📚 Year 7 WJEC PE: Formula & Theorem Quick Reference Guide | Year 7 WJEC 体育：公式定理速查手册
Welcome to your quick reference guide for Year 7 WJEC Physical Education. This handbook brings together all the essential formulas, principles and training theorems you will need throughout the year. Whether you are calculating training zones, analysing movement or setting fitness goals, these tools will help you understand how your body works and how to improve performance safely.
欢迎使用 Year 7 WJEC 体育的速查手册。这本手册汇集了你全年所需的所有关键公式、原理和训练定理。无论你是在计算训练区间、分析运动还是设定健身目标，这些工具都将帮助你理解身体的运作方式，并安全地提升运动表现。
1. Maximum Heart Rate (MHR) Formula | 最大心率公式
Maximum heart rate is the highest number of beats per minute your heart can achieve during all‑out exercise. The most common estimation method for a 12‑year‑old student is the simple equation: MHR = 220 − age. For example, if you are 12, your estimated MHR would be 208 beats per minute. This value is used to set training intensities and avoid overexertion.
最大心率是你在全力以赴运动时，心脏每分钟能达到的最高跳动次数。对于12岁的学生，最常用的估算方法是简单公式：最大心率 = 220 − 年龄。例如，如果你12岁，估算最大心率就是每分钟208次。这个数值用于设定训练强度并避免过度疲劳。
HRₘₐₓ = 220 − age (in years)
HRₘₐₓ = 220 − 年龄（岁）
2. Target Heart Rate Zone & Karvonen Formula | 目标心率区间与卡氏公式
To improve cardiovascular fitness, you need to exercise within a target heart rate zone. A more precise method than using a simple percentage of MHR is the Karvonen formula, which takes your resting heart rate (RHR) into account. The formula calculates heart rate reserve (HRR) = MHR − RHR, then applies the desired intensity. For a moderate‑intensity workout at 60‑75 % intensity, the target heart rate = (HRR × intensity) + RHR.
要改善心血管健康，你需要在目标心率区间内锻炼。比单纯使用最大心率百分比更精确的方法是卡氏公式，它将你的静息心率（RHR）考虑在内。该公式先计算心率储备（HRR）= 最大心率 − 静息心率，然后乘以所需的强度。进行中等强度60‑75 %的运动时，目标心率 = （HRR × 强度%）+ 静息心率。
Target HR = ((HRₘₐₓ − RHR) × intensity%) + RHR
目标心率 = ((HRₘₐₓ − 静息心率) × 强度% ) + 静息心率
For a 12‑year‑old with a resting heart rate of 70 bpm, the 65 % target would be: ((208 − 70) × 0.65) + 70 ≈ 160 bpm. Always start at the lower end of the zone and gradually progress.
对于一个静息心率为70 bpm的12岁学生，65%强度的目标心率计算为：((208 − 70) × 0.65) + 70 ≈ 每分钟160次。始终从强度区间的下限开始，逐步提升。
3. Body Mass Index (BMI) | 身体质量指数
BMI is a screening tool used to assess whether a person has a healthy body weight for their height. It is not a direct measure of body fat, but it helps identify weight categories that may lead to health problems. For Year 7 students, it provides a simple starting point for understanding body composition.
身体质量指数是一种筛查工具，用于评估一个人的体重相对身高是否健康。它并不直接测量体脂肪，但有助于识别可能导致健康问题的体重类别。对七年级学生来说，它是了解身体成分的一个简单起点。
BMI = weight (kg) ÷ (height (m))²
BMI = 体重（千克）÷（身高（米））²
For example, a student weighing 45 kg and 1.50 m tall would have a BMI of 45 ÷ (1.50 × 1.50) = 20.0 kg/m². Remember that children’s BMI is interpreted using age‑ and sex‑specific centile charts, not adult cut‑offs.
例如，一名体重45千克、身高1.50米的学生，其BMI为45 ÷ (1.50 × 1.50) = 20.0 千克/米²。请记住，儿童的BMI要使用按年龄和性别划分的百分位图表进行解读，而非成人界限值。
4. Speed, Distance and Time | 速度、距离和时间
Understanding the relationship between speed, distance and time is fundamental in many sports, from sprinting to cycling. The formula allows you to calculate one variable if the other two are known. In practical PE lessons, you will use this to analyse performance in running events, swimming races or team games where covering distance quickly matters.
