📚 GCSE Eduqas Physical Education: Quick Reference Guide to Formulas and Principles | GCSE Eduqas 体育：公式定理速查手册
Mastering the core formulas and principles is essential for success in GCSE Eduqas Physical Education. This quick-reference handbook brings together all the key equations and concepts you need, from cardiovascular training zones to lever mechanics, presented in a clear and exam-focused format. Use it to reinforce your understanding, check your knowledge, and build confidence before the big day.
掌握核心公式与原理对于 GCSE Eduqas 体育考试的成功至关重要。这本速查手册将所有关键公式和概念汇集一处，从心血管训练区间到杠杆力学，并以清晰、紧扣考纲的方式呈现。用它来巩固理解、检验知识，并在大考前建立信心。
1. Maximum Heart Rate and Training Zones | 最大心率与训练区间
Maximum Heart Rate (MHR) is the highest number of beats per minute your heart can achieve during maximal exercise. It is estimated using a simple age-based formula and forms the basis for calculating training zones.
最大心率 (MHR) 是你在极限运动中心脏每分钟所能达到的最高跳动次数。它用一个基于年龄的简单公式估算，并构成计算训练区间的基础。
MHR = 220 − age (years)
Once MHR is known, training zones can be identified to target different fitness components. The aerobic training zone typically lies between 60% and 80% of MHR, improving cardiovascular endurance. The anaerobic training zone, between 80% and 90% of MHR, develops the ability to work at high intensities without oxygen.
一旦知道了最大心率，就可以确定训练区间来针对不同的体适能要素。有氧训练区间通常位于最大心率的 60% 至 80% 之间，能改善心血管耐力。无氧训练区间在最大心率的 80% 至 90% 之间，能发展在缺氧情况下进行高强度运动的能力。
| Training Zone | % of MHR | Primary Benefit |
|---|---|---|
| Warm-up / Recovery | 50–60% | Improves blood flow, aids recovery |
| Aerobic (Endurance) | 60–80% | Enhances stamina and cardiovascular health |
| Anaerobic (High Intensity) | 80–90% | Develops speed, power, and lactate tolerance |
| Maximal Effort | 90–100% | Peak performance, short bursts only |
2. Karvonen Formula for Target Heart Rate | 卡沃宁目标心率公式
The Karvonen formula provides a more personalised target heart rate by incorporating resting heart rate (RHR). It calculates the heart rate reserve (HRR) and then applies the desired intensity percentage.
卡沃宁公式通过纳入静息心率 (RHR) 提供了一个更加个性化的目标心率。它先计算心率储备 (HRR)，然后乘以所需的强度百分比。
Heart Rate Reserve (HRR) = MHR − RHR
Target Heart Rate = RHR + (HRR × Intensity %)
For example, a 16-year-old performer with RHR of 60 bpm wanting to train at 70% intensity would have: MHR = 220 − 16 = 204 bpm; HRR = 204 − 60 = 144 bpm; Target = 60 + (144 × 0.70) = 160.8 bpm (≈ 161 bpm). This method ensures the exercise intensity reflects the individual’s fitness level more accurately than using MHR alone.
例如，一位 16 岁的运动员静息心率 60 bpm，希望以 70% 强度训练：MHR = 220 − 16 = 204 bpm；HRR = 204 − 60 = 144 bpm；目标心率 = 60 + (144 × 0.70) = 160.8 bpm（约 161 bpm）。与单独使用最大心率相比，这种方法能更准确地反映个人的体能水平。
3. Body Mass Index (BMI) | 体重指数（BMI）
BMI is a simple screening tool used to classify individuals as underweight, normal weight, overweight or obese based on height and mass. It does not distinguish between muscle and fat, so athletes with high muscle mass may be misclassified.
BMI 是一种简单的筛查工具，用于根据身高和体重将个体划分为体重不足、正常、超重或肥胖。它不区分肌肉和脂肪，因此肌肉量高的运动员可能被错误分类。
BMI = body mass (kg) ÷ height² (m²)
| BMI Range (kg/m²) | Classification |
|---|---|
| Less than 18.5 | Underweight |
| 18.5 – 24.9 | Normal weight |
| 25.0 – 29.9 | Overweight |
| 30.0 and above | Obese |
4. Waist-to-Hip Ratio | 腰臀比
Waist-to-hip ratio (WHR) is an indicator of fat distribution and associated health risks. A higher ratio suggests central obesity, which is linked to cardiovascular disease and type 2 diabetes.
腰臀比 (WHR) 是脂肪分布及相关健康风险的指标。比值较高表明中心性肥胖，这与心血管疾病和 2 型糖尿病相关。
WHR = waist circumference (cm) ÷ hip circumference (cm)
Health risk categories differ by gender. For men, a WHR above 0.90 indicates high risk; for women, the threshold is 0.85. WHR is a practical measurement used alongside BMI for a fuller picture of body composition.
