📚 Year 11 Cambridge PE: Quick Reference Formulas & Theorems | Year 11 剑桥体育：公式定理速查手册
This quick reference handbook brings together the essential formulas, equations and key theoretical principles needed for the Cambridge IGCSE Physical Education (0413) examination. Use it to revise cardiovascular calculations, biomechanics, training loads, energy systems and more, with each entry presented in a clear bilingual format.
这本速查手册汇集了剑桥 IGCSE 体育（0413）考试所需的核心公式、方程式和关键理论原理。你可以用它复习心血管计算、生物力学、训练负荷、能量系统等内容，每个条目都以清晰的中英双语呈现。
1. Cardiovascular System Formulas | 心血管系统公式
Maximum heart rate (HRmax) can be estimated by subtracting age from 220. This simple estimation is widely used to set exercise intensity zones.
HRmax = 220 - age
最大心率（HRmax）可用 220 减去年龄来估算。这个简单估算被广泛用于设定运动强度区间。
The Karvonen formula calculates target heart rate using resting heart rate (HRrest) to provide a more personalised training zone.
Target HR = ((HRmax - HRrest) × %intensity) + HRrest
卡氏公式利用安静心率（HRrest）计算目标心率，提供了更个性化的训练区间。
Stroke volume (SV) is the amount of blood pumped per beat. Cardiac output (Q) is the product of stroke volume and heart rate.
Q = SV × HR
每搏输出量（SV）是每次心跳泵出的血量。心输出量（Q）是每搏输出量与心率的乘积。
2. Respiratory System Formulas | 呼吸系统公式
Minute ventilation (VE) is the volume of air moved into and out of the lungs per minute. It depends on tidal volume and breathing frequency.
VE = TV × f
分钟通气量（VE）是每分钟进出肺的气体量。它取决于潮气量和呼吸频率。
Maximal oxygen uptake (VO₂max) is the product of maximal cardiac output and maximal arteriovenous oxygen difference. It is the gold standard for aerobic fitness.
VO₂max = Qmax × (a-v)O₂ diff max
最大摄氧量（VO₂max）是最大心输出量与最大动静脉氧差的乘积。它是评价有氧适能的黄金标准。
3. Biomechanics: Linear Motion | 生物力学：线性运动
Speed is the rate at which distance is covered. It is a scalar quantity.
Speed = Distance ÷ Time
速度是单位时间内经过的距离，是标量。
Velocity is displacement per unit time and includes direction. Acceleration is the rate of change of velocity.
Velocity = Displacement ÷ Time
速度（矢量）是单位时间的位移，包含方向。加速度是速度的变化率。
Acceleration = (Final Velocity - Initial Velocity) ÷ Time
加速度 =（末速度 - 初速度）÷ 时间。
4. Biomechanics: Force, Momentum & Impulse | 生物力学：力、动量与冲量
Newton's Second Law states that net force equals mass times acceleration.
F = m × a
牛顿第二定律指出，合外力等于质量乘以加速度。
Momentum is the product of mass and velocity. Impulse equals change in momentum and is also force multiplied by time.
Momentum = m × v
动量是质量与速度的乘积。冲量等于动量的变化，也等于力乘以时间。
Impulse = F × t = Δ(mv)
冲量 = 力 × 时间 = 动量变化量。
5. Angular Motion & Levers | 角运动与杠杆
Angular velocity (ω) measures how quickly an object rotates, usually in radians per second.
ω = θ ÷ t
角速度（ω）表示物体转动的快慢，常用弧度/秒表示。
Moment of inertia (I) depends on mass and its distribution from the axis of rotation. Angular momentum is conserved when no external torque acts.
Angular Momentum = I × ω
转动惯量（I）取决于质量及其相对于转轴的分布。当无外力矩作用时，角动量守恒。
Levers are classified into three classes. Mechanical advantage (MA) is the ratio of effort arm to resistance arm.
MA = Effort Arm ÷ Resistance Arm
杠杆分为三类。机械利益（MA）是力臂与阻力臂的比值。
6. Training Principles & Load Calculations | 训练原则与负荷计算
One-repetition maximum (1RM) can be estimated from submaximal repetitions using the Brzycki formula.
1RM = Weight ÷ (1.0278 - 0.0278 × Reps)
一次最大重复次数（1RM）可利用亚极量次数通过布莱茨基公式估算。
The FITT principle (Frequency, Intensity, Time, Type) underpins training programme design. Progressive overload requires gradual increase of these variables.