理解速度、距离和时间之间的关系是许多运动中的基础，从短跑到自行车运动都是如此。如果你知道其中两个变量，这个公式就可以计算出第三个。在体育实践课中，你会用它来分析跑步项目、游泳比赛或要求快速覆盖距离的团队运动中的表现。
speed = distance ÷ time
速度 = 距离 ÷ 时间
If you run 100 metres in 14 seconds, your average speed is 100 ÷ 14 ≈ 7.14 m/s. You can rearrange the equation: distance = speed × time, and time = distance ÷ speed. Always keep units consistent — metres and seconds, or kilometres and hours.
如果你在14秒内跑完100米，平均速度就是100 ÷ 14 ≈ 7.14 米/秒。你可以将方程变形为：距离 = 速度 × 时间，以及时间 = 距离 ÷ 速度。务必保持单位一致——同时使用米和秒，或公里和小时。
5. Work and Power in Physical Activity | 体育活动中的功与功率
Work is done when a force moves an object through a distance in the direction of the force. Power measures how quickly that work is performed. These concepts explain why explosive athletes can generate high forces in very short time frames and why technique that reduces wasted motion can improve efficiency.
当力使物体沿力的方向移动一段距离时就做了功。功率衡量的是完成功的快慢。这些概念解释了为什么爆发力强的运动员能在极短的时间内产生很大的力，以及为什么减少多余动作的技术能提高效率。
work = force × distance
功 = 力 × 距离
power = work ÷ time
功率 = 功 ÷ 时间
Imagine lifting a 5 kg medicine ball vertically through 2 metres. The force needed is approximately the weight, 5 kg × 10 m/s² = 50 N (using g ≈ 10 m/s²). Work done = 50 N × 2 m = 100 J. If you complete the lift in 0.5 seconds, power output = 100 J ÷ 0.5 s = 200 W. Higher power output means more explosive strength.
设想将一个5千克的药球垂直举起2米。所需的力大约为其重量，5 kg × 10 m/s² = 50 N（取g ≈ 10 m/s²）。做功 = 50 N × 2 m = 100 J。如果在0.5秒内完成这次举球，输出功率 = 100 J ÷ 0.5 s = 200 W。更高的输出功率意味着更强的爆发力。
6. Newton’s Laws of Motion in Sport | 运动中的牛顿定律
Sir Isaac Newton’s three laws of motion form the basis of biomechanics and explain how forces affect movement in every sport. Understanding these laws will help you improve starting technique, tackle safely in rugby, or hit a ball with greater control and power.
艾萨克·牛顿爵士的三大运动定律构成了生物力学的基础，并解释了力如何在各项运动中影响运动表现。理解这些定律有助于你改进起跑技术、在橄榄球中安全擒抱，或以更强的控制和力量击球。
First Law (Inertia): An object remains at rest or in uniform motion unless acted upon by an external force. A football will stay still on the penalty spot until kicked. A sprinter will continue moving forward after the finish line unless they apply braking forces.
第一定律（惯性定律）：物体将保持静止或匀速直线运动状态，除非有外力迫使它改变。足球在点球点上会保持静止，直到被踢起。短跑运动员冲过终点后仍会继续向前运动，除非他们施加制动力量。
Second Law (Acceleration): Force = mass × acceleration. The harder you throw a lighter shot put (or use a heavier shot with the same force), the greater the acceleration change. This explains why technique must match force application.
第二定律（加速度定律）：力 = 质量 × 加速度。你以相同的方式投掷较轻的铅球（或用同样的力投掷更重的铅球），加速度的变化会不同。这说明了为什么技术必须与力量运用相匹配。
Third Law (Action‑Reaction): For every action there is an equal and opposite reaction. When you push backwards against the starting blocks, the blocks push you forward. This is how swimmers propel themselves off the wall.
第三定律（作用力与反作用力定律）：每一个作用力都有一个大小相等、方向相反的反作用力。当你向后蹬起跑器时，起跑器会给你一个向前的推力。游泳运动员蹬壁就是这样获得推进力的。
7. Levers and Mechanical Advantage in the Body | 人体杠杆与机械效益
Your skeleton acts as a system of levers. A lever has a pivot (fulcrum), an effort force and a load. There are three classes of lever, and knowing which one is operating helps you understand why certain muscles are so strong or can move limbs quickly.