健康风险分类因性别而异。男性腰臀比高于 0.90 表示高风险；女性的阈值为 0.85。腰臀比是一种实用的测量方法，与 BMI 结合使用可以更全面地了解身体成分。
5. Speed, Acceleration, and Momentum | 速度、加速度与动量
These three fundamental mechanical quantities describe how quickly a performer moves, how that movement changes, and how much motion the body possesses.
这三个基本的力学量描述了运动员移动的快慢、运动的变化方式以及身体拥有多大的运动量。
Speed (m/s) = distance (m) ÷ time (s)
Acceleration (m/s²) = (final velocity − initial velocity) ÷ time taken
Momentum (kg m/s) = mass (kg) × velocity (m/s)
For instance, a 70 kg sprinter running at 9 m/s has a momentum of 630 kg m/s. The greater the momentum, the harder it is to change direction or stop – a key consideration in tackling and collision sports.
例如，一名 70 公斤的短跑运动员以 9 m/s 的速度奔跑，其动量为 630 kg m/s。动量越大，改变方向或停下来就越难——这在拦截和碰撞类运动中是一个关键考虑因素。
6. Force, Work, and Power | 力、功与功率
Force causes movement or deformation; work is done when a force moves an object; power reflects how quickly that work is performed. These terms describe the physical demands of sport.
力引起运动或形变；当一个力使物体移动时就做了功；功率反映了做功的快慢。这些术语描述了运动的物理需求。
Force (N) = mass (kg) × acceleration (m/s²)
Work done (J) = force (N) × distance moved in direction of force (m)
Power (W) = work done (J) ÷ time (s) or Power = force (N) × velocity (m/s)
A weightlifter lifting 1000 N through 2 m in 0.8 seconds produces 2000 J of work and a power output of 2500 W. Explosive athletes require high power production within short time frames.
一位举重运动员在 0.8 秒内将 1000 N 的重量举起 2 米，做功 2000 J，输出功率达 2500 W。爆发力型运动员需要在短时间内产生高功率。
7. Levers and Mechanical Advantage | 杠杆与机械效益
Levers in the human body consist of a bone (lever arm), a joint (fulcrum), a muscle effort, and a load. The arrangement determines mechanical advantage, which influences the trade-off between force and speed of movement.
人体中的杠杆由骨（杠杆臂）、关节（支点）、肌肉作用力和负荷组成。它们的排列方式决定了机械效益，这影响着力量与运动速度之间的权衡。
Mechanical Advantage (MA) = effort arm ÷ resistance arm
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A mechanical advantage greater than 1 means the lever amplifies force – a large load can be moved with a smaller effort, but over a shorter distance and at lower speed (e.g., second-class lever like calf raise).
机械效益大于 1 意味着杠杆放大了力量——可以用较小的力移动较重的负荷，但移动距离更短且速度更慢（例如，提踵属于第二类杠杆）。
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MA less than 1 allows greater range of motion and speed at the expense of force (e.g., third-class lever like bicep curl). Most levers in the body are third-class, favouring speed and range over strength.
机械效益小于 1 则允许更大的运动范围和速度，但会牺牲力量（例如，肱二头肌弯举属于第三类杠杆）。人体中大多数杠杆是第三类，优先考虑速度和范围而非力量。
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First-class levers (MA can be >, <, or = 1) are less common; the head nodding movement is an example, where the fulcrum lies between effort and load.
第一类杠杆（MA 可大于、小于或等于 1）较少见；点头动作就是一个例子，其支点位于作用力和负荷之间。
8. Stability and Centre of Mass | 稳定性与重心
Stability is the ability of a body to resist being displaced. It is influenced by the height of the centre of mass, the size of the base of support, and the line of gravity’s relationship to that base.
稳定性是指身体抵抗位移的能力。它受重心高度、支撑面积大小以及重力线相对于该支撑面位置的影响。
A body is more stable when: centre of mass is low; base of support is wide; line of gravity falls inside the base.
In sport, a wrestler lowers their centre of mass and widens their stance to become harder to topple. Conversely, a sprinter in the ‘set’ position raises the centre of mass slightly and shifts the line of gravity forward to facilitate quick acceleration. There is no single numerical formula, but these principles can be applied to analyse any static or dynamic position.
在体育运动中，摔跤手降低重心并加宽站姿以使自己更难被摔倒。相反，短跑运动员在“预备”姿势中略微抬高重心，并将重力线前移，以利于快速起跑。虽然没有单一的数值公式，但这些原理可用于分析任何静态或动态姿势。
9. Cardiac Output and Minute Ventilation | 心输出量与每分通气量
Understanding how the cardiovascular and respiratory systems respond to exercise requires these two central equations. Cardiac output (Q) measures the volume of blood the heart pumps per minute, while minute ventilation (VE) measures the volume of air breathed per minute.
