📚 Year 9 WJEC PE: Formula and Principles Quick Reference Guide | Year 9 WJEC 体育：公式定理速查手册
This quick reference guide covers the essential formulas and principles you need for Year 9 WJEC Physical Education. From calculating heart rate zones to understanding basic mechanics, these fundamentals will support your practical performance and theory exams. Use this handbook to revise key equations, training concepts and movement science.
本速查手册涵盖 Year 9 WJEC 体育课程所需的基本公式和原理。从计算心率区间到理解基础力学，这些基础知识将助力你的实践表现和理论考试。使用本手册复习关键公式、训练概念和运动科学。
1. Maximum Heart Rate and Target Heart Rate Zones | 最大心率与靶心率区间
The maximum heart rate (HRmax) is the theoretical highest number of times your heart can beat per minute during exhaustive exercise. It is commonly estimated using a simple age-based formula.
最大心率（HRmax）是理论上的在力竭运动中你心脏每分钟可以跳动的最高次数。通常使用基于年龄的简单公式进行估算。
HRmax = 220 – age (in years)
For example, a 14‑year‑old student has an estimated HRmax of 206 beats per minute (bpm). This value serves as the baseline for setting training intensities.
例如，一名 14 岁学生的估算 HRmax 为 206 次/分（bpm）。该值可作为设定训练强度的基准。
To train effectively, you should work within target heart rate zones expressed as a percentage of your HRmax. Moderate‑intensity exercise typically uses 50–70% HRmax, while vigorous activity targets 70–85% HRmax.
为了有效训练，你应在以 HRmax 百分比表示的靶心率区间内运动。中等强度运动通常使用 50–70% HRmax，而高强度活动则瞄准 70–85% HRmax。
Target HR = Intensity % × (220 – age)
If a 14‑year‑old aims for vigorous training at 80% intensity: Target HR = 0.80 × (220 – 14) = 0.80 × 206 ≈ 165 bpm.
如果一位 14 岁学生以 80% 强度进行高强度训练：靶心率 = 0.80 × (220 – 14) = 0.80 × 206 ≈ 165 次/分。
A more precise method uses the Karvonen formula, which incorporates resting heart rate (RHR) to calculate heart rate reserve (HRR). This accounts for individual fitness levels.
更精确的方法使用 Karvonen 公式，该公式纳入静息心率（RHR）来计算心率储备（HRR），考虑了个体体能水平。
Target HR = RHR + Intensity % × (HRmax – RHR)
Measuring RHR first thing in the morning provides a baseline. As fitness improves, RHR typically decreases, and training zones can be adjusted.
晨起首先测量 RHR 提供基线。随着体能提升，RHR 通常下降，训练区间可相应调整。
2. Body Mass Index (BMI) | 身体质量指数 (BMI)
Body Mass Index is a simple screening tool used to categorise weight status relative to height. It is widely applied in health and fitness assessments.
身体质量指数是一种简单的筛查工具，用于根据身高划分体重类别，广泛应用于健康与体能评估。
BMI = body mass (kg) ÷ (height in metres)²
nstance, a person weighing 55 kg with a height of 1.65 m has a BMI of 55 ÷ (1.65)² = 20.2.
计算 BMI 时，用公斤体重除以身高（米）的平方。例如，体重 55 公斤、身高 1.65 米的人，BMI = 55 ÷ (1.65)² = 20.2。
The standard classification system interprets BMI values as follows: underweight (less than 18.5), normal weight (18.5–24.9), overweight (25–29.9), and obese (30 or above).
标准分类系统将 BMI 值解读为：低于 18.5 为体重过轻，18.5–24.9 为正常体重，25–29.9 为超重，30 及以上为肥胖。
Although BMI is useful for population studies, it does not distinguish between muscle and fat mass. Very muscular athletes may have a high BMI but low body fat percentage.
虽然 BMI 在群体研究中有用，但它不能区分肌肉与脂肪质量。肌肉发达的运动员可能 BMI 较高但体脂百分比较低。
3. Metabolic Equivalent (MET) and Calorie Expenditure | 代谢当量与卡路里消耗
A MET expresses the energy cost of physical activities. One MET is defined as the resting metabolic rate, roughly 3.5 millilitres of oxygen consumed per kilogram of body mass per minute.
MET 表示身体活动的能量消耗。1 MET 被定义为静息代谢率，大约为每公斤体重每分钟消耗 3.5 毫升氧气。
1 MET = 3.5 ml O₂ · kg⁻¹ · min⁻¹
Activities are assigned MET values: sitting quietly is 1 MET, brisk walking is about 4 METs, and running at 8 km/h is roughly 8 METs. The total energy expenditure can be estimated using weight and duration.
