📚 IGCSE Cambridge Physical Education: Formula & Principles Quick Reference Handbook | IGCSE Cambridge 体育：公式定理速查手册
This quick-reference handbook brings together the essential formulas, equations and training principles tested in the Cambridge IGCSE Physical Education syllabus. It is designed for revision, classroom use and exam preparation, with each section pairing the core relationship with a practical sporting example.
本速查手册汇总了 Cambridge IGCSE 体育课程中考查的核心公式、方程与训练原则。每个部分都将关键关系与运动实例配对，适合备考、课堂复习和考前速查。
1. Cardiac Output and Stroke Volume | 心输出量与每搏输出量
Cardiac output (Q) is the volume of blood pumped by the left ventricle in one minute. It is calculated by multiplying stroke volume—the volume ejected per beat—by heart rate.
心输出量 (Q) 是左心室每分钟泵出的血液量。它等于每搏输出量（每次心跳射血量）乘以心率。
Q = Stroke volume × Heart rate
In a resting athlete, if stroke volume is 70 mL/beat and heart rate is 72 bpm, cardiac output is about 5.04 L/min. During exercise, both stroke volume and heart rate rise, so cardiac output can increase several-fold to deliver more oxygen to working muscles.
安静时，若每搏输出量为 70 mL/次、心率为 72 次/分，心输出量约为 5.04 L/min。运动时每搏输出量与心率均升高，心输出量可成倍增加，从而向工作肌肉输送更多氧气。
2. Heart Rate and Training Zones | 心率与训练区间
Maximum heart rate can be estimated using the simple age-based formula. This estimate helps athletes set aerobic and anaerobic training intensities.
最大心率可以用基于年龄的简单公式估算。该估算帮助运动员设定有氧与无氧训练强度。
Max HR ≈ 220 − age
For a 16-year-old, estimated maximum heart rate is 204 bpm. Light aerobic work is often prescribed at 60–70% of maximum heart rate, while high-intensity intervals may use 80–90%.
16 岁运动员的估算最大心率为 204 次/分。轻度有氧训练通常为最大心率的 60–70%，而高强度间歇训练可使用 80–90%。
A more personalised method is the Karvonen formula, which uses resting heart rate to calculate heart-rate reserve.
更个性化的方法是 Karvonen 公式，它利用安静心率计算心率储备。
Target HR = Resting HR + Intensity × (Max HR − Resting HR)
If a 16-year-old has a resting heart rate of 60 bpm and wants to train at 70% intensity, the target heart rate would be 60 + 0.70 × (204 − 60) = 160.8 bpm. This method better reflects fitness level because trained athletes often have lower resting heart rates.
若一名 16 岁运动员安静心率为 60 次/分，想以 70% 强度训练，目标心率为 60 + 0.70 × (204 − 60) = 160.8 次/分。该方法更能反映体能水平，因为训练有素的运动员安静心率通常较低。
3. Body Mass Index (BMI) | 身体质量指数
Body mass index is a simple screening tool that relates body mass to height squared. It is widely used to classify underweight, normal weight, overweight and obesity.
身体质量指数是一种简单筛查工具，将体重与身高平方关联起来，广泛用于分类体重过轻、正常、超重和肥胖。
BMI = mass (kg) ÷ height² (m²)
For example, a student with a mass of 64 kg and a height of 1.75 m has a BMI of 64 ÷ (1.75 × 1.75) = 20.9 kg/m², which is within the healthy range. BMI does not distinguish between muscle and fat, so very muscular athletes may be misclassified.
例如，一名体重 64 kg、身高 1.75 m 的学生 BMI 为 64 ÷ (1.75 × 1.75) = 20.9 kg/m²，属于健康范围。BMI 不能区分肌肉与脂肪，因此肌肉发达的运动员可能被误判。
In IGCSE Physical Education, BMI is discussed as one indicator of health and body composition, but it should be used alongside other measures such as skinfold thickness and waist-to-hip ratio.
