📚 GCSE AQA PE Formula & Theorem Quick Reference Guide | GCSE AQA 体育：公式定理速查手册
This quick reference guide brings together all the essential equations, formulas and key theorems you need to master for the AQA GCSE Physical Education specification. From cardiovascular calculations to mechanical principles, each entry is clearly stated and followed by its Chinese translation so that you can revise effectively in both languages. Use this handbook to check your understanding, support your exam practice, and build confidence in applying numbers to sport and exercise science.
本速查手册汇集了 AQA GCSE 体育课程所必需的全部核心方程、公式和重要定理。从心血管计算到力学原理，每个条目均清晰呈现并配有中文翻译，帮助你高效进行双语复习。你可以利用本手册检验理解程度、辅助考试练习，并在将数字应用于运动与锻炼科学时建立信心。
1. Maximum Heart Rate and Training Zones | 最大心率与训练区域
Maximum heart rate (HRmax) is the highest number of beats per minute your heart can achieve during all-out exercise. It is commonly estimated using a simple age-based formula. Knowing your HRmax allows you to set personalised training zones that are fundamental to planning aerobic and anaerobic workouts.
最大心率（HRmax）是指心脏在全力运动时每分钟所能达到的最高搏动次数。通常使用一个基于年龄的简单公式来估算。了解你的最大心率有助于设定个性化的训练区域，这是制定有氧与无氧训练计划的基础。
HRmax = 220 − age
The aerobic training zone targets improvements in cardiovascular endurance and is typically set at 60–80% of HRmax. Exercising in this zone uses oxygen to break down fuels and can be sustained for long periods.
有氧训练区域旨在提高心血管耐力，通常设定为最大心率的 60%–80%。在此区域内运动，身体利用氧气分解燃料，并可长时间持续进行。
Target HR (aerobic) = HRmax × 0.6 to HRmax × 0.8
The anaerobic training zone is used to develop speed, power and lactic acid tolerance. It lies between 80% and 90% of HRmax. Work in this zone can only be maintained for short bursts before fatigue sets in.
无氧训练区域用于发展速度、爆发力和乳酸耐受能力，位于最大心率的 80%–90% 之间。该区域内的运动只能持续短暂爆发，随即出现疲劳。
Target HR (anaerobic) = HRmax × 0.8 to HRmax × 0.9
2. Heart Rate Reserve (Karvonen Formula) | 心率储备（卡沃宁公式）
The Karvonen method uses heart rate reserve (HRR) to provide a more individualised target heart rate that accounts for resting heart rate (HRrest). It is particularly useful for fitter individuals whose resting pulse is lower than average.
卡沃宁法利用心率储备（HRR）来计算更为个性化的目标心率，因为它考虑到了安静心率（HRrest）。对于安静心率低于平均水平的体能较好者，该方法尤其适用。
HRR = HRmax − HRrest
Once HRR is known, the target heart rate for any desired intensity is calculated by adding a percentage of HRR back to the resting value. This gives a training zone that reflects true physiological strain more accurately than fractions of HRmax alone.
一旦得出 HRR，即可通过将一定百分比的 HRR 加上安静心率来计算任意期望强度下的目标心率。这样得出的训练区域比仅使用最大心率的百分比更能准确反映真实的生理负荷。
Target HR = (HRR × intensity) + HRrest
Intensity is written as a decimal, e.g. 0.6 for 60%. | 强度以小数表示，例如 0.6 代表 60%。
3. Cardiac Output | 心输出量
Cardiac output (Q) is the volume of blood pumped by the heart in one minute. It is the product of heart rate (HR) and stroke volume (SV), which is the amount of blood ejected per beat. This relationship is central to understanding how the cardiovascular system adapts to exercise.
