📚 Year 7 CCEA PE: Formula & Theorem Quick-Reference Handbook | 七年级CCEA体育：公式定理速查手册
Welcome to your go-to quick-reference guide for the essential formulas, theorems, and calculations you need to master in Year 7 CCEA Physical Education. Whether you are analysing your fitness test results, planning a training session, or simply trying to understand how your body responds to exercise, these formulas will help you measure, monitor, and improve your performance. Each section pairs an English explanation with a Chinese translation so you can learn both the language and the science behind the numbers.
欢迎使用这本速查手册，这里汇集了七年级CCEA体育课程中你必须掌握的核心公式、定理和计算方法。无论你是在分析体能测试成绩、设计训练计划，还是想了解身体对运动的反应，这些公式都能帮助你量化、监测并提升运动表现。每个小节都配有英文解释和中文翻译，让你同时学习语言和数据背后的科学。
1. Maximum Heart Rate (MHR) Formula | 最大心率公式
Your maximum heart rate (MHR) is the highest number of beats per minute your heart can safely achieve during all-out exercise. The most common estimation used in Year 7 is: MHR = 220 − age. For a typical 11‑year‑old student, this gives an estimated maximum of 209 bpm. Although individual fitness levels can cause variations, this formula gives you a simple starting point for setting training intensities.
最大心率（MHR）是指你在全力运动中每分钟心跳能达到的最高次数。七年级最常用的估算公式是：MHR = 220 − 年龄。对典型的11岁学生来说，估算最大心率约为209次/分钟。尽管个体差异会影响实际值，但这个公式为你设定训练强度提供了一个简单的起点。
MHR = 220 − age (years)
2. Target Heart Rate: Karvonen Method | 靶心率：卡沃宁公式
To exercise safely and effectively, you need to know your target heart rate (THR) zone. The Karvonen formula uses your resting heart rate (RHR) and desired intensity to give a personalised range. The calculation is: THR = ((MHR − RHR) × intensity%) + RHR. For example, if your MHR is 209 bpm and your RHR is 70 bpm, working at 60% intensity gives a target of ((209−70) × 0.6) + 70 = 153 bpm. This method ensures you work at the right level to build fitness without overdoing it.
为了安全有效地运动，你需要知道自己的靶心率（THR）区间。卡沃宁公式利用你的静息心率（RHR）和目标强度来给出个性化范围。计算方法是：THR = ((MHR − RHR) × 强度%) + RHR。例如，如果你的MHR是209 bpm，RHR是70 bpm，以60%强度运动时，靶心率为 ((209−70) × 0.6) + 70 = 153 bpm。这种方法能确保你在合适的心率水平上锻炼，提升体能又不过量。
THR = ((MHR − RHR) × intensity%) + RHR
3. Body Mass Index (BMI) | 身体质量指数
BMI is a simple tool that compares your weight to your height to assess whether you are underweight, healthy, overweight, or obese. The formula is: BMI = weight (kg) ÷ (height (m))². In Year 7 PE, you learn that BMI does not distinguish between muscle and fat, so it is only a general screening tool. For example, a student weighing 45 kg and measuring 1.55 m tall has a BMI of 45 ÷ (1.55)² ≈ 18.7, which falls within the healthy range for children of this age on the centile charts.
BMI是一种简单的工具，它通过比较体重与身高来评估你是否偏瘦、健康、超重或肥胖。公式为：BMI = 体重（kg）÷（身高（m））²。在七年级体育课上你会学到，BMI无法区分肌肉和脂肪，因此它只是一个粗略的筛查工具。例如，一名体重45公斤、身高1.55米的学生，其BMI为45 ÷ (1.55)² ≈ 18.7，在同龄儿童的百分位图表中属于健康范围。
BMI = weight (kg) ÷ (height (m))²
4. Resting Heart Rate (RHR) & Why It Matters | 静息心率及其重要性
Resting heart rate (RHR) is the number of times your heart beats per minute while you are completely at rest. A lower RHR usually indicates a stronger, more efficient heart. To measure RHR accurately, take your pulse first thing in the morning before getting out of bed for several days and calculate the average. Typical RHR for an 11‑year‑old ranges from 70 to 100 bpm, though active children may have lower values. RHR is an essential variable in many training formulas, so tracking it helps you see improvements in your cardiovascular fitness over time.
