📚 Year 11 AQA PE: Formula & Theorem Quick Reference Handbook | Year 11 AQA 体育：公式定理速查手册
This quick reference handbook brings together every essential formula, equation and quantitative relationship required for the AQA GCSE Physical Education (8582) specification. Use it to revise calculations for training zones, cardiac dynamics, mechanics, lever systems and energy transfers. Each section presents the core formula with worked context, followed by its Chinese translation so you can check understanding instantly.
本速查手册汇集了 AQA GCSE 体育（8582）考试中必须掌握的每一个核心公式、方程式与数量关系。你可以用它复习训练区、心脏动力学、力学、杠杆系统和能量转换的计算。每一节都先给出核心公式并加以解释，紧接着提供中文对照，帮助你立即查验理解。
1. Maximum Heart Rate & Training Zones | 最大心率与训练区间
Maximum heart rate (HRmax) is estimated as 220 minus your age in years. It forms the baseline for prescribing aerobic and anaerobic training intensities. The aerobic training zone is 60–80% of HRmax, while the anaerobic training zone is 80–90% of HRmax.
最大心率（HRmax）的估算公式为 220 减去你的年龄。它是制定有氧和无氧训练强度的基础。有氧训练区为 HRmax 的 60–80%，无氧训练区为 HRmax 的 80–90%。
HRmax = 220 − age (years)
Aerobic target: 60–80% HRmax | Anaerobic target: 80–90% HRmax
For a 16‑year‑old, HRmax = 204 bpm; the aerobic zone is roughly 122–163 bpm and the anaerobic zone is 163–184 bpm. Always use the lower and upper boundaries to fine‑tune interval sessions.
以 16 岁为例，HRmax = 204 次/分；有氧区大约为 122–163 次/分，无氧区为 163–184 次/分。训练时请始终使用上下边界来精确调整间歇安排。
2. Karvonen Formula (Heart Rate Reserve) | 卡沃宁公式（心率储备法）
The Karvonen method incorporates resting heart rate (RHR) to create personalised target zones. It uses the heart rate reserve (HRR) — the difference between HRmax and RHR — multiplied by the desired intensity percentage, then added back to RHR.
卡沃宁法纳入了安静心率（RHR）以制定个性化的目标区间。它使用心率储备（HRR），即 HRmax 与 RHR 的差值，乘以目标强度百分比，再加回安静心率。
Target HR = RHR + [Intensity% × (HRmax − RHR)]
If RHR is 60 bpm, HRmax is 200 bpm, and you want to work at 70% intensity, the target HR is 60 + 0.7 × (200 − 60) = 158 bpm. This formula is particularly useful for athletes with very low resting heart rates.
若安静心率为 60 次/分，HRmax 为 200 次/分，希望以 70% 强度运动，则目标心率 = 60 + 0.7 × (200 − 60) = 158 次/分。该公式对有极低安静心率的运动员特别实用。
3. Cardiac Output (Q) | 心输出量（Q）
Cardiac output is the volume of blood ejected by the left ventricle per minute. It is the product of heart rate and stroke volume. During exercise, both components rise, causing Q to increase dramatically.
心输出量是指左心室每分钟泵出的血液量。它是心率与每搏输出量的乘积。运动时这两个成分均会升高，使心输出量大幅增加。
Q = HR × SV
Q is measured in litres per minute (L/min). Stroke volume is the amount of blood pumped per beat (ml/beat, but often converted to L/beat). For example, HR = 180 bpm, SV = 0.1 L/beat → Q = 18 L/min.
Q 的单位为升/分（L/min）。每搏输出量是每次心跳泵出的血量（ml/次，通常转换为 L/次）。例如 HR=180 次/分，SV=0.1 L/次 → Q=18 L/min。
4. Minute Ventilation (VE) | 分钟通气量（VE）
Minute ventilation describes the total volume of air moved into and out of the lungs per minute. It depends on tidal volume — the depth of each breath — and breathing frequency.
