📚 Year 11 CIE Physical Education: Formula & Principle Quick Reference | 剑桥IGCSE体育公式定理速查手册
Success in CIE IGCSE Physical Education requires not only understanding the theory but also recalling the key formulas and principles that underpin movement analysis, training and human physiology. This quick reference guide compiles all essential equations, laws and measurement tools you need for your Year 11 exams, covering biomechanics, energy systems, cardiovascular responses, training planning and body composition. Keep this handbook handy while revising written paper topics and when completing your coursework.
想在 CIE IGCSE 体育考试中取得成功，既要理解理论，也要熟记支撑运动分析、训练和人体生理的关键公式与原理。这份速查手册整理了 Year 11 考试所需的全部核心方程、定律和测量工具，覆盖生物力学、能量系统、心血管反应、训练计划与身体成分等领域。在复习笔试内容和完成课程作业时，随时查阅本手册。
1. Linear Motion & Kinematics | 直线运动与运动学
Speed (v) is the rate at which distance is covered. Average speed = total distance (d) / total time (t). The formula for speed is:
速度 (v) 是距离变化的快慢。平均速度 = 总距离 (d) / 总时间 (t)。速度公式：
v = d / t
Acceleration (a) measures how quickly velocity changes. It is calculated from the change in velocity (Δv) over time taken (Δt):
加速度 (a) 衡量速度变化的快慢，由速度变化量 (Δv) 除以时间 (Δt) 求出：
a = (v – u) / t
where u is the initial velocity and v is the final velocity. In sporting contexts, a sprinter’s acceleration out of the blocks or a ball’s deceleration when caught can be analysed using these expressions.
其中 u 为初速度，v 为末速度。在运动情景中，短跑选手的起跑加速或接球时球的减速都可以用这些表达式进行分析。
2. Forces and Newton’s Laws | 力与牛顿定律
Newton’s second law gives the relationship between net force (F), mass (m) and acceleration (a):
牛顿第二定律给出了合力 (F)、质量 (m) 和加速度 (a) 的关系：
F = m a
Weight is the force of gravity acting on a mass. Near the Earth’s surface, weight (W) is calculated as:
重力是作用在物体上的万有引力，在地表附近，重力 (W) 按下式计算：
W = m g
where g is the gravitational field strength (10 m/s² or 9.8 m/s²). Understanding force and weight is crucial when analysing jumping, throwing and landing mechanics in physical education.
其中 g 是重力加速度 (10 m/s² 或 9.8 m/s²)。在体育中分析跳跃、投掷与落地力学时，理解力和重力至关重要。
The three laws of motion underpin all human movement: inertia (Law I), F = ma (Law II) and action–reaction (Law III). For example, a swimmer pushes water backward and the water exerts an equal forward force on the swimmer.
运动三定律是一切人体运动的基石：惯性定律（第一定律）、F = ma（第二定律）和作用力与反作用力定律（第三定律）。例如，游泳运动员向后推水，水同时给运动员一个等大向前的力。
3. Momentum and Impulse | 动量与冲量
Momentum (p) is the product of a body’s mass and its velocity:
动量 (p) 是物体质量与速度的乘积：
p = m v
Impulse is the product of the average force applied and the time over which it acts. It equals the change in momentum:
冲量是施加的平均力与作用时间的乘积，它等于动量的变化量：
Impulse = F Δt = Δp
In sport, increasing the time of impact reduces the force and helps prevent injuries. Landing with bent knees extends the time of deceleration, reducing the force on joints. Conversely, a quick strike in tennis or cricket maximises impulse transfer to the ball.
在运动中，增加撞击时间可减小作用力，有助于预防损伤。落地时屈膝可以延长减速时间，从而减少关节所受的力。反过来，网球或板球的快速击球则最大限度地传递冲量。
4. Work, Energy and Power | 功、能量与功率
Work (W) is done when a force moves an object in the direction of the force:
力使物体沿力的方向运动时，就做了功 (W)：
W = F d
Kinetic energy (KE) is the energy of motion:
动能 (KE) 是运动物体具有的能量：
KE = ½ m v²
Gravitational potential energy (GPE) is stored energy due to an object’s height:
重力势能 (GPE) 是因物体被举高而储存的能量：
GPE = m g h
Power (P) is the rate of doing work or transferring energy. It can also be expressed as force multiplied by velocity:
功率 (P) 是做功或能量转换的速率，也可用力与速度的乘积表示：
P = W / t = F v
These concepts explain why a weightlifter generates high power during the explosive second pull, and why a cyclist’s sustained power output is critical for time-trial performance.
这些概念解释了为什么举重运动员在爆发式二次提拉时输出高功率，以及为什么自行车选手在计时赛中持续输出功率极为关键。
5. Levers and Torque | 杠杆与力矩
A lever consists of a fulcrum (pivot), an effort force and a load. The turning effect of a force is called the moment or torque:
杠杆由支点、动力和阻力组成。力的转动效应称为力矩或转矩：
Moment = Force × perpendicular distance from pivot
There are three classes of levers in the human body, classified according to the relative positions of the fulcrum (F), load (L) and effort (E):
人体中存在三类杠杆，根据支点 (F)、阻力 (L) 和动力 (E) 的相对位置分类：
| Lever Class | Arrangement | Example in Body |
|---|---|---|
| First class | Fulcrum between load and effort (L–F–E) | Neck joint nodding |
| Second class | Load between fulcrum and effort (F–L–E) | Ankle during plantar flexion (standing on toes) |
| Third class | Effort between fulcrum and load (F–E–L) | Elbow flexion (biceps curl) |
Third‑class levers are the most common in the body; they favour speed and range of motion at the expense of force. Understanding lever systems helps coaches optimise technique for generating maximum force or speed.