静息心率（RHR）指你在完全休息状态下每分钟心跳的次数。较低的RHR通常意味着心脏更加强壮、高效。准确测量RHR的方法是连续几天早晨醒来后、下床前测量脉搏，然后计算平均值。11岁儿童的典型静息心率在70到100 bpm之间，而经常运动的孩子可能更低。RHR是许多训练公式中的关键变量，因此跟踪它可以让你看到心血管耐力随时间改善的情况。
5. Five Training Zones Based on %MHR | 基于最大心率百分比的五大训练区域
Training zones help you understand the different benefits of exercising at various heart rate intensities. They are calculated using simple percentages of your maximum heart rate. The table below summarises the five zones, their typical uses, and the fuel source mainly used.
训练区域帮助你理解在不同心率强度下运动所带来的不同效果。这些区域是根据你最大心率的简单百分比计算出来的。下表概括了五大区域、它们的典型用途以及主要供能物质。
| Zone | %MHR | Benefit | Fuel |
|---|---|---|---|
| 1 – Very Light | 50–60% | Warm‑up, recovery | Fat |
| 2 – Light | 60–70% | Basic endurance, fat burning | Fat |
| 3 – Moderate | 70–80% | Aerobic fitness | Carbohydrate & fat |
| 4 – Hard | 80–90% | Anaerobic threshold | Carbohydrate |
| 5 – Maximum | 90–100% | Speed, power | Carbohydrate |
6. Speed, Distance, Time Relationship | 速度、距离、时间的关系
In many Year 7 practical activities, you will record how fast you run, swim, or cycle over a set distance. The fundamental formula linking speed, distance, and time is: Speed = Distance ÷ Time. You can rearrange this triangle to find Distance = Speed × Time and Time = Distance ÷ Speed. Always make sure the units match—if distance is in metres and time in seconds, speed is in metres per second (m/s). In PE this formula helps you calculate your sprint speed or set pacing goals.
在七年级的许多实践活动中，你会记录自己在固定距离内跑步、游泳或骑行的有多快。速度、距离和时间之间的基本关系公式为：速度 = 距离 ÷ 时间。你可以通过三角变形得到：距离 = 速度 × 时间，以及时间 = 距离 ÷ 速度。务必保证单位一致——如果距离以米为单位，时间以秒为单位，速度的单位就是米/秒（m/s）。在体育课中，这个公式可以帮助你计算冲刺速度或制定配速目标。
Speed (m/s) = Distance (m) ÷ Time (s)
7. Predicting VO₂max from the Multi‑Stage Fitness Test | 哔声测试预测最大摄氧量
The multi‑stage fitness test (bleep test) is a common way to estimate your maximal oxygen uptake, or VO₂max, which measures aerobic endurance. While direct lab measurement is accurate, your PE teacher may use a simple equation based on the level and shuttle you reach. One widely used formula is: VO₂max (ml/kg/min) = 3.46 × (Level + (Shuttles / (Level × 0.4325 + 7.0048))) + 12.2. However, at Year 7 level you will more likely use a conversion table provided by CCEA. The key takeaway is that a higher test score reflects a higher VO₂max and better stamina.
