📚 Year 7 CAIE Physical Education: Formula & Principle Quick Reference Handbook | Year 7 CAIE 体育：公式定理速查手册
Welcome to your handy quick-reference guide for Year 7 Cambridge Physical Education. This handbook brings together the essential formulas, principles, and quick calculations you will use when learning about fitness, training, and human movement. Keep it close when revising for tests, planning a personal exercise programme, or simply checking how to measure your own health-related fitness.
欢迎使用 Year 7 剑桥体育速查手册。本手册汇集了在学习体能、训练和人体运动时所需的基础公式、原理和速算方法。在复习考试、制定个人锻炼计划或测量自身健康体适能时，请随时翻阅。
1. Maximum Heart Rate (MHR) | 最大心率 (MHR)
Your maximum heart rate is the highest number of beats per minute (bpm) your heart can safely reach during all-out exercise. The simplest and most widely used formula is MHR = 220 − age. For a 12‑year‑old, this gives 208 bpm. Remember, this is an estimate – individual differences can be ±10 bpm.
最大心率是指你在全力运动中每分钟心跳的最高次数。最简单通用的公式是 MHR = 220 − 年龄。对 12 岁学生，结果是 208 bpm。请注意这是估算值，个体差异可达 ±10 bpm。
2. Target Heart Rate Zones | 靶心率区间
To train effectively you need to exercise within a target heart rate zone. A simple percentage‑based zone uses: Target HR = MHR × (intensity %). For moderate exercise, 50–70% of MHR is typical. A more accurate method is the Karvonen formula, which includes your resting heart rate (RHR): THR = ((MHR − RHR) × %intensity) + RHR. Always measure RHR first thing in the morning.
想要高效训练，就需要在靶心率区间内运动。基于百分比的简易区间为：靶心率 = 最大心率 × (强度%)。中等强度通常取最大心率的 50–70%。更精确的方法是卡沃宁公式，纳入了安静心率 (RHR)：靶心率 = ((最大心率 − 安静心率) × 强度%) + 安静心率。请在清晨刚醒时测量安静心率。
3. Body Mass Index (BMI) | 身体质量指数
Body Mass Index gives a quick indication of whether a person’s weight is healthy for their height. The formula is: BMI = weight (kg) ÷ height² (m²). For example, a student weighing 45 kg and 1.50 m tall has a BMI of 45 ÷ (1.50 × 1.50) = 20.0 kg/m². General classifications: underweight <18.5, normal 18.5–24.9, overweight 25–29.9, obese ≥30. However, BMI does not distinguish muscle from fat, so athletes may be misclassified.
身体质量指数能快速判断体重是否在健康范围内。公式：BMI = 体重 (kg) ÷ 身高² (m²)。例如一名 45 kg、1.50 m 的学生，BMI = 45 ÷ (1.50 × 1.50) = 20.0 kg/m²。大致分类为：过轻 <18.5，正常 18.5–24.9，过重 25–29.9，肥胖 ≥30。但 BMI 无法区分肌肉与脂肪，因此运动员可能被误判。
4. FITT Principle: Frequency, Intensity, Time, Type | FITT 原则：频率、强度、时间、类型
The FITT principle is used to design a balanced training programme. Each element can be expressed numerically: Frequency (sessions per week), Intensity (% MHR or Rate of Perceived Exertion), Time (minutes per session) and Type (aerobic, anaerobic, resistance). When you want to improve, you adjust one or more FITT variables – for example, increasing frequency from 3 to 4 times per week.
FITT 原则用于设计均衡的训练计划。每个要素都可以量化：频率（每周训练次数）、强度（最大心率百分比或自觉用力程度）、时间（每次训练分钟数）和类型（有氧、无氧、抗阻）。想要提升时，可以调整一个或多个 FITT 变量——比如将每周频率从 3 次增加到 4 次。
5. SPORT Training Principles | SPORT 训练原则
SPORT stands for Specificity, Progression, Overload, Reversibility and Tedium. While not mathematical formulas, these are key ‘theorems’ of training. Specificity means training must match the sport’s demands. Progression requires gradual increases in workload – using the FITT formula helps here. Overload means working harder than normal to force adaptation. Reversibility reminds us that fitness is lost when you stop training. Tedium warns against boredom; variety keeps you motivated.
SPORT 分别代表专项性、渐进性、超负荷、可逆性和枯燥性。虽然它们不是计算公式，却是训练中的重要“定理”。专项性指训练必须符合运动项目要求。渐进性要求逐渐增加负荷——此时可借助 FITT 公式。超负荷 意为比以往更努力以促使身体适应。可逆性提醒我们停止训练后体适能会下降。枯燥性告诫要避免乏味，多样化的练习能保持动力。
6. Calculating Speed | 计算速度
Speed is a fundamental measure in many sports. The formula is: Speed = distance ÷ time. Standard units are metres per second (m/s). If a runner covers 100 m in 12.5 s, speed = 100 ÷ 12.5 = 8.0 m/s. To convert m/s to km/h, multiply by 3.6.
速度是许多运动中的基础衡量指标。公式为：速度 = 距离 ÷ 时间。标准单位为米/秒 (m/s)。若一名跑者用 12.5 秒完成 100 米，速度 = 100 ÷ 12.5 = 8.0 m/s。要把 m/s 转换为 km/h，只需乘以 3.6。
7. Pace, Time and Distance | 配速、时间与距离
Pace is often more practical than speed, especially in endurance events. Pace = time ÷ distance. It is usually expressed in minutes per kilometre (min/km). If an athlete completes a 3 km run in 15 minutes, their pace is 15 ÷ 3 = 5 min/km. The relationship triangle is: Distance = speed × time, and Time = distance ÷ speed. Rearranging these lets you predict race times.
