A-Level CAIE Physical Education: Formula & Principle Quick Reference Handbook | A-Level CAIE 体育：公式定理速查手册

📚 A-Level CAIE Physical Education: Formula & Principle Quick Reference Handbook | A-Level CAIE 体育：公式定理速查手册

This quick reference guide compiles essential formulas, laws and principles covered in the Cambridge International A-Level Physical Education syllabus (9396). Mastering these quantitative and theoretical foundations is crucial for Paper 1 (Anatomy, Physiology, Biomechanics) and also supports applied sections in training and sport psychology.

本速查手册汇编了剑桥国际A-Level体育课程（9396）所涉及的核心公式、定律和原理。掌握这些量化和理论基础对于试卷一（解剖学、生理学、生物力学）以及训练学和运动心理学等应用部分都至关重要。

1. Cardiovascular System Formulas | 心血管系统公式

Heart rate (HR) is measured in beats per minute (bpm). Stroke volume (SV) is the volume of blood ejected per beat (mL·beat⁻¹). Cardiac output (Q) is the product of HR and SV: Q = HR × SV. A typical resting Q for an adult is about 5 L·min⁻¹. During exercise, both HR and SV increase, raising Q to deliver more oxygen to working muscles.

心率（HR）以次/分钟（bpm）表示。每搏输出量（SV）是每次搏动射出的血量（毫升/次）。心输出量（Q）等于 HR 与 SV 的乘积：Q = HR × SV。成人静息 Q 通常约为 5 升/分钟。运动中 HR 和 SV 均升高，Q 增大，从而为工作肌群输送更多氧气。

Mean arterial pressure (MAP) can be estimated as MAP = DBP + ⅓(SBP − DBP), where DBP is diastolic and SBP systolic pressure. MAP drives blood flow and is elevated during dynamic exercise to maintain perfusion.

平均动脉压（MAP）可估算为 MAP = 舒张压 + ⅓(收缩压 − 舒张压)。MAP 推动血液流动，在动力性运动时会升高以维持组织灌注。

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2. Respiratory System Formulas | 呼吸系统公式

Minute ventilation (VE) is the volume of air breathed each minute: VE = VT × f, where VT is tidal volume (L·breath⁻¹) and f is breathing frequency (breaths·min⁻¹). Alveolar ventilation (VA) accounts for dead space (VD): VA = (VT − VD) × f. Only VA participates in gas exchange.

分钟通气量（VE）为每分钟吸入或呼出的气体量：VE = VT × f，VT 为潮气量（升/次），f 为呼吸频率（次/分钟）。肺泡通气量（VA）需扣除死腔量（VD）：VA = (VT − VD) × f。仅 VA 参与气体交换。

Maximal oxygen uptake (VO₂ max) is the upper limit of O₂ consumption, determined by the Fick equation: VO₂ max = Q × a-vO₂ diff. The arterial-venous O₂ difference (a-vO₂ diff) represents how much O₂ is extracted by tissues per litre of blood.

最大摄氧量（VO₂ max）是人体利用氧气的上限，可由菲克原理表达：VO₂ max = Q × a-vO₂ diff。动静脉氧差（a-vO₂ diff）表示每升血液被组织提取的氧气量。

The forced expiratory ratio is FEV₁/FVC. A healthy ratio is typically above 0.7, and a decrease indicates airway obstruction or respiratory limitation during exercise.

用力肺活量比为 FEV₁/FVC。健康者的比值通常大于 0.7，该值下降提示运动时存在气道阻塞或通气限制。

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3. Energy Systems and Metabolism | 能量系统与代谢

One metabolic equivalent (MET) is the resting O₂ consumption: 1 MET = 3.5 mL·kg⁻¹·min⁻¹. Activity energy expenditure can be estimated as kilocalories using METs: Energy (kcal) = MET × body mass (kg) × time (h).

1 代谢当量（MET）等于静息摄氧量：1 MET = 3.5 毫升·千克⁻¹·分钟⁻¹。活动能耗可用 MET 估算为千卡：能量 (kcal) = MET × 体重 (kg) × 时间 (h)。

Mechanical efficiency describes how much of the metabolic energy is converted into external work: Efficiency (%) = (work output / energy expenditure) × 100. In cycling, net efficiency is typically 20–25%.

