📚 IGCSE CAIE Physical Education: Quick Formula & Theorem Handbook | IGCSE CAIE 体育：公式定理速查手册
This revision guide consolidates the essential formulae, equations, and biomechanical principles required for the IGCSE CAIE Physical Education syllabus. Whether you are calculating speed, analysing levers, or evaluating cardiovascular efficiency, a firm grasp of these quantitative foundations will strengthen your exam answers and practical understanding.
本复习手册汇总了 IGCSE CAIE 体育课程要求掌握的基本公式、方程和生物力学原理。无论是计算速度、分析杠杆还是评估心血管效率，扎实掌握这些量化基础都能提升你的考试作答质量和实践理解。
1. Speed, Distance, Time | 速度、距离与时间
Speed is the rate at which distance is covered, a fundamental concept in movement analysis.
Speed = Distance ÷ Time (v = d / t)
速度表示单位时间内通过的距离，是运动分析中的基础概念。
速度 = 距离 ÷ 时间 (v = d / t)
- v = speed (m/s), d = distance (m), t = time (s)
- v = 速度 (米/秒), d = 距离 (米), t = 时间 (秒)
Average speed can be calculated when the total distance and total time are known. In many sports, instantaneous speed (e.g., maximum sprint speed) is more relevant to performance analysis.
当总距离和总时间已知时，可以计算平均速度。在许多运动中，瞬时速度（例如最大冲刺速度）与运动表现分析更相关。
2. Acceleration | 加速度
Acceleration measures how quickly velocity changes. It is vital for assessing explosiveness and changes of direction.
Acceleration = (Final velocity – Initial velocity) ÷ Time (a = (v-u) / t)
加速度衡量速度变化的快慢，对于评估爆发力和变向能力至关重要。
加速度 = (末速度 – 初速度) ÷ 时间 (a = (v-u) / t)
- a = acceleration (m/s²), v = final velocity (m/s), u = initial velocity (m/s), t = time (s)
- a = 加速度 (米/秒²), v = 末速度 (米/秒), u = 初速度 (米/秒), t = 时间 (秒)
Negative acceleration (deceleration) occurs when an object slows down, common when a player stops or changes direction rapidly.
负加速度（减速）发生在物体放缓时，常见于运动员急停或快速变向时。
3. Force and Newton’s Second Law | 力与牛顿第二定律
Force causes an object to accelerate. The relationship is expressed by Newton’s Second Law.
Force = Mass × Acceleration (F = m × a)
力使物体产生加速度，这一关系由牛顿第二定律表达。
力 = 质量 × 加速度 (F = m × a)
- F = force (N, Newtons), m = mass (kg), a = acceleration (m/s²)
- F = 力 (牛顿), m = 质量 (千克), a = 加速度 (米/秒²)
In sport, greater force applied to an object (e.g., a shot put) results in greater acceleration, provided mass remains constant. Similarly, a heavier opponent requires greater force to move.
在运动中，施加在物体（如铅球）上的力越大，产生的加速度就越大（假设质量不变）。同理，移动体重更大的对手需要更大的力。
4. Weight and Mass | 重量与质量
Weight is the force due to gravity acting on a mass. It should not be confused with mass, which is the amount of matter.
Weight = Mass × Gravitational field strength (W = m × g)
重量是重力作用于质量产生的力，不应与表示物质多少的质量混淆。
重量 = 质量 × 重力场强度 (W = m × g)
- W = weight (N), m = mass (kg), g = 10 m/s² (on Earth, IGCSE approximation)
- W = 重量 (牛顿), m = 质量 (千克), g = 10 米/秒² (IGCSE 中地球取值)
An athlete’s mass stays constant, but weight appears different on other planets. In biomechanics, weight acts through the centre of mass and influences stability and balance.
运动员的质量保持不变，但在其他行星上重量会不同。生物力学中，重量通过重心作用，影响稳定性和平衡。
5. Work, Energy, Power | 功、能量、功率
Work is done when a force moves an object. Power is the rate of doing work.
Work = Force × Distance moved in direction of force (W = F × d)
Power = Work ÷ Time (P = W / t) or Power = Force × Velocity (P = F × v)
当力使物体移动时，就做了功。功率是做功的速率。
功 = 力 × 沿力方向移动的距离 (W = F × d)
功率 = 功 ÷ 时间 (P = W / t) 或 功率 = 力 × 速度 (P = F × v)
- Work (Joules), Power (Watts)
- 功 (焦耳), 功率 (瓦特)
Explosive athletes (sprinters, jumpers) produce high power outputs by applying large forces at high speeds. Endurance athletes sustain lower power over longer times.
爆发力型运动员（短跑、跳跃选手）通过以高速施加大力来产生高功率输出。耐力型运动员则在较长时间内维持较低功率。
6. Efficiency | 效率
Efficiency compares useful energy output to total energy input, often expressed as a percentage. The human body constantly loses energy as heat.
Efficiency (%) = (Useful work output ÷ Total energy input) × 100
效率比较有效能量输出与总能量输入，通常以百分比表示。人体不断以热的形式散失能量。
效率 (%) = (有效功输出 ÷ 总能量输入) × 100
Muscular efficiency is typically around 20-25% during physical activities. Improving technique in sport can reduce wasted energy and increase mechanical efficiency.
身体活动中的肌肉效率通常在 20-25% 左右。改善运动技术可以减少能量浪费并提高机械效率。
7. Mechanical Advantage and Velocity Ratio | 机械利益与速度比
Levers and pulley systems in the body and equipment provide mechanical advantages.
