📚 Year 9 Edexcel Physical Education: Formula & Theorem Quick Reference Handbook | 九年级爱德思体育：公式定理速查手册
Welcome to your go-to revision guide for every calculation and scientific principle you need to master in Year 9 Edexcel Physical Education. From heart rate training zones to lever mechanics, this handbook breaks down each formula with a clear English explanation, immediately followed by its Chinese counterpart, so you can confidently apply the right equation under exam conditions. Use this resource regularly to strengthen both your theoretical understanding and your ability to interpret sporting data.
欢迎使用这本专为九年级爱德思体育设计的公式与定理速查手册。从心率训练区间到杠杆力学，本手册将每一个公式都附上清晰的英文解释，并紧接中文对应说明，帮助你在考试条件下自信地运用正确的方程。经常查阅这份资料，能巩固你的理论理解，并提升你解读运动数据的能力。
1. Maximum Heart Rate (MHR) | 最大心率
The simplest and most widely used estimate of maximum heart rate is:
最简单且使用最广泛的最大心率估算公式为：
MHR = 220 – Age
For a 14-year-old student, MHR would be 220 – alue serves as the baseline for calculating all training intensity zones, though it can vary with fitness level and genetics.
对于一名14岁的学生，最大心率约为220 – 14 = 206次/分（bpm）。该数值是计算所有训练强度区间的基准，尽管它会因体能水平和遗传因素存在个体差异。
2. Karvonen Formula – Heart Rate Reserve (HRR) | 卡沃宁公式——心率储备
The Karvonen formula introduces resting heart rate (RHR) for a more personalised training intensity:
卡沃宁公式引入安静心率，使训练强度更个性化：
Target HR = RHR + (Intensity % × (MHR – RHR))
First, calculate your heart rate reserve (MHR – RHR). Multiply this reserve by the desired percentage (e.g., 0.6 for 60%), then add your RHR. For a student with RHR = 70 bpm and MHR = 206, 60% intensity yields 70 + 0.6×(206–70) = 151.6 bpm.
首先算出心率储备（MHR – RHR）。将储备值乘以目标百分比（如60%为0.6），再加回安静心率。以一名安静心率70次/分、最大心率206次/分的学生为例，60%强度对应心率为70 + 0.6×(206–70) = 151.6次/分。
3. Target Heart Rate Zones | 目标心率区间
Edexcel expects you to identify five main training zones based on MHR:
爱德思考纲要求你掌握基于最大心率的五个主要训练区间：
| Training Zone / 训练区间 | % MHR | Primary Benefit / 主要作用 |
|---|---|---|
| Healthy Heart Zone / 健康心脏区 | 50–60% | Warm-up, recovery / 热身、恢复 |
| Fat Burning Zone / 燃脂区 | 60–70% | Aerobic base, fat metabolism / 有氧基础、脂肪代谢 |
| Aerobic Zone / 有氧区 | 70–80% | Cardiovascular endurance / 心血管耐力 |
| Anaerobic Threshold / 无氧阈 | 80–90% | Lactate tolerance, speed / 乳酸耐受、速度 |
| Red Line / 红线区 | 90–100% | Max effort, sprint / 极限努力、冲刺 |
Remember: the ‘fat burning’ zone uses a higher proportion of fat as fuel, but total calorie burn is lower than at higher intensities.
注意：所谓“燃脂区”虽然脂肪供能比例最高，但总热量消耗低于高强度运动。
4. Body Mass Index (BMI) | 身体质量指数
BMI is a simple screening tool used to classify weight relative to height:
BMI 是一种根据身高和体重评估体型的简便筛查工具：
BMI = Body mass (kg) ÷ (Height (m))²
kg and standing 1.65 m tall has a BMI of 55 ÷ (1.65)² ≈ 20.2 kg/m², which falls within the ‘normal weight’ range (18.5–). BMI does not differentiate between muscle and fat, so it is less accurate for athletes.
例如，一名体重55 kg、身高1.65 m的学生，其BMI为55 ÷ (1.65)² ≈ 20.2 kg/m²，属于“正常体重”范围（18.5–24.9）。由于BMI无法区分肌肉与脂肪，因此对运动员的评估并不精确。
5. Basal Metabolic Rate (BMR) | 基础代谢率
BMR estimates the minimum energy required to maintain vital functions at rest. In GCSE PE, a simplified generic equation is often used; however, the most recognised estimation is the Harris–Benedict equation:
BMR 是维持静息状态下基本生命活动所需的最低能量。在GCSE体育中，常使用简化通用公式，但最被认可的还是 Harris–Benedict 方程：
Male BMR = 66 + (13.7 × W) + (5 × H) – (6.8 × Age)
Female BMR = 655 + (9.6 × W) + (1.8 × H) – (4.7 × Age)
ht in centimetres. This BMR is then multiplied by a physical activity level (PAL) to estimate total daily energy expenditure (TDEE).
其中 W = 体重(kg)，H = 身高(cm)。将BMR与身体活动水平系数(PAL)相乘，可估算每日总能量消耗(TDEE)。
6. Energy Balance Equation | 能量平衡方程
Weight management in sport comes down to this fundamental relationship:
运动中的体重管理归根结底取决于这一基本关系：
Energy Intake (kcal) – Energy Expenditure (kcal) = Energy Balance
A positive balance leads to weight gain, a negative balance to weight loss. Athletes must carefully adjust their energy intake to match training loads. In practical analysis, you may be given food intake and exercise data to determine whether someone is in surplus or deficit.
