📚 Year 10 Eduqas PE: Formula & Theorem Quick Reference Guide | Eduqas十年级体育：公式定理速查手册
Welcome to the Year 10 Eduqas PE Formula & Theorem Quick Reference Guide. This resource compiles essential formulas and principles across physiology, biomechanics, and training that you need to master for your assessments. Use it regularly to reinforce your understanding and sharpen your calculation skills.
欢迎使用Year 10 Eduqas体育公式定理速查手册。本资源汇总了生理学、生物力学与训练学中你必须掌握的核心公式与原理，助你巩固理解、提升计算能力，轻松应对考试。
1. Heart Rate & Maximum Heart Rate | 心率与最大心率
The simplest estimate of maximum heart rate (MHR) is given by the equation:
最大心率（MHR）的最简单估算公式为：
MHR = 220 - age
but actual MHR can vary by ±12 beats per minute depending on genetics and fitness levels.
此公式提供基础估值，但实际最大心率会因遗传和体能水平产生±12次/分钟的偏差。
It is important to remember that MHR is not increased by training; it tends to decline slightly with age.
重要的是要记住，训练不会提高最大心率；它通常会随着年龄增长而略微下降。
For adolescents, the 220 - age rule still applies, although individual monitoring during maximal exercise is more accurate.
对于青少年来说，220减去年龄的法则同样适用，尽管在极量运动中进行个体监测会更准确。
2. Karvonen Formula for Target Heart Rate | 卡氏目标心率公式
The Karvonen formula uses heart rate reserve (HRR) to prescribe exercise intensity more precisely:
卡氏公式利用心率储备（HRR）更精确地制定运动强度：
Target HR = Resting HR + (Intensity × (MHR - Resting HR))
Here, Intensity is expressed as a decimal (e.g., 0.6 for 60%).
式中，强度用小数表示（如0.6代表60%）。
For example, a 15-year-old with a resting HR of 70 bpm wants to train at 70% intensity. MHR = 205 bpm. Target HR = 70 + 0.7 × (205 - 70) = 70 + 94.5 = 164.5 bpm.
例如，一名15岁学生，静息心率70次/分，想以70%强度训练。MHR=205次/分。目标心率= 70 + 0.7 × (205 - 70) = 70 + 94.5 = 164.5次/分。
This formula accounts for fitness level via resting HR; a lower resting HR results in a higher training target for the same percentage.
该公式通过静息心率体现了体能水平；静息心率越低，相同百分比下的训练目标心率反而越高。
3. Training Zones & Percentages | 训练区间与百分比
Training zones can be defined using %MHR or %HRR. The most common zones for aerobic training are:
训练区间可用最大心率百分比或心率储备百分比定义。有氧训练最常见的区间如下：
| Zone | Intensity | 中文区间 | 强度 |
|---|---|---|---|
| Very Light | < 50% MHR | 极低强度 | < 50% MHR |
| Light | 50-60% MHR | 低强度 | 50-60% MHR |
| Moderate | 60-70% MHR | 中等强度 | 60-70% MHR |
| Hard | 70-85% MHR | 高强度 | 70-85% MHR |
| Maximal | > 85% MHR | 极大强度 | > 85% MHR |
Using HRR via the Karvonen formula gives similar zones but with slightly higher target numbers for fitter individuals.
通过卡氏公式使用心率储备会得出相似的区间，但体能较好者的目标心率数值会略高。
Aerobic training usually aims for 60-80% MHR or 60-80% HRR to improve cardiovascular endurance.
有氧训练通常以60-80%最大心率或60-80%心率储备为目标，以改善心血管耐力。
4. Cardiac Output (Q) | 心输出量
Cardiac output is the volume of blood pumped by the heart per minute. The formula is:
心输出量是心脏每分钟泵出的血液量。公式为：
Q = Stroke Volume (SV) × Heart Rate (HR)
Stroke volume is the amount of blood pumped per beat, typically 70 ml at rest for an untrained person.
每搏输出量是每次心跳泵出的血量，未经训练者静息时通常约为70毫升。
During maximal exercise, SV can double and HR can triple, causing Q to rise from about 5 L/min to over 20 L/min in athletes.
在极量运动中，每搏输出量可加倍，心率可增加两倍，使心输出量从约5升/分钟升至运动员的20升/分钟以上。
Training increases both SV and the heart's efficiency, so a trained person achieves the same Q with a lower HR at rest.
训练能同时提高每搏输出量和心脏效率，因此受过训练的人用较低的静息心率即可达到同样的心输出量。
5. Pulmonary Ventilation (VE) | 肺通气量
Minute ventilation refers to the volume of air moved in and out of the lungs per minute:
每分通气量指每分钟进出肺部的空气量：
VE = Tidal Volume (TV) × Respiratory Frequency (f)
Tidal volume is the air exchanged per breath (approx. 500 ml at rest), and f is breaths per minute (approx. 12-15 at rest).
潮气量为每次呼吸交换的空气量（静息时约500毫升），f为每分钟呼吸次数（静息时约12-15次）。
Thus, resting ventilation is about 6-7.5 L/min, but during intense exercise it can increase dramatically to over 100 L/min.
因此，静息肺通气量约为6-7.5升/分钟，但在剧烈运动时可急剧升至100升/分钟以上。
Training improves respiratory muscle endurance and maintains higher TV without a proportional rise in f, making breathing more efficient.
训练能提高呼吸肌耐力，维持更高的潮气量而不使呼吸频率成正比上升，从而使呼吸更高效。
6. Body Mass Index (BMI) | 身体质量指数
BMI is a simple screening tool for weight categories. It is calculated as:
BMI是一种简单的体重分类筛查工具。计算公式为：
BMI = Weight (kg) / (Height (m))²
eight of 1.70 m has a BMI of 65 / (1.70²) = 22.5 kg/m², which is within the healthy range.
