📚 Year 7 AQA Physical Education: Quick Reference Formula & Theorem Handbook | 七年级 AQA 体育：公式定理速查手册
This handbook pulls together the most important equations, principles and rules you need in Year 7 AQA Physical Education. From heart‑rate calculations to the mechanics of movement, every formula is explained with a clear example so you can apply it in lessons, homework and assessments. Keep it handy when you revise for end‑of‑topic tests or prepare practical training plans.
本手册汇集了七年级 AQA 体育课程中最关键的公式、原则和定理。从心率计算到运动力学，每条公式都配有清晰的解释和示例，帮助你在课堂、作业和测评中灵活运用。复习单元测试或设计训练计划时，记得随时查阅。
1. Maximum Heart Rate (MHR) | 最大心率
The simplest way to estimate your maximum heart rate is the age‑based formula. MHR gives the highest number of beats per minute your heart can safely reach during all‑out exercise. It is the starting point for setting training zones.
估算最大心率最简单的方法是基于年龄的公式。最大心率表示你在全力运动中每分钟心跳的最高安全值，是设定训练区间的起点。
MHR = 220 – age (years)
For a Year 7 student aged 11, MHR ≈ 220 – This is a theoretical maximum and varies between individuals, but it works well for whole‑class planning.
以一名 11 岁的七年级学生为例，MHR ≈ 220 – 11 = 209 次/分。这是理论值，存在个体差异，但在全班计划中应用效果良好。
2. Target Heart Rate Zones | 目标心率区间
Once you know MHR, you can calculate the heart‑rate bands that produce different fitness benefits. Moderate intensity builds basic endurance; vigorous intensity develops cardiovascular fitness more quickly.
确定最大心率后，就可以计算不同健身目标对应的心率区间。中等强度有助建立基础耐力；剧烈强度则能更快提升心血管适能。
Moderate zone = 50% – 70% × MHR
Vigorous zone = 70% – 85% × MHR
Example for age 11 (MHR 209 bpm): Moderate = 105–146 bpm; Vigorous = 146– k your pulse for 15 seconds and multiply by 4 to see if you are working in the right zone.
以 11 岁（MHR 209 次/分）为例：中等强度区间为 105–146 次/分；剧烈强度区间为 146–178 次/分。在实操课上，你可以测量 15 秒脉搏并乘以 4，判断自己是否处于目标区间。
3. Heart Rate Reserve & the Karvonen Formula | 储备心率与卡沃宁公式
The Karvonen formula uses resting heart rate (RHR) to make personal training zones more accurate. It calculates how many beats you have 'in reserve' above rest, then adds a percentage of that reserve back to RHR.
卡沃宁公式引入静息心率（RHR），使个人训练区间更精确。它先算出你安静时以上的“储备”心跳数，再按训练强度取百分数加回静息心率。
Target HR = RHR + [Intensity % × (MHR – RHR)]
Measure RHR first thing in the morning. If a 12‑year‑old has RHR = 70 bpm and MHR = 208 bpm, the reserve is 138 bpm. For 60% 8 = 70 + 83 = 153 bpm. This method is frequently used in GCSE PE and worth learning early.
静息心率应在清晨醒来时测量。假设一名 12 岁学生 RHR = 70 次/分，MHR = 208 次/分，储备心率为 138 次/分。按 60% 强度计算：目标心率 = 70 + 0.6×138 = 153 次/分。该方法在 GCSE 体育中常用，值得尽早掌握。
4. Body Mass Index (BMI) | 身体质量指数
BMI is a quick screening tool that relates body mass to height. Although it does not distinguish between muscle and fat, it is used in AQA fitness units to discuss healthy weight ranges.
BMI 是一项快速筛查指标，将体重与身高关联。虽然它不能区分肌肉和脂肪，但在 AQA 健康体适能单元中用于探讨健康体重范围。
BMI = weight (kg) ÷ height² (m²)
g/m². This falls in the healthy weight category. Always practise converting height from cm to m before squaring.