能量摄入大于能量消耗导致体重增加，反之则体重减少。运动员需要谨慎调整能量摄入以匹配训练负荷。在实际分析题中，题目可能会提供饮食摄入和运动数据，要求你判断处于能量盈余还是亏空。
7. Speed, Distance, Time | 速度、距离、时间
The core relationship linking movement in any sport is:
任何运动中关于位移的核心关系为：
Speed (m/s) = Distance (m) ÷ Time (s)
eed. For example, a runner covering 100 m in 12.5 s achieves an average speed of 8 m/s. This formula is essential for analysing performance in sprinting, swimming, and cycling events.
求距离：距离 = 速度 × 时间。求时间：时间 = 距离 ÷ 速度。例如，一名短跑运动员用12.5秒跑完100米，其平均速度为8米/秒。该公式是分析短跑、游泳及自行车项目表现的基础。
8. Acceleration | 加速度
Acceleration describes how quickly velocity changes, which is crucial in explosive movements:
加速度描述速度变化的快慢，这对爆发性动作至关重要：
Acceleration (m/s²) = Change in velocity (m/s) ÷ Time taken (s)
If a footballer accelerates from rest (0 m/s) to 9 m/s in 3 seconds, acceleration = (9 – hen an object slows down. This equation explains how quickly athletes can reach top speed.
若一名足球运动员从静止（0 m/s）在3秒内加速至9 m/s，加速度为(9 – 0) ÷ 3 = 3 m/s²。当物体减速时，加速度为负值。该方程可以解释运动员达到最高速度的快慢。
9. Force, Mass, Acceleration (Newton's Second Law) | 力、质量、加速度（牛顿第二定律）
Understanding how force affects motion is fundamental to sports biomechanics:
理解力如何影响运动是运动生物力学的基础：
Force (N) = Mass (kg) × Acceleration (m/s²)
d force, the greater the acceleration for a given mass. Athletes train to generate more force to improve their explosive power.
一位铅球运动员对4 kg的铅球施加120 N的力，产生的加速度为120 ÷ 4 = 30 m/s²。对于给定质量，施加的力越大，加速度越大。运动员通过训练产生更大的力来提升爆发力。
10. Levers – Mechanical Advantage | 杠杆——机械优势
In the body, bones act as levers, joints as fulcrums, and muscles provide the effort. Mechanical advantage determines whether a lever favours speed or strength:
在人体中，骨起杠杆作用，关节为支点，肌肉提供动力。机械优势决定了一个杠杆是偏向速度还是偏向力量：
Mechanical Advantage = Effort Arm Length ÷ Resistance Arm Length
When the effort arm is longer than the resistance arm, a relatively small effort can move a larger resistance (high mechanical advantage, e.g., standing on tiptoes). When the resistance arm is longer, the lever amplifies speed and range of motion (low mechanical advantage, e.g., elbow extension during throwing).
当动力臂长于阻力臂时，较小的动力就能移动较大的阻力（高机械优势，如提踵站立）。当阻力臂长于动力臂时，杠杆可放大速度和动作幅度（低机械优势，如投掷时的伸肘动作）。
11. Principles of Training (FITT) | 训练原则（FITT）
Although not a numerical formula, the FITT principle is a theorem-like framework used to design effective training programmes. It stands for:
尽管不是数学公式，但FITT原则是一种类似于定理的框架，用于设计有效的训练计划。它代表：
- Frequency – how often you train / 频率——训练次数
- Intensity – how hard you train / 强度——训练难度
- Time – duration of each session / 时间——每次训练的时长
- Type – the kind of exercise performed / 类型——进行的运动种类
By progressively adjusting one or more of these variables, you apply the principle of progressive overload. For example, to improve cardiovascular fitness, you might increase frequency from 3 to 4 sessions per week, or extend time from 30 to 45 minutes.
通过逐步调整其中一个或多个变量，你就在运用渐进超负荷原则。例如，要提高心血管适能，可将每周训练频率从3次增加到4次，或将每次训练时间从30分钟延长至45分钟。
12. Simplified VO₂ Max Prediction | 简化最大摄氧量预测
VO₂ max is the maximum volume of oxygen the body can use per minute per kilogram of body weight. While laboratory measurement requires sophisticated equipment, field tests often use the following relationship:
最大摄氧量（VO₂ max）是人体每分钟每公斤体重所能利用的最大氧气量。虽然实验室测定需要精密设备，但现场测试常用以下关系：
VO₂ max (ml/kg/min) ≈ Distance covered in 12 minutes (m) – 504.9 ÷ 44.73
This is derived from the Cooper 12-minute run test. A simpler proportional principle is: the greater the distance covered in a fixed time, the higher the predicted VO₂ max. Understanding this concept helps you appreciate how endurance performance relates to the body’s oxygen transport capacity.
该式源自库珀12分钟跑测试。一个更简单的比例原则是：在固定时间内跑得越远，预测的VO₂ max越高。理解这一概念有助于你领会耐力表现与机体氧气运输能力之间的关系。
Published by TutorHao | Physical Education Revision Series | aleveler.com
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