📚 Year 7 CAIE Physical Education: Formula & Theorem Quick Reference Handbook | Year 7 CAIE 体育：公式定理速查手册
This quick reference handbook brings together the essential formulas, principles and key facts you need for Year 7 CAIE Physical Education. Use it to check your understanding of heart rate calculations, body composition measures, training principles and the science behind human movement. Each section presents the core idea in both English and Chinese, with clear formulas and simple explanations.
这本速查手册汇集了 Year 7 CAIE 体育课程所需的关键公式、定理和重要知识点。你可以用它来检查自己对心率计算、身体成分测量、训练原则以及人体运动科学基础的理解。每个部分都以中英双语呈现核心概念，并配有清晰的公式和简明解释。
1. Maximum Heart Rate (MHR) & Target Zone | 最大心率 (MHR) 与目标区间
Your maximum heart rate is the highest number of beats per minute your heart can reach during all-out exercise. The simplest estimate uses your age.
最大心率是你在全力运动时心脏每分钟能跳动的最高次数。最简单的估算方法要用到你的年龄。
MHR = 220 − age (years)
To train your aerobic system safely and effectively, you should work inside your target heart rate zone. For most Year 7 students, this falls between 60% and 85% of MHR.
为了安全有效地锻炼有氧系统，你应该在目标心率区间内运动。对大多数 Year 7 学生来说，这个区间是最大心率的 60% 到 85%。
Target Heart Rate = MHR × (0.60 to 0.85)
For a 12-year-old student, MHR = 220 − 12 = 208 bpm. The target zone would be roughly 125– bpm. Staying in this zone improves cardiovascular fitness without overstraining the heart.
以 12 岁的学生为例，MHR = 220 − 12 = 208 次/分。目标心率区间大约是 125–177 次/分。保持在这个区间可以改善心血管健康，又不会让心脏负担过重。
2. Body Mass Index (BMI) | 身体质量指数 (BMI)
BMI is a quick screening tool that uses your height and weight to estimate whether you are underweight, healthy weight, overweight or obese. It is not a direct measure of body fat, but it gives a useful starting point.
BMI 是一种快速筛查工具，用你的身高和体重来估算体重是否过轻、正常、超重或肥胖。它不是直接测量体脂的方法，但能提供一个有用的起点。
BMI = weight (kg) ÷ height² (m²)
To calculate your BMI, first square your height in metres, then divide your weight in kilograms by that number.
计算 BMI 时，先用身高（米）的平方，再用体重（千克）除以这个数值。
m², BMI = 45 ÷ 2.25 = 20.0 kg/m². This falls within the healthy weight range for that age.
例如，一名体重 45 kg、身高 1.50 m 的学生：身高² = 1.50 × 1.50 = 2.25 m²，BMI = 45 ÷ 2.25 = 20.0 kg/m²。这在同龄人中属于健康体重范围。
3. The FITT Principle | FITT 原则
FITT stands for Frequency, Intensity, Time and Type. It is a framework for designing a personal exercise programme and for making sure your training keeps challenging your body.
FITT 分别代表频率（Frequency）、强度（Intensity）、时间（Time）和类型（Type）。它是设计个人锻炼计划、确保训练持续对身体构成挑战的框架。
| Element | 要素 | What It Means | 含义 | Example for Year 7 | Year 7 示例 |
|---|---|---|
| Frequency | 频率 | How often you exercise | 每周锻炼几次 | 3–5 times per week | 每周 3–5 次 |
| Intensity | 强度 | How hard you work | 运动有多费力 | 60–85% MHR or 'talking pace' | 60–85% 最大心率或 '说话配速' |
| Time | 时间 | Duration of each session | 每次锻炼时长 | 20–60 minutes | 20–60 分钟 |
| Type | 类型 | Kind of exercise | 运动种类 | Aerobic, strength, flexibility | 有氧、力量、柔韧性 |
When you want to improve, you can change one or more FITT variables. For instance, to build more endurance, you might increase the time you run each week while keeping the intensity moderate.
当你想取得进步时，可以调整一个或多个 FITT 变量。例如，想增强耐力，你可以把每周跑步的时间加长，同时保持中等强度。
4. SPOR Training Principles | SPOR 训练原则
SPOR helps you remember four training principles: Specificity, Progression, Overload and Reversibility. These ideas explain why some training programmes work and why fitness can be lost.
