📚 Year 10 SQA PE: Formula & Theorems Quick Reference Handbook | Year 10 SQA 体育：公式定理速查手册
This quick reference handbook brings together the essential formulas, principles and biomechanical theorems you need for SQA National 4/5 Physical Education. From calculating training heart rates to understanding Newton's laws on the field, each concept is explained clearly with both English and Chinese explanations side by side. Use this guide to support your data analysis tasks, factors impacting performance questions, and practical planning.
这本速查手册汇集了 SQA National 4/5 体育课程所需的关键公式、原理和生物力学定理。从计算训练心率到理解运动场上的牛顿定律，每一个概念都配有清晰的英文和中文对照解释。在学习影响因素、进行数据分析以及制定实践计划时，你都可以利用这本手册来加深理解。
1. Maximum Heart Rate (MHR) | 最大心率 (MHR)
Maximum Heart Rate is the highest number of beats per minute your heart can achieve during maximal exercise. The most common estimation used in school PE is the age-predicted formula. Knowing your MHR helps set safe training zones.
最大心率是指心脏在最大强度运动中每分钟能够达到的最高搏动次数。学校体育中最常用的估算方法是根据年龄推算的公式。了解自己的最大心率有助于设定安全的训练区间。
A simple and widely used equation is:
一个简单而广泛使用的公式是：
MHR = 220 - age
For a 15-year-old performer: MHR = 220 - 15 = 205 beats per minute (bpm).
以一名15岁的运动者为例：最大心率 = 220 - 15 = 205 次/分钟 (bpm)。
2. Heart Rate Reserve and Karvonen Formula | 心率储备与卡沃宁公式
The Karvonen method uses resting heart rate (RHR) to calculate a more personalised training intensity. Heart Rate Reserve (HRR) is the difference between MHR and RHR. This method helps athletes train at the precise intensity needed for aerobic or anaerobic development.
卡沃宁方法利用安静心率 (RHR) 来计算更个性化的训练强度。心率储备 (HRR) 是最大心率与安静心率之间的差值。这种方法能帮助运动员在恰好所需的有氧或无氧发展强度下进行训练。
Heart Rate Reserve (HRR) = MHR - RHR
Target Heart Rate = (HRR × intensity%) + RHR
Example: A 15-year-old with MHR of 205 bpm and RHR of 65 bpm wants to train at 70% intensity. HRR = 205 - 65 = 140 bpm. Target = (140 × 0.70) + 65 = 163 bpm.
例子：一名15岁运动员，最大心率为205 bpm，安静心率为65 bpm，希望在70%的强度下训练。HRR = 205 - 65 = 140 bpm。目标心率 = (140 × 0.70) + 65 = 163 bpm。
3. Aerobic Capacity (VO₂ max) | 有氧能力 (VO₂ max)
VO₂ max is the maximum volume of oxygen the body can use in one minute per kilogram of body weight. It is a key measure of cardiorespiratory endurance. While direct measurement requires laboratory equipment, some field tests like the Cooper 12-minute run provide estimated values.
VO₂ max 是身体每公斤体重每分钟能够使用的最大氧气量，它是衡量心肺耐力的关键指标。虽然直接测量需要实验室设备，但库珀12分钟跑等场地测试可以提供估算值。
A common estimation equation from the Cooper test is:
库珀测试常用的估算公式为：
VO₂ max = (distance covered in metres - 504.9) ÷ 44.73
student runs 2200 metres in 12 minutes: VO₂ max ≈ (2200 - 504.9) ÷ 44.73 ≈ 37.9 ml/kg/min.
例如，一名学生在12分钟内跑完2200米：VO₂ max ≈ (2200 - 504.9) ÷ 44.73 ≈ 37.9 毫升/公斤/分钟。
4. Newton's Laws of Motion in Sport | 运动中的牛顿运动定律
Newton's three laws form the foundation of biomechanics in PE. Understanding them helps explain how performers start, stop, change direction and apply force.
牛顿三大定律构成了体育生物力学的基础。理解这些定律有助于解释运动者如何启动、停止、改变方向以及施加力量。
First Law (Inertia): A body remains at rest or in uniform motion unless acted upon by an external force. A football stays still until kicked.
