📚 AQA GCSE PE Formula & Theorem Quick Reference | AQA 体育：公式定理速查手册
This quick reference handbook covers all the essential formulas and theorems you need for the AQA GCSE Physical Education examination. From heart rate calculations to lever mechanics, every equation is explained clearly with worked examples to help you master the quantitative aspects of the course. Use this guide for last‑minute revision or as a daily study companion.
本速查手册涵盖 AQA 体育（GCSE）考试中所有必考的公式与定理。从心率计算到杠杆力学，每个公式都配有清晰的说明和例题，助你掌握课程中涉及计算的每个环节。可用作考前冲刺复习，也可日常翻阅巩固。
1. Maximum Heart Rate (MHR) | 最大心率
The simplest way to estimate your maximum heart rate is using the 220 − age formula. While individual variation exists, this equation gives a reliable baseline for setting training intensities. For a 15‑year‑old, MHR ≈ 220 − 15 = 205 beats per minute (bpm).
估算最大心率最简单的方法是使用 220 − 年龄 公式。虽然个体存在差异，但该方程为设定运动强度提供了可靠的基准。例如，15 岁运动员的最大心率 ≈ 220 − 15 = 205 次/分 (bpm)。
MHR = 220 − age
2. Training Zones Based on % of MHR | 最大心率百分比训练区间
Training zones are typically expressed as percentages of MHR. The aerobic training zone is 60–80% MHR, while the anaerobic zone is 80–90% MHR. To find a target heart rate, multiply MHR by the lower and upper percentage limits.
训练区间通常以最大心率的百分比表示。有氧训练区间为 60–80% MHR，无氧训练区间为 80–90% MHR。要计算目标心率，可将最大心率分别乘以区间的下限和上限百分比。
| Zone | % MHR | Example for age 15 (MHR=205) |
|---|---|---|
| Aerobic | 60–80% | 123–164 bpm |
| Anaerobic | 80–90% | 164–185 bpm |
Target HR = MHR × Percentage (as a decimal)
3. Karvonen Formula & Target Heart Rate | 卡沃南公式与目标心率
The Karvonen formula uses heart rate reserve (HRR) to prescribe exercise intensity more accurately. HRR is the difference between MHR and resting heart rate (RHR). The target heart rate for a given intensity is then calculated by adding a percentage of HRR to RHR.
卡沃南公式利用心率储备 (HRR) 更准确地制定运动强度。HRR 是最大心率与安静心率 (RHR) 之差。按给定强度百分比计算的目标心率，是将 HRR 的一定比例加上 RHR 得出。
HRR = MHR − RHR
Target HR = (HRR × Intensity%) + RHR
If a 15‑year‑old has RHR = 60 bpm and wants to train at 70% en HRR = 205 − 60 = 145 bpm. Target HR = (145 × 0.70) + 60 = 101.5 + 60 = 161.5 ≈ 162 bpm.
若某 15 岁运动员安静心率为 60 次/分，拟以 70% 强度训练，则 HRR = 205 − 60 = 145 次/分。目标心率 = (145 × 0.70) + 60 = 101.5 + 60 = 161.5 ≈ 162 次/分。
4. Body Mass Index (BMI) | 身体质量指数
BMI is a simple screening tool that relates body weight to height. It is widely used to classify individuals as underweight, normal weight, overweight or obese. Remember that BMI does not distinguish between muscle and fat, so it has limitations for very muscular athletes.
BMI 是一个将体重与身高关联的简易筛查工具，广泛用于判断体重过轻、正常、超重或肥胖。须注意 BMI 并不能区分肌肉与脂肪，因此对肌肉发达的运动员存在局限。
BMI = Weight (kg) ÷ [Height (m)]²
kg and 1.70 m tall: BMI = 65 ÷ (1.70 × 1.70) = 65 ÷ 2.89 ≈ 22.5 kg/m², which falls in the 'normal' range.
例如体重 65 kg、身高 1.70 m 的学生：BMI = 65 ÷ (1.70 × 1.70) = 65 ÷ 2.89 ≈ 22.5 kg/m²，属于“正常”范围。
5. Speed, Distance and Time | 速度、距离与时间
Speed is a scalar quantity that describes how quickly an athlete moves. In GCSE PE you will be expected to calculate speed, distance or time when two of the three variables are known. The units must be consistent – typically metres per second (m/s) or kilometres per hour (km/h).