分钟通气量表示每分钟进出肺部的空气总体积。它取决于潮气量（每次呼吸的深度）和呼吸频率。
VE = TV × f
VE is expressed in litres per minute (L/min), TV in litres per breath, and f in breaths per minute. During intense exercise, TV can rise to ~3 L and f to ~60 breaths/min, yielding VE values exceeding 180 L/min.
VE 的单位为升/分（L/min），TV 的单位为升/次，f 的单位为次/分。剧烈运动时，TV 可升至约 3 L，f 约 60 次/分，使得 VE 超过 180 L/min。
5. Body Mass Index (BMI) | 身体质量指数（BMI）
BMI provides a rough guide to whether an individual’s weight is healthy for their height. It is not a direct measure of body fat, but AQA expects you to compute it and understand its limitations in athletic populations.
BMI 可粗略判断一个人的体重相对于身高是否健康。它不是体脂的直接测量，但 AQA 要求你会计算并理解它在运动员群体中的局限性。
BMI = weight (kg) ÷ [height (m)]²
A score of 18.5–24.9 kg/m² is generally considered healthy. For a 70 kg athlete standing 1.75 m tall, BMI = 70 ÷ (1.75 × 1.75) ≈ 22.9 kg/m². Muscular athletes may register as ‘overweight’ despite low body fat.
18.5–24.9 kg/m² 通常被视为健康范围。一位体重 70 kg、身高 1.75 m 的运动员，BMI = 70 ÷ (1.75 × 1.75) ≈ 22.9 kg/m²。肌肉发达的运动员即使体脂很低，也可能被归为“超重”。
6. Speed, Distance & Time | 速度、距离与时间
Speed is the rate at which distance is covered. It is a scalar quantity, meaning direction is not considered. This formula underpins everything from sprint times to pacing in endurance events.
速度是距离的变化率。它是标量，即不考虑方向。这个公式是短跑计时乃至耐力项目配速分析的基础。
Speed (m/s) = distance (m) ÷ time (s)
To find distance, rearrange as d = speed × time; to find time, use t = distance ÷ speed. Ensure units are consistent — convert minutes to seconds and kilometres to metres where necessary.
求距离时，改写为 d = 速度 × 时间；求时间时，t = 距离 ÷ 速度。务必保持单位统一——必要时将分钟转换为秒，千米转换为米。
7. Acceleration | 加速度
Acceleration is the rate of change of velocity. AQA often frames questions around a sprinter leaving the blocks or a ball being slowed by drag. Deceleration is simply negative acceleration.
加速度是速度的变化率。AQA 的题目常围绕短跑选手起跑或球因阻力减速来设计。减速就是负加速度。
a = (v − u) ÷ t
Where a = acceleration (m/s²), v = final velocity (m/s), u = initial velocity (m/s), t = time (s). If a 100 m sprinter increases velocity from 0 to 12 m/s in 3 seconds, a = (12 − 0) ÷ 3 = 4 m/s².
其中 a = 加速度（m/s²），v = 末速度（m/s），u = 初速度（m/s），t = 时间（s）。若一名 100 米短跑选手在 3 秒内速度从 0 增至 12 m/s，则 a = (12 − 0) ÷ 3 = 4 m/s²。
8. Force, Mass & Acceleration (Newton’s Second Law) | 力、质量与加速度（牛顿第二定律）
The resultant force acting on an object causes it to accelerate in proportion to the force and inversely proportional to its mass. This relationship is central to understanding sprint starts, tackles, and projectile motion.
作用在物体上的合外力会使它产生加速度，加速度与力的大小成正比，与物体质量成反比。这一关系是理解起跑、拦截和抛体运动的核心。
F = m × a
Force (F) is measured in newtons (N), mass (m) in kilograms (kg), and acceleration (a) in m/s². To accelerate a 70 kg athlete at 3 m/s² requires a force of 210 N.
