Year 7 Cambridge PE: Formula & Theorem Quick Reference Handbook | 剑桥7年级体育：公式定理速查手册

📚 Year 7 Cambridge PE: Formula & Theorem Quick Reference Handbook | 剑桥7年级体育：公式定理速查手册

This quick reference handbook brings together the essential formulas, principles, and ‘theorems’ you will encounter in Year 7 Cambridge Physical Education. From calculating speed and target heart rate to understanding Newton’s laws and the FITT principle, each entry is explained in clear, simple language. Use this guide to support your practical work, written assignments, and exam preparation.

本速查手册汇集了剑桥7年级体育课程中你将遇到的核心公式、原理与“定理”。从计算速度和目标心率到理解牛顿定律和FITT原则，每一条都使用清晰简单的语言解释。使用本指南辅助你的实践活动、书面作业和考试准备。

1. Speed Formula | 速度公式

Speed = Distance ÷ Time

In PE, speed is how quickly you cover a certain distance. It can be measured in metres per second (m/s) or kilometres per hour (km/h). The formula helps you work out who sprinted fastest over a short distance or track performance over longer distances.

在体育中，速度是指你覆盖一定距离的快慢程度。可以用米每秒（m/s）或公里每小时（km/h）来测量。该公式帮助你算出谁在短距离内冲刺最快，或评估更长距离的运动表现。

For example, if a student runs 100 metres in 12.5 seconds, their speed is 100 ÷ 12.5 = 8 m/s. Remember to keep units consistent – if time is in seconds, distance should be in metres.

例如，如果一名学生用12.5秒跑完100米，其速度为 100 ÷ 12.5 = 8 m/s。记住要保持单位一致——若时间以秒为单位，距离就应以米为单位。

2. Maximum Heart Rate (MHR) Formula | 最大心率公式

Maximum Heart Rate = 220 – Age (years)

Your maximum heart rate (MHR) is the highest number of beats your heart can achieve in one minute during all-out effort. The most common estimation for teenagers and adults is 220 minus your age. For a 12‑year‑old Year 7 student, estimated MHR = 220 – 12 = 208 beats per minute (bpm).

最大心率（MHR）是指你在全力运动时心脏每分钟能够达到的最高跳动次数。对于青少年和成年人，最常见的估算方法是 220 减去年龄。对一个12岁的7年级学生来说，估算的最大心率 = 220 – 12 = 208 次/分钟（bpm）。

This number is a guideline, not an exact limit. It helps you understand training intensity. Most aerobic training zones are set between 60% and 80% of MHR.

这个数字是一个参考值，并非精确极限。它有助于你理解训练强度。大多数有氧训练区域设置在最大心率的60%至80%之间。

3. Target Heart Rate – Karvonen Formula | 目标心率 – 卡沃宁公式

Target Heart Rate = [(MHR – Resting HR) × %Intensity] + Resting HR

The Karvonen formula is more precise because it takes your resting heart rate (RHR) into account, which reflects your basic fitness level. First measure your RHR in the morning while still lying down. Then calculate your heart rate reserve (MHR – RHR). Multiply by the desired intensity (e.g., 0.6 for 60%) and add back the RHR.

卡沃宁公式更为精确，因为它考虑了反映你基础体能水平的静息心率（RHR）。首先在早晨仍躺着时测量静息心率。然后计算你的心率储备（MHR – RHR）。乘以期望强度（例如0.6代表60%）并加回静息心率。

Example: A 12‑year‑old with RHR of 70 bpm wanting to work at 70% intensity: MHR = 208, reserve = 138, target = (138 × 0.7) + 70 = 166.6 bpm. This method personalises your training zone.

例子：一名12岁学生静息心率70 bpm，希望以70%强度运动：MHR = 208，储备心率138，目标心率 = (138 × 0.7) + 70 = 166.6 bpm。此方法可使训练区域个性化。

4. Body Mass Index (BMI) | 身体质量指数

BMI = Weight (kg) ÷ [Height (m)]²

BMI is a simple screening tool that compares weight to height. In Year 7 PE, it is used to start conversations about healthy weight ranges, but it does not measure body fat directly. Divide your weight in kilograms by your height in metres squared (height multiplied by itself).

BMI是一种简单的筛查工具，用于比较体重与身高的关系。在7年级体育中，它用来开启关于健康体重范围的讨论，但它并不能直接测量体脂。用体重（千克）除以身高（米）的平方（身高乘以自身）。

For example, weight = 45 kg, height = 1.55 m: BMI = 45 ÷ (1.55 × 1.55) = 18.7 kg/m². For children and teens, BMI is plotted on age‑ and gender‑specific growth charts rather than using fixed adult cut‑offs.