配速往往比速度更实用，尤其在耐力项目中。配速 = 时间 ÷ 距离，通常以分钟/公里 (min/km) 表示。若一名运动员用 15 分钟跑完 3 公里，其配速为 15 ÷ 3 = 5 min/km。三者的关系三角为：距离 = 速度 × 时间，时间 = 距离 ÷ 速度。灵活变换这些公式可以预测比赛用时。
8. Force, Mass and Acceleration (Newton’s Second Law) | 力、质量与加速度（牛顿第二定律）
In physical education we apply Newton’s Second Law to understand how forces produce movement. Force (N) = mass (kg) × acceleration (m/s²). A heavier object needs more force to accelerate at the same rate. If a football of mass 0.45 kg is kicked with an acceleration of 40 m/s², the force applied is 0.45 × 40 = 18 N. This principle helps explain throwing, sprint starts and tackling.
体育课上我们用牛顿第二定律理解力如何产生运动。力 (N) = 质量 (kg) × 加速度 (m/s²)。物体越重，要达到相同加速度所需的力就越大。假设一个 0.45 kg 的足球以 40 m/s² 的加速度被踢出，施加的力为 0.45 × 40 = 18 N。这一原理有助于解释投掷、起跑和抢断动作。
9. Work, Energy and Power | 功、能与功率
Work is done when a force moves an object. Work (J) = force (N) × distance (m). Power measures how quickly work is done: Power (W) = work (J) ÷ time (s). In sport, powerful movements like a vertical jump or a javelin throw require high power output. If a weightlifter lifts 600 N through a height of 2 m in 1.5 s, work = 600 × 2 = 1200 J, and power = 1200 ÷ 1.5 = 800 W.
力使物体移动时就做了功。功 (J) = 力 (N) × 距离 (m)。功率衡量做功的快慢：功率 (W) = 功 (J) ÷ 时间 (s)。在运动中，垂直跳或掷标枪等爆发性动作都需要高功率输出。如果一位举重运动员用 600 N 的力将杠铃向上推举 2 m，耗时 1.5 s，功 = 600 × 2 = 1200 J，功率 = 1200 ÷ 1.5 = 800 W。
10. Levers and Mechanical Advantage | 杠杆与机械效益
Most body movements are produced by lever systems formed by bones, joints and muscles. A simple equation for any lever is: effort × effort arm = resistance × resistance arm. Mechanical Advantage (MA) tells us whether the lever increases force or speed: MA = effort arm ÷ resistance arm. If MA > 1, the lever multiplies force; if MA < 1, it produces greater speed and range of motion. For example, during a bicep curl, the effort arm is much shorter than the resistance arm, giving MA < 1 – this favours speed and range over force.
人体大多数动作都由骨骼、关节和肌肉构成的杠杆系统产生。任何杠杆都满足：力 × 力臂 = 阻力 × 阻力臂。机械效益 (MA) 揭示了杠杆是放大力量还是加快速度：机械效益 = 力臂 ÷ 阻力臂。若 MA > 1，杠杆增大力量；若 MA < 1，则产生更大的速度和运动幅度。例如，在肱二头肌弯举中，力臂远比阻力臂短，MA < 1——这更有利于速度和幅度，而非力量。
11. Energy Expenditure Estimation | 能量消耗估算
Estimating how many Calories you burn helps with training and nutrition. A rough formula for running is: Energy (kcal) ≈ body mass (kg) × distance (km) × 1.036. For a 40 kg student running 3 km, energy ≈ 40 × 3 × 1.036 ≈ 124 kcal. Remember that precise values depend on speed, terrain and fitness level. For other activities, laboratory testing or fitness trackers provide more accurate numbers.
估算运动消耗的卡路里有助于训练和营养安排。跑步的一个粗略公式是：能量 (kcal) ≈ 体重 (kg) × 距离 (km) × 1.036。一名 40 kg 的学生跑 3 km，约消耗 40 × 3 × 1.036 ≈ 124 kcal。要记住，精确数值还取决于速度、地形和体能水平。对于其他运动，实验室测试或健身追踪器能提供更准确的数据。
12. Hydration and Sweat Rate | 水分补充与出汗率
Staying hydrated is vital for performance and safety. You can calculate your sweat rate to guide fluid replacement: Sweat rate (L/h) = (body mass before − body mass after + fluid intake) ÷ exercise time (hours). Always weigh yourself in minimal clothing. If a student loses 0.4 kg after a 1‑hour session and drank 0.3 L, sweat rate = (0.4 + 0.3) ÷ 1 = 0.7 L/h. This helps plan how much to drink during training.
保持充足水分对运动表现和安全至关重要。你可以计算出汗率来指导补液：出汗率 (L/h) = (运动前体重 − 运动后体重 + 饮水量) ÷ 运动时间 (小时)。称重时请穿着最少的衣物。如果一名学生 1 小时训练后体重减少 0.4 kg，期间饮水 0.3 L，出汗率 = (0.4 + 0.3) ÷ 1 = 0.7 L/h。这有助于规划训练中的饮水量。
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