力（F）的单位是牛（N），质量（m）单位为千克（kg），加速度（a）单位为 m/s²。要让 70 kg 的运动员获得 3 m/s² 的加速度，需施加 210 N 的力。
9. Momentum | 动量
Momentum is the product of mass and velocity. It is a vector quantity, meaning direction matters. In contact sports, understanding momentum helps explain why heavier or faster players are harder to stop.
动量是质量与速度的乘积。它是矢量，方向至关重要。在身体接触类运动中，理解动量有助于解释为什么更重或更快的球员更难被阻挡。
p = m × v
Momentum (p) is measured in kg·m/s. If an 80 kg rugby player moves at 6 m/s, his momentum is 480 kg·m/s. During a tackle, a change in momentum — impulse — links to the force applied over time.
动量（p）的单位是 kg·m/s。若一位 80 kg 的橄榄球球员以 6 m/s 移动，其动量为 480 kg·m/s。拦截时，动量的变化——冲量——与力作用的时间有关。
10. Mechanical Advantage in Levers | 杠杆的机械效益
Levers magnify the effort applied by muscles. Mechanical advantage (MA) compares the length of the effort arm to the length of the load arm. An MA greater than 1 means less effort is needed to move a large load, but the load moves a shorter distance.
杠杆能放大肌肉施加的力。机械效益（MA）比较力臂长度和负荷臂长度。MA 大于 1 意味着可以用较小的力移动较大的负荷，但负荷移动的距离较短。
Mechanical Advantage = effort arm length ÷ load arm length
In a first‑class lever like the neck extending, the effort arm is often very short, giving MA < 1 — this favours speed and range of motion. For a second‑class lever such as the ankle during plantar flexion, MA > 1, favouring force production.
在第一类杠杆（如颈部后伸）中，力臂通常很短，MA < 1——这有利于速度和运动幅度。在第二类杠杆（如踝关节跖屈）中，MA > 1，有利于产生力量。
11. Principle of Moments | 力矩原理
When a lever system is balanced (in equilibrium), the total clockwise moment equals the total anticlockwise moment. The moment of a force is the product of the force and the perpendicular distance from the pivot.
当杠杆系统平衡（处于平衡状态）时，顺时针总力矩等于逆时针总力矩。力矩是力与其到支点垂直距离的乘积。
Moment = Force × perpendicular distance from pivot
∑ clockwise moments = ∑ anticlockwise moments
For example, a 400 N effort applied 0.3 m from the pivot can balance a 600 N load placed 0.2 m from the pivot on the other side, because 400 × 0.3 = 600 × 0.2 = 120 Nm.
例如，在距支点 0.3 m 处施加 400 N 的力，可平衡距支点 0.2 m 的 600 N 负荷，因为 400 × 0.3 = 600 × 0.2 = 120 Nm。
12. Work Done & Power | 做功与功率
Work done measures the energy transferred when a force moves an object. Power is the rate at which work is performed — a key concept in evaluating athletic performance, especially in activities like rowing or cycling.
做功衡量力移动物体时传递的能量。功率是做功的速率——评估运动表现（尤其是在划船或自行车等项目中）的关键概念。
Work Done (J) = Force (N) × distance moved in direction of force (m)
Power (W) = Work Done (J) ÷ time (s) or Power = Force × velocity
If a weightlifter applies 1500 N to lift a barbell 0.8 m in 0.5 s, work done = 1500 × 0.8 = 1200 J, and power = 1200 ÷ 0.5 = 2400 W. The velocity form (P = F × v) is useful when speed is constant.
若举重运动员施加 1500 N 在 0.5 s 内将杠铃举起 0.8 m，做功 = 1500 × 0.8 = 1200 J，功率 = 1200 ÷ 0.5 = 2400 W。当速度恒定时，速度形式（P = F × v）尤其实用。
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