Mechanical Advantage (MA) = Load ÷ Effort
Velocity Ratio (VR) = Distance moved by effort ÷ Distance moved by load
身体内部的杠杆和器械中的滑轮系统会提供机械利益。
机械利益 (MA) = 负荷 ÷ 用力
速度比 (VR) = 用力端移动距离 ÷ 负荷端移动距离
- MA > 1 means the effort needed is less than the load (force multiplier). MA < 1 means greater range of motion at the expense of force.
- MA > 1 表示所需用力小于负荷（省力杠杆）。MA < 1 表示以牺牲力为代价获得更大运动范围。
In the human body, most levers are designed for speed and range of motion (MA < 1), e.g., the biceps acting at the elbow.
在人体内，大多数杠杆为速度和运动范围而设计 (MA < 1)，例如肱二头肌在肘关节的作用。
8. Levers and Moments | 杠杆与力矩
A moment is the turning effect of a force. It is central to understanding levers in movement analysis.
Moment of a force = Force × Perpendicular distance from pivot (M = F × d)
力矩是力的转动效应，是理解运动分析中杠杆的核心。
力矩 = 力 × 支点的垂直距离 (M = F × d)
- M = moment (Nm), F = force (N), d = perpendicular distance from pivot (m)
- M = 力矩 (牛·米), F = 力 (牛), d = 与支点的垂直距离 (米)
For a lever to be in equilibrium, the clockwise moments must equal the anticlockwise moments. This principle explains how muscles balance body segments against resistance.
要使杠杆平衡，顺时针力矩必须等于逆时针力矩。这一原理解释了肌肉如何平衡身体环节对抗阻力。
9. Momentum and Impulse | 动量与冲量
Momentum is the product of mass and velocity, while impulse is the change in momentum caused by a force over time.
Momentum (p) = Mass × Velocity (p = m × v)
Impulse = Force × Time = Change in momentum (F × t = mv – mu)
动量是质量与速度的乘积，冲量是力在时间上积累造成的动量变化。
动量 (p) = 质量 × 速度 (p = m × v)
冲量 = 力 × 时间 = 动量变化 (F × t = mv – mu)
Increasing the time over which a force is applied (follow-through in throwing, hitting) increases impulse and therefore momentum transfer. In catching, extending the hands increases time and reduces impact force.
增加施力时间（投掷或击球中的随挥动作）可增大冲量，从而增加动量传递。接球时手的后收延长了作用时间，减小了冲击力。
10. Cardiovascular Calculations | 心血管计算
Cardiovascular endurance depends on the relationship between heart rate, stroke volume, and cardiac output.
Cardiac Output = Stroke Volume × Heart Rate (Q = SV × HR)
心血管耐力取决于心率、每搏输出量和心输出量之间的关系。
心输出量 = 每搏输出量 × 心率 (Q = SV × HR)
- Q = cardiac output (L/min), SV = stroke volume (L or mL per beat), HR = heart rate (beats per minute, bpm)
- Q = 心输出量 (升/分钟), SV = 每搏输出量 (升或毫升/次), HR = 心率 (次/分钟)
During exercise, cardiac output increases due to a rise in both heart rate and stroke volume. A trained athlete has a higher stroke volume, allowing a lower resting heart rate.
运动中，心率和每搏输出量均上升，使心输出量增加。训练有素的运动员每搏输出量更高，因而静息心率较低。
11. Body Mass Index (BMI) | 体重指数
BMI is a simple index used to classify underweight, normal weight, overweight, and obesity in populations.
BMI = Mass (kg) ÷ (Height in metres)² (BMI = m / h²)
BMI 是一种用于人群体重分类（过轻、正常、超重、肥胖）的简易指数。
BMI = 体重 (公斤) ÷ (身高 (米))² (BMI = m / h²)
- BMI ranges (adults): Underweight < 18.5; Normal 18.5–24.9; Overweight 25–29.9; Obese ≥ 30
- BMI 范围（成人）：过轻 < 18.5；正常 18.5–24.9；超重 25–29.9；肥胖 ≥ 30
BMI does not distinguish between muscle and fat; therefore, very muscular athletes may be classified as overweight. It remains a useful population-level screening tool.
BMI 不能区分肌肉和脂肪，因此肌肉发达的运动员可能被归为超重。尽管如此，它仍是一种有用的人群筛查工具。
12. Target Heart Rate Zones (Karvonen Formula) | 靶心率区域（卡沃宁公式）
Setting exercise intensity using heart rate reserve ensures training is specific to an individual’s fitness level.
Target Heart Rate = Resting HR + Intensity × (Max HR – Resting HR)
Where Max HR ≈ 220 – Age
利用心率储备设定运动强度可确保训练针对个人的体能水平。
靶心率 = 静息心率 + 运动强度 × (最大心率 – 静息心率)
其中 最大心率 ≈ 220 – 年龄
- Intensity is expressed as a decimal (e.g., 0.6 for 60%, 0.8 for 80%)
- 强度以小数表示 (例如 0.6 表示 60%，0.8 表示 80%)
For aerobic training, intensity is typically set between 60-80% of heart rate reserve. Anaerobic training uses intensities above 80%. This principle guides effective programme design.
有氧训练的强度通常设定在心率储备的 60-80% 之间。无氧训练则使用 80% 以上的强度。这一原理指导着有效的训练计划设计。
Published by TutorHao | Physical Education Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply