📚 Year 8 SQA Physical Education: Formula and Theorem Quick Reference Handbook | Year 8 SQA 体育：公式定理速查手册
Welcome to your quick reference handbook for key formulae and theorems in SQA Physical Education. Understanding these will help you analyse performance, improve fitness, and apply scientific principles to sport. Keep this guide handy for revision and exam preparation.
欢迎使用 SQA 体育关键公式和定理的速查手册。理解这些内容将帮助你分析运动表现、改善健康状况，并将科学原理应用于体育运动中。请妥善保存本指南，用于复习和备考。
1. Maximum Heart Rate (MHR) | 最大心率 (MHR)
Your Maximum Heart Rate is the highest number of beats per minute your heart can safely achieve during maximal exercise. It is often estimated using the formula MHR = 220 – age. For a typical Year 8 pupil aged 12-13, MHR is approximately 207-208 bpm. This value is essential for planning safe and effective training zones.
最大心率是指你在最大强度运动时，心脏每分钟能安全达到的最高跳动次数。通常使用公式 MHR = 220 – 年龄 进行估算。对于12-13岁的典型Year 8学生，MHR 约为 207-208 次/分钟。这个数值对于制定安全有效的训练区间至关重要。
2. Target Heart Rate Zones (Karvonen Formula) | 目标心率区间 (卡沃宁公式)
To train more precisely, the Karvonen formula uses your resting heart rate (RHR): Target HR = ((MHR – RHR) × Intensity%) + RHR. Intensity is expressed as a decimal (e.g. 0.6 for 60%). This method helps you exercise in moderate (60-70%) or vigorous (70-85%) zones to achieve specific fitness goals.
为了更精确地训练，卡沃宁公式引入了安静心率 (RHR)：目标心率 = ((MHR – RHR) × 强度%) + RHR。强度以小数表示（例如 60% 即为 0.6）。这种方法能帮助你在中等强度 (60-70%) 或高强度 (70-85%) 区间进行锻炼，从而达成特定的健身目标。
3. Body Mass Index (BMI) | 身体质量指数 (BMI)
Body Mass Index is a simple measure of body fat based on height and weight. The formula is BMI = weight (kg) ÷ height (m)². For instance, a pupil weighing 50 kg with a height of 1.60 m has a BMI of 50 ÷ (1.60 × 1.60) = 19.5. General classification: under 18.5 underweight, 18.5-24.9 healthy, 25-29.9 overweight, 30+ obese.
身体质量指数是根据身高和体重衡量体脂的简便方法。公式为 BMI = 体重 (kg) ÷ 身高 (m)²。例如，一名学生体重50公斤，身高1.60米，其 BMI = 50 ÷ (1.60 × 1.60) = 19.5。大致分类如下：低于18.5为偏瘦，18.5-24.9为健康，25-29.9为超重，30及以上为肥胖。
4. Speed | 速度
Speed measures how fast an object moves. The formula is Speed = Distance ÷ Time, often written as v = d / t. In sports, speed is typically recorded in metres per second (m/s). For example, if a sprinter covers 100 m in 12 seconds, her average speed is 100 ÷ 12 ≈ 8.33 m/s.
速度衡量物体移动的快慢。公式为 速度 = 距离 ÷ 时间，常写作 v = d / t。在体育中，速度通常以米/秒 (m/s) 为单位。例如，一名短跑选手在12秒内跑完100米，她的平均速度为 100 ÷ 12 ≈ 8.33 m/s。
5. Acceleration | 加速度
Acceleration is the rate at which velocity changes. It is calculated using the formula Acceleration = Change in velocity ÷ Time taken, or a = (v – u) / t, where v is final velocity, u is initial velocity, and t is time. If a football player accelerates from 0 to 5 m/s in 2 seconds, his acceleration is (5 – 0) ÷ 2 = 2.5 m/s².
加速度是速度变化的快慢。计算公式为 加速度 = 速度变化量 ÷ 所用时间，即 a = (v – u) / t，其中 v 为末速度，u 为初速度，t 为时间。如果一名足球运动员在2秒内从 0 m/s 加速到 5 m/s，他的加速度为 (5 – 0) ÷ 2 = 2.5 m/s²。
6. Force, Mass and Acceleration (Newton’s Second Law) | 力、质量与加速度 (牛顿第二定律)
Newton’s Second Law explains the relationship between force, mass, and acceleration: Force = Mass × Acceleration, or F = m × a. Force is measured in newtons (N), mass in kilograms (kg), and acceleration in m/s². For example, kicking a 0.4 kg football so it accelerates at 20 m/s² requires a force of 0.4 × 20 = 8 N.
牛顿第二定律阐释了力、质量和加速度之间的关系：力 = 质量 × 加速度，即 F = m × a。力的单位是牛顿 (N)，质量用千克 (kg)，加速度用 m/s²。例如，要使一个0.4 kg的足球以 20 m/s² 的加速度运动，需要施加 0.4 × 20 = 8 N 的力。
7. Work Done | 做功
Work is done when a force moves an object. It is calculated using Work Done = Force × Distance moved in the direction of the force, or W = F × d. Work is measured in joules (J). If you lift a 10 kg weight (force ≈ 100 N) through a height of 0.5 m, the work done is 100 × 0.5 = 50 J.
当一个力使物体移动时，便做了功。计算公式为 做功 = 力 × 沿力方向移动的距离，即 W = F × d。功的单位是焦耳 (J)。如果你将一个10公斤的杠铃（力约为100 N）向上举起0.5米，所做的功为 100 × 0.5 = 50 J。
8. Power | 功率
Power measures how quickly work is done. It is given by Power = Work Done ÷ Time, or P = W / t. Power is expressed in watts (W), where 1 W = 1 J/s. An athlete who performs 500 J of work in 2 seconds generates a power output of 250 W. Explosive movements like jumping require high power.
功率衡量做功的快慢。公式为 功率 = 做功 ÷ 时间，即 P = W / t。功率的单位是瓦特 (W)，1 W = 1 J/s。一名运动员在2秒内做了500 J的功，其功率输出为250 W。爆发性动作如跳跃需要较高的功率。
9. Moment of a Force (Torque) | 力矩 (扭矩)
A moment is the turning effect of a force around a pivot. It is calculated as Moment = Force × Perpendicular distance from pivot, or M = F × d. Moments are measured in newton-metres (Nm). In the body, muscles create moments at joints; for example, the biceps exerts a moment at the elbow to lift a weight. Increasing distance (e.g. longer lever arm) makes it easier to turn an object.
力矩是力绕支点产生的转动效应。计算公式为 力矩 = 力 × 支点到力作用线的垂直距离，即 M = F × d。力矩的单位是牛·米 (Nm)。在人体中，肌肉在关节处产生力矩；例如，肱二头肌在肘关节处产生力矩以举起物体。增加力臂距离（如更长的杠杆臂）可以使转动物体更省力。
10. The FITT Principle | FITT 原则
The FITT principle is a classic theorem for designing effective training programmes. It stands for: Frequency (how often you train), Intensity (how hard you work), Time (duration of each session), and Type (the kind of exercise). By manipulating these four variables, you can apply the overload principle safely and progressively improve fitness.
FITT 原则是设计有效训练计划的经典定理。它代表：频率（训练频次）、强度（训练难度）、时间（每次训练时长）和类型（运动种类）。通过合理调整这四个变量，你可以安全地运用超负荷原则，逐步提升体能水平。
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