📚 Quick Revision Handbook: Key Formulas and Theorems in AQA Year 8 Physical Education | AQA 八年级体育公式定理速查手册
This handbook brings together the essential formulas, principles, and theorems that underpin Year 8 AQA Physical Education. Being able to calculate training intensities, analyse body composition, and understand the mechanics of movement will deepen your grasp of human performance. Use this guide to support your practical lessons, homework, and exam revision.
本手册汇集了支撑 AQA 八年级体育课程的核心公式、原理与定理。学会计算训练强度、分析身体成分以及理解运动力学，能让你更深刻地掌握人体运动表现。请用这份指南来辅助你的实践课、作业和考试复习。
1. Maximum Heart Rate (MHR) Formula | 最大心率公式
The simplest way to estimate your maximum heart rate is the age-based formula: MHR = 220 – age (in years). This number represents the highest number of beats per minute your heart can safely achieve during all-out exercise. While individual variation exists, it provides a useful starting point for setting training zones.
估算最大心率最简单的方法是年龄公式：最大心率 = 220 – 年龄（岁）。这个数字代表你在全力运动中，心脏每分钟能安全达到的最高跳动次数。虽然存在个体差异，但它为设定训练区间提供了一个实用的起点。
MHR = 220 – age
For a Year 8 pupil aged 13, MHR = 220 – 13 = 207 bpm (beats per minute). This value will be used in many of the other calculations below.
对于一名 13 岁的八年级学生，最大心率 = 220 – 13 = 207 次/分钟。该数值将用于下文的许多其他计算。
2. Karvonen Formula for Target Heart Rate | 卡沃宁靶心率公式
A more precise way to set training intensity is the Karvonen method, which accounts for your resting heart rate (RHR). The formula is: Target Heart Rate = (MHR – RHR) × desired intensity + RHR. RHR should be measured first thing in the morning while still lying down.
一种更精确设定训练强度的方法是卡沃宁公式，它考虑了你的静息心率（RHR）。公式为：靶心率 =（最大心率 – 静息心率）× 目标强度 + 静息心率。静息心率应在清晨刚醒来仍躺卧时测量。
Target HR = (MHR – RHR) × Intensity + RHR
If a 13-year-old has an RHR of 65 bpm and wants to train at 70% intensity, the target heart rate = (207 – 65) × 0.70 + 65 = 142 × 0.70 + 65 = 99.4 + 65 ≈ 164 bpm. This method helps athletes train in precise energy system zones.
如果一名 13 岁学生的静息心率为 65 次/分钟，想以 70% 的强度训练，靶心率计算为：(207 – 65) × 0.70 + 65 = 142 × 0.70 + 65 = 99.4 + 65 ≈ 164 次/分钟。这种方法可帮助运动员在精确的能量系统区间内训练。
3. Aerobic and Anaerobic Training Zones | 有氧与无氧训练区间
Training zones are typically expressed as percentages of your maximum heart rate. Each zone elicits different physiological adaptations. The table below summarises the key zones and their primary benefits.
训练区间通常以最大心率的百分比来表示。每个区间会引发不同的生理适应。下表总结了关键区间及其主要益处。
| Zone Name | 区间名称 | % of MHR | 最大心率百分比 | Main Benefit | 主要益处 |
|---|---|---|
| Recovery / 恢复区 | 50–60% | Aids recovery, very light effort / 促进恢复，极低强度 |
| Fat-burning / 燃脂区 | 60–70% | Improves basic endurance, burns fat / 提高基础耐力，燃烧脂肪 |
| Aerobic / 有氧区 | 70–80% | Develops cardiovascular fitness / 发展心血管体能 |
| Anaerobic / 无氧区 | 80–90% | Increases lactate threshold, speed / 提高乳酸阈，提升速度 |
| Maximal / 极限区 | 90–100% | Develops maximal speed and power / 发展最大速度与爆发力 |
To find your personal zone boundaries, simply multiply your MHR by the lower and upper percentages. For a 13-year-old with MHR 207 bpm, the aerobic zone (70–80%) runs from 145 to 166 bpm.
要找到你的个人区间边界，只需将最大心率乘以区间的下限和上限百分比。例如，一个最大心率为 207 次/分钟的 13 岁学生，有氧区（70–80%）为 145 到 166 次/分钟。
4. Body Mass Index (BMI) | 身体质量指数
BMI is a simple screening tool used to categorise individuals based on their weight relative to height. It does not measure body fat directly but is widely used in health and fitness settings.
BMI 是一种简易的筛查工具，用于根据相对于身高的体重对个体进行分类。它虽然不直接测量体脂，但在健康和健身领域被广泛使用。
BMI = body mass (kg) ÷ height² (m²)
For a student who weighs 50 kg and is 1.60 m tall: BMI = 50 ÷ (1.60 × 1.60) = 50 ÷ 2.56 ≈ 19.5 kg/m². The classification table is shown below.
一名学生体重 50 公斤，身高 1.60 米：BMI = 50 ÷ (1.60 × 1.60) = 50 ÷ 2.56 ≈ 19.5 kg/m²。分类表如下所示。
| Classification | 分类 | BMI Range (kg/m²) | 范围 |
|---|---|
| Underweight / 过轻 | Below 18.5 |
| Normal weight / 正常 | 18.5 – 24.9 |
| Overweight / 超重 | 25.0 – 29.9 |
| Obese / 肥胖 | 30.0 and above |
It is important to remember that BMI does not differentiate between muscle and fat. Very muscular athletes may be classified as overweight despite having low body fat.
务必记住，BMI 不能区分肌肉和脂肪。肌肉发达的运动员可能被归为超重，尽管他们的体脂率很低。
5. Basal Metabolic Rate (BMR) | 基础代谢率
BMR is the number of calories your body needs to maintain basic life functions at complete rest. A rough estimate for adolescents can be obtained by multiplying body mass by a constant factor. This gives an approximate daily energy requirement for resting metabolism.
基础代谢率是指身体在完全休息状态下，维持基本生命活动所需的热量。对于青少年，可以通过体重乘以一个常数因子来粗略估算，得出休息代谢的每日能量需求近似值。
BMR (kcal/day) ≈ body mass (kg) × 24
This is a simplification. More accurate equations like the Mifflin-St Jeor formula consider age, height, and sex, but for quick checks the mass × 24 rule is useful. For a 50 kg student, BMR ≈ 50 × 24 = 1200 kcal per day. Total daily energy expenditure is BMR multiplied by a physical activity factor.
此为简化计算。更准确的公式（如 Mifflin-St Jeor）会考虑年龄、身高和性别，但快速估算时，体重 × 24 法则很实用。对于 50 公斤的学生，基础代谢率 ≈ 50 × 24 = 1200 千卡/天。每日总能量消耗是基础代谢率乘以体力活动系数。
6. Rate of Perceived Exertion (RPE) Scale | 主观疲劳感知量表
The RPE scale is a subjective method to quantify exercise intensity based on how hard you feel you are working. The original Borg scale runs from 6 (no exertion at all) to 20 (maximal exertion). A simplified 0–10 scale is also common in school settings.
RPE 量表是一种主观方法，根据你感觉自己在多大强度下运动来量化训练负荷。原始的博格量表从 6 分（毫不费力）到 20 分（极限努力）。在学校场景中，简化的 0–10 分量表也很常见。
| Borg 6–20 RPE | 博格 6–20 分 | Feeling / 感受 | Simplified 0–10 / 简化 0–10 分 |
|---|---|---|
| 6 | No exertion / 毫不费力 | 0 |
| 7–8 | Extremely light / 极轻 | 1 |
| 9–10 | Very light / 很轻 | 2–3 |
| 11–12 | Light / 轻 | 4 |
| 13–14 | Somewhat hard / 有点吃力 | 5–6 |
| 15–16 | Hard / 吃力 | 7–8 |
| 17–18 | Very hard / 很吃力 | 9 |
| 19 | Extremely hard / 极吃力 | – |
| 20 | Maximal exertion / 极限努力 | 10 |
A common target for steady cardio training is RPE 12–14 (somewhat hard), which roughly corresponds to 60–70% of MHR. This connection helps students learn to listen to their bodies.