SPOR 帮你记住四项训练原则：专项性（Specificity）、渐进性（Progression）、超负荷（Overload）和可逆性（Reversibility）。这些概念解释了为什么有些训练计划有效，以及体能为何会下降。
- Specificity | 专项性： Training must match the sport or goal. A swimmer needs to train in the water, not just lift weights. | 训练必须与运动项目或目标匹配。游泳运动员需要在水里训练，而不只是举重。
- Progression | 渐进性： You should gradually increase the difficulty. Going too hard too soon leads to injury. | 应逐步增加难度。操之过急会导致受伤。
- Overload | 超负荷： To improve, you must work harder than your body is used to. This can be done by manipulating the FITT variables. | 要进步，就必须超出身体习惯的负荷。可以通过调整 FITT 变量来实现。
- Reversibility | 可逆性： Fitness is lost when you stop training. 'Use it or lose it' applies to muscles, endurance and flexibility. | 一旦停止训练，体能就会下降。'用进废退'适用于肌肉、耐力和柔韧性。
Many teachers also add a 'T' for Tedium, reminding you that training should be varied and enjoyable to avoid boredom.
很多老师还会加上 'T' 表示枯燥（Tedium），提醒自己训练要丰富有趣，避免无聊。
5. Speed, Distance and Time | 速度、距离与时间
The relationship between speed, distance and time is one of the most useful formulas in physical education. It helps you analyse performance in running, swimming, cycling and many other activities.
速度、距离和时间的关系是体育中最有用的公式之一。它能帮你分析跑步、游泳、骑行及许多其他运动中的表现。
Speed = Distance ÷ Time
From this you can also rearrange the formula:
由此还可以推导出：
Distance = Speed × Time
Time = Distance ÷ Speed
Always make sure your units match. If distance is measured in metres and time in seconds, speed will be in metres per second (m/s). To compare with everyday speeds, you may convert to kilometres per hour (km/h).
一定要确保单位一致。如果距离用米、时间用秒，速度就是米每秒（m/s）。为了和日常速度比较，可以换算为千米每小时（km/h）。
e to km/h, multiply by 3.6, giving about 25.7 km/h. This sort of calculation is often used in fitness testing.
示例：一名学生 14 秒跑完 100 米。速度 = 100 ÷ 14 ≈ 7.14 m/s。换算为 km/h 乘 3.6，大约是 25.7 km/h。这种计算经常用在体能测试中。
6. Lever Systems in Movement | 动作中的杠杆系统
Our bones act as levers, our joints are the fulcrums and our muscles provide the effort to overcome a load. Understanding this helps you see why some body positions give you a mechanical advantage.
我们的骨骼充当杠杆，关节是支点，肌肉提供克服阻力的动力。理解这一点，你就会明白为什么某些身体姿势能带来机械优势。
Effort × Effort Arm = Load × Load Arm
In a first-class lever, the fulcrum sits between effort and load (e.g. the head nodding). In a second-class lever, the load is between fulcrum and effort (e.g. standing on tiptoe). In a third-class lever, the effort is between fulcrum and load (e.g. biceps curl). The majority of body levers are third-class, which favour speed and range of movement over raw force.
在一类杠杆中，支点在动力和阻力之间（如点头动作）。二类杠杆中，阻力在支点和动力之间（如踮脚站立）。三类杠杆中，动力在支点和阻力之间（如肱二头肌弯举）。人体大部分杠杆是第三类，其优势在于速度和动作范围而非纯粹的力量。
The formula explains why a longer effort arm makes a movement easier: for the same load, a longer effort arm requires less muscular effort.
这个公式解释了为什么更长的力臂会让动作更轻松：同样的负荷下，较长的力臂需要的肌肉力更小。
7. Health-Related Fitness Components | 健康相关体能组成
The five health-related fitness components are directly linked to your overall health and ability to perform everyday tasks. You do not need a formula to understand them, but you should know how each component is improved.
五项健康相关体能组成与你的整体健康和日常生活能力直接相关。理解它们不需要公式，但你应知道如何提升每一项。
| Component | 组成 | What It Means | 含义 | How to Improve | 如何改善 |
|---|---|---|
| Cardiovascular Endurance | 心血管耐力 | Ability of heart and lungs to deliver oxygen during long exercise | 心肺长时间供氧的能力 | Continuous running, cycling, swimming | 持续跑、骑行、游泳 |
| Muscular Strength | 肌肉力量 | Maximum force a muscle can produce | 肌肉能产生的最大力量 | Heavy weights, low reps | 大重量、低次数 |
| Muscular Endurance | 肌肉耐力 | Ability to repeat muscle contractions without fatigue | 肌肉反复收缩而不疲劳的能力 | Light weights, high reps | 小重量、高次数 |
| Flexibility | 柔韧性 | Range of motion around a joint | 关节的活动范围 | Static and dynamic stretching | 静态和动态拉伸 |
| Body Composition | 身体成分 | Ratio of fat to lean tissue | 脂肪与瘦体重的比例 | Balanced diet and regular exercise | 均衡饮食和定期锻炼 |
These components form the foundation of physical fitness and are regularly tested in school fitness assessments.
