📚 IGCSE Edexcel PE: Formula & Theorem Quick Reference | IGCSE Edexcel 体育：公式定理速查手册
This quick reference handbook compiles every essential formula, equation, principle and biomechanical law required for the IGCSE Edexcel Physical Education specification. Use it to sharpen your calculations for heart rate zones, movement analysis, training indices and energy system chemistry – all explained in clear, paired English and Chinese text.
本速查手册汇总了 IGCSE Edexcel 体育学科所有必备的公式、方程式、原理及生物力学定律，涵盖心率区域、运动分析、训练指数和能量系统化学等计算的清晰讲解，以中英对照的方式呈现，助你精准掌握各类定量考点。
1. Maximum Heart Rate & Karvonen Formula | 最大心率与卡沃内公式
Maximum heart rate (HRmax) is the highest number of beats per minute your heart can safely achieve during maximal exercise. A simple age-based estimate is universally applied in IGCSE PE.
HRmax = 220 – age (years)
最大心率是指心脏在最大强度运动中每分钟能够达到的最高安全搏动次数，IGCSE 体育统一采用基于年龄的简易估算。
HRmax = 220 – 年龄（岁）
Heart rate reserve (HRR) indicates the range between resting and maximum heart rate. The Karvonen formula uses HRR to calculate a personalised target heart rate for aerobic training zones, typically between 60% and 80% of HRR.
HRR = HRmax – Resting HR
Target HR = Resting HR + (Desired % × HRR)
心率储备反映了安静心率与最大心率之间的区间。卡沃内公式运用心率储备计算个性化目标心率，常用于设定 60%–80% 强度的有氧训练区域。
HRR = HRmax – 安静心率
目标心率 = 安静心率 + (目标强度百分比 × HRR)
2. Body Mass Index (BMI) | 身体质量指数（BMI）
BMI is a simple ratio of mass to height squared, used to classify individuals as underweight, normal weight, overweight or obese. Though it does not distinguish fat from muscle, it remains a common health screening tool.
BMI = body mass (kg) / height² (m²)
BMI 是体重与身高平方的简易比值，用于划分过轻、正常、超重和肥胖等类别。尽管它无法区分脂肪与肌肉，但仍是常见的健康筛查指标。
BMI = 体重（kg）/ 身高²（m²）
For a performer weighing 65 kg with a height of 1.70 m, BMI = 65 / (1.70 × 1.70) ≈ 22.5 kg/m², which falls in the healthy range. This calculation often appears alongside fitness test interpretation.
例如，体重 65 kg、身高 1.70 m 的运动员，BMI = 65 / (1.70 × 1.70) ≈ 22.5 kg/m²，属于健康范围。这类计算常伴随体能测试结果一起考查。
3. Levers, Moments and Mechanical Advantage | 杠杆、力矩与机械优势
In the human body, bones act as levers, joints as fulcrums, and muscles supply the effort. The moment (turning effect) of a force is the product of force and the perpendicular distance from the fulcrum.
Moment (Nm) = Force (N) × Perpendicular distance from fulcrum (m)
人体骨骼如同杠杆，关节为支点，肌肉提供动力。力矩是力产生转动效应的量度，等于力与力臂的乘积。
力矩（牛顿·米）= 力（N）× 力臂（支点到力作用线的垂直距离，m）
When a lever is balanced, the clockwise moment equals the anticlockwise moment, leading to the equilibrium equation Effort × effort arm = Load × load arm. Mechanical advantage (MA) quantifies the efficiency of a lever system.
Effort × effort arm = Load × load arm
Mechanical Advantage (MA) = Effort arm / Load arm
当杠杆平衡时，顺时针力矩等于逆时针力矩，即动力 × 动力臂 = 阻力 × 阻力臂。机械优势用于衡量杠杆系统的效率。
动力 × 动力臂 = 阻力 × 阻力臂
机械优势 (MA) = 动力臂 / 阻力臂
A second-class lever (e.g. calf raise) has MA > 1, favouring force production. A third-class lever (e.g. biceps curl) has MA < 1, favouring speed and range of motion. First-class levers can have MA equal to, greater or less than 1.
第二类杠杆（如提踵）的 MA 大于 1，省力；第三类杠杆（如肱二头肌弯举）MA 小于 1，有利于速度和运动幅度。第一类杠杆的 MA 可等于、大于或小于 1。
4. Linear Motion: Speed, Velocity and Acceleration | 直线运动：速率、速度与加速度
Speed is the rate of change of distance, a scalar quantity without direction. Velocity is the rate of change of displacement and includes direction. Acceleration is the rate of change of velocity.
Speed (m/s) = distance (m) / time (s)
Acceleration (m/s²) = (final velocity – initial velocity) / time
速率是距离的变化率，为标量，无方向。速度是位移的变化率，具有方向。加速度则是速度的变化率。
速率（m/s）= 距离（m）/ 时间（s）
加速度（m/s²）=（末速度 – 初速度）/ 时间
On a distance–time graph, the gradient gives speed; on a velocity–time graph, the gradient gives acceleration and the area under the graph gives displacement. These graphs are frequently used to analyse sprints, swimming or cycling events.
距离—时间图中，斜率表示速率；速度—时间图中，斜率表示加速度，面积表示位移。这些图形常用于分析短跑、游泳或自行车赛事中的运动表现。
5. Newton’s Laws of Motion | 牛顿运动定律
Newton’s three laws underpin virtually all movement analysis in sport. They are stated qualitatively in IGCSE but are frequently tested through sporting examples.