稳定有氧训练的常见目标是 RPE 12–14 分（有点吃力），大约对应于 60–70% 的最大心率。这种关联有助于学生学会倾听自己的身体。
7. FITT Principle | FITT 训练原则
The FITT principle is a framework for designing a safe and effective training programme. It stands for Frequency, Intensity, Time, and Type. Although it is not a mathematical formula, it governs how training variables are adjusted to achieve progression or manage recovery.
FITT 原则是设计安全有效训练计划的框架。它代表频率、强度、时间和类型。尽管不是数学公式，但它控制着训练变量的调整，以实现渐进或管理恢复。
- Frequency (F) | 频率：How often you train, e.g., 3–5 times per week. / 每周训练多少次，例如每周 3–5 次。
- Intensity (I) | 强度：How hard you train, measured by % MHR, RPE, or weight lifted. / 训练有多努力，可用最大心率百分比、RPE 或举起重量来衡量。
- Time (T) | 时间：Duration of each session, e.g., 30–60 minutes. / 每次训练的时长，例如 30–60 分钟。
- Type (T) | 类型：The mode of exercise, such as running, cycling, or resistance training. / 运动模式，如跑步、骑车或抗阻训练。
When a performer wants to improve aerobic endurance, they might apply FITT by increasing frequency from 3 to 4 sessions, raising intensity to 75% MHR, extending time to 45 minutes, and choosing continuous running as the type.
当运动员想提升有氧耐力时，可通过 FITT 将频率从 3 次提高到 4 次，强度增加到 75% 最大心率，时间延长至 45 分钟，并选择持续跑为运动类型。
8. Speed, Distance, and Time | 速度、距离与时间
The relationship between speed, distance, and time is fundamental in sports analytics. It is expressed by the simple equation below. Units must be consistent: speed in metres per second (m/s), distance in metres (m), and time in seconds (s).
速度、距离与时间之间的关系是运动分析的基础。可用下列简单方程表示。单位必须统一：速度以米/秒（m/s）计，距离以米（m）计，时间以秒（s）计。
Speed = Distance ÷ Time
If a pupil runs 100 metres in 14 seconds, speed = 100 ÷ 14 ≈ 7.14 m/s. To find distance when speed and time are known: Distance = Speed × Time. To find time: Time = Distance ÷ Speed. This formula helps in analysing sprint times, swimming speeds, and game movements.
如果一名学生用 14 秒跑完 100 米，速度 = 100 ÷ 14 ≈ 7.14 m/s。已知速度和时间求距离：距离 = 速度 × 时间。求时间：时间 = 距离 ÷ 速度。该公式有助于分析短跑成绩、游泳速度以及比赛中的移动。
9. Force, Mass, and Acceleration | 力、质量与加速度
Newton’s second law of motion states that the acceleration of an object depends on the net force acting upon it and the object’s mass. In PE, this helps explain how athletes generate movement and how equipment behaves.
牛顿第二运动定律指出，物体的加速度取决于作用在它上面的净力以及物体的质量。在体育中，这有助于解释运动员如何产生运动以及器材的表现。
Force = mass × acceleration (F = m × a)
Force is measured in newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²). A 0.45 kg football kicked with an acceleration of 200 m/s² experiences a force of 0.45 × 200 = 90 N. The larger the force applied, the greater the acceleration for a given mass.
力的单位是牛顿（N），质量单位是千克（kg），加速度单位是米/秒²（m/s²）。一个质量为 0.45 公斤的足球以 200 m/s² 的加速度被踢出，受到的力为 0.45 × 200 = 90 牛顿。对于给定质量，施加的力越大，加速度就越大。
10. Lever Systems and Mechanical Advantage | 杠杆系统与机械优势
Levers in the human body consist of a bone acting as the lever arm, a joint as the fulcrum (pivot), and a muscle providing the effort. Understanding the three classes of levers helps analyse movement efficiency.