例如，体重65千克、身高1.70米的人，其BMI为65/(1.70²)=22.5千克/米²，处于健康范围。
tions are: Underweight (<18.5), Healthy (18.5-24.9), Overweight (25-29.9), Obese (≥30).
一般分类为：偏瘦（<18.5）、健康（18.5-24.9）、超重（25-29.9）、肥胖（≥30）。
Although BMI does not distinguish muscle from fat, it remains a useful indicator in population studies and for initial health screening.
尽管BMI不能区分肌肉和脂肪，但在人群研究和初步健康筛查中仍然是一个有用的指标。
7. Speed, Velocity & Acceleration | 速率、速度与加速度
In biomechanics, we distinguish between scalar and vector quantities:
在生物力学中，我们区分标量和向量：
Speed (m/s) = Distance (m) / Time (s)
Velocity (m/s) = Displacement (m) / Time (s)
Displacement is the shortest straight-line distance from start to finish, with direction.
位移是从起点到终点的最短直线距离，且带有方向。
Acceleration is the rate of change of velocity. It is positive when speeding up in the direction of motion.
加速度是速度的变化率。在运动方向上加速时，加速度为正。
Acceleration (m/s²) = (Final Velocity - Initial Velocity) / Time
a = (v - u) / t
For example, a sprinter who increases velocity from 3 m/s to 9 m/s over 2 seconds has an acceleration of 3 m/s².
例如，短跑运动员在2秒内将速度从3米/秒增加到9米/秒，其加速度为3米/秒²。
Negative acceleration (deceleration) occurs when slowing down. Understanding these concepts helps analyse sprint starts and agility movements.
负加速度（减速）发生在速度降低时。理解这些概念有助于分析起跑和敏捷性动作。
8. Force, Mass & Acceleration (Newton's Second Law) | 力、质量与加速度（牛顿第二定律）
Newton's second law links the force applied to an object, its mass, and the resulting acceleration:
牛顿第二定律将施加于物体的力与其质量和产生的加速度联系起来：
Force (N) = Mass (kg) × Acceleration (m/s²)
In sport, this explains why a heavier shot put requires more force to achieve the same acceleration, or why increasing force application in a kick accelerates the ball more.
在运动中，这解释了为何更重的铅球需要更大的力才能达到相同的加速度，以及为何踢球时加大用力会使球加速更快。
It also applies to the athlete's own body: to jump higher, the athlete must push against the ground with enough force to create upward acceleration greater than gravity (9.8 m/s²).
这同样适用于运动员自身：要跳得更高，运动员必须向地面施加足够的力，产生大于重力（9.8米/秒²）的向上加速度。
Impulse is the product of force and time; applying force over a longer time can increase momentum change.
冲量是力与时间的乘积；在较长时间内施加力可以增加动量变化。
9. Levers & Mechanical Advantage | 杠杆与机械效益
In the human body, bones act as levers, joints as fulcrums, and muscles provide the effort. The mechanical advantage (MA) of a lever system determines its efficiency:
在人体中，骨骼充当杠杆，关节充当支点，肌肉提供动力。杠杆系统的机械效益（MA）决定了其效率：
Mechanical Advantage = Effort Arm / Resistance Arm
The effort arm is the distance from the fulcrum to the point of muscle attachment; the resistance arm is the distance from the fulcrum to the load.
力臂为支点到肌肉附着点的距离；阻力臂为支点到负荷的距离。
First-class levers (e.g., nodding the head) have the fulcrum between effort and load. Second-class levers (e.g., calf raise) have the load between fulcrum and effort, always giving MA > 1. Third-class levers (e.g., biceps curl) have the effort between fulcrum and load, usually MA < 1, favouring speed and range of motion over force.
第一类杠杆（如点头动作）支点在动力与负荷之间。第二类杠杆（如提踵）负荷在支点和动力之间，机械效益总大于1。第三类杠杆（如肱二头肌弯举）动力在支点和负荷之间，机械效益通常小于1，以牺牲力量换取速度和活动幅度。
Most human movements involve third-class levers, which explains why we are fast but relatively weak compared to the loads our muscles must move.
大多数人体运动以第三类杠杆为主，这解释了为什么我们动作快但在克服负荷时力量相对较弱。
10. Energy Expenditure & METs | 能量消耗与代谢当量
cost. 1 MET = resting metabolic rate (≈3.5 ml O₂/kg/min). To estimate energy expenditure:
代谢当量（MET）是估算能量消耗的单位。1 MET = 静息代谢率（≈3.5毫升氧气/千克/分钟）。要估算能量消耗：
Energy (kcal) = METs × Body Mass (kg) × Time (hours)
A 60 kg person jogging for 30 minutes (0.5 h) burns approximately 8 × 60 × 0.5 = 240 kcal.
例如，以8千米/小时慢跑的能耗约8 METs。一名60千克的人慢跑30分钟（0.5小时）消耗约8 × 60 × 0.5 = 240千卡。
Different activities have standard MET values: walking 3 METs, cycling moderate 6 METs, playing football 7-10 METs.
不同活动有标准MET值：步行3 METs、中等强度骑行6 METs、踢足球7-10 METs。
Understanding METs helps athletes plan fuelling strategies and manage weight balance by comparing energy intake with expenditure.
理解METs有助于运动员制定补给策略，并通过比较能量摄入与消耗来管理体重平衡。
For precise calorie tracking, these estimates are useful but should be adjusted for individual differences in efficiency and body composition.
对于精确热量追踪，这些估算值很有用，但应根据个体效率和身体成分差异进行调整。
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