📚 Year 8 CIE PE: Quick Reference Formula & Theorem Handbook | Year 8 CIE 体育：公式定理速查手册
Welcome to your go-to handbook for the essential formulas and theorems you need in Year 8 CIE Physical Education. Keeping these equations at your fingertips will help you understand how your body responds to exercise, how to measure fitness, and how to design safe and effective training programmes.
欢迎使用这本为你准备的 Year 8 CIE 体育学科必备公式定理速查手册。把这些方程牢记在心，可以帮助你理解身体对运动的反应、如何测量体能水平，以及如何设计安全有效的训练计划。
1. Maximum Heart Rate (MHR) | 最大心率
Your maximum heart rate is the highest number of beats per minute your heart can safely achieve during maximal exercise. The simplest way to estimate it is: MHR = 220 – age. This formula gives a general guide, although individual differences exist.
最大心率是你在极限运动中，心脏每分钟能够安全达到的最高搏动次数。最简单的估算方法是：最大心率 = 220 – 年龄。这个公式提供了一个大致的参考，但人与人之间会存在差异。
For a 13-year-old student, estimated MHR = 220 – 13 = 207 bpm. Knowing your MHR is the first step to calculating training zones.
以一名 13 岁的学生为例，估算最大心率 = 220 – 13 = 207 次/分。了解最大心率是计算训练区间的第一步。
2. Target Heart Rate Zones | 目标心率区间
Different training intensities produce different fitness benefits. Heart rate zones are expressed as percentages of MHR. For general aerobic fitness, you often work at 60-80% of MHR; for high-intensity intervals, you may reach 85-95%.
不同的训练强度会带来不同的健身效果。心率区间以最大心率的百分比来表示。对于一般的有氧健身，通常会控制在最大心率的 60-80% 进行运动；而在高强度间歇训练中，可能会达到 85-95%。
| Zone | % of MHR | Benefit |
|---|---|---|
| Warm-up/Recovery | 50-60% | Gentle movement, aids recovery |
| Aerobic/Fat burning | 60-70% | Improves basic endurance and fat metabolism |
| Aerobic threshold | 70-80% | Strengthens cardiovascular system |
| Anaerobic threshold | 80-90% | Increases lactate tolerance and speed |
| Maximum effort | 90-100% | Develops peak power and speed |
3. Karvonen Formula (Heart Rate Reserve) | 卡沃宁公式（储备心率）
A more personalised method uses heart rate reserve (HRR): Target HR = [(MHR – resting HR) x % intensity] + resting HR. This takes into account your individual resting heart rate, making the training zones more accurate for you.
一种更加个性化的方法是使用储备心率（HRR）：目标心率 = [(最大心率 – 安静心率) × 强度百分比] + 安静心率。这个方法考虑了你的个人安静心率，使训练区间对你来说更加精确。
For a student with resting HR of 70 bpm and MHR of 207, training at 70% intensity would give: [(207-70) x 0.70] + 70 = (137 x 0.70) + 70 = 95.9 + 70 ≈ 166 bpm. This is a great tool when you begin to take training seriously.
对于一个安静心率为 70 次/分、最大心率为 207 的学生，如果以 70% 强度进行训练，计算得出：[(207-70) × 0.70] + 70 = (137 × 0.70) + 70 = 95.9 + 70 ≈ 166 次/分。当你开始认真对待训练时，这是一个非常棒的工具。
4. Body Mass Index (BMI) | 身体质量指数
BMI is a quick screening tool to estimate whether a person’s body weight is healthy for their height. It is calculated as: BMI = mass (kg) / height² (m²). Always remember to convert height to metres before squaring it.
身体质量指数（BMI）是一个快速筛查工具，用来估计一个人的体重是否在其身高范围内处于健康状态。计算公式为：BMI = 体重（千克）/ 身高²（米²）。要记得先把身高单位换算成米，再平方。
A student weighing 50 kg and 1.55 m tall would have a BMI of 50 / (1.55 x 1.55) = 50 / 2.4025 ≈ 20.8 kg/m², which falls in the normal weight range. However, BMI does not distinguish between muscle and fat, so very muscular individuals may be classified incorrectly.
一名体重 50 千克、身高 1.55 米的学生，其 BMI 为 50 / (1.55 × 1.55) = 50 / 2.4025 ≈ 20.8 千克/米²，落在正常体重范围内。不过，BMI 无法区分肌肉和脂肪，因此肌肉非常发达的人可能会被错误归类。
5. FITT Principle | FITT 原则
The FITT principle is the foundation of any training programme. It stands for Frequency, Intensity, Time and Type. Adjusting any one of these variables changes the overload placed on your body.