机械效率反映代谢能转化为外功的比例：效率 (%) = (做功输出 / 能量消耗) × 100。骑行的净效率通常为 20–25%。

The respiratory exchange ratio (RER) is RER = VCO₂ / VO₂. RER of 0.7 reflects fat oxidation, 1.0 reflects carbohydrate oxidation, and >1.0 indicates anaerobic buffering.

呼吸交换率（RER）定义为 RER = VCO₂ / VO₂。RER 0.7 对应脂肪氧化，1.0 对应碳水化合物氧化，大于 1.0 提示无氧代谢参与缓冲。

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4. Newton’s Laws of Motion | 牛顿运动定律

First Law (Inertia): A body remains at rest or in uniform motion unless acted upon by a net external force. This explains why a sprinter must apply force to start, and why a football continues moving until friction or another force acts.

第一定律（惯性）：物体在不受净外力作用时将保持静止或匀速直线运动状态。这解释了短跑选手为何需发力起跑，以及足球为什么会持续运动直到摩擦或其他力作用。

Second Law (Acceleration): F = m a. The acceleration of an object is proportional to the net force and inversely proportional to its mass. A greater force produces a larger acceleration for a given mass; for example, a shot‑putter must generate large force to accelerate the shot.

第二定律（加速度）：F = m a。物体的加速度与净外力成正比，与质量成反比。在质量一定时，更大的力产生更大加速度；例如铅球运动员必须产生大力量才能使铅球加速。

Third Law (Action–Reaction): For every action force there is an equal and opposite reaction force. When a swimmer pushes water backwards, the water pushes the swimmer forwards. Ground reaction force is essential in running and jumping.

第三定律（作用力与反作用力）：每一个作用力都有一个大小相等、方向相反的反作用力。游泳者向后推水时，水向前推游泳者。地面反作用力是跑步和跳跃的关键。

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5. Levers and Mechanical Advantage | 杠杆与机械利益

The turning effect of a force is torque (τ): τ = F × d, where F is force and d is the perpendicular distance from the axis of rotation (moment arm). For equilibrium, the sum of clockwise torques equals the sum of anticlockwise torques.

力的转动效应称为力矩（τ）：τ = F × d，F 为力，d 为力臂（转轴到力作用线的垂直距离）。平衡时，顺时针力矩之和等于逆时针力矩之和。

Mechanical advantage (MA) = effort arm / resistance arm. When MA > 1, a small effort can move a large resistance (third‑class levers like the biceps curl have MA < 1 but allow large range and speed). Levers are classified into first, second and third class depending on the relative positions of effort, load and fulcrum.

机械利益（MA） = 动力臂 / 阻力臂。MA > 1 时，较小的动力可克服较大阻力；像肱二头肌弯举这样的第三类杠杆 MA < 1，但能提供大范围活动和高速度。杠杆根据动力、阻力和支点的相对位置分为第一、第二和第三类。

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6. Kinematics and Projectile Motion | 运动学与抛体运动

Speed (v) and acceleration (a) are defined as v = Δs / Δt and a = Δv / Δt. For constant acceleration, three key equations apply: v = u + a t, s = u t + ½ a t², and v² = u² + 2 a s (u = initial velocity, s = displacement).

速度和加速度定义为 v = Δs / Δt 和 a = Δv / Δt。在匀加速度下，三个基本方程为：v = u + a t、s = u t + ½ a t² 及 v² = u² + 2 a s（u 为初速度，s 为位移）。

For projectile motion, assuming air resistance is negligible, the horizontal and vertical components are independent. Horizontal displacement: sₓ = u cos θ × t. Vertical displacement: sᵧ = (u sin θ) t − ½ g t², where g = 9.81 m·s⁻². The optimum release angle for distance on level ground is 45°.

对于抛体运动，忽略空气阻力时，水平与垂直分量相互独立。水平位移：sₓ = u cos θ × t；垂直位移：sᵧ = (u sin θ) t − ½ g t²，g = 9.81 米·秒⁻²。平地上最大远度的最佳出手角度为 45°。

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7. Forces, Momentum and Impulse | 力、动量与冲量

Momentum (p) is the product of mass and velocity: p = m v. Impulse is the change in momentum caused by a force acting over time: F Δt = Δp. In a tackle, increasing contact time reduces the force experienced.

动量 (p) 为质量与速度的乘积：p = m v。冲量 是力作用一段时间引起的动量变化：F Δt = Δp。在抢断中，延长接触时间可减小

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