📚 Year 10 AQA PE: Formula & Theorem Quick Reference Handbook | Year 10 AQA 体育：公式定理速查手册
This quick reference handbook brings together the essential formulas and theorems covered in Year 10 AQA GCSE Physical Education. From calculating training zones to understanding levers and energy expenditure, these equations are vital for both exam success and practical application in sport. Use this guide to memorise, revise, and apply each formula confidently.
这本速查手册汇总了 Year 10 AQA GCSE 体育课程中的关键公式与定理。从计算训练区间到理解杠杆和能量消耗，这些公式对考试成功和体育实践都至关重要。请用本手册帮助记忆、复习并熟练应用每一个公式。
1. Maximum Heart Rate & Training Zones | 最大心率与训练区间
Maximum heart rate (MHR) is the highest number of beats per minute (bpm) your heart can achieve during maximal exercise. The most common estimation is based on age. Once MHR is known, training zones are calculated as percentages to target specific fitness adaptations.
最大心率 (MHR) 是人体在极限运动中每分钟心跳可达的最高次数 (bpm)。最常用的估算方法基于年龄。确定 MHR 后，便可按百分比计算不同训练区间，以针对性地提升体能。
MHR = 220 − age
For an aerobic base, train at 60–80% of MHR. Anaerobic threshold work typically falls between 80–90% MHR. Always use these figures as estimates; individual variation can be significant.
有氧基础训练通常在 MHR 的 60–80% 区间进行。无氧阈值训练一般落在 MHR 的 80–90% 之间。请注意这些数值仅为估算，个体差异可能很大。
- Aerobic zone: 60–80% MHR
- Anaerobic zone: 80–90% MHR
- 有氧区间：60–80% MHR
- 无氧区间：80–90% MHR
2. Karvonen Formula (Heart Rate Reserve) | 卡沃宁公式（心率储备）
The Karvonen formula provides a more personalised target heart rate by incorporating resting heart rate (RHR). It accounts for fitness level and is particularly useful for endurance athletes.
卡沃宁公式通过引入静息心率 (RHR) 来计算更个性化的目标心率。该公式考虑了体能水平，对耐力运动员尤为实用。
Target HR = RHR + Intensity × (MHR − RHR)
Intensity is expressed as a decimal (e.g. 0.7 for 70%). For a 15‑year‑old with RHR of 60 bpm aiming at 70% intensity: MHR = 205, HR reserve = 145, so target = 60 + 0.7 × 145 ≈ 162 bpm.
强度以小数表示（如 0.7 代表 70%）。例如一名 15 岁学生，静息心率 60 bpm，想以 70% 强度训练：MHR = 205，心率储备 = 145，目标心率 = 60 + 0.7 × 145 ≈ 162 bpm。
3. Cardiac Output (Q) | 心输出量 (Q)
Cardiac output is the volume of blood pumped by the heart per minute. It reflects how efficiently the cardiovascular system delivers oxygen to working muscles.
心输出量是心脏每分钟泵出的血液体积，反映心血管系统向工作肌肉输氧的效率。
Q = HR × SV
HR is heart rate (bpm) and SV is stroke volume (ml/beat), the amount ejected per contraction. During exercise, both increase, raising Q dramatically. Elite athletes can achieve Q values above 30 L/min.
HR 为心率 (bpm)，SV 为每搏输出量 (ml/次)，即每次收缩泵出的血量。运动时两者均上升，使 Q 显著提高。优秀运动员的心输出量可超过 30 L/min。
4. Body Mass Index (BMI) | 身体质量指数 (BMI)
BMI is a simple index of weight‑for‑height used to classify underweight, normal weight, overweight and obesity.
BMI 是一种根据体重和身高评估身体胖瘦程度的简易指标，用于分类体重不足、正常体重、超重和肥胖。
BMI = weight (kg) ÷ height² (m²)
ight of 1.70 m: BMI = 65 ÷ (1.70²) = 22.5 kg/m², which falls within the normal range (18.5–24.9).
例如，一名体重 65 kg、身高 1.70 m 的学生：BMI = 65 ÷ (1.70²) = 22.5 kg/m²，处于正常范围 (18.5–24.9)。
5. Speed, Velocity & Acceleration | 速度、速率与加速度
Speed is the rate at which distance is covered. Velocity includes direction. Acceleration describes how quickly velocity changes, which is crucial in analysing sprints, throws and tackles.
速率是移动距离的快慢程度，速度包含方向。加速度则描述速度变化的快慢，在分析冲刺、投掷和拦截时十分关键。
v = d ÷ t
a = (v − u) ÷ t
.5 s has an average speed of 8 m/s. If they accelerate from 0 to 8 m/s in 2 s, a = 4 m/s².