心输出量（Q）是心脏在一分钟内泵出的血液总量。它是心率（HR）与每搏输出量（SV，即每一次搏动射出的血量）的乘积。这一关系对于理解心血管系统如何适应运动至关重要。
Q = HR × SV
During exercise, both heart rate and stroke volume increase, leading to a dramatic rise in cardiac output. Trained athletes often achieve a higher stroke volume, which allows them to maintain a given cardiac output at a lower heart rate compared with untrained individuals.
运动期间，心率和每搏输出量均会增加，从而使心输出量大幅上升。训练有素的运动员通常能够达到更高的每搏输出量，因此他们能够以比未经训练者更低的心率维持相同的心输出量。
4. Minute Ventilation | 每分钟通气量
Minute ventilation (VE) is the total volume of air moved into and out of the lungs per minute. It is calculated by multiplying tidal volume (TV) – the amount of air inhaled or exhaled in a single breath – by breathing frequency (f).
每分钟通气量（VE）是每分钟进出肺部的空气总体积。它通过潮气量（TV，即单次呼吸吸入或呼出的空气量）乘以呼吸频率（f）来计算。
VE = TV × f
During physical activity, both tidal volume and breathing frequency rise, sharply elevating minute ventilation. This ensures that more oxygen is taken in and more carbon dioxide is removed to meet the demands of working muscles.
在体力活动期间，潮气量和呼吸频率同时上升，使每分钟通气量急剧增加。这确保了更多氧气的摄入和更多二氧化碳的排出，以满足工作肌肉的需求。
5. Body Mass Index (BMI) | 身体质量指数（BMI）
Body Mass Index is a simple screening tool used to classify a person’s weight status in relation to their height. It is important in health-related fitness and is often discussed in connection with the risks of obesity and underweight.
身体质量指数是一种简单的筛查工具，用于依据身高对人的体重状态进行分类。它在健康相关体适能中十分重要，并经常与肥胖和体重过轻的风险一同讨论。
BMI = body mass (kg) ÷ height² (m)
Although BMI does not distinguish between fat and lean mass, it provides a useful starting point for assessing whether an individual may need to adjust their diet and physical activity levels to improve health.
尽管 BMI 无法区分脂肪质量与瘦体重，但它为评估个体是否需要调整饮食和身体活动水平以改善健康提供了一个有用的起点。
6. Speed, Distance and Time | 速度、距离与时间
Speed is a scalar quantity that describes how quickly an athlete covers a certain distance. The relationship between distance travelled, time taken and speed forms one of the most fundamental equations in movement analysis.
速度是一个标量，用于描述运动员覆盖一定距离的迅速程度。移动距离、所用时间与速度之间的关系构成了运动分析中最基本的方程之一。
speed = distance ÷ time ( v = d / t )
Rearranging the equation allows you to calculate distance or time when the other two variables are known. This is regularly applied in sporting contexts, such as timing a sprint or estimating the pace needed to break a personal record.
重新整理该公式，可在已知另外两个变量的情况下计算距离或时间。这在体育情境中经常被应用，例如为短跑计时，或估算打破个人记录所需的速度。
7. Acceleration and Force | 加速度与力
Acceleration is the rate at which velocity changes. It can be calculated from the difference between final velocity and initial velocity over time, and it is essential for analysing starts, sprints and changes of direction in sport.
加速度是速度变化的快慢。它可以通过最终速度与初始速度之差随时间的变化来计算，对于分析运动中的起跑、冲刺和变向至关重要。
a = (v − u) / t
Newton’s second law of motion links force, mass and acceleration. The greater the force applied to an object, the more it accelerates, provided its mass remains constant. This principle explains how athletes generate speed through force application.
牛顿第二运动定律将力、质量和加速度联系在一起。在质量不变的情况下，施加于物体的力越大，其加速度就越大。这一原理解释了运动员如何通过施加力量产生速度。
F = m × a
8. Momentum | 动量
Momentum is the product of an object’s mass and its velocity. It describes the quantity of motion an athlete possesses and helps explain why heavier athletes or those moving faster are harder to stop on the field.
