📚 Year 11 WJEC PE: Quick Reference Formula & Principle Handbook | Year 11 WJEC 体育：公式定理速查手册
This quick reference handbook brings together every formula, equation and scientific principle you need for the WJEC GCSE Physical Education examination. Keep it close for last-minute revision, classroom activities and homework support. Each entry is paired with clear explanations in both English and Chinese to help you memorise and apply the concepts with confidence.
本速查手册汇集了 WJEC GCSE 体育考试所需的所有公式、方程与科学原理。适合考前冲刺、课堂练习与家庭作业参考。每个条目均配有清晰的中英文双语解释，帮助你牢固记忆并自信运用。
1. Maximum Heart Rate and Training Zones | 最大心率与训练区间
Maximum heart rate (MHR) is estimated using the simple formula: MHR = 220 − age. This value forms the baseline for setting exercise intensity.
最大心率（MHR）可通过公式估算：最大心率 = 220 − 年龄。该数值是设定运动强度的基础。
Training zones are expressed as percentages of MHR and target different physiological adaptations:
训练区间以最大心率的百分比表示，分别针对不同的生理适应：
- Aerobic zone (60–80% MHR): develops cardiovascular endurance, uses fat as fuel. Ideal for steady-state running, cycling and swimming.
- Anaerobic zone (80–90% MHR): improves speed and power, accumulates lactic acid.
Used in interval training and short bursts. - Red line zone (90–100% MHR): maximal effort, only sustainable for very short periods. Used sparingly by elite performers.
- 有氧区间（最大心率的60–80%）：发展心血管耐力，以脂肪为燃料，适合匀速跑步、骑行和游泳。
- 无氧区间（最大心率的80–90%）：提高速度与爆发力，产生乳酸，用于间歇训练和短时冲刺。
- 红线区间（最大心率的90–100%）：极限强度，仅能维持极短时间，高水平运动员偶有使用。
2. Karvonen Formula (Heart Rate Reserve) | 卡沃宁公式（心率储备）
The Karvonen formula calculates a target heart rate based on your resting heart rate (RHR) and heart rate reserve (HRR).
卡沃宁公式依据安静心率（RHR）与心率储备（HRR）来计算目标心率。
First, find the heart rate reserve: HRR = MHR − RHR.
Then determine the target heart rate: Target HR = RHR + (HRR × desired % intensity).
首先计算心率储备：心率储备 = 最大心率 − 安静心率。
然后计算目标心率：目标心率 = 安静心率 + (心率储备 × 期望强度百分比)。
For example, a 16-year-old with RHR 60 bpm training at 70% intensity: MHR = 204, HRR = 144, target HR = 60 + (144 × 0.70) = 160.8 bpm.
例如，一名16岁学生安静心率60次/分，以70%强度训练：MHR = 204，HRR = 144，目标心率 = 60 + (144 × 0.70) = 160.8 次/分。
3. Cardiac Output (Q) | 心输出量
Cardiac output is the volume of blood pumped by the heart each minute. It is the product of stroke volume (SV) and heart rate (HR).
心输出量是心脏每分钟泵出的血量，等于每搏输出量（SV）与心率（HR）的乘积。
Q = SV × HR
- Q = cardiac output (L/min)
- SV = stroke volume (mL/beat, often converted to litres)
- HR = heart rate (beats per minute, bpm)
- Q = 心输出量（升/分钟）
- SV = 每搏输出量（毫升/次，常换算为升）
- HR = 心率（次/分钟）
During exercise, both SV and HR increase, raising Q to deliver more oxygen to working muscles. Elite endurance athletes can achieve a Q of over 30 L/min.
运动时，SV与HR同时上升，使心输出量增加，为工作肌群输送更多氧气。优秀耐力运动员的心输出量可超过30升/分钟。
4. Body Mass Index (BMI) | 身体质量指数
BMI is a screening tool used to classify weight status. It relates body mass to height.
BMI 是一种体重分级筛查工具，将体重与身高相关联。
BMI = weight (kg) ÷ height² (m)
Standard classification (adults):
| BMI (kg/m²) | Category |
|---|---|
| <18.5 | Underweight |
| 18.5–24.9 | Normal weight |
| 25–29.9 | Overweight |
| ≥30 | Obese |
中文分类：
| BMI（千克/米²） | 类别 |
|---|---|
| <18.5 | 偏瘦 |
| 18.5–24.9 | 正常体重 |
| 25–29.9 | 超重 |
| ≥30 | 肥胖 |
BMI has limitations: it does not distinguish between muscle and fat mass, so a very muscular athlete may be classified as overweight.
BMI有局限性：无法区分肌肉与脂肪，因此肌肉发达的运动员可能被归入超重类别。
5. Speed, Distance, Time and Acceleration | 速度、距离、时间与加速度
Average speed is the distance travelled per unit of time. It can be rearranged to find distance or time.
平均速度是单位时间内通过的距离。该公式可变形求距离或时间。
v = d / t
- v = speed (m/s)
- d = distance (m)
- t = time (s)
- v = 速度（米/秒）
- d = 距离（米）
- t = 时间（秒）
Acceleration measures how quickly velocity changes. It is positive when speeding up and negative (deceleration) when slowing down.
加速度衡量速度变化的快慢。加速时为正，减速时为负（负加速度）。
a = Δv / t = (v − u) / t
- a = acceleration (m/s²)
- Δv = change in velocity (m/s)
- u = initial velocity (m/s)
- v = final velocity (m/s)
- t = time (s)
- a = 加速度（米/秒²）
- Δv = 速度变化量（米/秒）
- u = 初速度（米/秒）
- v = 末速度（米/秒）
- t = 时间（秒）
celerating from 0 to 12 m/s in 2.5 s has an acceleration of a = (12 − 0) / 2.5 = 4.8 m/s².