第一定律（惯性）： 一切物体总保持匀速直线运动状态或静止状态，直到有外力迫使它改变。足球在被踢之前保持静止。
Second Law (Acceleration): onal to the net force and inversely proportional to its mass. This is expressed as F = ma.
第二定律（加速度）： 物体加速度的大小与受到的合外力成正比，与物体的质量成反比。公式为 F = ma。
Third Law (Reaction): For every action, there is an equal and opposite reaction. When a swimmer pushes water backward, the water pushes the swimmer forward.
第三定律（作用力与反作用力）： 两个物体之间的作用力和反作用力总是大小相等，方向相反。游泳者向后推水时，水给游泳者一个向前的推力。
5. Force Calculation | 力计算 (F = ma)
Force can be calculated when mass and acceleration are known. In sporting contexts, this principle shows how increasing acceleration or the mass being moved affects the force needed.
当质量和加速度已知时，可以计算力的大小。在运动情境中，这一原理显示了增加加速度或移动质量如何影响所需力量。
Force = mass × acceleration
Units: Newtons (N). Mass is measured in kilograms (kg) and acceleration in metres per second squared (m/s²). For instance, a 0.5 kg basketball shot with acceleration of 12 m/s² experiences a force of 6 N.
单位：牛顿 (N)。质量以千克 (kg) 为单位，加速度以米每二次方秒 (m/s²) 为单位。例如，一个0.5 kg的篮球以12 m/s² 的加速度被投出时，受到的力为6 N。
6. Moment of Force and Levers | 力矩与杠杆
A moment is the turning effect of a force around a pivot. In the body, bones act as levers, joints are pivots, and muscles provide the effort to overcome a load.
力矩是力绕支点产生的转动效应。在人体中，骨充当杠杆，关节为支点，肌肉提供动力来克服阻力。
Moment (Nm) = Force (N) × distance from pivot (m)
The three classes of levers (first, second and third) depend on the relative positions of pivot, effort and load. Most movements in the body are third-class levers, such as a bicep curl, where the effort lies between pivot (elbow) and load (hand).
三类杠杆（第一类、第二类和第三类）取决于支点、动力点和阻力点的相对位置。人体大多数动作属于第三类杠杆，例如二头肌弯举，动力点（肌肉附着点）位于支点（肘关节）和阻力点（手）之间。
7. Centre of Gravity and Stability | 重心与稳定性
The centre of gravity (CoG) is the point where all of an object’s weight appears to act. In humans, it is typically located around the hips and changes with posture and movement.
重心 (CoG) 是物体所有重量看似集中的那一点。对于人体，重心通常位于髋部附近，并随着姿势和运动而变化。
Stability is increased when the centre of gravity is low, the base of support is wide, and the line of gravity falls centrally within the base. A defensive stance in basketball therefore keeps the body more stable.
当重心较低、支撑面较宽且重力线落在支撑面中心时，稳定性增强。因此篮球防守中的低姿态站姿会使身体更加稳定。
The relationship can be summarised: Stability ∝ Base of Support × 1/height of CoG.
这一关系可概括为：稳定性 ∝ 支撑面宽度 × 1/重心高度。
8. Kinematics Equations for Movement Analysis | 运动学方程用于动作分析
Kinematics describes motion without considering its causes. Useful quantities include speed, velocity, acceleration and displacement. These equations can be applied to start times, sprint phases or projectile motion in games like shot put.
运动学描述运动本身，而不考虑其成因。常用的量包括速率、速度、加速度和位移。这些公式可以应用于起跑时间、冲刺阶段或推铅球等项目的抛体运动分析。
g v = final velocity, u = initial velocity, a = acceleration, s = displacement, t = time):
关键公式（设 v 为末速度，u 为初速度，a 为加速度，s 为位移，t 为时间）：
v = u + at
s = ut + ½at²
v² = u² + 2as
from rest (u = 0) with acceleration of 3 m/s² for 2 seconds will reach v = 3 × 2 = 6 m/s.
