📚 Year 8 CAIE Physical Education: Formula & Theorem Quick Reference Handbook | 8 年级 CAIE 体育：公式定理速查手册
Welcome to your go-to revision companion for Year 8 CAIE Physical Education. This handbook condenses the key formulas, principles, and quick-reference facts you need to analyse performance, training, and the human body in sport. Use it to sharpen your exam technique and deepen your understanding of how science underpins physical activity.
欢迎使用你的 8 年级 CAIE 体育备考速查伴侣。本手册浓缩了你在分析运动表现、训练和人体在运动中的反应时所需的关键公式、原理和速查要点。用它来打磨你的考试技巧，并加深你对科学如何支撑身体活动的理解。
1. Maximum Heart Rate (MHR) | 最大心率
The simplest estimation of MHR is 220 minus your age. For a 13-year-old student, this gives 207 beats per minute (bpm).
最大心率最简单的估算方法是 220 减去你的年龄。对于 13 岁的学生，这将得出 207 次/分。
MHR = 220 − age
MHR = 220 − 年龄
This estimate is used to set training zones. However, more precise lab tests exist, but for Year 8, 220−age is the standard reference.
这个估算值用于设定训练区间。尽管存在更精确的实验室测试，但对于 8 年级来说，220−年龄是标准参考。
2. Target Heart Rate Zone (Karvonen Formula) | 靶心率区间（卡沃宁公式）
The Karvonen formula uses resting heart rate (RHR) to give a more personalised training zone. It calculates the heart rate reserve first.
卡沃宁公式利用静息心率来给出更个性化的训练区间。它首先计算心率储备。
Target HR = ((MHR − RHR) × %Intensity) + RHR
靶心率 = ((最大心率 − 静息心率) × 强度百分比) + 静息心率
For moderate aerobic work (60–70% intensity), you can plug in your own RHR taken first thing in the morning. This method ensures that a fitter person with a lower RHR trains at an appropriate heart rate.
对于中等强度的有氧运动（60–70% 强度），你可以代入自己早晨刚醒时测量的静息心率。这个方法确保更健康、静息心率更低的人能以合适的心率训练。
3. Body Mass Index (BMI) | 身体质量指数
BMI is a quick screening tool to classify weight status. It is not a direct measure of body fat, but it is widely used in population studies.
BMI 是一种快速筛查体重状态的工具。它并非身体脂肪的直接测量指标，但广泛用于群体研究。
BMI = weight (kg) ÷ height² (m²)
BMI = 体重（千克）÷ 身高²（米²）
For example, a pupil weighing 50 kg and 1.60 m tall has a BMI of 50 ÷ (1.60×1.60) = 19.5 kg/m², which falls in the healthy range. Remember, BMI does not distinguish between muscle and fat mass.
例如，一个体重 50 千克、身高 1.60 米的学生 BMI 为 50 ÷ (1.60×1.60) = 19.5 千克/米²，处于健康范围。请记住，BMI 不区分肌肉和脂肪质量。
4. Calorie Expenditure Using METs | 利用代谢当量计算卡路里消耗
Metabolic Equivalent of Task (MET) indicates how many times more energy an activity uses compared to resting. Resting is 1 MET. Running at 8 km/h is about 8 METs.
代谢当量表示一项活动消耗的能量是静息时的多少倍。静息为 1 MET。以 8 公里/小时的速度跑步约为 8 METs。
Calories burned ≈ MET × weight (kg) × time (hours)
消耗热量 ≈ MET × 体重（千克） × 时间（小时）
So a 50 kg student playing football (7 METs) for 1 hour will burn roughly 7 × 50 × 1 = 350 kcal. This is an estimate – actual energy cost varies with fitness and body composition.
因此，一名 50 千克的学生踢足球（7 METs）1 小时大约消耗 7 × 50 × 1 = 350 千卡。这只是一个估算值——实际能量消耗因体能和身体成分而异。
5. Training Load | 训练负荷
Training load represents the overall stress placed on the body. It is often calculated as the product of intensity and duration (volume).
训练负荷代表施加于身体的总压力。通常用强度与时间（训练量）的乘积来表示。
Training Load = Intensity × Duration
训练负荷 = 强度 × 持续时间
Intensity can be measured by heart rate, RPE, or percentage of one-repetition maximum (1RM). Keeping a training diary helps monitor load and avoid overtraining.
强度可以通过心率、主观用力感觉或单次最大重量的百分比来衡量。记录训练日记有助于监控负荷，避免过度训练。
6. The FITT Principle | FITT 原则
The FITT principle is a framework for designing an effective exercise programme. It stands for Frequency, Intensity, Time, and Type.
FITT 原则是设计有效锻炼计划的一个框架。它代表频率、强度、时间和类型。
- Frequency – how often you exercise per week.
- 频率 – 每周锻炼的次数。
- Intensity – how hard you work (e.g., % MHR, RPE).
- 强度 – 你的努力程度（如 %MHR，主观用力感觉）。
- Time – duration of each session.
- 时间 – 每次训练的持续时间。
- Type – the kind of exercise (e.g., aerobic, strength, flexibility).