百米跑中，一名运动员2.5秒内从0加速到12米/秒，其加速度为 a = (12 − 0) / 2.5 = 4.8 米/秒²。
6. Newton's Second Law: Force, Mass and Acceleration | 牛顿第二定律：力、质量与加速度
An object's acceleration depends on the net force acting on it and its mass. This is expressed by the equation:
物体的加速度取决于作用在其上的净力与自身质量，等式表达为：
F = m × a
- F = force (N)
- m = mass (kg)
- a = acceleration (m/s²)
- F = 力（牛顿）
- m = 质量（千克）
- a = 加速度（米/秒²）
Weight is a specific force caused by gravity: Weight (W) = m × g, where g = 9.8 m/s² (10 N/kg is often used for GCSE calculations).
重力是由引力产生的特定力：体重（W）= 质量 × 重力加速度（g），g 通常取9.8米/秒²（GCSE计算中常用10牛/千克）。
A rugby player of mass 90 kg accelerating at 2 m/s² requires a force of 180 N. The larger the force applied, the greater the acceleration if mass remains constant.
一名90千克的橄榄球运动员以2米/秒²加速需要180牛的力。质量不变时，施加的力越大，加速度越大。
7. Work and Power | 功与功率
Work done occurs when a force moves an object over a distance. Work is measured in joules (J).
功是力使物体沿力的方向移动一段距离时所做的功，单位为焦耳（J）。
W = F × d
- W = work done (J)
- F = force (N)
- d = distance moved in the direction of the force (m)
- W = 功（焦耳）
- F = 力（牛顿）
- d = 沿力方向移动的距离（米）
Power is the rate at which work is done, measured in watts (W).
功率是做功的快慢，单位为瓦特（W）。
P = W / t
- P = power (W)
- W = work done (J)
- t = time (s)
- P = 功率（瓦）
- W = 功（焦耳）
- t = 时间（秒）
Since W = F × d, power can also be written as: P = (F × d) / t. When movement is at constant velocity, power = force × velocity.
由于 W = F × d，功率也可写作：P = (F × d) / t。当匀速运动时，功率 = 力 × 速度。
8. Moment of Force and Lever Balance | 力矩与杠杆平衡
A moment is the turning effect of a force about a pivot. The perpendicular distance from the pivot to the line of action of the force is the moment arm.
力矩是力绕支点的转动效应。从支点到力作用线的垂直距离称为力臂。
M = F × d
- M = moment (Nm)
- F = force (N)
- d = perpendicular distance from pivot to line of action of force (m)
- M = 力矩（牛·米）
- F = 力（牛顿）
- d = 支点到力作用线的垂直距离（米）
For a lever to be in rotational equilibrium, the sum of clockwise moments must equal the sum of anticlockwise moments.
杠杆处于转动平衡时，顺时针力矩之和等于逆时针力矩之和。
Sum of clockwise moments = Sum of anticlockwise moments
Applying this principle in sport: during a bicep curl, the effort (bicep) must produce a moment large enough to overcome the resistance (weight in hand).
该原理在运动中应用：肱二头肌弯举时，动力（肱二头肌）必须产生足够力矩来克服阻力（手中重量）。
9. Lever Systems and Mechanical Advantage | 杠杆系统与机械效益
A lever consists of a rigid bar, a pivot (fulcrum), an effort force and a resistance load. The arrangement determines the lever class.
杠杆由刚性杆、支点（枢纽）、动力和阻力组成。三者的排列决定杠杆类别。
- First-class lever: fulcrum between effort and resistance (e.g., neck joint, see-saw).
- Second-class lever: resistance between fulcrum and effort (e.g., standing on tiptoes, wheelbarrow).
- Third-class lever: effort between fulcrum and resistance (e.g., bicep curl). Most body levers are third-class.
- 一级杠杆：支点在动力与阻力之间（如颈部关节、跷跷板）。
- 二级杠杆：阻力在支点与动力之间（如踮脚站立、手推车）。
- 三级杠杆：动力在支点与阻力之间（如肱二头肌弯举）。人体多数杠杆为三级杠杆。
Mechanical advantage (MA) compares the effort arm (distance from effort to fulcrum) with the resistance arm (distance from resistance to fulcrum).
机械效益（MA）表示动力臂（动力到支点的距离）与阻力臂（阻力到支点的距离）的比值。
MA = Effort arm / Resistance arm
- MA > 1: requires less effort to move a larger resistance (second-class lever).
- MA < 1: effort travels a shorter distance but resistance moves faster and over a larger range (third-class lever).
- MA > 1：省力，用较小力移动较大阻力（二级杠杆）。
- MA < 1：动力移动距离短，阻力端移动速度快、范围大（三级杠杆）。
10. Newton's Three Laws of Motion | 牛顿运动三定律
First Law (Inertia): An object remains at rest or in uniform motion in a straight line unless acted upon by an external resultant force.
第一定律（惯性定律）：一切物体在没有受到外力作用时，总保持静止状态或匀速直线运动状态。
In sport: a football will stay at rest until kicked; a moving ice hockey puck continues sliding until friction or a stick alters its motion.
运动实例：足球静止直到被踢；冰球滑动直到摩擦或球杆改变其运动。
Second Law (Acceleration): nal to the resultant force acting on it and inversely proportional to its mass. F = m × a.
第二定律（加速度定律）：物体加速度的大小与所受合外力成正比，与物体质量成反比，F = m × a。 Published by TutorHao | Year 11 体育 Revision Series | aleveler.com
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