人体中的杠杆由作为杠杆臂的骨、作为支点的关节以及提供动力的肌肉组成。理解这三类杠杆有助于分析动作效率。
- First-class lever | 第一类杠杆：Fulcrum between effort and load (e.g., nodding the head). / 支点在动力与阻力之间（如点头）。
- Second-class lever | 第二类杠杆：Load between fulcrum and effort (e.g., standing on tiptoes). / 阻力在支点和动力之间（如踮脚站立）。
- Third-class lever | 第三类杠杆：Effort between fulcrum and load (e.g., biceps curl). / 动力在支点和阻力之间（如肱二头肌弯举）。
Mechanical advantage (MA) is calculated as the length of the effort arm divided by the length of the resistance arm. When MA > 1, the lever magnifies force; when MA < 1, it favours speed and range of motion. Most human levers are third-class and favour speed over force.
机械优势（MA）的计算方法为动力臂长度除以阻力臂长度。当 MA > 1 时，杠杆省力；当 MA < 1 时，杠杆有利于速度和运动范围。人体大多数杠杆属于第三类，以速度换力量。
Mechanical Advantage = Effort arm length ÷ Resistance arm length
11. Power Calculation | 功率计算
Power measures how quickly work is done or energy is transferred. It is a crucial component of explosive activities like jumping, throwing, and sprinting. The standard formula relates work and time.
功率衡量做功或能量转移的快慢。它是跳跃、投掷和短跑等爆发性活动的关键因素。标准公式将功和时间关联起来。
Power = Work ÷ Time or Power = (Force × Distance) ÷ Time
Work is measured in joules (J), time in seconds (s), and power in watts (W). If a weightlifter lifts 600 J of work in 2 seconds, the power output is 600 ÷ 2 = 300 W. In vertical jump assessments, a simplified equation sometimes used is: Peak Power = Force × Velocity, but in school contexts the work-time formula is primary.
功的单位是焦耳（J），时间的单位是秒（s），功率的单位是瓦特（W）。如果一名举重运动员在 2 秒内做了 600 焦耳的功，那么功率输出为 600 ÷ 2 = 300 瓦。在垂直跳测评中，有时会用到简化的公式：峰值功率 = 力 × 速度，但在学校场景下，功–时间公式是基础。
12. Simple Body Composition Formulae | 身体成分简易公式
Body composition refers to the proportion of fat mass and fat-free mass in the body. While precise measurement requires laboratory equipment, some simple indices can be calculated from basic measurements to track changes over time.
身体成分指体内脂肪重量与去脂体重的比例。虽然精确测量需要实验室设备，但可以根据基本测量计算一些简易指数，以追踪一段时间内的变化。
Body Fat Percentage = (Fat Mass ÷ Total Body Mass) × 100
Fat mass can be estimated using skinfold calipers and prediction equations, often beyond Year 8 scope. A simpler school-based approach is to calculate the waist-to-height ratio: Waist circumference (cm) ÷ Height (cm). A ratio below 0.5 is generally associated with healthy body composition in adolescents. Lean body mass can also be estimated as total body mass minus fat mass.
脂肪重量可使用皮褶卡尺和预测方程来估算，这通常超出八年级范围。一个更简单的校园方法是计算腰围身高比：腰围（厘米）÷ 身高（厘米）。比率低于 0.5 通常表明青少年的身体成分较为健康。去脂体重也可通过总体重减去脂肪重量来估算。
Tracking the waist-to-height ratio alongside BMI offers a clearer picture of central adiposity risk. Always remember that single numbers do not define fitness — they are tools to support a healthy, active lifestyle.
将腰围身高比与 BMI 一起追踪，可以更清晰地反映中心性肥胖风险。请始终记住，单一数字并不能定义健康——它们只是支持健康积极生活方式的工具。
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