牛顿三大定律几乎支撑着所有体育运动中的运动分析，IGCSE 考试以定性描述为主，但常结合运动实例考查。
First Law (Inertia): A body remains at rest or moves at constant velocity unless acted upon by an external resultant force. Example: a football stays still until kicked; a cyclist coasts when no net force is applied.
第一定律（惯性定律）： 任何物体都保持静止或匀速直线运动状态，直到有外力迫使它改变。例如：足球被踢前保持静止，自行车手在合力为零时保持滑行。
Second Law (Acceleration): The acceleration of an object is directly proportional to the net force and inversely proportional to its mass.
F = m × a
第二定律（加速度定律）： 物体的加速度与所受合力成正比，与质量成反比。
F = m × a
Third Law (Action–Reaction): For every action force there is an equal and opposite reaction force. In swimming, the hand pushes water backward, and the water pushes the swimmer forward.
第三定律（作用与反作用）： 作用力与反作用力大小相等、方向相反。游泳时，手向后推水，水则向前推动游泳者。
6. Momentum and Impulse | 动量与冲量
Momentum is the product of mass and velocity, describing the quantity of motion an object possesses. Impulse is the product of force and the time for which it acts, equal to the change in momentum.
Momentum (kg m/s) = mass (kg) × velocity (m/s) (p = m v)
Impulse (N s) = Force (N) × time (s) = Δp = mv – mu
动量是质量与速度的乘积，描述物体的运动量。冲量是力与作用时间的乘积，等于动量的变化。
动量（kg·m/s）= 质量（kg）× 速度（m/s） (p = m v)
冲量（N·s）= 力（N）× 时间（s）= 动量变化量 = mv – mu
These concepts explain injury prevention techniques: catching a ball with ‘giving’ hands extends the impact time, reducing the force felt. In tackling, following through increases contact time and transfers more momentum to the opponent.
这些概念能解释运动损伤预防原理：接球时顺势后收双手可延长作用时间，减小受力。拦截时顺势前送则增加接触时间，将更多动量传递给对手。
7. Bernoulli’s Principle & Magnus Effect | 伯努利原理与马格努斯效应
Bernoulli’s principle states that faster fluid (air) flow over a surface creates lower pressure, while slower flow creates higher pressure. This pressure difference produces a lift or swing force on projectiles and airfoils.
伯努利原理指出，流体（空气）在表面流速较快处压强较小，流速较慢处压强较大。这一压力差会对抛射体或翼型产生升力或侧向力。
The Magnus effect applies Bernoulli’s principle to spinning balls. A spinning ball drags air faster on one side and slower on the opposite side, causing a pressure imbalance and making the ball curve. Topspin in tennis dips the ball; backspin extends flight; sidespin generates curved trajectories in football and volleyball.
马格努斯效应将伯努利原理应用于旋转球体：旋转的球带动一侧空气加速、对面侧减速，产生压力差，使球路弯曲。网球的“上旋”令球下沉，“下旋”延长飞行，足球和排球中的“侧旋”则形成弧线轨迹。
8. Harvard Step Test Index | 哈佛台阶测试指数
The Harvard Step Test measures cardiovascular endurance by recording the pulse recovery after a fixed step-up protocol. A higher index indicates better aerobic fitness.
Fitness Index = (exercise time in seconds × 100) / (2 × sum of three pulse counts)
哈佛台阶测试通过测量固定登阶运动后的脉搏恢复情况来评定心血管耐力，指数越高，有氧适能越好。
体能指数 =（运动持续时间 秒 × 100）/（2 × 三次脉搏数之和）
The three pulse counts are taken at 1–1.5 min, 2–2.5 min and 3–3.5 min after exercise. For example, a 300 s step test with post-exercise pulse sums of 80+75+70 = 225 gives an index of (300×100)/(2×225) = 66.7, which is ‘average’ on standard tables.
三次脉搏分别在运动结束后 1–1.5 分钟、2–2.5 分钟和 3–3.5 分钟测量。如运动 300 秒后三次脉搏之和为 80+75+70=225，则体能指数为 (300×100)/(2×225) = 66.7，在标准表中属于“一般”水平。
9. Cooper Test & VO₂max Estimation | 库珀测试与最大摄氧量估算
The 12-minute Cooper run/walk test assesses maximal oxygen uptake (VO₂max) indirectly. The distance covered is inserted into a regression equation to estimate VO₂max in ml/kg/min.
VO₂max (ml/kg/min) = (22.351 × distance in km) – 11.288
库珀 12 分钟跑/走测试间接评定最大摄氧量（VO₂max），将 12 分钟内完成的距离代入回归方程即可估算出 VO₂max。
VO₂max（ml/kg/min）= (22.351 × 距离 km) – 11.288
If an athlete covers 2.8 km in 12 minutes, estimated VO₂max = (22.351 × 2.8) – 11.288 = 62.58 – 11.288 ≈ 51.3 ml/kg/min, a level often classified as excellent. This test is widely used in schools because it requires minimal equipment.
若运动员 12 分钟跑完 2.8 km，估算的 VO₂max = (22.351 × 2.8) – 11.288 = 62.58 – 11.288 ≈ 51.3 ml/kg/min，通常属于优秀等级。该测试因所需器械少而在学校普遍使用。
10. Energy System Equations | 能量系统化学方程式
Understanding the three energy systems and their chemical reactions is fundamental to IGCSE PE. The ATP–PC system (anaerobic alactic) provides immediate energy via the breakdown of stored ATP and creatine phosphate.
Published by TutorHao | IGCSE 体育 Revision Series | aleveler.com
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