FITT 原则是任何训练计划的基础。它分别代表频率（Frequency）、强度（Intensity）、时间（Time）和类型（Type）。调整其中任何一个变量，都会改变施加在身体上的超负荷刺激。
- Frequency: how often you train per week. 每周练几次。
- Intensity: how hard you work (e.g., % MHR, RPE). 训练时有多努力（如 %最大心率、自觉劳累等级）。
- Time: duration of each session. 每次训练的持续时间。
- Type: the kind of exercise (e.g., running, cycling, resistance). 运动的种类（如跑步、骑行、抗阻训练）。
To improve fitness progressively, you must increase one or more FITT components over time. This is known as progressive overload.
要使体能逐步提升，必须随着时间的推移增加 FITT 中一项或多项要素。这就是所谓的渐进式超负荷。
6. Speed, Distance, Time | 速度、距离、时间
These three variables are linked by the simple relationship: Speed = Distance / Time. Rearranging this gives Distance = Speed x Time and Time = Distance / Speed. Being able to switch between them is essential for analysing performance in running, swimming and other timed events.
这三个变量由一个简单的关系式连接：速度 = 距离 / 时间。经过变形，可以得到：距离 = 速度 × 时间，以及时间 = 距离 / 速度。能够在这几个公式之间灵活转换，对于分析跑步、游泳以及其他计时项目的表现至关重要。
If a student runs 100 metres in 14 seconds, their average speed is 100 / 14 = 7.14 m/s. To estimate how long it would take to cover 1500 m at that speed, Time = 1500 / 7.14 ≈ 210 seconds, or 3 minutes 30 seconds.
如果一名学生用 14 秒跑完 100 米，那么其平均速度为 100 / 14 = 7.14 米/秒。如果要估算以该速度跑完 1500 米需要多长时间，则时间 = 1500 / 7.14 ≈ 210 秒，即 3 分 30 秒。
7. Energy Balance | 能量平衡
Energy balance is the relationship between calories consumed through food and drink and calories expended through metabolism and physical activity. The basic equation is: Energy Balance = Energy Intake – Energy Expenditure.
能量平衡是指通过食物和饮料摄入的热量与通过新陈代谢及体力活动消耗的热量之间的关系。基本方程式为：能量平衡 = 能量摄入 – 能量消耗。
A positive balance (intake > expenditure) leads to weight gain; a negative balance (expenditure > intake) leads to weight loss. For maintaining a healthy weight, aim for a balance over time.
正平衡（摄入 > 消耗）会导致体重增加；负平衡（消耗 > 摄入）会导致体重减轻。要维持健康体重，目标应当是长期保持动态平衡。
1 kg of body fat ≈ 7,700 kcal
This approximation helps you understand why small daily changes can add up over weeks and months.
这个近似值可以帮助你理解，为什么每天小小的改变，累积数周或数月后效果就会很明显。
8. Force, Mass and Acceleration | 力、质量与加速度
According to Newton’s Second Law of Motion, the acceleration of an object depends on the net force acting on it and its mass: Force = Mass x Acceleration (F = m × a). In sport, this explains how a stronger shot is produced with greater force or how a lighter ball accelerates faster.
根据牛顿第二运动定律，物体的加速度取决于作用在其上的净力与物体的质量：力 = 质量 × 加速度（F = m × a）。在体育运动中，这解释了为什么用更大的力可以打出力量更大的球，或者质量较轻的球会加速得更快。
If a footballer kicks a 0.43 kg ball with an average force of 65 N, the acceleration of the ball is a = F / m = 65 / 0.43 ≈ 151 m/s². This immense acceleration is why the ball leaves the foot so rapidly.
如果一名足球运动员用 65 牛的平均力去踢一个质量为 0.43 千克的足球，那么球的加速度为 a = F / m = 65 / 0.43 ≈ 151 米/秒²。如此巨大的加速度，正是球瞬间离开脚面的原因。
9. Lever Systems | 杠杆系统
Levers in the human body help us produce force, speed or a large range of motion. A lever consists of a fulcrum (joint), load (resistance) and effort (muscle force). The arrangement of these three components determines the lever class.
人体内的杠杆能够帮助我们产生力量、速度或较大的动作范围。一个杠杆由支点（关节）、负荷（阻力）和力（肌肉力量）组成。这三者的排列方式决定了杠杆的类别。
| Class | Arrangement | Example in Body |
|---|---|---|
| First class | Fulcrum between load and effort | Nodding the head (atlanto-occipital joint) |
| Second class | Load between fulcrum and effort | Standing on tip-toes (ball of foot as fulcrum) |
| Third class | Effort between fulcrum and load | Bicep curl (elbow joint) |
Most levers in the body are third-class levers, which favour speed and range of movement over raw force.
人体内大多数杠杆属于第三类杠杆，它们以牺牲纯力量为代价，换取速度和动作范围的优势。
10. Training Intensity and RPE Scale | 训练强度与自觉劳累等级量表
The Rating of Perceived Exertion (RPE) is a subjective way to measure exercise intensity on a scale of 6 to 20 (original Borg scale) or 0 to 10. It is useful when heart rate monitors are not available, and it correlates well with actual heart rate: RPE x 10 ≈ heart rate (bpm) for the 6-20 scale.
自觉劳累等级（RPE）是一种主观衡量运动强度的方法，量表范围通常为 6 到 20（原始的博格量表）或 0 到 10。在没有心率监测设备时，这种方法非常有用，而且它与实际心率有很好的相关性：对于 6-20 级的量表，RPE × 10 ≈ 心率（次/分钟）。
A rating of 12-13 (somewhat hard) often corresponds to around 120-130 bpm and is suitable for moderate aerobic training. Learning to listen to your body is a key skill in PE.
等级 12-13（有点吃力）通常对应大约 120-130 次/分钟的心率，适合中等强度的有氧训练。学会倾听自己的身体，是体育课中的一项关键技能。
11. Oxygen Deficit and EPOC (Basic) | 氧亏与运动后过量氧耗（基础）
At the start of exercise, the oxygen demand of your muscles increases instantly, but your oxygen supply systems take time to catch up. This temporary shortfall is called oxygen deficit. During this period, anaerobic energy systems cover the demand.
运动开始时，肌肉对氧气的需求立刻增加，但供氧系统需要一定时间才能跟上。这个暂时的缺口称为氧亏。在此期间，无氧能量系统会补上这部分能量需求。
After exercise, your body continues to consume extra oxygen to restore normal conditions (repay the deficit). This is called Excess Post-exercise Oxygen Consumption (EPOC), sometimes referred to as the “afterburn.” Although at Year 8 we keep the concept simple, it explains why you keep breathing heavily after a sprint.
运动结束后，你的身体仍会持续额外耗氧，以恢复正常状态（偿还氧亏）。这被称为运动后过量氧耗（EPOC），有时也俗称“后燃效应”。虽然在 Year 8 我们只需要掌握简单概念，但它能解释为什么冲刺完之后你还会大口喘气。
12. Training Zones for Skill and Fitness | 技能与体能训练区间
Understanding which energy system you are training is useful. Very broadly: activities lasting 0-10 seconds at maximum effort (e.g., a 30 m sprint) primarily use the ATP-PC system; 10-90 seconds (e.g., a 200 m run) rely heavily on anaerobic glycolysis; and efforts longer than 2-3 minutes shift toward the aerobic system.
了解你在训练哪一套能量系统很有用。非常粗略地概括：0-10 秒的最大强度运动（如 30 米冲刺）主要依靠 ATP-PC 系统供能；10-90 秒（如 200 米跑）严重依赖无氧糖酵解；而持续超过 2-3 分钟的运动则会转向有氧供能系统。
As a quick reference, you can use the “duration = dominant system” rule to plan your interval training:
你可以用“持续时间 = 主导供能系统”的规则，作为安排间歇训练的快速参考：
- Short sprints (≤10 s): develop power and speed. 极短冲刺（≤10 秒）：发展爆发力和速度。
- Medium efforts (30-90 s): improve lactic acid tolerance. 中等时间全力运动（30-90 秒）：提高乳酸耐受能力。
- Long efforts (2 min +): enhance aerobic capacity. 长时间运动（2 分钟以上）：增强有氧能力。
Combine these insights with the heart rate formulas above, and you have a complete toolkit for designing your own fitness sessions safely and effectively.
把这些知识跟前面的心率公式结合起来，你就拥有了一套完整的工具，可以安全有效地设计属于自己的体能训练课了。
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