📚 Year 10 OCR PE: Formula & Theorem Quick Reference Handbook | Year 10 OCR 体育：公式定理速查手册
This quick reference handbook covers the essential formulas and theorems for the Year 10 OCR GCSE Physical Education course. Mastering these equations and principles will strengthen your exam answers, coursework analysis and practical evaluation skills. All formulas are presented with clear units and practical sports examples.
本速查手册涵盖 Year 10 OCR GCSE 体育课程的核心公式和定理。掌握这些方程与原理，能帮助你提升考试答题、课程作业分析和实践评估的能力。每个公式都配有明确单位和运动实例。
1. Maximum Heart Rate (MHR) | 最大心率公式
Maximum heart rate is the highest number of beats per minute (bpm) your heart can achieve during all-out exercise. It is commonly estimated using a simple age-based equation:
MHR = 220 – Age (years)
最大心率是心脏在极限运动时每分钟跳动的最高次数，通常用基于年龄的简单方程估算：MHR = 220 – 年龄（岁）。
2. Karvonen Formula (Heart Rate Reserve) | 卡沃宁公式（心率储备）
The Karvonen method uses resting heart rate (RHR) to personalise training zones. First calculate heart rate reserve (HRR):
HRR = MHR – RHR
卡沃宁法利用静息心率 (RHR) 制定个性化训练区间。首先计算心率储备：HRR = MHR – RHR。
Then the target heart rate for a given intensity is:
Target HR = RHR + (HRR × desired intensity %)
Example: at 60% intensity, Target HR = RHR + (HRR × 0.60)
随后可根据强度计算靶心率：靶心率 = RHR + (HRR × 目标强度%)。例如 60% 强度时，靶心率 = RHR + (HRR × 0.60)。
3. Body Mass Index (BMI) | 身体质量指数
BMI assesses whether a person has a healthy body mass relative to their height:
BMI = body mass (kg) ÷ [height (m)]²
BMI 用于评估体重相对于身高是否健康：BMI = 体重 (kg) ÷ 身高 (m)²。
The result places individuals into categories such as underweight, normal weight, overweight or obese. Remember that BMI does not distinguish between muscle and fat.
结果可将人分为偏瘦、正常、超重或肥胖等类别。注意 BMI 不区分肌肉与脂肪。
4. Energy Expenditure Using METs | 用 MET 估算能量消耗
Metabolic Equivalent of Task (MET) values describe the energy cost of activities. Energy expenditure can be estimated as:
Energy (kcal) ≈ MET × body mass (kg) × time (hours)
代谢当量 (MET) 值描述活动的能量消耗水平，可用以下公式估算：能量 (kcal) ≈ MET × 体重 (kg) × 时间 (小时)。
For example, jogging at 8 km/h (about 8 METs) for 30 minutes by a 60 kg person: 8 × 60 × 0.5 = 240 kcal.
举例：体重 60 kg 的人以 8 km/h 慢跑 30 分钟 (约 8 METs)，消耗约 8 × 60 × 0.5 = 240 kcal。
5. Speed and Acceleration | 速度与加速度
Average speed is a scalar quantity calculated by dividing distance travelled by time taken:
v = d / t (m/s)
平均速度是标量，用移动距离除以时间计算：v = d / t (m/s)。
Acceleration is the rate of change of velocity. When initial velocity (u) and final velocity (v) are known over a time interval (t):
a = (v – u) / t (m/s²)
加速度是速度变化率。已知初速度 u、末速度 v 和时间 t 时：a = (v – u) / t (m/s²)。
6. Newton’s Second Law of Motion | 牛顿第二定律
The acceleration of an object is proportional to the resultant force acting on it and inversely proportional to its mass:
F = m × a
Resultant Force (N) = mass (kg) × acceleration (m/s²)
物体的加速度与所受合力成正比，与其质量成反比：合力 (N) = 质量 (kg) × 加速度 (m/s²)。
This law explains why a footballer kicking a lighter ball can generate a higher acceleration using the same force.
该定律解释了为何用相同力量踢一个更轻的足球能产生更大的加速度。
7. Momentum | 动量
Momentum is a vector quantity given by the product of an object’s mass and velocity:
p = m × v (kg m/s)
动量是矢量，等于物体质量与速度的乘积：p = m × v (kg m/s)。
In tackling or collisions, momentum is conserved in a closed system. A larger mass or faster velocity gives greater momentum, making the athlete harder to stop.
在防守擒抱或碰撞中，封闭系统内动量守恒。质量更大或速度更快则动量更大，使运动员更难被停止。
8. Moment of Force and Levers | 力矩与杠杆
A moment (turning effect) is calculated by multiplying the force applied by the perpendicular distance from the pivot:
Moment = Force × perpendicular distance from fulcrum (Nm)
力矩（转动效应）等于作用力乘以从支点出发的垂直距离：力矩 = 力 × 支点垂直距离 (Nm)。
For a lever to balance, the clockwise moment equals the anticlockwise moment:
Effort × effort arm = Load × load arm
杠杆平衡时，顺时针力矩等于逆时针力矩：动力 × 动力臂 = 阻力 × 阻力臂。
In the body, joints act as fulcrums, muscles provide effort and body segments or external weights act as loads.
在人体中，关节作为支点，肌肉提供动力，身体节段或外部重量作为阻力。
9. Work and Power | 功与功率
Work is done when a force moves an object in the direction of the force:
Work (W) = Force (F) × distance moved in direction of force (d) (Joules, J)
当一个力使物体沿力的方向移动时就做了功：功 (W) = 力 (F) × 沿力方向移动的距离 (d) (J)。
Power is the rate at which work is done. It can be calculated from work and time, or from force and velocity:
P = W / t (Watts, W)
P = F × v (when velocity is constant)
功率是做功的速率，可从功和时间或力和速度计算：P = W / t (W) 或 P = F × v (匀速时)。
10. Cooper 12-Minute Run Test (VO₂
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