📚 Year 9 Edexcel PE: Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This quick-reference handbook brings together the essential formulas and principles covered in the Year 9 Edexcel Physical Education curriculum. It includes key equations for fitness testing, training zones, basic biomechanics, and training principles. Use these summaries to reinforce your revision and to sharpen your ability to apply theory to practical examples.
本速查手册汇集了 Year 9 Edexcel 体育课程中的核心公式和定理，涵盖体能测试、训练区间、基础生物力学以及训练原则的关键方程。利用这些总结强化复习，并提升将理论应用于实践的能力。
1. Maximum Heart Rate (MHR) | 最大心率
The maximum heart rate (MHR) is the highest number of beats per minute your heart can achieve during all‑out exercise. A simple estimate, widely used in schools, is calculated by subtracting your age from 220. This value helps set safe exercise intensity limits.
最大心率（MHR）是指尽全力运动时心脏每分钟能够达到的最高搏动次数。学校中普遍使用的简单估算方法是220减去年龄，该数值有助于设定安全的运动强度上限。
MHR = 220 − age
2. Heart Rate Reserve & Karvonen Method | 心率储备与卡式公式
e zones for aerobic training, making it more personalised than using a percentage of MHR alone. The formula is: Target HR = RHR + (Intensity × HRR). Intensity is expressed as a decimal (e.g., 0.6 for 60%).
心率储备（HRR）是最大心率与安静心率（RHR）之差。卡式公式利用心率储备计算有氧训练的目标心率区，比单纯使用最大心率百分比更个性化。公式为：目标心率 = 安静心率 + (运动强度 × 心率储备)。强度以小数表示（如60%写为0.6）。
HRR = MHR − RHR
Target HR = RHR + (Intensity × HRR)
3. Body Mass Index (BMI) | 身体质量指数
Body Mass Index provides a rough guide to whether a person has a healthy weight for their height. It is calculated by dividing weight in kilograms by height in metres squared. While easy to use, BMI does not distinguish between lean mass and fat mass.
身体质量指数是衡量体重与身高比例的一个粗略指标，计算方法是体重（kg）除以身高（m）的平方。BMI使用简便，但无法区分瘦体重与脂肪重量。
BMI = weight (kg) ÷ [height (m)]²
4. Speed, Distance and Time | 速度、距离与时间
Speed describes how quickly an athlete covers a distance. It is a scalar quantity, meaning it only has magnitude. The average speed can be found by dividing the total distance travelled by the time taken. This formula is used in sprint analysis and many field tests.
速度描述运动员移动一段距离的快慢程度，它是标量，仅有大小。平均速度等于总路程除以所用时间，常用于短跑分析和多项实地测试。
Average speed (v) = distance (d) ÷ time (t)
5. Acceleration | 加速度
Acceleration is the rate at which velocity changes. It is a vector quantity, so direction matters. If an athlete speeds up, slows down or changes direction, acceleration is present. The average acceleration is the change in velocity divided by the time taken for that change.
加速度描述速度变化的快慢，是矢量，方向至关重要。运动员加速、减速或改变方向时均存在加速度。平均加速度等于速度变化量除以发生该变化的时间。
a = Δv ÷ t
where Δv = final velocity − initial velocity
6. Force, Mass and Newton’s Second Law | 力、质量与牛顿第二定律
Newton’s Second Law states that the force applied to an object equals its mass multiplied by its acceleration. In sport, this explains how a greater force applied to a shot, ball, or sprinter’s legs results in greater acceleration, provided mass remains constant.
牛顿第二定律指出，施加在物体上的力等于其质量乘以加速度。在运动中，这解释了为什么在对铅球、球或短跑运动员双腿施加的力更大时，只要质量不变，加速度就更大。
Force (F) = mass (m) × acceleration (a)
Units: Newtons (N), kg, m/s²
7. Work, Energy and Power | 功、能与功率
Work is done when a force moves an object. Energy is the capacity to do work, and power measures how quickly work is performed. In sport, explosive actions demand high power output. The formulas below link these concepts and help analyse athletic performance.
当力使物体移动时即做了功。能量是做功的本领，功率则衡量做功的快慢。运动中爆发性动作需要高功率输出。下列公式连接这些概念，有助于分析运动表现。
| Work (W) = Force (F) × distance (d) | 单位：焦耳 (J) |
| Power (P) = Work (W) ÷ time (t) | 单位：瓦特 (W) |
| Power (P) = Force (F) × velocity (v) | 用于恒定速度时 |
8. Levers and Moments | 杠杆与力矩
Levers consist of a rigid bar, a fulcrum (pivot), an effort force and a load. The turning effect of a force is called a moment. The moment depends on the size of the force and the perpendicular distance from the fulcrum. In the human body, bones act as levers, joints are fulcrums, and muscles provide the effort.
杠杆由刚性杆、支点、动力和阻力组成。力的转动效应称为力矩，其大小取决于力的大小及其到支点的垂直距离。人体中，骨骼为杠杆，关节为支点，肌肉提供动力。
Moment (M) = Force (F) × perpendicular distance from fulcrum (d)
单位：牛顿米 (Nm)
9. Mechanical Advantage | 机械优势
Mechanical advantage (MA) indicates how effectively a lever amplifies an effort force. It is the ratio of the effort arm length to the resistance arm length. An MA greater than 1 means the lever multiplies the effort, making it easier to move a heavy load, while an MA less than 1 allows faster, wider movements at the expense of force.
机械优势（MA）反映杠杆省力的程度，等于动力臂长度与阻力臂长度之比。MA大于1时，杠杆省力，便于移动重物；MA小于1时，能以牺牲力为代价换取更大、更快的运动幅度。
Mechanical Advantage = Effort arm length ÷ Resistance arm length
10. Principle of Moments & Equilibrium | 力矩原理与平衡
For a lever to be in equilibrium (balanced), the total clockwise moment must equal the total anticlockwise moment. This principle is fundamental to understanding balance and stability in static positions, such as a gymnastic handstand or a start position in sprinting.
杠杆平衡的条件是总顺时针力矩等于总逆时针力矩。该原理对理解静止姿势（如体操手倒立或短跑起跑姿势）中的平衡与稳定性至关重要。
Total clockwise moment = Total anticlockwise moment
11. FITT Principle (Training) | FITT 训练原则
The FITT principle provides a framework for designing an effective exercise programme. It stands for Frequency, Intensity, Time and Type. By manipulating these variables, athletes can apply overload and continue making progress. The FITT principle works alongside specificity, ensuring the training is tailored to the activity.
FITT原则为设计有效锻炼计划提供了框架，分别代表频率、强度、时间和类型。通过调整这些变量，运动员可施加超负荷并持续取得进步。FITT原则与专项性原则结合，确保训练针对特定活动量身定制。
| FITT Component | Description |
|---|---|
| Frequency | How often training occurs (e.g., sessions per week) |
| Intensity | How hard the exercise is (e.g., % of MHR, weight lifted) |
| Time | Duration of each session or activity |
| Type | Mode of exercise (e.g., running, swimming, resistance) |
12. SPORT & RRR Principles | SPORT 与 RRR 原则
The principles of training are often remembered using SPORT and the three R's. SPORT stands for Specificity, Progression, Overload, Reversibility and Tedium. The three R's — Rest, Recovery and Reversibility — remind us that adaptation occurs during recovery, and without rest or if training ceases, fitness gains are lost.
训练原则常用SPORT和三个R来记忆。SPORT代表专项性、渐进性、超负荷、可逆性和单调性。三个R（休息、恢复和可逆性）强调适应发生在恢复期；缺乏休息或停止训练，体能增益会丢失。
- Specificity: training must match the demands of the sport. / 训练须匹配运动项目需求。
- Progression: gradually increase workload as the body adapts. / 随着身体适应，逐步增加负荷。
- Overload: work beyond the normal level using FITT. / 通过FITT使机体承受超出日常的负荷。
- Reversibility: fitness declines when training stops. / 停止训练后体能会下降。
- Tedium: variety prevents boredom and maintains motivation. / 训练多样性避免枯燥并保持动力。
Adaptation = Training stimulus + Recovery
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