理解心血管和呼吸系统对运动的反应需要这两个核心公式。心输出量 (Q) 衡量心脏每分钟泵出的血量，而每分通气量 (VE) 衡量每分钟呼吸的空气量。
Cardiac Output (L/min) = stroke volume (mL) × heart rate (bpm)
Minute Ventilation (L/min) = tidal volume (L) × breathing frequency (breaths/min)
During exercise, both stroke volume and heart rate increase, so cardiac output rises significantly to deliver more oxygen to working muscles. Simultaneously, tidal volume and breathing rate increase, which boosts minute ventilation. Trained athletes often develop a larger stroke volume and lower resting heart rate, making their circulatory systems more efficient.
运动时，每搏输出量和心率都会增加，因此心输出量显著上升，为工作肌肉输送更多氧气。同时，潮气量和呼吸频率增加，从而提高了每分通气量。经过训练的运动员通常每搏输出量更大、静息心率更低，这让他们的循环系统效率更高。
10. Energy Balance and Caloric Expenditure | 能量平衡与热量消耗
Body weight is maintained when energy intake (calories consumed) equals energy expenditure (calories burned). A sustained positive energy balance leads to weight gain; a negative balance leads to weight loss. While the exact metabolic equations are beyond GCSE requirements, the principle is vital for health and performance nutrition.
当能量摄入（消耗的卡路里）等于能量消耗（燃烧的卡路里）时，体重得以维持。持续的正能量平衡导致体重增加；负平衡导致体重减轻。虽然精确的代谢公式超出 GCSE 要求，但这原理对健康和运动营养至关重要。
Energy balance = energy intake (from food and drink) − energy expenditure (basal metabolism + physical activity + thermic effect of food)
Physical activity can be quantified in METs (Metabolic Equivalents), where 1 MET is the energy used at rest. An activity of 8 METs uses eight times the resting energy. For a rough calculation of kilocalories burned: kcal = METs × body mass (kg) × duration (hours). This helps performers plan appropriate nutritional strategies for their training demands.
身体活动可以用 MET（代谢当量）来量化，1 MET 是静息时的能量消耗。强度为 8 METs 的活动消耗的能量是静息时的八倍。粗略计算消耗的千卡数：千卡 = METs × 体重 (kg) × 持续时间 (小时)。这有助于运动员根据训练需求规划适当的营养策略。
11. Training Load and Progressive Overload | 训练负荷与渐进超负荷
Progressive overload is the gradual increase in training stress to drive adaptation and improvement. It can be monitored and adjusted using simple volume-load formulas. Without overload, fitness plateaus; too much overload risks injury and burnout.
渐进超负荷是逐渐增加训练压力以驱动适应和进步的过程。可使用简单的训练量—负荷公式进行监测和调整。没有超负荷，体能会停滞；超负荷过多则有受伤和过度训练的风险。
Training Load = frequency × intensity × time × type (FITT principle)
Volume-load (resistance training) = sets × repetitions × weight lifted (kg)
For example, if a performer does 3 sets of 10 reps at 50 kg, the volume-load is 3 × 10 × 50 = 1500 kg. To progressively overload, they might increase the weight, add sets, or add reps in the next session. Coaches use these load calculations to ensure safe and effective programme design.
例如，一名运动员以 50 公斤的重量完成 3 组 10 次，训练量负荷为 3 × 10 × 50 = 1500 公斤。为了渐进超负荷，他们在下一次训练中可以增加重量、增加组数或增加重复次数。教练员利用这些负荷计算来确保安全有效的训练计划设计。
12. Summary of Key Units and Conversions | 关键单位与换算汇总
Using correct units is critical in examination answers. Below is a quick reference table of the quantities, their SI units, and common conversions you should know for the Eduqas GCSE course.
在考试答案中使用正确的单位至关重要。以下是一个关键量、其国际单位制以及你需要掌握的常见换算的速查表，适用于 Eduqas GCSE 课程。
| Quantity | Unit | Notes |
|---|---|---|
| Distance / Height | metre (m) | 1 km = 1000 m |
| Time | second (s) | 1 min = 60 s; 1 h = 3600 s |
| Mass | kilogram (kg) | Often given in grams; 1 kg = 1000 g |
| Force | newton (N) | Weight = mass × gravity (g ≈ 10 m/s²) |
| Work / Energy | joule (J) | 1 kJ = 1000 J |
| Power | watt (W) | 1 W = 1 J/s |
| Speed / Velocity | metre per second (m/s) | May also see km/h; convert as needed |
Always show your units in calculation questions and double-check that they match. Converting all values to SI units before substituting into a formula helps avoid errors and is expected in exam mark schemes.
在计算题中务必写出单位并再次检查它们是否匹配。在代入公式前将所有数值转换为国际单位制有助于避免错误，这也是考试评分方案所要求的。
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