第三类杠杆是人体中最常见的类型，它牺牲力来换取速度和活动范围。理解杠杆系统有助于教练优化技术，以产生最大力量或速度。
6. Cardiovascular & Respiratory Measures | 心血管与呼吸指标
Maximum heart rate is commonly estimated with the simple formula:
最大心率通常用以下简单公式估算：
HRmax = 220 – age (years)
Heart rate reserve (HRR) is the difference between maximum and resting heart rate:
心率储备 (HRR) 是最大心率与静息心率之差：
HRR = HRmax – HRrest
The Karvonen formula uses HRR to prescribe target heart rate zones for aerobic training:
卡氏公式利用心率储备来设定有氧训练的目标心率区间：
Target HR = HRrest + (HRR × %intensity)
Cardiac output (Q) represents the volume of blood pumped by the heart per minute:
心输出量 (Q) 是心脏每分钟泵出的血量：
Q = HR × SV
where SV is stroke volume, the amount of blood ejected per beat. Minute ventilation (VE) describes the total volume of air inhaled or exhaled per minute:
其中 SV 为每搏输出量，即每次心跳泵出的血量。每分通气量 (VE) 表示每分钟吸入或呼出的气体总量：
VE = f × VT
where f is respiratory rate and VT is tidal volume. In an exercise test, VO2 max can be determined from the Fick equation: VO2 = Q × (a–v)O2 difference, illustrating the link between cardiovascular delivery and oxygen extraction.
其中 f 为呼吸频率，VT 为潮气量。在运动测试中，VO2 max 可由菲克方程求得：VO2 = Q × (动静脉氧差)，体现了心血管供氧与组织摄氧之间的关系。
7. Training Principles & FITT | 训练原则与 FITT
Effective training programmes are built on the principles of specificity, progressive overload, reversibility and individuality. Overload can be manipulated through the FITT variables:
有效的训练计划基于专项性、渐进超负荷、可逆性和个体差异等原则。超负荷可通过 FITT 变量来调节：
- Frequency – how often training occurs
- Intensity – how hard the exercise is (often prescribed using % of HRmax or % of VO2 max)
- Time – duration of each session
- Type – mode of activity (continuous, interval, resistance, etc.)
- 频率 (Frequency) – 每周训练次数
- 强度 (Intensity) – 运动难度（通常用 %HRmax 或 %VO2 max 设定）
- 时间 (Time) – 每次训练的持续时间
- 类型 (Type) – 运动方式（持续训练、间歇训练、抗阻训练等）
Training intensity can be quantified as a percentage of HRmax:
训练强度可以量化为最大心率的百分比：
Intensity (%) = (HRexercise / HRmax) × 100
For cardiorespiratory fitness, the recommended zone is typically 60–85% of HRmax. Using these formulas, athletes and coaches can create precise, progressive overload strategies while monitoring for overtraining.
对心肺适能而言，推荐训练区间通常为 60–85% HRmax。利用这些公式，运动员和教练可以制定精确的渐进超负荷策略，同时监控过度训练风险。
8. Body Composition & Anthropometry | 身体成分与人体测量
Body Mass Index (BMI) provides a simple measure of body mass relative to height:
体重指数 (BMI) 是一个简单的体重与身高比例衡量指标：
BMI = mass (kg) / height² (m²)
Waist‑to‑hip ratio (WHR) evaluates fat distribution and health risk:
腰臀比 (WHR) 评估脂肪分布与健康风险：
WHR = waist circumference / hip circumference
Body fat percentage can be estimated from skinfold thickness measurements. A common approach uses the sum of four skinfolds (biceps, triceps, subscapular, suprailiac) and applies the Durnin & Womersley equations or an appropriate population‑specific formula. The general Siri equation for converting body density (BD) to body fat percentage is:
体脂百分比可通过皮褶厚度测量进行估算。常用方法是测量四处皮褶（肱二头肌、肱三头肌、肩胛下、髂嵴上）的总和，再运用 Durnin & Womersley 方程或适合特定人群的公式。常用的 Siri 方程可将体密度 (BD) 转换为体脂百分比：
Body fat % = (495 / BD) – 450
While the Siri equation itself rarely appears in Year 11 papers, understanding the principle that skinfold thickness can predict body density and hence fat percentage is often required.
虽然 Siri 方程不太可能直接出现在 Year 11 考卷中，但理解“皮褶厚度可推算体密度进而得到体脂率”的原理常常是考查内容。
9. Nutrition & Energy Balance | 营养与能量平衡
Energy balance is the relationship between energy intake (food) and energy expenditure (basal metabolism + physical activity). Basal metabolic rate (BMR) can be estimated using the Mifflin‑St Jeor equation, for instance for males:
能量平衡指能量摄入（
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