活动被赋予 MET 值：静坐为 1 MET，快走约为 4 METs，以 8 公里/小时的速度跑步约为 8 METs。总能量消耗可根据体重和持续时间进行估算。
Calories burned = MET × body mass (kg) × time (hours)
ly 6 × 50 × 0.75 = 225 kcal. This formula helps plan weight management and energy balance.
例如，一名 50 公斤的学生以 6 METs 骑车 45 分钟（0.75 小时），大约消耗 6 × 50 × 0.75 = 225 千卡。该公式有助于规划体重管理和能量平衡。
4. Speed, Distance and Time | 速度、距离与时间
Speed is the rate at which an object covers distance. In sport, analysing speed helps athletes monitor performance and pacing strategies.
速度是物体通过距离的速率。在运动中，分析速度有助于运动员监测表现和配速策略。
Speed = Distance ÷ Time
. For longer events, speed is often expressed in metres per minute or kilometres per hour.
如果一名 100 米短跑选手以 12.5 秒完成，平均速度为 100 ÷ 12.5 = 8 米/秒。对于更长距离的项目，速度常以米/分钟或公里/小时表示。
Rearranging the formula allows you to solve for any missing variable: Distance = Speed × Time and Time = Distance ÷ Speed. These relationships are fundamental in time‑based sports.
通过变形公式可求解任一变量：距离 = 速度 × 时间 以及 时间 = 距离 ÷ 速度。这些关系在时间主导的运动项目中至为基础。
5. Acceleration | 加速度
Acceleration describes the change in velocity over a period. It is especially relevant in sprint starts, jumping and rapid changes of direction.
加速度描述一段时间内的速度变化，在冲刺起跑、跳跃和快速变向中尤为重要。
Acceleration (a) = (final velocity – initial velocity) ÷ time
a = (v – u) ÷ t
rugby player accelerates from rest (0 m/s) to 6 m/s in 1.5 seconds, the acceleration is (6 – 0) ÷ 1.5 = 4 m/s². A negative value indicates deceleration or braking.
如果一位橄榄球运动员从静止（0 米/秒）加速到 6 米/秒用时 1.5 秒，加速度为 (6 – 0) ÷ 1.5 = 4 米/秒²。负值表示减速或制动。
In many team games, the ability to accelerate quickly can be more important than top speed, allowing players to evade opponents or close down space.
在许多团队比赛中，快速加速的能力可能比最高速度更为重要，能使运动员摆脱对手或压缩空间。
6. Newton’s Second Law: Force, Mass and Acceleration | 牛顿第二定律：力、质量与加速度
Newton’s second law explains how the motion of an object changes when a force is applied. This principle underpins almost every movement in sport.
牛顿第二定律解释了当力作用于物体时其运动如何改变。该原理是体育中几乎所有动作的基础。
Force (F) = mass (m) × acceleration (a)
g experiencing an acceleration of 40 m/s², the applied force is 0.5 × 40 = 20 N (newtons).
用更大力量踢足球时，球加速更快。对于质量为 0.5 公斤、加速度为 40 米/秒² 的球，施加的力为 0.5 × 40 = 20 牛（牛顿）。
In throwing events, the athlete aims to generate a large force over the implement’s mass to maximise acceleration. The same law also governs braking and landing forces, which must be managed to avoid injury.
在投掷项目中，运动员力图对器械质量产生大力以最大化加速度。同一规律也支配着制动力与落地冲击力，必须加以控制以避免受伤。
7. Work Done and Power | 做功与功率
Work done measures the energy transferred when a force moves an object. It is directly related to the force applied and the distance moved in the direction of the force.
做功衡量力移动物体时转移的能量，与施加的力及沿力方向移动的距离直接相关。
Work Done (W) = Force (F) × Distance (d)
of approximately 100 N (10 kg × 10 m/s²). The work done is 100 N × 1.5 m = 150 J (joules).
将 10 公斤的重物垂直提升 1.5 米需要约为 100 牛的力（10 kg × 10 m/s²），做功为 100 N × 1.5 m = 150 焦耳（J）。
Power indicates the rate of work or energy transfer. It is crucial for explosive activities such as jumping and sprinting.
功率表示做功或能量传递的速率，对跳跃和冲刺等爆发性活动至关重要。
Power (P) = Work Done ÷ Time
or Power = Force × Velocity
output is 150 ÷ 0.5 = 300 W (watts). Developing power is a key aim in plyometric training.
