IGCSE OCR Physical Education: Quick Reference Formula & Theorem Handbook | IGCSE OCR 体育：公式定理速查手册

📚 IGCSE OCR Physical Education: Quick Reference Formula & Theorem Handbook | IGCSE OCR 体育：公式定理速查手册

This handbook provides a concise collection of essential formulas and key principles for the IGCSE OCR Physical Education specification. Use it to quickly revise calculations for heart rate, mechanical advantage, power, cardiac output, and more. Understanding these relationships will help you analyse sporting performance and apply physiological concepts in exam questions.

本手册汇集了IGCSE OCR体育课程中的核心公式和重要原理。可用于快速复习心率、机械优势、功率、心输出量等计算。理解这些关系有助于分析运动表现，并在考试中应用生理学概念。

1. Max Heart Rate (MHR) | 最大心率

Maximum heart rate is the highest number of beats per minute your heart can achieve during maximal exercise. It provides a baseline for setting training zones.

最大心率是进行最大强度运动时心脏每分钟所能达到的最高搏动次数，为设定训练区间提供了基准。

The simplest estimation formula, widely used in exercise science, is:

运动科学中最广泛使用的估算公式为：

MHR = 220 − Age

For a 16‑year‑old athlete, MHR = 220 − 16 = 204 bpm. This value can then be used to calculate training zones such as aerobic or anaerobic thresholds.

对于16岁的运动员，MHR = 220 − 16 = 204次/分。该数值随后可用于计算有氧阈或无氧阈等训练区间。

While the formula is convenient, individual variation exists due to genetics, training status and mode of exercise. Field testing provides a more accurate MHR.

尽管该公式很方便，但因遗传、训练水平和运动方式不同，个体差异显著。实地测试可获得更准确的最大心率。

2. Target Heart Rate Zone (Karvonen Formula) | 目标心率区间（卡沃宁公式）

The Karvonen method offers a more personalised target heart rate by incorporating resting heart rate (RHR) and heart rate reserve (HRR).

卡沃宁法通过纳入安静心率（RHR）和心率储备（HRR），提供了更个性化的目标心率。

First, calculate the heart rate reserve:

首先计算心率储备：

HRR = MHR − RHR

Then apply the desired training intensity percentage:

然后乘以期望的训练强度百分比：

Target HR = (HRR × %Intensity) + RHR

For a 16‑year‑old with RHR = 60 bpm, MHR = 204 bpm and HRR = 144 bpm. At 70% intensity, target HR = (144 × 0.7) + 60 = 160.8 bpm, typically rounded to 161 bpm.

对于一个16岁、安静心率60次/分的人，MHR=204次/分，HRR=144次/分。强度70%时，目标心率 = (144 × 0.7) + 60 = 160.8次/分，通常取整数161次/分。

3. Body Mass Index (BMI) | 身体质量指数

BMI is a simple screening tool that uses mass and height to classify weight status in populations.

BMI是一种利用体重和身高对人群进行体重分类的简易筛查工具。

BMI = Weight (kg) ÷ [Height (m)]²

The World Health Organization defines the following cut‑offs: below 18.5 underweight, 18.5–24.9 healthy weight, 25–29.9 overweight, and 30 or above obese.

世界卫生组织界定：低于18.5为体重过轻，18.5–24.9为健康体重，25–29.9为超重，30及以上为肥胖。

A gymnast weighing 52 kg with a height of 1.60 m has a BMI = 52 ÷ (1.60)² = 20.3, which falls in the healthy range.

一名体重52千克、身高1.60米的体操运动员BMI = 52 ÷ (1.60)² = 20.3，属于健康范围。

4. Speed | 速度

Speed describes the rate at which an athlete covers distance. It is a scalar quantity, meaning direction is not considered.

速度描述运动员通过距离的快慢率，是标量，不考虑方向。

Speed = Distance ÷ Time

Common units are metres per second (m/s) or kilometres per hour (km/h). To convert m/s to km/h, multiply by 3.6.

常用单位为米/秒（m/s）或公里/小时（km/h）。将 m/s 转换为 km/h，需乘以3.6。

If a swimmer completes 50 m in 25 s, average speed = 50 ÷ 25 = 2.0 m/s. The same movement in km/h is 2.0 × 3.6 = 7.2 km/h.

如果游泳运动员25秒完成50米，平均速度 = 50 ÷ 25 = 2.0 m/s。同样速度按km/h计为2.0 × 3.6 = 7.2 km/h。

5. Mechanical Advantage | 机械优势

Mechanical advantage (MA) describes how much a lever system multiplies the effort force. It is determined by the length of the effort arm relative to the resistance arm.

机械优势描述杠杆系统放大动力的倍数，由力臂与阻力臂的相对长度决定。

MA = Effort Arm ÷ Resistance Arm

When MA > 1, the lever amplifies force, making it easier to lift a heavy load (e.g. a wheelbarrow). When MA < 1, the lever allows a small effort to move a resistance quickly over a large range (e.g. biceps curl at the elbow).

当MA > 1时，杠杆放大力，使举起重负荷更省力（如手推车）。当MA < 1时，杠杆允许较小的动力快速大范围移动阻力（如肘部的肱二头肌弯举）。

In the elbow during a biceps curl, the effort arm (distance from elbow joint to biceps insertion) is shorter than the resistance arm (distance from joint to the hand holding the weight). The MA is less than 1, favouring speed over force.

在肱二头肌弯举中，力臂（肘关节到肱二头肌附着点的距离）短于阻力臂（关节到手上负重的距离），MA小于1，偏向速度而非力量。

6. Power | 功率

Power measures the rate of work performed or energy transferred, a crucial factor in explosive activities such as sprinting, jumping and throwing.

功率衡量做功或能量转移的速率，是短跑、跳跃和投掷等爆发性活动的关键因素。

Power = Work ÷ Time

Another expression, combining force and velocity, is frequently used in biomechanics:

另一种结合力与速度的表达式在生物力学中常用：

Power = Force × Velocity

Unit: watt (W), where 1 W = 1 J/s. A weightlifter performing 2000 J of work in 2 s produces a power output of 1000 W.

单位：瓦特（W），1瓦 = 1焦耳/秒。一位举重运动员在2秒内做了2000焦耳的功，输出功率为1000瓦。

7. Cardiac Output (Q) | 心输出量

Cardiac output is the total volume of blood pumped by the left ventricle per minute. It reflects the heart’s ability to meet the oxygen demands of working muscles.

心输出量是左心室每分钟泵出的血液总量，反映心脏满足运动肌肉需氧量的能力。

Q = Heart Rate (HR) × Stroke Volume (SV)

At rest, Q is approximately 5 L/min. During maximal exercise in trained athletes, it can rise to 35 L/min or more.

安静时，心输出量约5升/分；训练有素的运动员在最大强度运动时可升至35升/分甚至更高。

Resting example: HR = 70 bpm, SV = 70 mL, Q = 70 × 70 = 4900 mL/min = 4.9 L/min.

安静时示例：HR=70次/分，SV=70毫升，Q = 70 × 70 = 4900毫升/分 = 4.9升/分。

8. Stroke Volume (SV) | 每搏输出量

Stroke volume is the amount of blood ejected by the left ventricle with each contraction. It is the difference between the volume of blood in the ventricle just before contraction and the volume remaining after contraction.

每搏输出量是左心室每次收缩射出的血量，即心室收缩前血量与收缩

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IGCSE OCR Physical Education: Quick Reference Formula & Theorem Handbook | IGCSE OCR 体育：公式定理速查手册