多阶段体能测试（哔声测试）通常用来估算你的最大摄氧量（VO₂max），这项指标衡量有氧耐力。虽然实验室直接测量最为准确，但你的体育老师可能会根据你跑到的级别和折返次数使用一个简单的公式。其中一个广泛使用的公式是：VO₂max (ml/kg/min) = 3.46 × (级别 + (折返次数 / (级别 × 0.4325 + 7.0048))) + 12.2。不过在七年级阶段，你更可能使用CCEA提供的换算表。重要的是，测试分数越高，意味着VO₂max越高，耐力越好。
8. Calories Burned per Minute Using METs | 用代谢当量估算每分钟热量消耗
A MET (Metabolic Equivalent of Task) represents the energy cost of an activity compared to resting. One MET equals approximately 1 kcal per kg of body weight per hour at rest. To estimate calories burned per minute during an activity, you can use: Calories per minute = (MET × body mass (kg) × 3.5) / 200. For example, jogging at about 8 km/h has a MET value of roughly 8.0. For a 45 kg student, this gives (8.0 × 45 × 3.5) / 200 ≈ 6.3 kcal per minute. Understanding METs helps you compare how different exercises burn energy.
MET（代谢当量）表示某项活动相对于静息状态的能量消耗。1 MET约等于每公斤体重每小时消耗1千卡。要估算某项运动每分钟消耗的卡路里，可以使用公式：每分钟卡路里 = (MET × 体重（kg）× 3.5) / 200。例如，以大约8公里/小时的速度慢跑，其MET值约为8.0。对一名45公斤的学生来说，(8.0 × 45 × 3.5) / 200 ≈ 每个钟消耗6.3千卡。了解MET值有助于你比较不同运动燃烧能量的情况。
Calories/min ≈ (MET × body mass (kg) × 3.5) / 200
9. Heart Rate Recovery (HRR) | 心率恢复
Heart rate recovery measures how quickly your heart returns to normal after exercise. It is a simple indicator of fitness: a faster drop in heart rate means your heart is more efficient. A straightforward method is to record your peak heart rate at the end of exercise, then measure it again one minute later. The formula is: HRR (1 min) = peak HR − HR after 1 minute. For example, if your peak was 185 bpm and after one minute it drops to 135 bpm, your recovery is 50 bpm. Elite athletes may see drops of 60 bpm or more. Tracking HRR over several weeks shows whether your aerobic fitness is improving.
心率恢复衡量的是运动后心率恢复到正常水平的速度。它是判断体能状态的简单指标：心率下降得越快，意味着心脏效率越高。一个简单的方法是记录运动结束瞬间的峰值心率，然后在一分钟后再测量一次。公式为：1分钟恢复值 = 峰值心率 − 1分钟后心率。例如，如果峰值是185 bpm，一分钟后降到135 bpm，恢复值为50 bpm。优秀运动员的恢复值可达60 bpm甚至更高。持续数周追踪你的心率恢复情况，可以看出有氧能力是否在提高。
10. Sweat Loss Calculation for Hydration | 出汗量计算与补水
Staying hydrated is essential for performance and safety. You can estimate how much fluid you lose through sweat during exercise by weighing yourself before and after a session. The formula is: Sweat loss (litres) = body mass before (kg) − body mass after (kg) + fluid consumed during exercise (litres) − urine output (litres). For each kilogram of body mass lost, you need to drink approximately 1.2–1.5 litres of fluid to fully rehydrate. In Year 7, we simplify this to: Fluid to replace (ml) = weight lost (g) × 1.5. This practical formula helps you maintain hydration and avoid heat-related illnesses.
保持水分充足对运动表现和安全至关重要。你可以通过在运动前后称量体重来估算运动中通过出汗流失了多少体液。公式为：出汗量（升）= 运动前体重（kg）− 运动后体重（kg）+ 运动时饮水量（升）− 排尿量（升）。每减轻1公斤体重，大约需要补充1.2–1.5升液体才能完全补水。七年级我们将其简化为：需补液量（ml）= 体重减少量（g）× 1.5。这个实用公式有助于你保持水分平衡，预防热相关疾病。
Fluid to replace (ml) ≈ weight loss (g) × 1.5
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