📚 Year 8 AQA Physical Education: Formula & Theorem Quick Reference Guide | Year 8 AQA 体育：公式定理速查手册
This quick reference guide brings together the essential formulae and theorems you need for Year 8 AQA Physical Education. It covers heart rate training, biomechanics, fitness testing, and energy systems. Each entry shows the formula, explains what it means, and gives a worked example to help you apply it confidently in lessons and assessments.
本速查手册汇集了 Year 8 AQA 体育学科所需的核心公式与定理，涵盖心率训练、运动生物力学、体能测试和能量系统。每个条目都展示公式、解释其含义，并给出具体示例，帮助你在课堂和考试中自信应用。
1. Maximum Heart Rate (MHR) | 最大心率公式
The maximum heart rate (MHR) is the highest number of beats your heart can achieve in one minute during all‑out exercise. The simplest and most widely used estimation is the age‑based formula.
最大心率（MHR）是心脏在极限运动中一分钟内能达到的最高跳动次数。最简单、最常用的估算方法就是基于年龄的公式。
MHR = 220 − Age
For a Year 8 student aged 12, MHR = 220 − 12 = 208 bpm. This value is a guide, not a fixed limit, and individual variation exists.
对于一名12岁的 Year 8 学生，最大心率 = 220 − 12 = 208 次/分钟。该数值仅为参考，并非绝对上限，存在个体差异。
2. Training Zones | 训练心率区间
Training zones are ranges of heart rate expressed as percentages of MHR. They help you work at the right intensity to develop specific aspects of fitness, such as aerobic endurance or anaerobic power.
训练心率区间是以最大心率百分比表示的心率范围。它们帮助你在合适的强度下训练，以发展特定的体能要素，如有氧耐力或无氧爆发力。
The table below summarises the key training zones for a 12‑year‑old with an MHR of 208 bpm.
下表总结了一名12岁、最大心率208次/分钟学生的关键训练区间。
| Training Zone (English) | 训练区间（中文） | %MHR | Approx. HR (12 yr) |
| Aerobic Endurance | 有氧耐力区 | 60–80% | 125–166 bpm |
| Anaerobic Threshold | 无氧阈区 | 80–90% | 166–187 bpm |
| Maximum Effort | 极限努力区 | 90–100% | 187–208 bpm |
To calculate a lower or upper limit, multiply MHR by the decimal form of the percentage. For instance, the aerobic zone lower limit: 208 × 0.60 = 124.8 bpm.
要计算区间下限或上限，只需将最大心率乘以百分数对应的小数。例如，有氧区下限：208 × 0.60 = 124.8 次/分钟。
3. Body Mass Index (BMI) | 身体质量指数
Body Mass Index is a screening tool that uses height and weight to estimate whether a person has a healthy body mass for their height. It does not measure body fat directly but is useful in population studies.
身体质量指数是一种利用身高和体重来估算体重是否健康的筛查工具。它并非直接测量体脂，但在人群研究中十分有用。
BMI = Mass (kg) ÷ Height² (m)
For a student of mass 45 kg and height 1.55 m: BMI = 45 ÷ (1.55 × 1.55) = 45 ÷ 2.4025 ≈ 18.7 kg/m². A BMI between 18.5 and 24.9 is generally considered healthy for adults; for children, age‑ and sex‑specific centile charts are used.
一名体重45千克、身高1.55米的学生：BMI = 45 ÷ (1.55 × 1.55) = 45 ÷ 2.4025 ≈ 18.7 kg/m²。成人 BMI 在18.5–24.9间通常视为健康；儿童需使用按年龄和性别划分的百分位曲线。
4. Speed, Distance and Time | 速度、距离与时间
Speed describes how quickly an object or athlete covers a distance. In sport, it is often expressed in metres per second (m/s) or kilometres per hour (km/h).
速度描述物体或运动员覆盖距离的快慢。在体育中，常用米每秒（m/s）或千米每小时（km/h）表示。
Speed = Distance ÷ Time
If a sprinter covers 100 m in 12 seconds, speed = 100 ÷ 12 ≈ 8.33 m/s. To convert m/s to km/h, multiply by 3.6: 8.33 × 3.6 ≈ 30 km/h.
