📚 SQA Physical Education: Formula & Theorem Quick-Reference Handbook | SQA 体育：公式定理速查手册
Welcome to your quick-reference handbook for the essential formulas and theorems in SQA National 5 Physical Education. This guide compiles the key equations you need to analyse performance, monitor training load and understand the scientific principles underlying human movement. Keep it handy as you prepare for written assessments, practical analysis tasks and your personal development portfolio.
欢迎使用 SQA National 5 体育必备公式定理速查手册。本指南汇总了分析运动表现、监测训练负荷以及理解人体运动科学原理所需的核心公式。在你准备笔试、实践分析任务和个人发展档案时，请将这份手册随时放在手边。
1. Maximum Heart Rate and Training Zones | 最大心率与训练区间
Your heart rate is one of the simplest physiological markers you can use to gauge exercise intensity. The most widely used prediction for maximum heart rate (HRmax) is derived from age alone.
心率是衡量运动强度最简单、最常用的生理指标之一。最普遍的最大心率（HRmax）预测公式仅基于年龄。
HRmax = 220 − age
However, this equation gives an estimated value with a standard error of about ±10– method incorporates resting heart rate (HRrest) to calculate the heart rate reserve (HRR).
然而，该公式给出的是一个估计值，标准误差大约为 ±10–12 次/分；因此个体差异总是存在的。为了更精确地制定运动强度，卡沃内（Karvonen）方法引入了静息心率（HRrest）来计算心率储备（HRR）。
Target HR = (HRmax − HRrest) × Intensity % + HRrest
Once your target heart rate ranges are established, you can assign them to standard training zones. The table below maps typical percentage ranges to their physiological purpose.
确定目标心率范围后，就可以将其分配到标准训练区间。下表列出了常见的百分比范围及其生理学目的。
| Training Zone | % HRmax | Purpose |
|---|---|---|
| Recovery | 50–60% | Active recovery, warm-up, cool-down |
| Aerobic Base | 60–70% | Develop basic endurance and fat metabolism |
| Aerobic Endurance | 70–80% | Improve maximal oxygen uptake (VO₂ max) |
| Anaerobic Threshold | 80–90% | Tolerate lactate accumulation, high-intensity intervals |
| Maximal Effort | 90–100% | Speed, sprinting, peak power output |
In a training programme, spending the right amount of time in each zone allows you to target specific adaptations without causing overtraining. Remember to always use the same formula or measurement when comparing training loads over time.
在训练计划中，恰当地分配在每个区间的时间，能针对性地引发生理适应，同时避免过度训练。请记住，随着时间推移比较训练负荷时，务必使用相同的公式或测量方法。
2. Body Mass Index and Body Composition | 身体质量指数与身体成分
Body Mass Index (BMI) is a straightforward screening tool that uses body mass and stature to classify individuals into weight categories. It does not differentiate between fat mass and lean mass, yet it remains a useful population-level indicator.
身体质量指数（BMI）是一种简单的筛查工具，利用体重和身高将人群划分为不同体重等级。它不能区分脂肪重量与瘦体重，但仍然是一个有用的群体指标。
BMI = mass (kg) / [height (m)]²
cations apply from the World Health Organization: underweight (<18.5), normal weight (18.5–24.9), overweight (25– and obese (≥30). For adolescents, age- and sex-specific percentile charts should be used.
世界卫生组织的标准成人分类为：体重过轻（<18.5）、正常体重（18.5–24.9）、超重（25–29.9）和肥胖（≥30）。对于青少年，应使用按年龄和性别划分的百分位曲线图。
Because BMI does not reveal fat distribution, the waist-to-hip ratio (WHR) is often calculated alongside it to assess central obesity and associated health risk.
因为 BMI 无法体现脂肪分布，通常还会同时计算腰臀比（WHR），以评估中心性肥胖及其相关健康风险。
WHR = waist circumference / hip circumference
A high WHR (above 1.0 for males, above 0.85 for females) suggests increased cardiovascular risk. Athletes with high muscle mass may have an elevated BMI but a healthy WHR and low body fat percentage; therefore, both figures should be interpreted with caution.
较高的腰臀比（男性 >1.0，女性 >0.85）提示心血管疾病风险增加。肌肉含量高的运动员可能 BMI 偏高，但腰臀比正常且体脂率较低；因此，两个指标都应谨慎解读。
3. Speed, Velocity and Acceleration | 速率、速度与加速度
In sport science, the distinction between scalar and vector quantities is essential. Speed quantifies how fast an athlete moves, while velocity also reports the direction of motion.
在体育科学中，区分标量与矢量至关重要。速率衡量运动员移动的快慢，而速度还需指明运动方向。
v = d / t
Here d is the total distance covered; the result is average speed. Velocity, on the other hand, is displacement (Δs) divided by time (Δt). Displacement is the straight-line distance in a given direction from start to finish.
这里的 d 是总路程，所得结果为平均速率。而速度则是位移（Δs）除以时间（Δt）。位移是指定方向上从起点到终点的直线距离。
v = Δs / Δt
Acceleration measures the rate at which velocity changes. A positive value indicates speeding up; a negative value (deceleration) indicates slowing down.
加速度衡量速度变化的快慢。正值表示加速，负值（减速）表示减速。
a = (v − u) / t
e final velocity. For an athlete starting from rest, u = 0, and the equation simplifies to a = v / t. Uniform acceleration also links displacement: s = ut + ½ a t², which is useful when analysing sprints or throws.
其中 u 为初速度，v 为末速度。如果运动员从静止开始，u = 0，公式简化为 a = v / t。匀加速直线运动还可联系到位移：s = ut + ½ a t²，在分析短跑或投掷项目时非常有用。
4. Work, Energy and Power | 功、能量与功率
Mechanical work is done when a force moves an object through a distance in the direction of the force. In the gym or on the field, every muscular contraction
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