速度是标量，描述运动员移动的快慢。GCSE 体育考试要求能够根据已知的两个变量计算速度、距离或时间。单位必须统一——通常为米/秒 (m/s) 或 公里/时 (km/h)。
Speed = Distance ÷ Time
5 s, speed = 100 ÷ 12.5 = 8 m/s. To convert to km/h, multiply by 3.6: 8 × 3.6 = 28.8 km/h.
若短跑运动员 12.5 秒跑完 100 米，则速度 = 100 ÷ 12.5 = 8 m/s。转换为公里/时，乘以 3.6：8 × 3.6 = 28.8 km/h。
6. Work, Force and Distance | 功、力与距离
Work is done whenever a force moves an object. In sporting contexts, calculating work helps understand energy transfer during activities like pushing a tackle sled or lifting a weight. The force must act in the direction of the movement.
每当力使物体发生位移时就做了功。在运动情境中，计算功可帮助理解推拉训练橇或举起重物等活动的能量转移。力必须沿移动方向作用才做功。
Work (J) = Force (N) × Distance (m)
led with a force of 300 N over a distance of 10 m does 300 × 10 = 3000 joules (J) of work.
以 300 N 的力推训练橇前进 10 m 做功 300 × 10 = 3000 焦耳 (J)。
7. Power | 功率
Power is the rate at which work is done, reflecting an athlete's explosiveness. The faster a given amount of work is performed, the greater the power output. Power can also be expressed as force multiplied by velocity.
功率是做功的快慢，反映运动员的爆发力。在相同做功量下，用时越短，功率输出越大。功率也可用力乘以速度表示。
Power (W) = Work (J) ÷ Time (s)
Power (W) = Force (N) × Velocity (m/s)
r who does 2000 J of work in 0.5 s achieves a power output of 2000 ÷ 0.5 = 4000 W (watts).
一名举重运动员在 0.5 秒内做功 2000 J 时，功率输出为 2000 ÷ 0.5 = 4000 W (瓦特)。
8. Moment and Levers | 力矩与杠杆
A moment is the turning effect of a force. In the body, muscles create moments around joints, forming lever systems. The size of a moment depends on both the force and the perpendicular distance from the pivot (the moment arm).
力矩是力产生的转动效应。人体中肌肉绕关节产生力矩，构成杠杆系统。力矩大小取决于力的大小以及力到支点的垂直距离（力臂）。
Moment (Nm) = Force (N) × Distance from pivot (m)
In a second‑ cle). If the force is 800 N and the moment arm is 0.05 m, the moment = 800 × 0.05 = 40 Nm.
在提踵这类第二类杠杆中，负荷（体重）位于支点（前脚掌）与动力（小腿肌）之间。若力为 800 N，力臂长 0.05 m，则力矩 = 800 × 0.05 = 40 Nm。
9. Mechanical Advantage of Levers | 杠杆的机械利益
Mechanical advantage (MA) tells you how much a lever multiplies the effort force. A value greater than 1 means the effort arm is longer than the resistance arm, making it easier to move a heavy load. Second‑class levers typically have MA > 1.
机械利益 (MA) 表示杠杆将动力放大了多少倍。数值大于 1 表示动力臂长于阻力臂，移动重负荷更省力。第二类杠杆通常机械利益大于 1。
Mechanical Advantage = Effort Arm ÷ Resistance Arm
If the effort arm of a wheelbarrow (second‑ sistance arm is 0.4 m, MA = 1.2 ÷ 0.4 = 3. This means the effort is magnified three times.
若手推车（第二类杠杆）的动力臂长 1.2 m，阻力臂长 0.4 m，则 MA = 1.2 ÷ 0.4 = 3。这意味着动力被放大了三倍。
10. Training Load – RPE × Duration | 训练负荷——自觉用力程度 × 持续时间
Training load is a simple measure of the overall stress placed on an athlete during a session. By multiplying the session’s rating of perceived exertion (RPE, on a scale of 1–10) by the duration in minutes, coaches can monitor internal load and adjust programming to avoid overtraining.
训练负荷是衡量一次训练课对运动员施加总压力的简易指标。将自觉用力程度 (RPE，1–10级) 乘以持续时间（分钟），教练员可监控内部负荷，调整计划以预防过度训练。
Training Load (AU) = RPE × Duration (min)
A 45‑ itrary units (AU). Comparing weekly loads helps identify spikes that could lead to injury.
一节 45 分钟、RPE 评为 7 的训练课，其训练负荷 = 7 × 45 = 315 任意单位 (AU)。对比周负荷可识别可能导致受伤的负荷突增。
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