📚 Year 11 Edexcel PE: Formula & Theorem Quick Reference Handbook | 爱德思体育公式定理速查手册
Mastering the key formulas and theorems is essential for success in Edexcel Year 11 Physical Education. This quick reference handbook compiles all the vital calculations you need, from heart rate training zones to biomechanics and fitness testing indices. Each formula is presented clearly, with paired English and Chinese explanations to reinforce your understanding and help you apply them confidently in exam scenarios.
掌握关键公式和定理是学好爱德思 Year 11 体育的基础。这份速查手册汇集了所有重要的计算，从心率训练区到生物力学，再到体能测试指数。每个公式都清晰地呈现，并配有中英文对照解释，帮助你加深理解，在考试情境中自信应用。
1. Maximum Heart Rate (MHR) | 最大心率
The simplest and most widely used method to estimate your maximum heart rate is subtracting your age from 220. This value serves as a baseline for setting aerobic and anaerobic training zones.
估算最大心率最简单、最常用的方法是用 220 减去你的年龄。这个数值是设定有氧和无氧训练区的基础。
MHR = 220 – age
For example, a 16-year-old student would have an estimated MHR of 204 beats per minute (bpm). Although individual variations exist, this formula gives a reliable starting point for exercise intensity planning.
例如，一名 16 岁学生的预估最大心率为 204 次/分。尽管存在个体差异，该公式为运动强度规划提供了一个可靠的起点。
2. Karvonen Formula for Target Heart Rate | 卡沃宁靶心率公式
The Karvonen formula calculates your target heart rate zone more accurately by factoring in your resting heart rate (RHR). This method identifies the heart rate needed to work at a specific percentage of your heart rate reserve.
卡沃宁公式通过带入静息心率，更精确地计算靶心率区间。该方法能确定达到特定心率储备百分比所需要的心率。
Target HR = (MHR – RHR) × Intensity% + RHR
If an athlete has a resting heart rate of 60 bpm and wants to train at 70% intensity, their target heart rate would be [(204 – 60) × 0.7] + 60 = 160.8 bpm. This calculation ensures workouts are tailored to the individual’s fitness level.
如果一名运动员静息心率为 60 次/分，想以 70% 强度训练，其靶心率则为 [(204 – 60) × 0.7] + 60 = 160.8 次/分。这一计算确保训练与个人体能水平相匹配。
3. Body Mass Index (BMI) | 身体质量指数
Body Mass Index is a simple indicator of body composition, categorising individuals as underweight, healthy weight, overweight or obese. It uses weight in kilograms and height in metres.
身体质量指数是衡量身体成分的简易指标，可将人群划分为偏瘦、健康体重、超重或肥胖。它使用以千克为单位的体重和以米为单位的身高。
BMI = weight (kg) ÷ height² (m²)
A student weighing 65 kg with a height of 1.75 m has a BMI of 65 ÷ (1.75)² = 21.2 kg/m², which falls within the healthy range. While BMI does not distinguish between muscle and fat, it remains a useful screening tool in sport and health.
一名体重 65 公斤、身高 1.75 米的学生，BMI 为 65 ÷ (1.75)² = 21.2 kg/m²，处于健康范围。虽然 BMI 不能区分肌肉和脂肪，但它仍是运动与健康中实用的筛查工具。
4. Harvard Step Test Fitness Index | 哈弗台阶测试体能指数
The Harvard Step Test measures cardiovascular endurance by evaluating how quickly the heart recovers after a standardised stepping exercise. The fitness index combines exercise duration and post-exercise pulse counts.
哈弗台阶测试通过评估标准化台阶运动后心率恢复的快慢，衡量心血管耐力。体能指数结合了运动时长和运动后脉搏计数。
Fitness Index = (duration in seconds × 100) ÷ (2 × sum of three pulse counts)
Pulse counts are taken for 30 seconds at 1–1.5, 2–2.5, and 3–3.5 minutes after completing the step test. A longer exercise time and lower heart rate sum produce a higher index, indicating superior aerobic fitness. This formula often appears in Edexcel data-analysis questions.
脉搏计数在完成台阶测试后 1–1.5 分钟、2–2.5 分钟和 3–3.5 分钟各测 30 秒。运动时间越长、心率总和越低，得出的指数越高，表明有氧体能更优秀。该公式常在爱德思数据分析题中出现。
5. Cooper 12-Minute Run VO₂max Prediction | 库珀 12 分钟跑最大摄氧量预测
The Cooper test predicts maximal oxygen uptake (VO₂max) based on the distance covered in 12 minutes. VO₂max is a gold-standard measure of aerobic power.
库珀测试根据 12 分钟内跑过的距离预测最大摄氧量。最大摄氧量是衡量有氧能力的黄金标准。
VO₂max (ml/kg/min) = (distance in metres – 504.9) ÷ 44.73
If a performer runs 2800 metres, their estimated VO₂max is (2800 – 504.9) ÷ 44.73 ≈ 51.3 ml/kg/min. While this formula provides an estimate, it is highly useful for tracking changes in aerobic performance without laboratory equipment.
如果一名参与者跑了 2800 米，其预测最大摄氧量为 (2800 – 504.9) ÷ 44.73 ≈ 51.3 ml/kg/min。虽然该公式仅提供估算值，但它在无需实验室设备的情况下，对追踪有氧表现变化非常实用。
6. Speed, Distance and Time | 速度、距离和时间
Speed is a fundamental measure in many sports. It is calculated by dividing the distance travelled by the time taken. This relationship helps analyse sprint performance, race pacing and game movements.
速度是许多运动中的基本测量指标。它通过距离除以时间来计算。这一关系有助于分析短跑表现、比赛配速和比赛中的移动。
Speed = distance ÷ time
For instance, a 100-metre sprinter finishing in 11.5 seconds has an average speed of approximately 8.7 m/s. You can rearrange the formula to find distance or time when the other variables are known, a common requirement in exam calculations.
例如，一名 100 米短跑运动员用时 11.5 秒，其平均速度约为 8.7 米/秒。你可以变换公式来求距离或时间，这是考试计算中的常见要求。
7. Work and Power | 功与功率
Work is done when a force moves an object over a distance. Power measures how quickly that work is performed, reflecting an athlete’s explosive capacity and muscular endurance.
当力使物体移动一段距离时，就做了功。功率衡量做功的快慢，反映运动员的爆发力和肌肉耐力。
Work (J) = force (N) × distance (m)
Power (W) = work ÷ time
If a weightlifter applies a force of 1500 N to lift a barbell 2 metres, the work done is 3000 J. If the lift takes 3 seconds, the power output is 1000 W. Understanding these equations links physical performance to mechanical principles.
如果一名举重运动员施加 1500 牛的力将杠铃举起 2 米，所做功为 3000 焦。如果完成举重用了 3 秒，则功率输出为 1000 瓦。理解这些等式可将运动表现与力学原理联系起来。
8. Levers and Moment of Force | 杠杆与力矩
A lever system consists of a fulcrum, an effort and a load. The moment of force (torque) quantifies the turning effect produced by a force acting around the fulcrum. It is central to analysing movement efficiency in the human body.
杠杆系统由支点、动力和阻力组成。力矩量化了力绕支点产生的转动效果。它是分析人体动作效率的核心。
Moment (Nm) = force (N) × perpendicular distance from fulcrum (m)
In a third-class lever like the bicep curl, the effort lies between fulcrum and load. Although this arrangement sacrifices mechanical advantage, it allows a large range of motion and speed. Edexcel questions often ask you to calculate moments or identify lever classes.
在肱二头肌弯举这类第三类杠杆中，动力位于支点和阻力之间。虽然这种结构牺牲了机械效益，但它实现了大幅度的活动范围和速度。爱德思考题常要求计算力矩或辨识杠杆类别。
9. Mechanical Advantage | 机械效益
Mechanical advantage describes the efficiency of a lever system by comparing the effort arm length to the resistance arm length. A value above 1 means less effort is needed to move a given load.
机械效益通过比较动力臂与阻力臂的长度，描述杠杆系统的效率。数值大于 1 时，表示移动某一负荷需要的动力更小。
Mechanical Advantage = effort arm ÷ resistance arm
For example, in a second-class lever such as standing on tiptoes, the effort arm is longer than the resistance arm, producing a mechanical advantage greater than 1. This principle explains why some body movements feel easier because they amplify force.
例如，在踮脚尖这类第二类杠杆中，动力臂长于阻力臂，产生的机械效益大于 1。这一原理解释了为何某些身体动作因增力而感觉更省力。
10. 1RM Percentage Load Calculation | 1RM 百分比负荷计算
One-repetition maximum (1RM) is the heaviest weight you can lift once with proper form. Training loads are often prescribed as a percentage of 1RM to target specific fitness goals, such as muscular endurance, hypertrophy or maximal strength.
一次最大重复重量是指用标准动作只能完成一次的最大重量。训练负荷通常以 1RM 的百分比来设定，以针对特定的训练目标，如肌耐力、肌肥大或最大力量。
Training load = 1RM × desired percentage
If an athlete’s bench press 1RM is 80 kg and the programme requires a hypertrophy set at 75% intensity, the training load becomes 80 × 0.75 = 60 kg. Using this formula ensures safe and progressive overload, a key concept in the Edexcel fitness training topic.
如果一名运动员卧推 1RM 为 80 公斤，训练方案要求以 75% 强度进行肌肥大组训练，则训练负荷为 80 × 0.75 = 60 公斤。使用该公式可确保安全渐进超负荷，这是爱德思体能训练专题中的关键概念。
11. Acceleration | 加速度
Acceleration measures how quickly an object or performer changes velocity. It is particularly relevant when analysing sprints, jumps and changes of direction in invasion games.
加速度衡量物体或运动员改变速度的快慢。在分析短跑、跳跃和攻防转换变向时，加速度尤为重要。
Acceleration (m/s²) = (final velocity – initial velocity) ÷ time
A footballer accelerating from 0 m/s to 8 m/s in 2 seconds has an acceleration of 4 m/s². A negative acceleration (deceleration) occurs when velocity decreases, helping you interpret motion graphs presented in Edexcel exam papers.
一名足球运动员在 2 秒内从 0 米/秒加速到 8 米/秒，其加速度为 4 米/秒²。当速度减小时出现负加速度，有助于你解读爱德思考卷中出现的运动图表。
12. Impulse and Momentum Relationship | 冲量与动量关系
The impulse–momentum theorem states that the change in momentum of an object equals the impulse applied. This principle explains why extending the time of applied force reduces impact force, important in techniques like landing and striking.
冲量-动量定理指出，物体动量的变化等于作用的冲量。该原理解释了为何延长作用力时间能减小冲击力，这在落地和击打等技术中很重要。
Impulse (Ns) = force × time = change in momentum
Momentum (kg m/s) = mass × velocity
Cricketers follow through when catching a ball to increase contact time, reducing the force felt. While Edexcel may not always require momentum calculations in isolation, the concept links biomechanics and injury prevention, enriching your long-answer responses.
板球运动员接球时顺势缓冲以增加接触时间，从而减小感受到的力。虽然爱德思可能不单独要求动量计算，但这一概念连接了生物力学和损伤预防，可丰富你的长篇回答。
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