FITT 原则（频率、强度、时间、类型）是训练计划设计的基础。渐进超负荷要求逐步增加这些变量。
Training volume is often calculated as the product of repetitions, sets and load.
Volume Load = Reps × Sets × Weight
训练量通常以重复次数、组数和负重之积来计算。
7. Energy Systems & Metabolic Equivalents | 能量系统与代谢当量
ATP-PC system provides immediate energy for up to about 10 seconds. The lactate system dominates high-intensity efforts lasting 10-90 seconds.
ATP-PC 系统提供约 10 秒内的即时能量。乳酸系统主导持续 10-90 秒的高强度运动。
Aerobic system uses oxygen to resynthesise ATP during prolonged submaximal exercise.
有氧系统在长时间亚极量运动中使用氧气再合成 ATP。
Metabolic equivalent (MET) expresses energy cost. 1 MET = 3.5 mL O₂/kg/min (resting VO₂).
1 MET = 3.5 mL O₂ · kg⁻¹ · min⁻¹
代谢当量（MET）表示能量消耗。1 MET = 3.5 毫升/千克/分钟（安静摄氧量）。
8. Body Composition & Nutrition | 身体成分与营养
Body Mass Index (BMI) is a simple screening tool for weight status.
BMI = Weight (kg) ÷ (Height (m))²
身体质量指数（BMI）是一项简单的体重状况筛查工具。
Energy balance is the relationship between energy intake and energy expenditure. Basal metabolic rate (BMR) can be estimated via the Mifflin-St Jeor equations.
Male BMR = (10 × weight kg) + (6.25 × height cm) - (5 × age) + 5
Female BMR = (10 × weight kg) + (6.25 × height cm) - (5 × age) - 161
能量平衡是能量摄入与消耗之间的关系。基础代谢率（BMR）可通过 Mifflin-St Jeor 方程估算。
9. Skill Acquisition & Reaction Time | 技能习得与反应时
Hick's Law describes the logarithmic relationship between the number of stimulus-response choices and reaction time.
RT = a + b log₂(n)
希克定律描述了刺激-反应选择数量与反应时间之间的对数关系。
Simple reaction time involves one stimulus, while choice reaction time involves multiple stimuli, increasing processing demands.
简单反应时涉及单一刺激，而选择反应时涉及多个刺激，增加了加工需求。
Movement time is the duration of the motor response, while response time is the sum of reaction time and movement time.
Response Time = Reaction Time + Movement Time
动作时是运动反应持续的时间，而反应时是反应时间与动作时间之和。
10. Psychology: Arousal Theories | 心理学：唤醒理论
ationship between arousal and performance: performance = habit strength × drive (arousal).
Performance = Habit × Drive
驱力理论认为唤醒与表现呈线性关系：表现 = 习惯强度 × 驱力（唤醒）。
The Inverted-U hypothesis states that performance increases with arousal to an optimum point, then declines.
倒U型假说指出，表现随唤醒增加而提高，达到最佳点后下降。
Catastrophe theory proposes that when cognitive anxiety is high, performance drops suddenly after passing the optimal arousal level.
突变理论提出，当认知焦虑较高时，表现超过最佳唤醒水平后会突然下降。
11. Power, Work & Efficiency | 功率、功与效率
Work is the product of force and distance moved in the direction of the force.
Work = Force × Distance
功是力与在力的方向上移动的距离之积。
Power measures the rate of doing work or energy transfer per unit time.
Power = Work ÷ Time = Force × Velocity
功率衡量做功的速率，或单位时间内的能量转移。
Mechanical efficiency is the percentage of total energy expended that produces useful work.
Efficiency (%) = (Useful Work ÷ Total Energy Expended) × 100
机械效率是用于产生有用功的总能量消耗的百分比。
12. Additional Key Formulas & Ratios | 其他关键公式与比值
Respiratory exchange ratio (RER) is the ratio of carbon dioxide produced to oxygen consumed; it indicates fuel utilisation.
RER = VCO₂ ÷ VO₂
呼吸交换率（RER）是二氧化碳产生量与氧气消耗量的比值，它指示燃料利用情况。
essure and total peripheral resistance, but in sport science the SV×HR formula is primary.
心输出量也可用平均动脉压和总外周阻力表示，但在运动科学中主要使用 SV×HR 公式。
Static friction is crucial for grip and traction; it is proportional to the normal reaction force.
F_friction_max = μ_s × N
静摩擦对于抓握和牵引至关重要，它与法向反作用力成正比。
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