若 150 J 的功在 0.5 秒内完成，则输出功率为 150 ÷ 0.5 = 300 瓦（W）。发展功率是爆发力训练的核心目标。
8. Moments and Levers | 力矩与杠杆
A moment is the turning effect of a force around a pivot, commonly observed in the body’s joint actions. Muscles create moments to produce movement.
力矩是力绕支点的转动效果，常见于身体的关节动作。肌肉产生力矩以产生运动。
Moment (torque) = Force × perpendicular distance from pivot
M = F × d
In a bicep curl, the elbow acts as the pivot, the bicep muscle provides the effort, and the weight in the hand is the load. The moment produced must overcome the opposing moment of the load.
在肱二头肌弯举中，肘关节为支点，肱二头肌提供施力，手中的重物为负荷。产生的力矩必须克服负荷的反向力矩。
Lever systems in the body are classified into three classes. Most sporting movements use third‑class levers, where the effort is between the pivot and the load, favouring speed and range of motion over force.
人体中的杠杆系统分为三级。多数体育动作采用第三类杠杆，施力位于支点和负荷之间，以牺牲部分力量为代价换取速度和活动范围。
9. Training Intensity and the FITT Principle | 训练强度与 FITT 原则
The FITT principle is a framework for designing exercise programmes. Each letter represents a variable that can be manipulated to achieve training goals.
FITT 原则是设计运动计划的一个框架。每个字母代表一个可调整的变量，以实现训练目标。
Frequency – How often you train per week. For general fitness, 3–5 sessions per week are recommended, allowing rest days in between.
频率（Frequency） – 每周训练几次。为保持一般体能，建议每周 3–5 次，并在其间安排休息日。
Intensity – How hard you work during a session. Intensity can be monitored using heart rate (as in Section 1), perceived exertion scales, or percentage of one‑repetition maximum in resistance training.
强度（Intensity） – 单次训练中的用力程度。强度可通过心率（如第 1 节）、主观疲劳量表或抗阻训练中单次最大重量的百分比进行监控。
Time – The duration of each exercise bout. For cardiovascular health, the recommendation is often 20–60 minutes of continuous or intermittent activity.
时间（Time） – 每次运动持续的时长。为心血管健康，通常建议进行 20–60 分钟的持续或间歇性活动。
Type – The mode of exercise, such as running, cycling, swimming or team sports. The type should be specific to the fitness component being developed.
类型（Type） – 运动方式，如跑步、骑行、游泳或团队运动。类型应针对正在发展的体能要素具有专项性。
By altering one or more FITT variables, you can apply progressive overload and avoid plateaus. For example, increasing frequency from three to four sessions per week adds training stimulus.
通过改变一个或多个 FITT 变量，你可以施加渐进超负荷并避免停滞。例如，将每周频率从三次增加到四次可增加训练刺激。
10. Overload and Recovery Principles | 超负荷与恢复原则
Progressive overload is the gradual increase of stress placed on the body during training. Without overload, the body does not adapt and performance stagnates.
渐进超负荷指训练过程中逐步增加对身体的压力。没有超负荷，身体不会适应，运动表现便会停滞。
The overload can be achieved by manipulating FITT variables: lifting heavier weights (intensity), performing more sets (time or frequency), or reducing rest intervals. The principle of specificity states that training must be relevant to the desired performance.
超负荷可通过调整 FITT 变量来实现：举起更重重量（强度）、增加组数（时间或频率）或缩短间歇。专项性原则指出训练必须与目标表现相关。
Reversibility warns that fitness gains are lost when training stops or decreases significantly. Even a few weeks of inactivity can reduce cardiovascular endurance and strength.
可逆性原则警示：当训练停止或显著减少时，体能增益会消失。即使几周不活动也可能降低心血管耐力和力量。
Variety helps maintain motivation and ensures all‑round development. Incorporating different activities and training methods reduces boredom and overuse injury risk.
多样性有助于保持动力并确保全面发展。融入不同活动和训练方法可减少枯燥感和过度使用损伤风险。
Adequate recovery, including sleep, nutrition and active rest, is essential for adaptation and performance improvement. The overload–recovery cycle must be balanced to avoid overtraining.
充足的恢复，包括睡眠、营养和积极休息，是适应和提升表现的关键。超负荷与恢复的循环必须平衡，以避免过度训练。
Published by TutorHao | Physical Education Revision Series | aleveler.com
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