IGCSE AQA PE: Formula and Theorem Quick Reference Handbook | IGCSE AQA 体育：公式定理速查手册

📚 IGCSE AQA PE: Formula and Theorem Quick Reference Handbook | IGCSE AQA 体育：公式定理速查手册

This quick-reference handbook collects all the key formulas and theorems required for the IGCSE AQA Physical Education exam. Each entry is paired with English and Chinese explanations so you can revise effectively wherever you are.

这本速查手册汇集了 IGCSE AQA 体育考试所需的关键公式和定理。每个条目均配有中英双语解释，方便随时高效复习。

1. Cardiovascular System Key Formulas | 心血管系统关键公式

The cardiovascular system delivers oxygen and nutrients during exercise. The following equations help you quantify cardiac function.

心血管系统在运动中输送氧气和养分，以下公式帮助你量化心脏功能。

Cardiac output (Q) is the volume of blood pumped by the heart per minute. It is calculated using heart rate (HR) and stroke volume (SV):

Q = HR × SV

心输出量（Q）是心脏每分钟泵出的血量，由心率（HR）与每搏输出量（SV）相乘得出：

心输出量 = 心率 × 每搏输出量

Stroke volume is the amount of blood ejected per beat. HR is measured in beats per minute (bpm). Typical resting Q is about 5 L/min, rising to 20–25 L/min during intense exercise.

每搏输出量是每次心跳射出的血量，心率以每分钟心跳次数（bpm）计算。安静时心输出量约为 5 升/分钟，剧烈运动时可升至 20–25 升/分钟。

Maximum heart rate (HRmax) is estimated with the simple age-based formula:

HRmax = 220 – age (years)

最大心率（HRmax）可通过简单公式估算：

最大心率 = 220 – 年龄（岁）

To set training zones precisely, use the Karvonen formula, which accounts for resting heart rate (HRrest) and desired intensity:

Target HR = ((HRmax – HRrest) × %Intensity) + HRrest

要精确设定训练区间，使用考虑安静心率的卡沃宁公式：

目标心率 = ((最大心率 – 安静心率) × 强度百分比) + 安静心率

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2. Respiratory System Key Formulas | 呼吸系统关键公式

Pulmonary ventilation moves air in and out of the lungs. Minute ventilation (VE) combines how deeply and how often you breathe.

肺通气使空气进出肺部。分钟通气量（VE）综合了呼吸深度和频率。

Tidal volume (TV) is the air moved per breath; breathing frequency (f) is the number of breaths per minute. Minute ventilation is given by:

VE = TV × f

潮气量（TV）是每次呼吸移动的空气量；呼吸频率（f）是每分钟呼吸次数。分钟通气量公式为：

分钟通气量 = 潮气量 × 呼吸频率

During exercise TV can rise from ~0.5 L to over 3 L, while f may increase from 12–15 to 40–60 breaths/min, dramatically boosting VE.

运动时潮气量可从约 0.5 升增加到 3 升以上，呼吸频率可从 12–15 次/分升至 40–60 次/分，从而显著提升分钟通气量。

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3. Body Composition | 身体成分

Body Mass Index (BMI) is a quick screening tool that relates mass to height. It does not measure body fat directly but is widely used in fitness assessments.

身体质量指数（BMI）是快速筛查工具，将体重与身高相关联，不能直接测量体脂，但广泛应用于健康评估。

BMI is calculated as:

BMI = weight (kg) ÷ height² (m²)

BMI 计算公式为：

BMI = 体重（kg）÷ 身高²（m²）

For example, a 70 kg athlete with a height of 1.75 m has a BMI of 70 ÷ (1.75)² ≈ 22.9 kg/m², which falls within the healthy range.

例如，一名 70 kg 的运动员身高 1.75 m，BMI = 70 ÷ (1.75)² ≈ 22.9 kg/m²，处于健康范围。

Accurate body fat percentage can be estimated using skinfold measurements or bioelectrical impedance, but BMI remains a convenient first indicator in IGCSE contexts.

精确的体脂百分比可通过皮褶测量或生物电阻抗法估算，但在 IGCSE 内容中 BMI 是便捷的初步指标。

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4. Linear Motion: Speed, Velocity and Acceleration | 直线运动：速率、速度与加速度

Understanding how bodies move is fundamental to analysing sports performance. Speed, velocity and acceleration are key mechanical quantities.

理解身体如何运动是分析运动表现的基础。速率、速度和加速度是关键力学量。

Speed (scalar) is the rate of change of distance:

speed = distance ÷ time

速率（标量）是距离的变化率：

速率 = 距离 ÷ 时间

Velocity (vector) is displacement over time, including direction:

v = Δs ÷ Δt

速度（矢量）是位移随时间的变化，包含方向：

速度 = 位移 ÷ 时间

Acceleration describes how quickly velocity changes:

a = (v – u) ÷ t

(where u = initial velocity, v = final velocity)

加速度描述速度变化的快慢：

加速度 = (末速度 – 初速度) ÷ 时间

In a 100 m sprint, the athlete’s velocity increases from 0 to around 12 m/s, giving an average acceleration of about 3–4 m/s².

在 100 米短跑中，运动员速度从 0 增至约 12 m/s，平均加速度约 3–4 m/s²。

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5. Newton’s Laws and Momentum | 牛顿定律与动量

Newton’s three laws govern the motion of all objects and are essential for explaining forces in sport.

牛顿三大定律支配着所有物体的运动，对解释运动中的力至关重要。

Newton’s First Law (inertia): an object stays at rest or moves uniformly unless acted on by a net external force.

牛顿第一定律（惯性）：物体保持静止或匀速直线运动，除非受到外力作用。

Newton’s Second Law links force, mass and acceleration:

F = m × a

牛顿第二定律联系了力、质量与加速度：

力 = 质量 × 加速度

Newton’s Third Law: for every action there is an equal and opposite reaction. When a sprinter pushes back on the blocks, the blocks push the sprinter forward.

牛顿第三定律：每一个作用力都有一个大小相等、方向相反的反作用力。短跑运动员向后蹬起跑器，起跑器就向前推动运动员。

Momentum (p) is the product of mass and velocity:

p = m × v

动量（p）是质量与速度的乘积：

动量 = 质量 × 速度

The impulse–momentum theorem states that the impulse (F × t) equals the change in momentum:

F × t = m(v – u)

冲量–动量定理指出，冲量（力 × 时间）等于动量的变化：

力 × 时间 = 质量 × (末速度 – 初速度)

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6. Levers and Mechanical Advantage | 杠杆与机械优势

Levers help the body and sports equipment multiply force or speed. The mechanical advantage (MA) tells you how effective a lever is.

杠杆帮助身体和运动器材增大力或速度。机械优势（MA）反映杠杆的效率。

Mechanical advantage is the ratio of the length of the effort arm to the length of the resistance arm:

MA = effort arm length ÷ resistance arm length

机械优势是力臂长度与阻力臂长度的比值：

机械优势 = 力臂长度 ÷ 阻力臂长度

When MA > 1, the lever multiplies force (e.g. a crowbar). When MA < 1

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