如果一名短跑运动员用12秒跑完100米，速度 = 100 ÷ 12 ≈ 8.33 m/s。要将 m/s 转换为 km/h，只需乘以3.6：8.33 × 3.6 ≈ 30 km/h。
The same triangle relationship can be rearranged to find distance (Distance = Speed × Time) or time (Time = Distance ÷ Speed).
同样的三角形关系可以变形求距离（距离 = 速度 × 时间）或时间（时间 = 距离 ÷ 速度）。
5. Power and Work | 功率与功
Power is the rate at which work is done or energy is transferred. Explosive athletes, such as jumpers and throwers, need high power outputs.
功率是做功或能量转换的速率。跳跃、投掷等爆发力项目运动员需要高功率输出。
Power = Work ÷ Time
Work is the product of force and the distance moved in the direction of that force: Work = Force × Distance. Therefore, Power can also be written as:
功是力与沿力方向移动距离的乘积：功 = 力 × 距离。因此，功率也可写作：
Power = (Force × Distance) ÷ Time
Lifting a 20 kg weight (force ≈ 200 N) through 1.5 m in 2 seconds gives: Work = 200 × 1.5 = 300 J, Power = 300 ÷ 2 = 150 W.
将一个20千克的重物（力约为200牛）在2秒内垂直上举1.5米：功 = 200 × 1.5 = 300焦，功率 = 300 ÷ 2 = 150瓦。
6. Levers and Mechanical Advantage | 杠杆与机械效益
Levers are rigid bars that rotate around a fulcrum. The relative lengths of the effort arm and resistance arm determine the mechanical advantage.
杠杆是绕支点转动的刚性杆。力臂和阻力臂的相对长度决定了机械效益。
Mechanical Advantage = Effort Arm ÷ Resistance Arm
When the effort arm is longer than the resistance arm, a smaller effort force can move a larger resistance — this is typical of second‑class levers (e.g. standing on tiptoe). In the body, most levers are third‑class, where the effort arm is shorter, favouring speed and range of motion over force.
当力臂长于阻力臂时，较小的努力力就能移动较大的阻力，这是第二类杠杆的典型特征（如踮脚尖）。人体中大多数杠杆为第三类，力臂较短，牺牲力的优势以换取速度和活动范围。
In a bicep curl, the effort (biceps) acts closer to the elbow fulcrum than the weight in the hand, so mechanical advantage is less than 1.
在肱二头肌弯举中，肱二头肌的着力点比手中的重物更靠近肘关节支点，因此机械效益小于1。
7. Force, Mass and Acceleration | 力、质量与加速度
Newton’s second law of motion relates the force applied to an object, its mass, and the resulting acceleration. This relationship explains how athletes generate speed and change direction.
牛顿第二运动定律将施加于物体的力、质量和产生的加速度联系起来。这一关系解释了运动员如何产生速度和改变方向。
Force = Mass × Acceleration
To accelerate a 70 kg athlete from 0 to 5 m/s² requires a net force of 70 × 5 = 350 N. The same athlete changing direction with a lateral acceleration of 3 m/s² needs a force of 210 N.
要使一名70千克的运动员从0加速到5 m/s²，需要净力70 × 5 = 350牛。同一运动员以横向加速度3 m/s²改变方向时，需要210牛的力。
8. Momentum and Impulse | 动量与冲量
Momentum is a measure of how difficult it is to stop a moving object. In contact sports and tackling, momentum helps explain impact forces.
动量是衡量阻止运动物体难易程度的物理量。在接触性运动和抢截中，动量有助于解释冲击力。
Momentum = Mass × Velocity
A 60 kg rugby player running at 8 m/s has a momentum of 480 kg·m/s. Impulse is the change in momentum and equals the average force applied times the contact time.
一名60千克的橄榄球运动员以8 m/s奔跑，其动量为480 kg·m/s。冲量是动量的变化量，等于平均施加力乘以接触时间。
Impulse = Force × Time = Change in Momentum
If a goalkeeper catches a ball of momentum 12 kg·m/s and brings it to rest in 0.2 s, the average force is 12 ÷ 0.2 = 60 N.
如果守门员接住一个动量为12 kg·m/s的球并在0.2秒内使其静止，平均力为12 ÷ 0.2 = 60牛。
9. Principles of Training (FITT) | 训练原则 (FITT)
The FITT principle provides a framework for designing effective training programmes. Each letter stands for a key variable that can be adjusted to ensure progression and avoid plateaus.