例如，短跑运动员从静止开始（u = 0），以3 m/s² 的加速度跑2秒，末速度将达到 v = 3 × 2 = 6 m/s。
9. Momentum and Impulse | 动量与冲量
Momentum is the product of mass and velocity and describes the quantity of motion a body possesses. Impulse relates the force applied over time to a change in momentum. These concepts are vital in tackling and striking sports.
动量是质量与速度的乘积，描述了物体所具有的运动量。冲量则反映了力在一段时间内的作用与动量变化的关系。这些概念在橄榄球擒抱和击球类运动中至关重要。
Momentum p = mass × velocity
Impulse = Force × time = change in momentum (Δp)
Increasing the time over which a force is applied, such as following through when kicking a football, increases impulse and therefore momentum change, leading to greater final velocity of the ball.
增加力作用的时长，例如踢足球时跟随球的动作，会增大冲量，从而引起更大的动量变化，使球的末速度更快。
10. Energy Expenditure and Calorie Calculation | 能量消耗与卡路里计算
ication of energy cost, where 1 MET = resting metabolic rate (approximately 3.5 ml O₂/kg/min).
在体育中，了解能量消耗有助于评估不同活动的运动强度。任务的代谢当量 (MET) 能反映能量消耗的大小，1 MET 等于安静代谢率（约3.5毫升氧气/公斤/分钟）。
A rough estimation for calories burned per minute is:
每分钟所消耗卡路里的粗略估算公式为：
Calories per minute = MET × body mass (kg) × 0.0175
60 kg student running for 1 minute would burn approximately 10 × 60 × 0.0175 = 10.5 kcal.
例如，以10公里/小时跑步的MET值约为10。一名60千克的学生跑1分钟，大约消耗 10 × 60 × 0.0175 = 10.5 千卡路里。
11. Body Mass Index (BMI) | 身体质量指数 (BMI)
BMI provides a simple way to assess whether a person's weight is appropriate for their height. While not a direct measure of body composition, it is used in PE settings to discuss health and performance indicators.
体重指数提供了一种评估体重是否适合身高的简单方法。尽管并非直接测量身体成分的指标，但在体育课堂中经常用来讨论健康与表现的相关因素。
BMI = weight (kg) ÷ height² (m²)
, BMI = 68 ÷ (1.75 × 1.75) = 22.2 kg/m², which falls within the healthy weight range (18.5 – 24.9).
对于一名身高1.75米、体重68公斤的学生，BMI = 68 ÷ (1.75 × 1.75) = 22.2 千克/平方米，属于健康体重范围（18.5 – 24.9）。
12. Training Principles – FITT and Overload | 训练原则 – FITT 与超负荷
The FITT principle guides the design of effective training programmes. Frequency, Intensity, Time and Type must be manipulated to ensure progressive overload, which is essential for continued fitness improvements without causing injury.
FITT 原则指导有效训练计划的设计。必须合理调控频率、强度、时间和类型，以确保渐进超负荷，这对于在不引发损伤的前提下持续提升体能至关重要。
While not a numerical formula, it can be applied with thresholds: to improve aerobic fitness, train at least 3 times per week (Frequency) at 60–80% of MHR (Intensity), for 20–30 minutes (Time), using continuous or interval methods (Type).
虽然这并不是一条数学公式，但它可以通过阈值来应用：要提高有氧能力，每周至少训练3次（频率），强度为最大心率的60–80%（强度），每次20–30分钟（时间），采用持续训练或间歇训练法（类型）。
The overload principle states that stress must gradually increase. If a performer can comfortably run 3 km, increasing to 3.5 km or running the same distance in a shorter time applies overload. The rate of progression is often guided by the 10% rule — do not increase training load by more than 10% per week.
超负荷原则要求负荷必须逐步增加。如果运动者能轻松跑完3公里，那么将距离增加到3.5公里，或者用更短的时间跑完相同距离，就是施加了超负荷。训练负荷的进阶速率通常遵循10%法则——每周训练负荷的增加不超过10%。
Published by TutorHao | Physical Education Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图