计算示例：一名学生体重 45 kg，身高 1.55 m。身高² = 1.55×1.55 = 2.4025 m²。BMI = 45 ÷ 2.4025 ≈ 18.7 kg/m²，属于健康体重范围。计算前务必先将身高从厘米换算为米再平方。
5. FITT Principle | FITT 原则
FITT is the framework used to design any exercise programme. Every session can be adjusted using its four elements, making it a powerful 'theorem' for progression.
FITT 是设计所有运动计划的框架。每个训练课都可以通过它的四个要素进行调整，是进步的核心“定理”。
Frequency – how often you exercise. Starting point: 3 days per week for beginners.
频率 – 运动的频繁程度。初学者可从每周 3 天起步。
Intensity – how hard you work, often measured by heart rate or RPE.
强度 – 运动强度，常用心率或主观疲劳量表衡量。
Time – duration of each session. Minimum 20 minutes of continuous activity for aerobic benefit.
时间 – 每次训练的持续时间。有氧益处的最低连续活动时间为 20 分钟。
Type – the kind of exercise, e.g. running, cycling, swimming, or team sports.
类型 – 运动种类，如跑步、骑行、游泳或团队运动。
To improve fitness, change one FITT variable at a time while keeping a training diary. This systematic approach is the foundation of all periodised plans.
提升体能时，每次只改变一个 FITT 变量并记录训练日志。这种系统方法是一切周期性训练计划的基础。
6. SPORT Training Principles | SPORT 训练原则
Beyond FITT, the broader principles of training are often remembered as SPORT. They explain how the body adapts and why rest is essential.
除了 FITT，更广泛的训练原则通常记为 SPORT。它们解释身体如何适应以及为什么休息至关重要。
Specificity – training must match the sport or goal. A sprinter practises short, fast bursts.
针对性 – 训练必须匹配运动项目或目标。短跑运动员练习短距离快速爆发。
Progression – gradually increase workload to keep challenging the body.
渐进性 – 逐步增加负荷，持续挑战身体。
Overload – work harder than normal to force adaptation. Use FITT to apply overload safely.
超负荷 – 通过高于平常的负荷迫使身体适应。利用 FITT 安全地施加超负荷。
Reversibility – fitness is lost when training stops. 'Use it or lose it' applies to all components of fitness.
可逆性 – 停止训练后体适能会下降。“用进废退”适用于所有体适能要素。
Tedium – avoid boredom by varying training. Variety keeps motivation high and works different muscle groups.
多样性 – 通过变化训练避免枯燥。多样性维持高动机并锻炼不同肌群。
7. Rating of Perceived Exertion (RPE) | 主观疲劳量表
RPE, also called the Borg Scale, rates exercise intensity from 6 (no exertion) to 20 (maximal exertion). It is especially useful when heart‑rate monitors are not available.
主观疲劳量表又称博格量表，将运动强度从 6（毫不费力）到 20（极度费力）进行分级。在没有心率监测设备时特别实用。
Estimated HR ≈ RPE × 10
If you rate your effort as 12, your heart rate is likely around 120 bpm. In Year 7, you mainly use the simpler 1–10 version where 1 is resting and 10 is maximum effort. Linking RPE to heart rate helps you tune into your body's signals.
若自评 12 级，心率大约在 120 次/分。七年级主要使用简化版 1–10 级量表，1 为静止，10 为最大努力。将 RPE 与心率关联，有助于你感知身体信号。
8. Speed, Distance and Time | 速度、距离与时间
The relationship between speed, distance and time underpins most movement analysis and is tested regularly in practical and written work.
速度、距离和时间之间的关系是大多数运动分析的基础，在实践与书面作业中经常考查。
Speed = Distance ÷ Time
Distance ÷ Speed. These three forms are essential for interpreting sprint times and multi‑stage fitness test data.