在 IGCSE 体育中，BMI 被视为健康和身体成分的一项指标，但应与皮褶厚度和腰臀比等其他测量方法结合使用。
4. Energy Balance and Caloric Intake | 能量平衡与热量摄入
Energy balance is the relationship between energy taken in through food and drink and energy expended through basal metabolism, thermogenesis and physical activity.
能量平衡指通过饮食摄入的能量与通过基础代谢、产热和身体活动消耗的能量之间的关系。
Energy balance = Energy intake − Energy expenditure
A positive energy balance leads to weight gain, while a negative balance leads to weight loss. Athletes in heavy training often need extra kilocalories to maintain performance, repair tissue and support growth.
能量正平衡导致体重增加，负平衡导致体重下降。大负荷训练的运动员常需额外千卡来维持运动表现、修复组织并支持生长。
The main macronutrients provide different amounts of energy: carbohydrate and protein provide approximately 4 kcal per gram, while fat provides approximately 9 kcal per gram. This affects dietary planning for endurance and strength athletes.
三大宏量营养素提供不同的能量：碳水化合物和蛋白质每克约提供 4 千卡，脂肪每克约提供 9 千卡。这会影响耐力和力量运动员的膳食安排。
5. Work, Power and Mechanical Efficiency | 功、功率与机械效率
Work is done when a force moves an object through a distance in the direction of the force. Power is the rate at which work is done or energy is transferred.
当力使物体沿力的方向移动一定距离时，力对物体做功。功率是做功或能量转移的速率。
Work = Force × distance
Power = Work ÷ time
Work is measured in joules (J) and power in watts (W). A sprinter producing a large force over a short time develops high power, which is more important for explosive events than total work alone.
功的单位是焦耳 (J)，功率单位是瓦特 (W)。短跑运动员在短时间内产生较大力量，输出高功率，这对爆发性项目比单纯的总功更重要。
Mechanical efficiency compares useful work output with the total chemical energy used.
机械效率比较有用功输出与总化学能消耗。
Efficiency = (Useful work output ÷ Total energy input) × 100%
Human movement is not perfectly efficient because energy is lost as heat. In cycling, mechanical efficiency is often around 20–25%, meaning only about one fifth to one quarter of the metabolic energy becomes useful work on the pedals.
人体运动并非完全高效，因为部分能量以热的形式散失。在自行车运动中，机械效率通常约为 20–25%，意味着只有约五分之一到四分之一的代谢能量转化为踏板上的有用功。
6. Speed, Velocity and Acceleration | 速率、速度与加速度
Speed is a scalar quantity describing how fast a body moves, while velocity is a vector quantity describing speed in a given direction. Acceleration measures how quickly velocity changes.
速率是标量，描述物体运动快慢；速度是矢量，描述某一方向上的运动快慢。加速度衡量速度变化的快慢。
Speed = distance ÷ time
Acceleration = (final velocity − initial velocity) ÷ time
In a 100 m sprint, if an athlete covers the distance in 12.5 s, average speed is 8 m/s. Acceleration is greatest at the start, when velocity rises rapidly from zero.
在 100 m 短跑中，若运动员用 12.5 s 跑完全程，平均速率为 8 m/s。起跑阶段速度从零迅速增大，加速度最大。
Acceleration is measured in metres per second squared (m/s²). If a cyclist increases velocity from 4 m/s to 10 m/s in 3 seconds, acceleration is (10 − 4) ÷ 3 = 2 m/s².
加速度的单位是米每二次方秒 (m/s²)。若一名自行车运动员在 3 秒内将速度从 4 m/s 提高到 10 m/s，加速度为 (10 − 4) ÷ 3 = 2 m/s²。
7. Force, Momentum and Newton’s Laws | 力、动量与牛顿定律
Force causes a mass to accelerate, changes an object’s shape, or changes its state of motion. Newton’s second law links force, mass and acceleration.
力使质量加速、改变物体形状或改变其运动状态。牛顿第二定律将力、质量与加速度联系起来。
Force = mass × acceleration (F = ma)
Momentum is the product
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