- 类型 – 运动种类（如有氧、力量、柔韧性）。
Applying FITT helps ensure progressive overload. As the body adapts, one or more FITT variables should be increased.
应用 FITT 原则有助于确保渐进超负荷。当身体适应后，应增加一项或多项 FITT 变量。
7. Speed, Distance, Time | 速度、距离、时间
The relationship between speed, distance, and time is fundamental in analysing athletic performance. The formula is used in running, cycling, swimming, and many team sports.
速度、距离和时间之间的关系是分析运动表现的基础。这一公式用于跑步、自行车、游泳和许多团队运动。
Speed = Distance ÷ Time
速度 = 距离 ÷ 时间
To calculate sprint speed, measure a known distance (e.g., 50 m) and record the time with a stopwatch. Then divide. Rearranging the formula lets you find time or distance as well.
要计算短跑速度，测量一个已知的距离（如 50 米）并用秒表记录时间，然后相除。将公式变形也可求出时间或距离。
8. Power | 功率
Power measures the rate at which work is done. In sport, explosive activities like jumping and throwing require high power output.
功率衡量做功的速率。在运动中，跳跃和投掷等爆发性活动需要高功率输出。
Power = Work ÷ Time
功率 = 功 ÷ 时间
And work is the product of force and distance moved in the direction of the force.
而功是力与在力的方向上移动距离的乘积。
Work = Force × Distance
功 = 力 × 距离
For a vertical jump, work equals body weight (in newtons) multiplied by jump height. Power tests like the Wingate test use a cycle ergometer to assess peak power.
对于垂直起跳，功等于体重（以牛顿计）乘以起跳高度。像 Wingate 测试等功率测试利用自行车测功计评估峰值功率。
9. Rate of Perceived Exertion (RPE) | 主观用力感觉量表
RPE scales let athletes self-rate how hard they feel an exercise is. The Borg 6–20 Scale is classic: 6 means no exertion at all, 20 means maximal effort.
主观用力感觉量表让运动员自我评估他们认为运动有多费力。经典的博格 6-20 量表中，6 表示毫不费力，20 表示最大努力。
An approximate heart rate can be estimated as RPE × 10. For example, an RPE of 12 suggests a heart rate around 120 bpm. The simpler 0–10 scale is also common, where 0 is rest and 10 is maximal exertion.
大致心率可以通过 RPE × 10 估算。例如，RPE 为 12 意味着心率约为 120 次/分。简单的 0-10 量表也很常用，0 表示休息，10 表示最大努力。
Using RPE helps people without heart rate monitors to train within safe and effective intensity zones.
使用主观用力感觉量表帮助没有心率监测器的人在安全有效的强度区间内训练。
10. Heart Rate Recovery (HRR) | 心率恢复
Heart rate recovery is the drop in heart rate after exercise stops. A faster recovery is linked to higher cardiovascular fitness.
心率恢复是指运动停止后心率的下降幅度。恢复越快，表明心血管健康水平越高。
HRR = HR at peak exercise − HR after 1 or 2 minutes rest
心率恢复 = 峰值运动心率 − 休息 1 分钟或 2 分钟后心率
A drop of 20 bpm or more in the first minute indicates good fitness. In tests, a standardised submaximal protocol is used, and recovery is tracked for several minutes.
第一分钟下降 20 次/分或更多表明良好的体能。在测试中，采用标准化的亚极量方案，并连续监测数分钟的恢复情况。
11. Levers and Mechanical Advantage | 杠杆与机械利益
In the human body, bones act as levers, joints as fulcrums, and muscles provide effort. Mechanical advantage tells us how efficiently a lever overcomes a resistance.
在人体中，骨骼充当杠杆，关节充当支点，肌肉提供动力。机械利益告诉我们杠杆克服阻力的效率如何。
Mechanical Advantage = Effort Arm Length ÷ Resistance Arm Length
机械利益 = 动力臂长度 ÷ 阻力臂长度
A mechanical advantage greater than 1 means less effort is needed to move a larger resistance, but over a smaller distance. Most body levers, like the biceps at the elbow, have mechanical disadvantage (MA < 1) but allow a large range and speed of movement.
机械利益大于 1 意味着用较小的力就能移动较大的阻力，但移动距离较短。大多数人体杠杆，如肘部的肱二头肌，处于机械劣势（MA < 1），但允许较大的运动幅度和速度。
12. Work-to-Rest Ratio | 运动与休息比例
In interval training, the work-to-rest ratio determines the energy systems targeted. A ratio of 1:1 or 1:2 targets the anaerobic alactic system; longer rest or lower effort uses aerobic systems.
在间歇训练中，运动与休息的比例决定了所针对的供能系统。1:1 或 1:2 的比例针对无氧非乳酸系统；更长的休息或较低的运动强度会使用有氧系统。
For example, a sprint training session might be 30 seconds work, 60 seconds rest (1:2). A HIIT circuit might use 40 seconds work, 20 seconds rest (2:1) to stress the lactic acid system. Adjusting the ratio changes the fitness adaptation.
例如，短跑训练课可能是运动 30 秒、休息 60 秒（1:2）。HIIT 循环可能使用运动 40 秒、休息 20 秒（2:1）来刺激乳酸系统。调整比例会改变身体适应的方式。
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