例如，体重45千克，身高1.55米：BMI = 45 ÷ (1.55 × 1.55) = 18.7 kg/m²。对于儿童和青少年，BMI需标注在年龄和性别特定的生长图表上，而不是使用固定的成人截断值。

5. FITT Principle | FITT 训练原则

F – Frequency, I – Intensity, T – Time, T – Type

The FITT principle is a framework for building an effective exercise plan. Frequency is how often you exercise (e.g., 3 times a week). Intensity is how hard you work (e.g., 70% of MHR). Time is the duration of each session (e.g., 30 minutes). Type is the kind of exercise (e.g., running, swimming, cycling).

FITT原则是构建有效锻炼计划的框架。Frequency（频率）指你多久锻炼一次（如每周3次）。Intensity（强度）指你运动得有多努力（如最大心率的70%）。Time（时间）指每次训练的持续时间（如30分钟）。Type（类型）指运动的种类（如跑步、游泳、骑自行车）。

Changing any one of these variables will alter the training effect. Over time, you can increase frequency, intensity or time to follow the progressive overload principle.

改变其中任何一个变量都会改变训练效果。你可以随着时间推移增加频率、强度或时间，以遵循渐进超负荷原则。

6. SPORT Principles of Training | 训练中的 SPORT 原则

S – Specificity, P – Progression, O – Overload, R – Reversibility, T – Tedium (Variation)

The SPORT principles help you plan a balanced training programme. Specificity means training should match the demands of your sport. Progression requires gradually increasing the challenge. Overload means working harder than normal to improve fitness. Reversibility warns that fitness is lost when you stop training. Tedium reminds you to vary activities to avoid boredom.

SPORT原则帮助你规划一个平衡的训练计划。Specificity（特异性）指训练应与你从事的运动需求相匹配。Progression（渐进性）要求逐步增加挑战。Overload（超负荷）意味着要比平时更努力才能提升体能。Reversibility（可逆性）警告你一旦停止训练，体能就会下降。Tedium（单调性，亦称变化性）提醒你要变换活动以避免枯燥。

For example, a footballer’s programme should include sprinting, agility and ball skills (specificity). Each week, the number of sprints can increase (progression and overload). If injured and resting, fitness declines (reversibility). Mixing drills with games keeps training enjoyable (tedium).

例如，一名足球运动员的训练计划应该包括冲刺、灵敏和球技（特异性）。每周冲刺次数可以增加（渐进性与超负荷）。若因伤休息，体能就会下降（可逆性）。将练习与比赛穿插进行可保持训练趣味性（单调性/变化性）。

7. Newton’s Laws of Motion | 牛顿运动定律

First Law (Inertia): An object stays at rest or moves at a constant speed in a straight line unless acted on by an unbalanced force. In sport, a football will not move until kicked.

第一定律（惯性）： 除非受到不平衡力的作用，否则物体将保持静止或匀速直线运动状态。在运动中，足球不会被移动，除非被踢。

Second Law (Acceleration): Force = Mass × Acceleration (F = m × a). Heavier objects need more force to accelerate. A shot‑putter must apply great force to accelerate the heavy shot.

第二定律（加速度）： 力 = 质量 × 加速度（F = m × a）。较重的物体需要更大的力来加速。推铅球运动员必须施加巨大的力才能使沉重的铅球加速。

Third Law (Action‑Reaction): For every action, there is an equal and opposite reaction. When a swimmer pushes water backwards, the water pushes the swimmer forwards.

第三定律（作用力与反作用力）： 对于每一个作用力，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，水将游泳者向前推。

These laws explain movement in almost every sport and are the foundation of biomechanics.

这些定律能解释几乎所有运动中的移动现象，是生物力学的基础。

8. Work and Power | 功和功率

Work = Force × Distance

Power = Work ÷ Time

Work measures the energy transferred when a force moves an object. It is measured in joules (J). If you lift a 20 N weight through 2 metres, you do 20 × 2 = 40 J of work. Power tells you how quickly that work is done, measured in watts (W). Power = work ÷ time; doing the same work in half the time doubles the power.

功衡量的是力使物体移动时所传递的能量，单位为焦耳（J）。如果你将一个20牛的物体向上举起2米，你做了20 × 2 = 40焦耳的功。功率表明做功的快慢，单位为瓦特（W）。功率 = 功 ÷ 时间；用一半时间完成同样的功，功率就翻倍。

In PE, power relates to explosive activities such as jumping, throwing and sprinting. An athlete who can generate more power in a short time will have a performance advantage.

在体育中，功率与跳跃、投掷和冲刺等爆发性活动相关。能够在短时间内产生更大功率的运动员会具有表现优势。

9. Levers in the Body | 人体中的杠杆

A lever is a rigid bar that rotates around a fulcrum. In the human body, bones act as levers, joints are the fulcrums, and muscles provide the effort force. The load is the weight being moved. Levers are classified into three classes depending on the arrangement of fulcrum, effort and load.