单位：体育情境中多用米/秒（m/s）。若一名学生用 15 秒跑完 100 米，速度 = 100 ÷ 15 = 6.67 m/s。公式变形：距离 = 速度 × 时间，时间 = 距离 ÷ 速度。这三个公式对分析短跑成绩和多阶段体能测试数据至关重要。
9. Force, Mass and Acceleration | 力、质量与加速度
Newton’s Second Law explains how an object’s motion changes when a force is applied. In sport, greater force production can lead to faster acceleration – a key concept for sprinters and throwers.
牛顿第二定律解释施加力后物体运动如何改变。在体育中，产生更大的力可带来更快的加速度——这对短跑和投掷运动员是关键概念。
Force = Mass × Acceleration (F = m × a)
Force is measured in newtons (N), mass in kilograms (kg) and acceleration in metres per second squared (m/s²). Example: a 2 kg medicine ball accelerated at 4 m/s² requires 8 N of force. Understanding this helps you analyse why lighter implements can be thrown faster.
力以牛顿（N）为单位，质量以千克（kg）为单位，加速度以米/秒²（m/s²）为单位。例如，将 2 kg 药球以 4 m/s² 加速度推出需 8 N 力。理解这一点能帮助你分析为何较轻的器械能被更快投出。
10. Levers and Mechanical Advantage | 杠杆与机械效益
Most body movements work as levers. Knowing the arrangement helps you judge whether a system is built for speed or for strength. Mechanical advantage tells you if effort is magnified.
大多数身体运动都是杠杆作用。了解杠杆排列能帮你判断一个系统是为速度还是为力量而设计。机械效益说明力量是否被放大。
Mechanical Advantage = Effort Arm ÷ Load Arm
In a second‑class lever (e.g. standing on tiptoes), the load is between the fulcrum and the effort, giving mechanical advantage > 1 – you can lift a heavy load with less effort. In a third‑class lever (e.g. biceps curl), the effort is between the fulcrum and load, producing high speed but low mechanical advantage. Year 7 students should recognise the three lever classes and label fulcrum, effort and load on simple diagrams.
在第二类杠杆（如踮脚尖）中，负荷位于支点与力点之间，机械效益 > 1，能以较小力举起重物。在第三类杠杆（如肱二头肌弯举）中，力点位于支点与负荷之间，产生高速但机械效益低。七年级学生应能辨认三类杠杆并在示意图上标出支点、力点和负荷。
11. Aerobic and Anaerobic Thresholds | 有氧与无氧阈值
Thresholds mark the exercise intensity at which the body’s energy systems shift. The aerobic threshold is where fat burning is optimised; the anaerobic threshold is the point where lactate accumulates quickly.
阈值标志着运动强度下身体供能系统的转换点。有氧阈值是燃脂最优化的强度点；无氧阈值是乳酸迅速堆积的临界点。
Aerobic threshold ≈ 60%–70% MHR
Anaerobic threshold ≈ 80%–90% MHR
For an 11‑year‑old, aerobic threshold ≈ 125–146 bpm; anaerobic threshold ≈ 167– below anaerobic threshold you can talk comfortably; above it, speaking becomes difficult.
对于 11 岁学生，有氧阈值约 125–146 次/分，无氧阈值约 167–188 次/分。七年级虽不要求精确的实验室测试，但你可以通过感受来区分：无氧阈值以下可以轻松交谈；超过后说话变得困难。
12. Work and Power in Simple Movements | 简单动作中的功与功率
Work measures the energy transferred when a force moves an object. Power tells you how quickly that work is done – the difference between a steady climb and an explosive jump.
功衡量力使物体移动所传递的能量。功率则表明做功能多快——这就是缓慢攀登与爆发跳跃的区别。
Work = Force × Distance (W = F × d)
Power = Work ÷ Time (P = W ÷ t)
10 = 25 W. You can use these equations to compare power output in standing jumps and step‑ups during fitness testing.
若将 10 kg 重物（力约 100 N）垂直上举 0.5 m，功 = 100 × 0.5 = 50 J。若在 10 秒内完成 5 次，总功 = 250 J，功率 = 250 ÷ 10 = 25 W。在体能测试中，你可以用这些方程比较纵跳和台阶练习的功率输出。
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