动量是物体质量与其速度的乘积。它描述了运动员所拥有的运动量，并有助于解释为什么体重较大的运动员或移动更快的运动员在场上更难被拦停。
p = m × v
In contact sports such as rugby, conservation of momentum is a key concept during tackles. A player with greater momentum will tend to continue moving in the same direction after a collision, provided external forces are equal.
在英式橄榄球等接触性运动中，动量守恒是抢断过程中的关键概念。如果外力相等，动量更大的球员在碰撞后往往会继续沿原方向移动。
9. Levers and Moments | 杠杆与力矩
A moment is the turning effect of a force about a pivot. In the human body, joints act as pivots and muscles provide the effort to overcome resistance. Understanding moments helps explain how lever systems can amplify force or speed.
力矩是力绕支点产生的转动效应。在人体中，关节充当支点，肌肉提供动力以克服阻力。理解力矩有助于解释杠杆系统如何放大力量或速度。
Moment = force × perpendicular distance from pivot
For a lever to be balanced or to produce efficient movement, the clockwise moments must equal the anticlockwise moments. Athletes unconsciously adjust technique to optimise moment arms and reduce the effort required for a given movement.
为了使杠杆平衡或产生高效的运动，顺时针力矩必须等于逆时针力矩。运动员会不自觉地调整技术以优化力臂，减少特定动作所需的力量。
10. Mechanical Advantage | 机械优势
Mechanical advantage (MA) describes how effectively a lever multiplies the effort applied to overcome a resistance. When the effort arm is longer than the resistance arm, a large load can be moved with a relatively small effort force.
机械优势（MA）用于描述杠杆将施加的动力放大以克服阻力的有效程度。当动力臂长于阻力臂时，能够用相对较小的力量移动较大的负荷。
MA = effort arm ÷ resistance arm
Second-class levers in the body, such as the ankle during plantar flexion, naturally have a mechanical advantage greater than 1. This means they favour force production, making them vital for powerful pushes in running and jumping.
人体中的第二类杠杆，例如跖屈时的踝关节，天然具有大于 1 的机械优势。这意味着它们有利于产生力量，因而对于跑步和跳跃中的有力蹬伸至关重要。
11. Power | 功率
Power is the rate at which work is done or energy is transferred. In sport, powerful athletes can exert large forces quickly, which is a key determinant of success in explosive events like throwing, jumping and sprinting.
功率是做功或能量转换的快慢。在体育运动中，爆发力强的运动员能够快速施加大力量，这是投掷、跳跃和短跑等爆发性项目取得成功的关键因素。
P = W / t
When the force applied and the velocity of movement are known, power can also be expressed as the product of force and velocity. This form is often more practical for analysing continuous sporting actions like cycling or rowing.
当已知施加的力量和运动速度时，功率还可以表示为力与速度的乘积。这种形式往往更适用于分析骑行或划船等连续性运动动作。
P = F × v
12. Calorie Expenditure and METs | 卡路里消耗与代谢当量
Metabolic equivalents (METs) express the energy cost of physical activities relative to resting metabolism. One MET is defined as the oxygen consumption of a person at rest and is approximately 3.5 ml of oxygen per kilogram of body mass per minute.
代谢当量（MET）表示身体活动相对于安静代谢的能量消耗。1 MET 被定义为人体在安静状态下的耗氧量，大约为每公斤体重每分钟消耗 3.5 毫升氧气。
1 MET ≈ 3.5 ml O₂ / kg / min
To estimate calorie expenditure during an activity, multiply the MET value of the activity by the individual’s body mass in kilograms and by the duration of the activity in hours. This approach is widely used in fitness monitoring and weight management programmes.
要估算某项活动中的卡路里消耗，可将该活动的 MET 值乘以个人体重（公斤）再乘以活动持续时间（小时）。这一方法被广泛用于健身监测和体重管理方案中。
Calories burned = METs × body mass (kg) × time (hours)
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