FITT 原则为设计有效的训练计划提供了一个框架。每个字母代表一个关键变量，可加以调整以保证进步并避免平台期。
F – Frequency: how often you train (e.g. 3 times per week).
I – Intensity: how hard you work (e.g. 70% MHR, or rate of perceived exertion).
T – Time: duration of each session (e.g. 30 minutes).
T – Type: the kind of exercise (e.g. cycling, swimming, resistance training).
F – 频率：训练频次（如每周3次）。
I – 强度：训练努力程度（如70%最大心率，或主观疲劳量表）。
T – 时间：每次持续时长（如30分钟）。
T – 类型：运动种类（如自行车、游泳、抗阻训练）。
A simple training load formula often used alongside FITT is: Training Load = Intensity × Time. Monitoring load helps reduce the risk of overtraining.
常与 FITT 配合使用的简单训练负荷公式为：训练负荷 = 强度 × 时间。监控负荷有助于降低过度训练风险。
10. Aerobic vs Anaerobic Respiration | 有氧与无氧呼吸
The body uses two main energy pathways. Knowing the word equations helps you understand how different activities are fuelled.
人体使用两条主要能量通路。了解文字方程式有助于理解不同运动是如何供能的。
Aerobic: Glucose + Oxygen → Carbon Dioxide + Water + Energy
有氧：葡萄糖 + 氧气 → 二氧化碳 + 水 + 能量
Anaerobic: Glucose → Lactic Acid + Energy
无氧：葡萄糖 → 乳酸 + 能量
Aerobic respiration releases energy slowly but can be sustained for long periods. Anaerobic respiration supplies energy very quickly but leads to lactate accumulation and fatigue within seconds to minutes.
有氧呼吸释放能量缓慢但能持续很长时间。无氧呼吸供能极快，但会导致乳酸堆积，在数秒至数分钟内引起疲劳。
11. Caloric Expenditure Estimation | 热量消耗估算
Estimating energy expenditure helps athletes manage diet and training load. A common method uses MET (Metabolic Equivalent of Task) values.
估算能量消耗有助于运动员管理饮食与训练负荷。常用的方法采用 MET（任务代谢当量）值。
Energy (kcal) = MET × Body Mass (kg) × Time (hours)
1 MET is the energy used at rest, roughly 1 kcal per kilogram per hour. Walking at 5 km/h is about 3.5 METs. For a 50 kg student walking for 1 hour: Energy = 3.5 × 50 × 1 = 175 kcal.
1 MET 为静息时的能耗，约为每千克体重每小时1千卡。以5千米/小时的速度步行约为3.5 MET。一名50千克的学生步行1小时：能量 = 3.5 × 50 × 1 = 175 千卡。
More intense activities have higher MET values: jogging ≈ 7 METs, basketball ≈ 6.5 METs, swimming (moderate) ≈ 8 METs.
强度越高的活动 MET 值越大：慢跑约为7 MET，篮球约为6.5 MET，中速游泳约为8 MET。
12. VO₂max Estimation (Cooper Test) | 最大摄氧量估算（库珀测试）
VO₂max is the maximum volume of oxygen the body can use per minute per kilogram of body mass. It is a gold‑standard measure of aerobic fitness. The 12‑minute Cooper run provides a field‑based estimate.
最大摄氧量（VO₂max）是身体每千克体重每分钟能利用的最大氧气量，是衡量有氧能力的黄金标准。12分钟库珀跑提供了一个现场估算方法。
VO₂max (ml/kg/min) = (Distance in metres − 504.9) ÷ 44.73
If a student covers 2400 m in 12 minutes: VO₂max = (2400 − 504.9) ÷ 44.73 = 1895.1 ÷ 44.73 ≈ 42.4 ml/kg/min. This value places the student in a good fitness category for their age.
如果一名学生12分钟跑完2400米：VO₂max = (2400 − 504.9) ÷ 44.73 = 1895.1 ÷ 44.73 ≈ 42.4 ml/kg/min。该数值让该学生处于同龄人中较好的体能水平。
Other prediction equations exist for different tests, such as the multistage fitness test, but the Cooper formula is one of the simplest and most widely used in schools.
其他测试（如多阶段体能测试）也有预测公式，但库珀公式是学校中最简单且最广泛使用的公式之一。
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