杠杆是一根绕支点转动的刚性棒。在人体中，骨骼充当杠杆，关节是支点，肌肉提供动力。负荷是被移动的重量。根据支点、动力和负荷的排列方式，杠杆分为三类。

• First‑class lever: fulcrum between effort and load – e.g., nodding the head (skull pivots on spine).
• 第一类杠杆： 支点在动力和负荷之间——比如点头动作（颅骨以脊柱为支点）。
• Second‑class lever: load between fulcrum and effort – e.g., standing on tiptoes (ball of foot as fulcrum, body weight as load).
• 第二类杠杆： 负荷在支点和动力之间——比如踮脚尖站立（前脚掌为支点，体重为负荷）。
• Third‑class lever: effort between fulcrum and load – the most common in the body, e.g., biceps curl (elbow fulcrum, effort at forearm, load in hand).
• 第三类杠杆： 动力在支点和负荷之间——人体中最常见，比如肱二头肌弯举（肘部为支点，前臂处提供动力，手中负荷）。

Understanding levers helps you analyse movement efficiency and the advantage offered by different joint actions.

理解杠杆有助于你分析动作效率以及不同关节活动带来的优势。

10. Energy Systems Overview | 能量系统概览

The body uses three energy systems to produce ATP (adenosine triphosphate), the energy currency for muscle contraction. The ATP‑PC system provides immediate energy for up to 10 seconds of maximum effort, such as a 100 m sprint. It does not require oxygen.

身体使用三个能量系统来产生ATP（三磷酸腺苷），这是肌肉收缩的能量货币。ATP‑PC系统为最多10秒的全力爆发提供即时能量，比如100米冲刺。它不需要氧气。

The lactic acid system (anaerobic glycolysis) fuels high‑intensity efforts lasting up to about 90 seconds, e.g., a 400 m run. It produces lactic acid as a by‑product, causing muscle fatigue. The aerobic system uses oxygen to supply energy for activities lasting longer than 2 minutes, such as distance running. It produces the most ATP but at a slower rate.

乳酸系统（无氧糖酵解）为持续长达约90秒的高强度运动供能，例如400米跑。它产生乳酸作为副产品，导致肌肉疲劳。有氧系统利用氧气为持续超过2分钟的活动（如长跑）供能。它产生的ATP最多，但速率较慢。

All three systems work together, but the dominant system depends on the intensity and duration of the exercise.

三个系统协同工作，但主导系统取决于运动的强度和持续时间。

11. Hydration and Fluid Balance | 水分与体液平衡

Fluid loss (% body weight) = (Weight before – Weight after) ÷ Weight before × 100

Staying hydrated is critical for performance and safety. Even a small fluid loss (1–2% of body weight) can reduce endurance, strength and concentration. Weigh yourself before and after a training session to estimate sweat loss. For every 1 kg lost, you need to replace roughly 1–1.5 litres of fluid.

保持水分充足对运动表现和安全至关重要。哪怕是体重1–2%的少量体液流失都可能降低耐力、力量和注意力。在训练前后称体重可以估算出汗流失量。每减轻1千克，你需要补充大约1至1.5升液体。

In PE lessons, especially in hot conditions, drink water before, during and after exercise. Aim for pale‑coloured urine as a quick hydration check.

在体育课上，尤其炎热天气下，运动前、中、后都要喝水。快速判断补水状况的方法是以尿液颜色清亮为目标。

12. Skill-related Fitness Components | 技能相关体能要素

While health‑related fitness includes body composition, cardiovascular endurance, flexibility, muscular endurance and strength, skill‑related fitness helps you perform effectively in sports. The six commonly recognised components are:

健康相关体适能包括身体成分、心血管耐力、柔韧性、肌肉耐力和肌肉力量，而技能相关体适能则有助于你在运动中有效发挥。六个公认的要素为：

• Agility – ability to change direction quickly (e.g., dodging in netball).
• 敏捷性 – 快速改变方向的能力（如无挡板篮球中的闪躲）。
• Balance – maintaining stability while still or moving (e.g., handstand).
• 平衡 – 在静止或移动中保持稳定（如手倒立）。
• Coordination – using senses together with body parts (e.g., catching a ball).
• 协调性 – 将感官与身体部位配合使用（如接球）。
• Power – combining strength and speed (e.g., long jump take‑off).
• 爆发力 – 力量与速度的结合（如跳远起跳）。
• Reaction time – quick response to a stimulus (e.g., sprint start off the gun).
• 反应时间 – 对刺激快速做出反应（如听到发令枪后起跑）。
• Speed – moving the body quickly over a distance (e.g., 100 m dash).
• 速度 – 在距离上快速移动身体（如百米冲刺）。

These components are not fixed ‘theorems’ but guiding concepts that underpin all sports performance. Coaches design drills to improve specific components relevant to the sport.

这些要素并非刻板的“定理”，而是支撑所有运动表现的指导概念。教练会设计练习来提升与特定运动相关的具体要素。

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