其中 v = 最终速率/速度，u = 初始速率/速度，d = 距离，t = 时间。一名 100 m 短跑运动员用时 12.5 s，平均速率为 8 m/s。若在 2 s 内从 0 加速到 8 m/s，则 a = 4 m/s²。
6. Newton's Second Law & Weight | 牛顿第二定律与重量
Newton's Second Law states that the acceleration of an object is proportional to the net force and inversely proportional to its mass. Weight is the force due to gravity acting on a mass.
牛顿第二定律指出，物体的加速度与所受合力成正比，与质量成反比。重量是引力场对物体质量施加的力。
F = m × a
W = m × g
g. So a 70 kg athlete has a weight of 700 N. When kicking a ball, the force applied determines its acceleration.
F = 合力 (N)，m = 质量 (kg)，a = 加速度 (m/s²)。在地球表面，引力场强度 g ≈ 10 N/kg。因此一名 70 kg 的运动员重约 700 N。踢球时，施加的力决定了球的加速度。
7. Momentum & Impulse | 动量与冲量
Momentum is the product of mass and velocity and is conserved in collisions. Impulse is the change in momentum caused by a force acting over time – important in tackling and striking.
动量是质量与速度的乘积，在碰撞中守恒。冲量是力在一段时间内引起的动量变化，在拦截和击打动作中十分重要。
p = m × v
F × t = Δp = m v − m u
m/s. When tackled and brought to rest, the impulse applied by the tackler equals 400 N s.
一名 80 kg 的橄榄球运动员以 5 m/s 奔跑，动量为 400 kg m/s。被擒抱并停下时，对方施加的冲量为 400 N s。
8. Levers & Mechanical Advantage | 杠杆与机械优势
Levers magnify the effect of a force. In the body, bones act as levers, joints as fulcrums and muscles provide the effort. Understanding lever systems helps optimise performance and reduce injury risk.
杠杆能放大力的作用。在人体中，骨骼充当杠杆，关节充当支点，肌肉提供动力。理解杠杆系统有助于优化运动表现并降低受伤风险。
Effort × Effort Arm = Load × Load Arm
Mechanical Advantage (MA) = Effort Arm ÷ Load Arm
When MA > 1, the lever amplifies force (e.g. calf raise). When MA < 1, it amplifies speed and range of motion (e.g. biceps curl). Most body levers favour speed over force.
当 MA > 1 时，杠杆放大力量（如提踵）。当 MA < 1 时，杠杆放大速度和运动幅度（如肱二头肌弯举）。人体大多数杠杆倾向于速度而非力量。
9. Energy Expenditure & MET | 能量消耗与代谢当量
/min, equivalent to resting metabolism. Using MET values allows estimation of energy burn.
MET (代谢当量) 表示体力活动的能耗强度。1 MET ≈ 3.5 ml O₂/kg/min，相当于静息代谢水平。利用 MET 值可以估算能量消耗。
Energy (kcal) = MET × weight (kg) × time (hours)
: 8 × 60 × 0.5 = 240 kcal. This formula helps design training and weight management plans.
一个体重 60 kg 的人步行 (3.5 MET) 1 小时：3.5 × 60 × 1 = 210 kcal。跑步 (8 MET) 30 分钟 (0.5 h)：8 × 60 × 0.5 = 240 kcal。该公式有助于制定训练和体重管理计划。
10. Minute Ventilation (VE) | 每分通气量
Minute ventilation is the total volume of air moved into and out of the lungs per minute. It rises sharply during exercise to meet increased oxygen demand.
每分通气量是每分钟进出肺部的空气总体积，在运动中会急剧增加以满足升高的氧气需求。
VE = TV × f
ing VE ≈ 6 L/min. During intense exercise, VE can exceed 100 L/min in trained individuals.
TV = 潮气量 (升/次)，f = 呼吸频率 (次/分)。静息时 TV ≈ 0.5 L，f ≈ 12，VE ≈ 6 L/min。剧烈运动时，训练有素者的 VE 可超过 100 L/min。
11. Estimating VO₂max | 最大摄氧量估算
VO₂max represents the maximal rate of oxygen consumption during incremental exercise and is a key indicator of cardiorespiratory fitness. It can be estimated without laboratory equipment using field tests like the Cooper 12‑minute run.
最大摄氧量 (VO₂max) 代表递增负荷运动中的最大耗氧速率，是心肺耐力的关键指标。可通过库珀 12 分钟跑等场地测试进行估算，无需实验室设备。
VO₂max (ml/kg/min) = (d − 504.9) ÷ 44.8
≈ 51.2 ml/kg/min. This formula works best for individuals with reasonable running ability.
d 是 12 分钟内跑步的距离 (米)。例如：跑 2800 m → (2800 − 504.9) ÷ 44.8 ≈ 51.2 ml/kg/min。该公式最适合具备一定跑步能力的个体。
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