你的骨骼就像一个杠杆系统。杠杆由支点、动力和阻力组成。杠杆分为三类，了解正在使用的是哪一类有助于你理解为什么某些肌肉力量强大，或者为什么某些动作能让肢体快速移动。
First‑class lever: Fulcrum is between effort and load, like the neck nodding movement. Second‑class lever: Load is between fulcrum and effort, like standing on tiptoe (calf muscle). This offers mechanical advantage for strength. Third‑class lever: Effort is between fulcrum and load, like a bicep curl. This is the most common lever in the body and favours range and speed of movement over force.
第一类杠杆：支点在动力与阻力之间，例如颈部点头动作。第二类杠杆：阻力在支点与动力之间，如踮脚尖站立（小腿肌肉）。这类杠杆为力量提供了机械效益。第三类杠杆：动力在支点与阻力之间，如肱二头肌弯举。这是人体中最常见的杠杆形式，以牺牲力量为代价换来更大的运动范围和速度。
Analyse a basketball shot: the elbow acts as the fulcrum, the triceps apply effort behind the fulcrum, and the ball in the hand is the load. It is a third‑class lever, designed for speed release.
分析投篮动作：肘部是支点，肱三头肌在支点后方施加力量，手中的篮球是阻力。这是一个第三类杠杆，专为快速出手而设计。
8. The FITT Principle for Training | 训练的FITT原则
The FITT principle is a set of guidelines to help you design a safe, effective exercise programme. FITT stands for Frequency, Intensity, Time and Type. By adjusting these variables, you can progress your training or target different components of fitness.
FITT原则是一套指导方针，帮助你设计安全有效的锻炼计划。FITT代表频率、强度、时间和类型。通过调整这些变量，你可以逐步推进训练，或针对不同的体能要素进行锻炼。
- Frequency: How often you exercise, e.g., 3‑5 times per week.
- 频率：锻炼的频率，例如每周3‑5次。
- Intensity: How hard you work, often measured via heart rate or RPE.
- 强度：锻炼的强度，通常用心率或RPE来衡量。
- Time: Duration of each session, e.g., 30‑60 minutes.
- 时间：每次锻炼的持续时间，例如30‑60分钟。
- Type: The kind of exercise performed, such as running, swimming or circuit training.
- 类型：所进行的运动种类，例如跑步、游泳或循环训练。
A Year 7 student aiming to improve aerobic endurance might start with Frequency 3 times/week, Intensity 65 % of MHR, Time 20 minutes continuous activity, and Type jogging. As fitness improves, one or more of the FITT factors can be increased.
一名七年级学生如果希望提高有氧耐力，可以从频率每周3次、强度65%最大心率、持续时间20分钟的连续活动，以及类型慢跑开始。随着体能提升，可以增加FITT中的一项或多项因素。
9. SMART Goal Setting in PE | 体育中的SMART目标设定
Setting clear goals is important for motivation and improvement. The SMART framework ensures your goals are Specific, Measurable, Achievable, Relevant and Time‑bound. This theorem of goal setting is used across sports and physical education to help you focus your efforts.
设定清晰的目标对激励和改进至关重要。SMART框架确保你的目标是具体的、可衡量的、可实现的、相关的并且有时间限制。这一目标设定原理广泛应用于体育运动中，以帮助你集中精力。
SMART breakdown: Specific — ‘I want to improve my bleep test score’; Measurable — ‘by 2 levels’; Achievable — ‘I will train twice a week’; Relevant — ‘this will help in football matches’; Time‑bound — ‘by the end of this half term’.
SMART细分：具体的——’我想提高我的哔哔声折返跑成绩’；可衡量的——’提升2级’；可实现的——’我将每周训练两次’；相关的——’这会有助于我的足球比赛’；有时间限制的——’在本半学期结束前’。
Without a deadline and a way to measure progress, goals often remain wishes. Use this theorem to turn broad aims into action plans.
