📚 Year 11 OCR PE: Quick-Reference Formulas & Theorem Handbook | Year 11 OCR 体育：公式定理速查手册
Welcome to your essential OCR GCSE Physical Education formulas and key principles quick-reference guide. This handbook summarises the critical calculations and biomechanical theorems you need to master for Paper 1 (Physical factors affecting performance) and Paper 2 (Socio-cultural issues and sports psychology). Whether you are revising cardiac outputs, training zones, levers, or Newton's laws, this page provides clear explanations paired with Chinese translations to support bilingual learning.
欢迎使用 OCR GCSE 体育核心公式与关键原理速查手册。本手册总结了试卷一（影响运动表现的生理因素）和试卷二（社会文化问题与运动心理学）中必须掌握的关键计算和生物力学定理。无论你是在复习心输出量、训练区间、杠杆还是牛顿定律，这里都提供清晰解释并配以中文翻译，助力双语学习。
1. Cardiac Output (Q) | 心输出量公式
ured in beats per minute (bpm), while SV is the amount of blood ejected per beat, typically expressed in millilitres (ml). To express Q in litres per minute (L/min), divide the product by 1000: Q (L/min) = (HR × SV) ÷ 1000. For a resting individual with HR = 72 bpm and SV = 70 ml, Q = (72 × 70) / 1000 = 5.04 L/min. During intense exercise, both HR and SV increase, elevating Q to supply working muscles with oxygen.
心输出量是心脏每分钟泵出的血液总量，计算公式为心输出量 = 心率 × 每搏输出量。心率单位是次/分 (bpm)，每搏输出量是每次心跳射出的血量 (ml)。表示成升/分钟需除以1000：Q (L/min) = (HR × SV) ÷ 1000。安静时心输出量约5 L/min，最大运动时训练有素的运动员可达20–40 L/min。
Q = HR × SV
2. Maximum Heart Rate and Training Zones | 最大心率与训练区间
ties that target specific fitness adaptations. The aerobic training zone corresponds to 60–80% ing cardiovascular endurance and fat burning. The anaerobic training zone falls between 80–90% w to quickly reference target heart rate ranges for a 16-year-old student (MHR = 204 bpm).
估算最大心率的最简单公式是最大心率 = 220 − 年龄。这一估算帮助设定针对特定适应的训练强度。有氧训练区为最大心率的60–80%，促进心血管耐力和脂肪消耗；无氧训练区在80–90% MHR，提升速度、爆发力和乳酸耐受。下表为16岁学生（MHR = 204 bpm）的目标心率参照表。
| Training Zone | % MHR | Example (Age 16, MHR=204 bpm) |
|---|---|---|
| Aerobic (moderate) | 60–80% | 122–163 bpm |
| Anaerobic (vigorous) | 80–90% | 163–184 bpm |
3. Karvonen Formula (Heart Rate Reserve) | 卡沃宁公式（心率储备）
HRR), where HRR = MHR − RHR. The formula is Target HR = RHR + (Intensity × HRR), with intensity expressed as a decimal (e.g. 0.7 for 70%). For example, an athlete with RHR = 60 bpm, MHR = 200 bpm, and desired intensity 70% accounts for individual fitness levels and is widely used in personalised training plans.
采用心率储备法可以得到更精确的目标心率。它基于安静心率 (RHR) 和储备心率 (HRR = MHR − RHR)。公式为：目标心率 = RHR + (强度 × HRR)，强度以小数表示 (如70%对应0.7)。例如一名运动员安静心率60 bpm、最大心率200 bpm，进行70%强度训练时，目标心率 = 60 + 0.7 × (200 − 60) = 158 bpm。该方法因人而异，常用于个性化训练方案。
Target HR = RHR + (Intensity × (MHR − RHR))
4. Minute Ventilation (VE) | 分钟通气量
requency (f): VE = VT × f. Tidal volume is the amount of air inhaled or exhaled in one breath, typically around 0.5 L at rest. Breathing frequency is the number of breaths per minute. At rest, VE ≈ 0.5 L × 12 breaths/min = 6 L/min. During vigorous exercise, tidal volume can increase to 2–3 L and breathing rate to 40–60 breaths/min, raising VE well above 100 L/min to meet oxygen demands.
