Year 10 Cambridge IGCSE PE: Formula & Theorem Quick Reference Handbook | 剑桥IGCSE体育：公式定理速查手册

📚 Year 10 Cambridge IGCSE PE: Formula & Theorem Quick Reference Handbook | 剑桥IGCSE体育：公式定理速查手册

This handbook brings together the key formulas, laws and principles you will encounter in the Cambridge IGCSE Physical Education course. Understanding these quantitative and theoretical tools is essential for analysing human performance, designing training programmes and explaining movement. Keep this quick reference guide with you for revision and exam preparation.

本手册汇集了剑桥IGCSE体育课程中会接触到的关键公式、定律和原理。理解这些定量与理论工具对于分析人体运动表现、设计训练计划和解释运动动作至关重要。复习和备考时，请将这份速查手册带在身边。

1. Maximum Heart Rate (Max HR) | 最大心率公式

The maximum heart rate (Max HR) is the highest number of beats per minute your heart can achieve during maximal exercise. The age-predicted formula offers a quick estimate for setting training zones.

最大心率是心脏在极限运动时每分钟能跳动的最高次数。年龄预测公式提供了一个快速估算的方法，用于设定训练区域。

Max HR = 220 – age

For a 15-year-old student, Max HR = 220 – 15 = 205 beats per minute (bpm). Training intensities are then prescribed as percentages of this value, for example 60–80% for aerobic endurance work.

对于一名15岁的学生，最大心率=220–15=205次/分钟(bpm)。之后训练强度根据此值的百分比来设定，例如有氧耐力训练采用60–80%最大心率。

2. Heart Rate Reserve & Target Heart Rate (Karvonen Formula) | 心率储备与目标心率（卡尔沃宁公式）

The Karvonen method uses heart rate reserve (HRR) to calculate target heart rate more accurately than percentage of Max HR alone. HRR is the difference between Max HR and resting heart rate.

卡尔沃宁方法利用心率储备(HRR)来计算目标心率，比单纯使用最大心率百分比更为精确。心率储备是最大心率与安静心率的差值。

HRR = Max HR – Resting HR
Target HR = (HRR × %intensity) + Resting HR

If a 15-year-old has a resting HR of 60 bpm, then HRR = 205 – 60 = 145 bpm. To work at 65% intensity, target HR = (145 × 0.65) + 60 = 154 bpm. This formula ensures that individuals with different fitness levels train at the correct physiological load.

若15岁学生安静心率为60 bpm，则心率储备=205–60=145 bpm。要以65%强度训练，目标心率=(145×0.65)+60=154 bpm。该公式确保不同体能水平的人都能在正确的生理负荷下训练。

3. Cardiac Output | 心输出量

Cardiac output (Q) is the volume of blood pumped by the heart per minute. It is the product of stroke volume (SV) and heart rate (HR).

心输出量(Q)是心脏每分钟泵出的血液量。它是每搏输出量(SV)与心率(HR)的乘积。

Q = SV × HR

At rest, a typical stroke volume may be 70 mL and heart rate 70 bpm, giving a cardiac output of about 4.9 L/min. During intense exercise, stroke volume can rise to 120 mL and heart rate to 180 bpm, producing a cardiac output around 21.6 L/min. Endurance training increases stroke volume, allowing a lower heart rate for the same output.

安静时，典型每搏输出量约为70 mL，心率为70 bpm，心输出量约4.9 L/min。剧烈运动时，每搏输出量可增至120 mL，心率达180 bpm，心输出量可达21.6 L/min。耐力训练能增大每搏输出量，从而在相同输出量下心率更低。

4. Body Mass Index (BMI) | 身体质量指数

BMI is a simple tool for classifying body weight relative to height. It helps identify underweight, healthy weight, overweight and obesity categories.

BMI是根据身高和体重评估体型的简单工具，用于识别过轻、健康、超重和肥胖类别。

BMI = weight (kg) ÷ [height (m)]²

Classification	BMI (kg/m²)
Underweight	< 18.5
Normal weight	18.5 – 24.9
Overweight	25.0 – 29.9
Obese	≥ 30.0

For example, an athlete weighing 65 kg with a height of 1.75 m would calculate BMI = 65 / (1.75)² ≈ 21.2 kg/m², which falls within the normal range. BMI does not distinguish between muscle and fat mass, so it must be interpreted cautiously with muscular athletes.

例如，一名体重65 kg、身高1.75 m的运动员，BMI=65/(1.75)²≈21.2 kg/m²，属于正常范围。但BMI无法区分肌肉与脂肪，对肌肉发达的运动员应谨慎解读。

5. Speed and Acceleration | 速度与加速度

Speed is the rate at which distance is covered. Acceleration measures how quickly velocity changes.

速度是移动距离的变化率。加速度衡量速度变化的快慢。

Speed = distance ÷ time | Acceleration = (final velocity – initial velocity) ÷ time taken

A sprinter covering 100 m in 12.0 s has an average speed of 100 ÷ 12 = 8.33 m/s. If the same athlete accelerates from rest (0 m/s) to 10 m/s in 2.0 s, the acceleration is (10 – 0) ÷ 2 = 5 m/s². These calculations help coaches analyse performance in starts, sprints and change-of-direction moves.

一名短跑选手用12.0秒跑完100米，平均速度为100÷12=8.33 m/s。如果该选手从静止(0 m/s)在2.0秒内加速到10 m/s，加速度为(10–0)÷2=5 m/s²。这些计算有助于教练分析起跑、冲刺和变向动作的表现。

6. Moment of Force (Torque) | 力矩

A moment is the turning effect of a force. It depends on the size of the force and the perpendicular distance from the pivot to the line of action of the force.

力矩是力的转动效果。它取决于力的大小以及支点到力作用线的垂直距离。

Moment = Force × perpendicular distance from fulcrum

In sport, a longer lever arm increases the moment for the same muscle force. For example, in golf, a longer club shaft produces a greater moment on the ball, enabling longer shots. Conversely, in arm wrestling, gripping close to your opponent’s hand reduces their moment arm, giving you a mechanical advantage. Moments are measured in newton-metres (Nm).

在体育运动中，较长的杠杆臂在相同肌力下能增大力矩。例如在高尔夫中，更长的杆身对球产生的力矩更大，能打出更远的球。相反，扳手腕时握住对方靠近手部的位置会缩短其力臂，为你带来机械优势。力矩的单位是牛顿·米(Nm)。

7. Newton’s Laws of Motion | 牛顿运动定律

First Law (Inertia): An object will remain at rest or move at a constant velocity unless acted upon by an external unbalanced force. In sport, a

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Year 10 Cambridge IGCSE PE: Formula & Theorem Quick Reference Handbook | 剑桥IGCSE体育：公式定理速查手册