📚 IGCSE CAIE Physical Education: Formula & Theorem Quick Revision Handbook | IGCSE CAIE 体育：公式定理速查手册
This revision handbook summarises the essential formulas, laws and training thresholds required for the Cambridge IGCSE Physical Education syllabus. Use it for quick recall before written papers and for applying data to practical examples.
本速查手册汇总了剑桥 IGCSE 体育课程所需的公式、定律与训练阈值，适合笔试前快速回顾，也便于将数据应用到实际情境中。
1. Heart Rate & Training Zones | 心率与训练区间
Maximum heart rate (HRmax) is estimated by the formula HRmax = 220 − age in beats per minute. This is a population-level estimate, not a personal diagnostic value.
最大心率（HRmax）通常用公式 HRmax = 220 − 年龄（次/分）估算。这是人群水平估计值，并非个人诊断值。
HRmax = 220 − age
Aerobic training zone is usually 60–80% of HRmax. Anaerobic training zone is usually 80–90% of HRmax.
有氧训练区间一般为最大心率的 60–80%。无氧训练区间一般为最大心率的 80–90%。
| Age (years) | HRmax (bpm) | Aerobic 60–80% | Anaerobic 80–90% |
|---|---|---|---|
| 14 | 206 | 124–165 | 165–185 |
| 16 | 204 | 122–163 | 163–184 |
| 18 | 202 | 121–162 | 162–182 |
Example: a 16-year-old has HRmax ≈ 204 bpm; aerobic zone ≈ 122–163 bpm; anaerobic zone ≈ 163–184 bpm.
示例：16 岁学生 HRmax ≈ 204 次/分；有氧区间约为 122–163 次/分；无氧区间约为 163–184 次/分。
2. Karvonen Formula & Target Heart Rate | 卡式公式与目标心率
Karvonen formula uses heart rate reserve (HRR) to prescribe target heart rate: Target HR = ((HRmax − resting HR) × %intensity) + resting HR.
卡氏公式使用储备心率（HRR）来确定目标心率：目标心率 = （（最大心率 − 安静心率）× 强度百分比） + 安静心率。
Target HR = ((HRmax − resting HR) × %intensity) + resting HR
HRR = HRmax − resting HR. This method is more individualised because it accounts for resting fitness.
储备心率 = 最大心率 − 安静心率。该方法更个性化，因为考虑了安静心率水平。
Example: age 16, resting HR 70 bpm, HRmax 204 bpm, at 70% intensity: target HR = ((204 − 70) × 0.70) + 70 = 163.8 bpm.
示例：16 岁，安静心率 70 次/分，最大心率 204 次/分，70% 强度：目标心率 = ((204 − 70) × 0.70) + 70 = 163.8 次/分。
3. Body Mass Index | 身体质量指数
BMI = body mass (kg) ÷ height² (m²). It is a screening tool for underweight, healthy weight, overweight and obesity.
BMI = 体重（kg）÷ 身高²（m²）。它是筛查体重过轻、健康体重、超重和肥胖的工具。
BMI = body mass in kg ÷ height² in m²
IGCSE examples often require units: mass in kilograms, height in metres, BMI in kg/m².
IGCSE 例题通常要求单位：体重用千克，身高用米，BMI 单位是 kg/m²。
Example: 65 kg, 1.75 m: BMI = 65 ÷ (1.75²) = 21.2 kg/m².
示例：65 kg，1.75 m：BMI = 65 ÷ (1.75²) = 21.2 kg/m²。
Limitations: BMI does not distinguish muscle from fat, so athletes may be classed as overweight despite low body fat.
局限性：BMI 不能区分肌肉与脂肪，因此运动员即使体脂低也可能被归为超重。
4. Body Composition & Skinfold Estimation | 身体成分与皮褶厚度估算
Body fat percentage can be estimated from skinfold thickness using equations such as the Durnin–Womersley formula. IGCSE does not require the full regression equation, but you must interpret sum-of-skinfolds data.
体脂百分比可通过皮褶厚度使用 Durnin–Womersley 等公式估算。IGCSE 不要求完整回归方程，但必须能解释皮褶总和数据。
Common skinfold sites: triceps, biceps, subscapular, suprailiac. Measurements are taken in millimetres.
常见皮褶部位：肱三头肌、肱二头肌、肩胛下、髂前上棘。测量单位为毫米。
A higher sum of skinfolds generally indicates higher body fat. Reliability depends on tester skill and site consistency.
皮褶总和越高通常说明体脂越高。可靠性取决于测试者技能与测量部位一致性。
Body density and percentage body fat are indirect estimates; they have standard error and are not direct measures.
身体密度和体脂百分比是间接估计值，存在标准误差，并非直接测量。
5. Energy & Nutrient Calorific Values | 能量与营养素热量值
The main energy values per gram are: carbohydrate 4 kcal, protein 4 kcal, fat 9 kcal. Alcohol is 7 kcal/g but is not a performance nutrient.
主要营养素每克能量值：碳水化合物 4 千卡，蛋白质 4 千卡，脂肪 9 千卡。酒精为 7 千卡/克，但不属于运动表现营养素。
Energy balance: weight gain occurs when energy intake is greater than energy expenditure; weight loss occurs when intake is less than expenditure.
能量平衡：能量摄入大于能量消耗时体重增加；摄入小于消耗时体重下降。
Example: 100 g carbohydrate + 20 g fat + 50 g protein = (100 × 4) + (20 × 9) + (50 × 4) = 780 kcal.
示例：100 g 碳水 + 20 g 脂肪 + 50 g 蛋白质 = (100 × 4) + (20 × 9) + (50 × 4) = 780 千卡。
IGCSE questions may ask you to calculate total energy or compare meals using these factors.
IGCSE 题目可能要求用这些系数计算总能量或比较不同餐食。
6. Hydration & Sweat Loss | 水合与汗液流失
Sweat loss = pre-exercise body mass − post-exercise body mass + fluid consumed − urine output. Often simplified to body mass change.
汗液流失 = 运动前体重 − 运动后体重 + 摄入液体量 − 尿量。通常简化为体重变化。
1 kg of body mass lost is approximately equivalent to 1 L of fluid loss.
体重每下降 1 kg 约相当于流失 1 L 液体。
Example: pre-exercise 70.0 kg, post-exercise 69.2 kg = 0.8 kg loss ≈ 800 mL sweat loss.
示例：运动前 70.0 kg，运动后 69.2 kg = 下降 0.8 kg ≈ 800 mL 汗液流失。
Rehydration guidance: drink 1.2–1.5 L per 1 kg body mass lost, consumed gradually with electrolytes.
补水建议：每丢失 1 kg 体重补充 1.2–1.5 L 液体，逐渐饮用并补充电解质。
7. Linear Motion: Speed, Acceleration & Momentum | 直线运动：速度、加速度与动量
Speed (m/s) = distance (m) ÷ time (s). Average speed uses total distance; total displacement gives velocity.
速度（m/s）= 距离（m）÷ 时间（s）。平均速度使用总距离；总位移对应速度向量。
Speed = distance ÷ time
Acceleration (m/s²) = change in velocity (m/s) ÷ time (s). Deceleration is negative acceleration.
加速度（m/s²）= 速度变化量（m/s）÷ 时间（s）。减速是负加速度。
a = Δv ÷ t
Momentum (kg m/s) = mass (kg) × velocity (m/s). Momentum is conserved in a closed system.
动量（kg·m/s）= 质量（kg）× 速度（m/s）。封闭系统中
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