如果没有截止日期和衡量进步的方法，目标往往就只是愿望。运用这一原理可以将笼统的目标转化为行动计划。
10. Rate of Perceived Exertion (RPE) Scale | 主观疲劳感觉量表
RPE is a subjective scale that measures how hard you feel your body is working during exercise. It is closely linked to heart rate and can be used alongside or instead of heart rate monitors. The most common version is the modified 1‑10 scale where 1 represents ‘very light activity’ and 10 represents ‘maximal exertion’.
主观疲劳感觉量表是一种主观量表，用于衡量你在运动中感觉身体的努力程度。它与心率紧密相关，可以与心率监测器配合使用或替代之。最常用的版本是修正的1‑10级量表，其中1代表’非常轻松的活动’，10代表’极限用力’。
| RPE | Description | 描述 |
| 1‑2 | Very light | 非常轻松 |
| 3‑4 | Light to moderate | 轻松到中等 |
| 5‑6 | Moderate to somewhat hard | 中等至有些吃力 |
| 7‑8 | Hard | 吃力 |
| 9 | Very hard | 非常吃力 |
| 10 | Maximal effort | 极限用力 |
A practical relationship: RPE × 10 often approximates heart rate. For example, if you rate your exertion at 6, your heart rate may be around 140‑160 bpm depending on fitness. This helps you regulate intensity without stopping to take a pulse.
一个实用的关系：RPE × 10 通常近似心率。例如，如果评分为6，你的心率可能在140‑160 bpm左右，具体取决于体能状况。这有助于你在不停下来测脉的情况下调节强度。
11. Training Thresholds (Aerobic and Anaerobic) | 训练阈值（有氧与无氧）
Training thresholds mark the boundaries between different energy systems. The aerobic threshold is the intensity at which you shift from mainly fat burning to a higher reliance on carbohydrates. The anaerobic threshold is the point where the body starts producing lactate faster than it can be removed, leading to fatigue. These boundaries are often expressed as percentages of maximum heart rate.
训练阈值标志着不同能量系统之间的边界。有氧阈值是身体从主要燃烧脂肪转向更依赖碳水化合物的强度点。无氧阈值是身体开始产生乳酸的速度超过其清除速度的临界点，从而导致疲劳。这些边界通常以最大心率的百分比来表示。
Aerobic training zone: 60‑80 % HRₘₐₓ
有氧训练区：60‑80 % HRₘₐₓ
Anaerobic threshold approx. 80‑90 % HRₘₐₓ
无氧阈值约 80‑90 % HRₘₐₓ
For a 12‑year‑old, the aerobic zone would be approximately 125‑166 bpm. Training just below the anaerobic threshold (around 170 bpm) builds endurance, while short bursts above it develop speed and power. Year 7 activities like interval running or shuttle runs deliberately cross this threshold to improve fitness.
对于12岁的学生，有氧训练区大约为125‑166 bpm。刚好在无氧阈值（约170 bpm）以下进行训练可以提升耐力，而间歇性地突破该阈值的短距离冲刺则能发展速度和爆发力。七年级的间歇跑或折返跑等练习正是有目的地穿越这一阈值来改善体能。
12. Energy Balance Equation | 能量平衡方程
Body weight stays stable when energy intake from food and drink equals energy expenditure from basal metabolism and physical activity. This simple principle underpins all weight management in sport and health. For young athletes, energy balance must support growth, training and recovery.
当从饮食中摄入的能量等于基础代谢与身体活动消耗的能量时，体重保持稳定。这一简单原理是各类运动与健康体重管理的基础。对年轻运动员而言，能量平衡必须支持生长、训练和恢复。
Energy balance = energy in − energy out
能量平衡 = 能量摄入 − 能量消耗
If energy in exceeds energy out over time, weight gain occurs. In PE, you apply this theorem when you plan post‑match snacks or adjust meal patterns to fuel a morning cross‑country run. Kilocalories (kcal) and kilojoules (kJ) are the units used to measure energy.
如果长期能量摄入大于能量消耗，体重就会增加。在体育课中，当你规划赛后点心或为晨间越野跑调整饮食模式时，就是在应用这一定理。千卡（kcal）和千焦（kJ）是衡量能量的单位。
Published by TutorHao | PE Revision Series | aleveler.com
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