📚 Year 10 Eduqas PE: Formula & Theorem Quick-Reference Handbook | GCSE体育公式定理速查手册
This quick-reference handbook brings together the essential formulas, equations, and theoretical laws required for the Eduqas GCSE Physical Education specification. Whether you are calculating training zones, analysing movement, or understanding psychological theories, these pages provide a clear checklist to support your revision.
本速查手册汇集了Eduqas GCSE体育教学大纲要求的基本公式、方程式和理论定律。无论您是在计算训练区间、分析运动，还是理解心理学理论，这些内容都能为您的复习提供清晰的清单。
1. Heart Rate & Cardiac Formulas | 心率与心输出量公式
Maximum Heart Rate (MHR) = 220 – age
最大心率 (MHR) = 220 – 年龄
Heart Rate Reserve (HRR) = MHR – Resting Heart Rate (RHR). This represents the range available for exercise intensity.
心率储备 (HRR) = 最大心率 – 安静心率 (RHR)。它代表了可用于运动强度调节的范围。
Karvonen Formula: Target Heart Rate = RHR + (Intensity × HRR)
卡沃南公式：靶心率 = 安静心率 + (强度 × 心率储备)
troke Volume (SV) × Heart Rate (HR). Stroke volume is the amount of blood pumped per beat.
心输出量 (Q) = 每搏输出量 (SV) × 心率 (HR)。每搏输出量是心脏每跳动一次泵出的血液量。
2. Body Mass Index (BMI) | 身体质量指数
BMI = weight (kg) / height² (m²)
BMI = 体重 (kg) / 身高² (m²)
It classifies individuals as underweight, healthy weight, overweight or obese. Caution: BMI does not distinguish between muscle and fat mass.
它用于划分体重过轻、正常、超重或肥胖。注意：BMI无法区分肌肉与脂肪质量。
3. Energy Expenditure Using METs | 使用代谢当量计算能量消耗
Energy (kcal) = MET value × body mass (kg) × duration (hours)
能量 (kcal) = MET值 × 体重 (kg) × 时间 (hours)
1 MET represents resting metabolic rate (~1 kcal/kg/h). Physical activities: light < 3 METs, moderate 3–6 METs, vigorous > 6 METs.
1 MET代表静息代谢率（约1 kcal/kg/h）。身体活动等级：轻度 < 3 METs，中等3–6 METs，剧烈 > 6 METs。
4. Speed, Velocity & Acceleration | 速率、速度与加速度
Speed (m/s) = distance (m) / time (s). It is a scalar quantity.
速率 (m/s) = 距离 (m) / 时间 (s)，是一个标量。
Velocity = displacement / time. It is a vector – direction matters.
速度 = 位移 / 时间，是矢量——包含方向。
Acceleration (m/s²) = (final velocity – initial velocity) / time → a = (v – u) / t
加速度 (m/s²) = (末速度 – 初速度) / 时间 → a = (v – u) / t
Negative acceleration indicates deceleration.
负加速度表示减速。
5. 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 an external force.
第一定律（惯性）：一切物体在没有受到外力作用时，总保持静止或匀速直线运动状态。
Second Law (Acceleration): Force (N) = mass (kg) × acceleration (m/s²) → F = m a
第二定律（加速度）：力 (N) = 质量 (kg) × 加速度 (m/s²) → F = m a
Third Law (Action–Reaction): For every action, there is an equal and opposite reaction.
第三定律（作用力与反作用力）：两物体间的作用力和反作用力大小相等、方向相反。
6. Momentum & Impulse | 动量与冲量
Momentum (p) = mass (m) × velocity (v) → p = m v (unit: kg m/s)
动量 (p) = 质量 (m) × 速度 (v) → p = m v（单位：kg m/s）
Impulse = force (F) × time (t) = change in momentum → F t = m v – m u
冲量 = 力 (F) × 时间 (t) = 动量变化量 → F t = m v – m u
Increasing the time of impact reduces the average force – crucial in landing and protective equipment.
延长碰撞时间可减小平均作用力——这在落地技术和防护装备中尤为关键。
7. Work, Power & Energy | 功、功率与能量
Work done (J) = force (N) × distance moved in the direction of force (m) → W = F d
做功 (J) = 力 (N) × 沿力方向移动的距离 (m) → W = F d
Power (W) = work done / time taken → P = W / t. It can also be expressed as P = F × v (force × velocity).
功率 (W) = 做功 / 时间 → P = W / t。也可表示为 P = F × v（力 × 速度）。
Kinetic Energy: KE = ½ m v² | Gravitational Potential Energy: GPE = m g h (g = 9.8 m/s²).
动能：KE = ½ m v² | 重力势能：GPE = m g h（g = 9.8 m/s²）。
8. Levers & Mechanical Advantage | 杠杆与机械优势
Moment (torque) = force × perpendicular distance from fulcrum → M = F × d
力矩 = 力 × 到支点的垂直距离 → M = F × d
, second- and third-class levers. Mechanical Advantage (MA) = effort arm / resistance arm.
人体使用第一、第二和第三类杠杆。机械优势 (MA) = 力臂 / 阻力臂。
MA > 1 amplifies force (e.g. calf raise as a second-class lever); MA < 1 increases speed and range of motion (e.g. biceps curl as a third-class lever).
MA > 1 放大力量（如小腿提踵为第二类杠杆）；MA < 1 增大速度和动作幅度（如肱二头肌弯举为第三类杠杆）。
9. Projectile Motion Principles | 抛体运动原理
The optimal release angle for maximum horizontal range (ignoring air resistance) is 45°.
忽略空气阻力时，达到最大水平距离的最优出手角度为45°。
If release height exceeds landing height (e.g. shot put), the optimal angle is slightly less than 45°.
若出手点高于落点（如铅球），最优角度略小于45°。
Key factors affecting a projectile: release velocity, release angle, release height, and aerodynamic forces (Bernoulli principle, Magnus effect).
影响抛体运动的关键因素：出手速度、出手角度、出手高度和空气动力（伯努利原理、马格努斯效应）。
10. Training Zones & FITT Principles | 训练区间与FITT原则
FITT stands for Frequency, Intensity, Time, Type – the basis of any training programme design.
FITT 分别指频率、强度、时间、类型——这是任何训练计划设计的基础。
Intensity can be set using % of maximal heart rate (%MHR) or %1RM. Typical aerobic zone: 60–80% MHR; anaerobic zone: 80–90% MHR.
强度可用最大心率百分比 (%MHR) 或一次重复最大重量百分比 (%1RM) 设定。典型有氧区间：60–80% MHR；无氧区间：80–90% MHR。
Progressive Overload: to continue adapting, one or more FITT variables must be gradually increased.
渐进超负荷原则：为持续产生适应，必须逐步提高一项或多项FITT变量。
11. Inverted-U Theory & Drive Theory | 倒U理论与驱力理论
The Inverted-U hypothesis (Yerkes–Dodson law) states that performance improves with arousal up to an optimal point; beyond that, performance declines.
倒U假设（耶克斯–多德森定律）指出：随着唤醒水平提高，表现会上升至最佳点；超过最佳点后表现下降。
Optimal arousal depends on skill level, personality and task complexity. Simple, gross skills tolerate higher arousal; fine, complex skills require lower arousal.
最佳唤醒水平取决于技能水平、人格和任务复杂度。简单、粗大技能允许多一些唤醒；精细、复杂技能需要较低的唤醒。
al). This predicts a linear relationship but does not explain choking under high pressure.
驱力理论：表现 = 习惯强度 × 驱力（唤醒）。它预测线性关系，但无法解释高压下的发挥失常。
Published by TutorHao | PE 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