分钟通气量是每分钟吸入或呼出肺部的空气总量，由潮气量 (VT) 乘以呼吸频率 (f) 得出：VE = VT × f。安静时潮气量约0.5升，呼吸频率12次/分，VE ≈ 6 L/min。剧烈运动时潮气量可升至2–3升，呼吸频率加快至40–60次/分，使分钟通气量远超100 L/min，以满足氧气需求。
VE = VT × f
5. Body Mass Index (BMI) | 身体质量指数
. For an OCR PE context, you should know the standard categories: underweight (<18.5), normal weight (18.5–24.9), overweight (25– r athlete may be incorrectly classified as overweight. Use this formula to interpret health-related fitness data, but always consider its limitations.
身体质量指数是一种评估体重状况的工具，公式为 BMI = 体重 (kg) ÷ 身高² (m²)。OCR 体育要求掌握以下分类标准：偏瘦 (<18.5)、正常 (18.5–24.9)、超重 (25–29.9) 和肥胖 (≥30)。但 BMI 无法区分肌肉与脂肪，肌肉发达的运动员可能被错误归为超重。运用该公式分析健康体适能时，必须考虑其局限性。
BMI = mass (kg) / (height (m))²
6. Speed, Velocity, and Acceleration | 速度、速率与加速度
; it has the same magnitude as speed but includes direction. Acceleration is the rate of change of velocity, given by a = (v − u) / t, where u is initial velocity and v is final velocity. In sprinting, an athlete' Typical units used in OCR exams are m/s for speed and velocity, and m/s² for acceleration.
速率是标量，描述物体移动的快慢，公式为速率 = 距离 / 时间 (v = d / t)。速度是矢量，大小与速率相同但带有方向。加速度是速度的变化率，公式 a = (v − u) / t，其中 u 为初速度，v 为末速度。短跑起跑阶段的加速度即由该公式决定。OCR 考试常用单位：速率与速度用 m/s，加速度用 m/s²。
v = d / t
a = (v − u) / t
7. Newton's Laws of Motion | 牛顿运动定律
Newton' acted upon by an external resultant force. Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma). Third Law: For every action force, there is an equal and opposite reaction force. These laws explain sprint starts (reaction force), tackling (inertia and momentum), and throwing techniques (force-mass relationship).
牛顿三定律奠定了生物力学的基础。第一定律（惯性）：除非受到合外力作用，物体将保持静止或匀速直线运动状态。第二定律：加速度与合外力成正比，与质量成反比（F = ma）。第三定律：每一个作用力都有一个大小相等、方向相反的反作用力。这些定律解释了起跑（反作用力）、擒抱（惯性与动量）以及投掷技术（力-质量关系）。
First Law: Inertia – an object will not change its motion unless a force acts on it.
第一定律：惯性——若无外力，物体不改变其运动状态。
Second Law: F = ma – force produces greater acceleration; a heavier object accelerates less for the same force.
第二定律：F = ma ——力越大加速度越大；相同力作用下，质量越大加速度越小。
Third Law: Action-reaction – when pushing against the ground, the ground pushes back equally.
第三定律：作用与反作用——蹬地时，地面以同等大小的力将人体推向前。
8. Force, Mass, and Momentum | 力、质量与动量
duct of mass and velocity: p = mv, measured in kg·m/s. In contact sports, the change in momentum is linked to impulse (force × time). A tackle with a large force over a short time produces a rapid change in momentum, which can be used to stop an opponent effectively. Hitting a ball with a bat or racquet also illustrates how transferring momentum generates powerful shots.
合力导致加速度，遵循 F = ma，F 单位牛顿 (N)，m 单位千克 (kg)，a 单位 m/s²。动量 (p) 是质量与速度的乘积：p = mv，单位 kg·m/s。在身体接触项目中，动量的变化与冲量（力 × 时间）相关。短时间内施加大力可迅速改变对手动量，实现有效拦截。击球时，球拍将动量传递给球，产生有力回球。
F = m × a
p = m × v
9. Work Done (W) | 做功
s the applied force (newtons, N), and d is the distance moved in the direction of the force (metres). If the force is perpendicular to the displacement, no work is done. In physical education, you may use work done to estimate energy expenditure during activities such as lifting weights or climbing stairs. Example: lifting a 200 N barbell through 0.8 m does W = 200 × 0.8 = 160 J of work.
做功指力使物体沿力的方向移动时的能量转换，公式 W = F × d，其中 W 为功 (焦耳 J)，F 为力 (牛顿 N)，d 为沿力方向移动的距离 (米)。若力与位移垂直，则不做功。在体育中，可用于估算举重或爬楼梯等活动的能量消耗。例如将 200 N 的杠铃上举 0.8 m，做功 W = 200 × 0.8 = 160 J。
W = F × d
10. Power (P) | 功率
Power is the rate at which work is done or energy is
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