m³ = 1 000 000 cm³
• 1 dm³ = 1000 cm³ = 1 升

Example: Convert 54 km/h to m/s. Multiply by (1000 m / 1 km) and divide by (3600 s / 1 h). So 54 km/h = 54 × (1000/3600) = 15 m/s. This speed conversion appears frequently.

示例：将 54 千米/小时转换为 米/秒。乘以 (1000 m/1 km) 再除以 (3600 s/1 h)。因此 54 km/h = 54 × (1000/3600) = 15 m/s。这一速度换算经常出现。

2. Speed, Distance and Time | 速度、距离与时间

The relationship between speed, distance and time is fundamental. Use the formula:

speed = distance ÷ time   (v = s / t)

Rearrange to find distance (s = v × t) or time (t = s / v). The SI unit of speed is m/s, but you may also use km/h. Always ensure consistent units.

速度、距离和时间之间的关系是基础。使用公式：

速度 = 距离 ÷ 时间   (v = s / t)

变形以求得距离 (s = v × t) 或时间 (t = s / v)。速度的国际单位是 m/s，但也可使用 km/h。务必保证单位一致。

In IGCSE questions, you often need to read a distance–time graph. The gradient of a distance–time graph gives the speed. If the graph is curved, the speed is changing, and the instantaneous speed can be found by drawing a tangent.

在 IGCSE 考试中，常需要解读距离-时间图。距离-时间图的斜率表示速度。如果图线是弯曲的，速度正在变化，瞬时速度可通过画切线求得。

Example: A cyclist covers 420 m in 30 s. Speed = 420 / 30 = 14 m/s. How far at this speed in 2.5 minutes? Time in seconds = 150 s, distance = 14 × 150 = 2100 m.

示例：一名自行车手 30 s 内骑行 420 m。速度 = 420/30 = 14 m/s。以该速度 2.5 分钟能走多远？时间换算成秒 = 150 s，距离 = 14 × 150 = 2100 m。

3. Acceleration and Equations of Motion | 加速度与运动方程

Acceleration is the rate of change of velocity: a = (v – u) / t, where v is final velocity, u is initial velocity, and t is time. The unit is m/s². When acceleration is uniform, use the equations of motion: v = u + a t, and s = u t + ½ a t², where s is displacement.

加速度是速度的变化率：a = (v – u) / t，其中 v 是末速度，u 是初速度，t 是时间。单位为 m/s²。当加速度恒定时，使用运动方程：v = u + a t，以及 s = u t + ½ a t²，其中 s 是位移。

Example: A car accelerates from rest (u=0) to 20 m/s in 5 s. a = (20 – 0)/5 = 4 m/s². Distance travelled s = 0×5 + ½

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