这些组成是体能的基石，在学校体能评估中也经常进行测试。
8. Skill-Related Fitness Components | 技能相关体能组成
Skill-related fitness components are more about your ability to perform in sports and games. They help you react quickly, change direction and control your body.
技能相关体能组成更多关系到你在运动和比赛中的表现能力。它们帮助你快速反应、改变方向和控制身体。
- Agility | 敏捷： Ability to change direction quickly and accurately. | 快速而准确地改变方向的能力。
- Balance | 平衡： Ability to keep the body stable, whether still or moving. | 无论是静止还是移动，保持身体稳定的能力。
- Coordination | 协调： Ability to use two or more body parts smoothly together. | 顺畅地同时使用两个或多个身体部位的能力。
- Power | 爆发力： Combination of strength and speed (Power = Force × Velocity). | 力量与速度的结合（爆发力 = 力 × 速度）。
- Reaction Time | 反应时间： Time taken to respond to a stimulus. | 对刺激做出反应所需的时间。
- Speed | 速度： Ability to move body parts quickly over a distance. | 在距离上快速移动身体部位的能力。
In many sports, skill-related fitness can be more important than health-related fitness. A gymnast, for instance, relies heavily on balance and coordination.
在许多运动中，技能相关体能可能比健康相关体能更重要。例如，体操运动员高度依赖平衡和协调能力。
9. Rate of Perceived Exertion (RPE) | 自感劳累评分 (RPE)
RPE is a subjective way to measure exercise intensity without relying on heart rate monitors. It lets you listen to your body and adjust effort based on how you feel.
RPE 是一种不用心率监测仪就能测量运动强度的主观方法。它让你倾听身体的声音，根据自身感受调整用力程度。
The original Borg scale runs from 6 to 20, but an easier 0–10 scale is often used with younger students:
最初的博格量表是从 6 到 20 分，但对于年龄较小的学生，常使用更简单的 0–10 分量表：
| RPE (0–10) | 评分 | Effort Level | 用力程度 | Feeling | 感受 |
|---|---|---|
| 0 | Nothing at all | 毫无感觉 | Rest | 休息 |
| 2–3 | Light | 轻松 | Can sing | 可以唱歌 |
| 4–5 | Moderate | 中等 | Can talk comfortably | 能够轻松交谈 |
| 6–7 | Vigorous | 剧烈 | Breathing heavily, hard to talk | 呼吸急促，很难说话 |
| 8–9 | Very hard | 非常累 | Very breathless | 喘不过气 |
| 10 | Maximal | 极限 | Cannot continue | 无法继续 |
For improving aerobic fitness, aim to work at an RPE of about 4–6. This corresponds roughly to the moderate-to-vigorous intensity zone.
要改善有氧能力，目标 RPE 可以在 4–6 分左右。这大体对应中等至高强度区间。
10. Simple Energy Balance & Calorie Estimate | 简单能量平衡与卡路里估算
Weight management ultimately depends on energy balance: calories consumed versus calories burned. Physical activity is a key part of the 'calories out' side of the equation.
体重管理最终取决于能量平衡：摄入的卡路里与消耗的卡路里。身体活动是'消耗'这一侧的关键部分。
Energy Balance = Calories In − Calories Out
A rough estimate of calories burned during walking or running uses your body weight and distance:
对走路或跑步所消耗的卡路里，有一个基于体重和距离的粗略估算：
Calories burned ≈ Body weight (kg) × Distance (km) × 1.036
0 kcal. This is only an estimate; actual calorie burn depends on speed, fitness level and terrain.
例如，一名 45 kg 的学生跑 3 km，大约消耗 45 × 3 × 1.036 ≈ 140 kcal。这只是估算；实际消耗还取决于速度、体能水平和地形。
Understanding energy balance helps you make healthy choices about food and exercise. Even small daily changes, like walking an extra 1 km, can add up over time.
理解能量平衡有助于你在饮食和运动上做出健康选择。即使是很小的日常改变，比如每天多走 1 km，长期积累下来效果也很明显。
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