📚 IGCSE CCEA Physical Education: Formula and Theorem Quick Revision Handbook | IGCSE CCEA 体育：公式定理速查手册
This revision handbook summarises the essential formulas, equations and principles that frequently appear in IGCSE CCEA Physical Education. Use it alongside past-paper practice to check calculations, explain movement and justify training zones.
本速查手册总结了 IGCSE CCEA 体育中经常出现的基本公式、方程与原理。可结合历年真题练习，用于核对计算、解释动作并说明训练区间。
1. Maximum Heart Rate and Target Heart Rate | 最大心率与目标心率
Maximum heart rate (MHR) is an estimate of the highest beats per minute (bpm) the heart can reach during maximal exercise. The simplest formula used in IGCSE Physical Education is MHR = 220 − age. Target heart rate zones are then calculated as percentages of MHR.
最大心率（MHR）是心脏在最大强度运动中每分钟最高跳动次数的估算值。IGCSE 体育中最常用的公式是 最大心率 = 220 − 年龄。目标心率区间通常按最大心率的百分比计算。
MHR = 220 − age
Lower target HR = MHR × 0.50
Upper target HR = MHR × 0.85
Typical training zones are the health/fitness zone at 50–85% MHR, the aerobic zone at 60–80% MHR and the anaerobic zone at 80–90% MHR. For a 16-year-old, MHR = 220 − 16 = 204 bpm. The aerobic target range is therefore 204 × 0.60 = 122 bpm to 204 × 0.80 = 163 bpm.
常见训练区间包括：健康/健身区间为最大心率的 50–85%，有氧区间为 60–80%，无氧区间为 80–90%。以 16 岁学生为例，最大心率 = 220 − 16 = 204 次/分。因此有氧目标范围为 204 × 0.60 = 122 次/分 至 204 × 0.80 = 163 次/分。
2. Karvonen Formula and Heart Rate Reserve | 卡沃宁公式与储备心率
The Karvonen formula gives a more individualised training heart rate because it uses resting heart rate (RHR). First calculate heart rate reserve (HRR), then add a percentage of HRR back to RHR.
卡沃宁公式利用静息心率（RHR）计算更具个性化的训练心率。先计算储备心率（HRR），再将储备心率的一定百分比加回静息心率。
HRR = MHR − RHR
Target HR = RHR + (HRR × intensity)
For a 16-year-old with MHR = 204 bpm and RHR = 60 bpm, HRR = 204 − 60 = 144 bpm. At 70% intensity, target HR = 60 + (144 × 0.70) = 60 + 100.8 = 160.8 ≈ 161 bpm. This method reflects aerobic fitness because trained athletes usually have lower resting heart rates.
以一名 16 岁学生为例，最大心率 = 204 次/分，静息心率 = 60 次/分，储备心率 = 204 − 60 = 144 次/分。在 70% 强度下，目标心率 = 60 + (144 × 0.70) = 60 + 100.8 = 160.8 ≈ 161 次/分。该方法能反映有氧耐力水平，因为训练有素的运动员静息心率通常较低。
3. Cardiac Output and Stroke Volume | 心输出量与每搏输出量
Cardiac output (Q) is the volume of blood pumped by the left ventricle in one minute. It is the product of stroke volume (SV) and heart rate (HR). Stroke volume is the volume of blood ejected per beat.
心输出量（Q）是左心室每分钟泵出的血液量。它是每搏输出量（SV）与心率（HR）的乘积。每搏输出量是心脏每搏动一次射出的血液量。
Q = SV × HR
At rest, typical values are SV ≈ 70 mL, HR ≈ 72 bpm, so Q ≈ 70 ÷ 1000 × 72 = 5.04 L/min. During maximal exercise, SV may rise to about 120 mL and HR to about 180 bpm, giving Q ≈ 120 ÷ 1000 × 180 = 21.6 L/min. This increase in cardiac output helps deliver more oxygen to working muscles.
安静时，典型数值为 SV ≈ 70 毫升，HR ≈ 72 次/分，因此 Q ≈ 70 ÷ 1000 × 72 = 5.04 升/分。在最大强度运动时，SV 可升至约 120 毫升，HR 可升至约 180 次/分，此时 Q ≈ 120 ÷ 1000 × 180 = 21.6 升/分。心输出量增加有助于向工作肌肉输送更多氧气。
4. Minute Ventilation and Tidal Volume | 每分通气量与潮气量
Minute ventilation (VE) is the volume of air moved into or out of the lungs per minute. It is calculated from tidal volume (TV) and breathing frequency (f). Tidal volume is the air moved per breath.
每分通气量（VE）是每分钟吸入或呼出肺部的气体量。它由潮气量（TV）和呼吸频率（f）计算得出。潮气量是每次呼吸吸入或呼出的气体量。
VE = TV × f
At rest, TV ≈ 0.5 L and f ≈ 12–15 breaths/min, so VE ≈ 6 to 7.5 L/min. During intense exercise, TV can rise to about 3 L and f to about 40–50 breaths/min, producing VE values above 120 L/min. Both tidal volume and breathing frequency increase to supply more oxygen and remove more carbon dioxide.
安静时，潮气量约为 0.5 升，呼吸频率约为 12–15 次/分，因此每分通气量约为 6 至 7.5 升/分。在高强度运动中，潮气量可升至约 3 升，呼吸频率可升至约 40–50 次/分，每分通气量可超过 120 升/分。潮气量和呼吸频率同时增加，以供应更多氧气并排出更多二氧化碳。
5. Body Mass Index and Body Composition | 体重指数与身体成分
Body mass index (BMI) is a simple measure of body mass relative to height. It is used to classify underweight, normal weight, overweight and obesity in populations. It does not directly measure body fat.
体重指数（BMI）是衡量体重与身高关系的简单指标。它常用于人群中体重过轻、正常、超重和肥胖的分类，但并不能直接测量体脂。
BMI = mass (kg) ÷ height² (m²)
| BMI value | Classification |
|---|---|
| Below 18.5 | Underweight |
| 18.5–24.9 | Normal weight |
| 25.0–29.9 | Overweight |
| 30.0 and above | Obese |
For example, a performer with mass 64 kg and height 1.75 m has BMI = 64 ÷ (1.75²) = 64 ÷ 3.0625 = 20.9 kg/m², which is in the normal range. BMI has limitations for sports performers because muscle is dense, so a muscular athlete may be classified as overweight despite having low body fat.
例如，一名运动员体重 64 千克，身高 1.75 米，其 BMI = 64 ÷ (1.75²) = 64 ÷ 3.0625 = 20.9 千克/米²，属于正常范围。BMI 对运动员有一定局限，因为肌肉密度较大，肌肉发达的运动员即使体脂很低，也可能被划分为超重。
6. Work, Power and Mechanical Efficiency | 功、功率与机械效率
Work is done when a force moves an object in the direction of the force. Power is the rate at which work is done. Mechanical efficiency expresses how much of the energy input is converted into useful work.
当力使物体沿力的方向移动时，就做了功。功率是做功的速率。机械效率表示输入能量中有多少被转化为有用功。
Work = Force × distance
Power = Work ÷ time
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