📚 A-Level Eduqas Physical Education: Quick-Reference Formula & Theorem Handbook | A-Level Eduqas 体育：公式定理速查手册
This handbook brings together the essential equations, laws, and quick calculations you need for the Eduqas A-Level Physical Education specification. From biomechanics to exercise physiology, every formula is presented in a clear, exam-ready format with paired explanations to support both your revision and bilingual understanding.
本手册汇集了Eduqas A-Level 体育课程所需的核心公式、定律与速算方法。从生物力学到运动生理学，每条公式都以清晰、适合考试的形式呈现，并配有中英双语解释，帮助你在复习中融会贯通。
1. Maximum Heart Rate and Target Heart Rate Zones | 最大心率与目标心率区间
The simplest estimation of maximum heart rate (HRmax) is 220 minus age. This value is used to set training zones, most commonly the aerobic training zone between 60% and 80% of HRmax. For a more accurate prediction, the formula 207 – (0.7 × age) is sometimes used.
最大心率 (HRmax) 最简单的估算方法是 220 减去年龄。此数值用于设定训练区间，最常用的是有氧训练区间的 60% 至 80% HRmax。更精确的预测有时使用 207 – (0.7 × 年龄)。
HRmax = 220 – age
Target HR = HRmax × Intensity (e.g. 0.6–0.8)
For a 17-year-old athlete, HRmax ≈ 203 bpm; the aerobic training zone would be 122–162 bpm. This heart-rate-based prescription underpins much of the conditioning work in the specification.
对于 17 岁的运动员，HRmax ≈ 203 次/分；有氧训练区间为 122–162 次/分。这种基于心率的训练处方是本课程许多体能工作的基础。
2. Body Mass Index (BMI) | 身体质量指数 (BMI)
Body Mass Index provides a crude measure of body composition by relating mass to the square of height. The standard formula is weight in kilograms divided by the square of height in metres. Although it does not distinguish between lean mass and fat mass, it remains a useful epidemiological tool.
身体质量指数通过体重与身高平方的关系提供粗略的身体成分测量。标准公式为体重（公斤）除以身高（米）的平方。虽然它无法区分瘦体重与脂肪量，但仍是一个有用的流行病学工具。
BMI = mass (kg) / (height (m))²
A BMI of 18.5–24.9 kg/m² is generally considered healthy. For athletes with high muscle mass, BMI may misclassify them as overweight, so waist-to-hip ratio or skinfold measurements are often used alongside it.
BMI 在 18.5–24.9 kg/m² 之间通常被视为健康。对于肌肉量高的运动员，BMI 可能将其误判为超重，因此常配合腰臀比或皮褶厚度测量使用。
3. Respiratory Quotient (RQ) | 呼吸商 (RQ)
The respiratory quotient is the ratio of carbon dioxide produced to oxygen consumed during metabolism. It indicates which fuel is being predominantly used. A value of 1.0 suggests carbohydrate oxidation, while 0.7 indicates fat oxidation.
呼吸商是指代谢过程中产生的二氧化碳与消耗的氧气之比，用于判断主要供能物质。数值为 1.0 表明碳水化合物氧化，0.7 则表明脂肪氧化。
RQ = VCO₂ produced / VO₂ consumed
During high-intensity exercise, RQ rises toward 1.0 as carbohydrate becomes the dominant fuel. At rest and during low-intensity steady-state exercise, RQ approaches 0.7. This concept is linked to indirect calorimetry and energy expenditure calculations.
在高强度运动中，碳水化合物成为主导燃料，RQ 上升至接近 1.0。在休息和低强度稳态运动时，RQ 接近 0.7。此概念与间接热量测定法和能量消耗计算紧密相关。
4. Newton’s Laws of Motion | 牛顿运动定律
Newton’s three laws underpin all linear motion analysis in sport. The First Law (Inertia) states that a body remains at rest or in uniform motion unless acted upon by an external force. The Second Law quantifies acceleration: F = m × a. The Third Law describes action–reaction pairs.
牛顿三大定律是体育中所有线性运动分析的基础。第一定律（惯性）指出物体保持静止或匀速直线运动，直到外力作用。第二定律定量描述加速度：F = m × a。第三定律说明作用力与反作用力成对出现。
F = m a
When a sprinter pushes back against the blocks, the blocks exert an equal and opposite force forward (Third Law). The resulting forward acceleration is determined by the net force divided by the athlete’s mass (Second Law).
短跑运动员向后蹬起跑器时，起跑器施加相等且反向的前推力（第三定律）。由此产生的前向加速度由净力除以运动员质量决定（第二定律）。
5. Speed, Acceleration, and Momentum | 速度、加速度与动量
Speed, velocity, and acceleration are fundamental descriptors of motion. Momentum, the product of mass and velocity, is a conserved quantity in closed systems and is central to collision and impulse analysis in sport.
速率、速度和加速度是运动的基本描述量。动量是质量与速度的乘积，在封闭系统中守恒，是体育中碰撞和冲量分析的核心。
v = Δs / Δt
a = Δv / Δt
p = m v
In a rugby tackle, the total momentum before impact equals the total momentum after impact (conservation of momentum). The change in momentum over time equals the impulse (F × t), explaining why following through increases force application.
在橄榄球擒抱中，撞击前的总动量等于撞击后的总动量（动量守恒）。动量随时间的变化等于冲量 (F × t)，这解释了为什么随挥动作能增加力量施加。
6. Work, Energy, and Power | 功、能量与功率
Mechanical work is done when a force moves a body through a displacement. Kinetic energy relates to motion, while gravitational potential energy relates to position. Power is the rate of doing work, a critical performance indicator.
机械功是力使物体沿位移方向移动时所做的功。动能与运动有关，而重力势能与位置有关。功率是做功的速率，是关键的竞技表现指标。
W = F d cosθ
KE = ½ m v²
GPE = m g h
P = W / t = F v
A weightlifter raising 100 kg by 2.0 m against gravity does work of about 1960 J. If the lift took 1.5 s, the average power output would be approximately 1307 W. This power calculation helps compare explosive strength across athletes.
举重运动员将 100 公斤杠铃举起 2.0 米，克服重力做功约 1960 J。若该次试举耗时 1.5 秒，平均功率输出约为 1307 W。这一功率计算有助于比较运动员的爆发力。
7. Levers and Moments | 杠杆原理与力矩
The moment of a force is its turning effect, calculated as force × perpendicular distance from the fulcrum. In the body, bones act as levers, joints as fulcrums, and muscles provide the effort. Understanding lever classes helps analyse mechanical advantage.
力矩是力的转动效应，计算为力 × 到支点的垂直距离。在人体中，骨骼充当杠杆，关节为支点，肌肉提供动力。理解杠杆类别有助于分析机械效益。
Moment = F × d (perpendicular distance)
A third-class lever, such as the elbow joint during a biceps curl, has the effort between the fulcrum and the resistance. This arrangement favours range and speed of movement over force. For equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments.
第三类杠杆，如肱二头肌弯举中的肘关节，动力在支点和阻力之间。这种排列有利于动作幅度和速度，而非力量。若要平衡，顺时针力矩之和等于逆时针力矩之和。
8. Angular Kinematics | 角运动学
Rotational motion is described by angular displacement, angular velocity, and angular acceleration. These quantities are the angular analogues of linear kinematics and are essential for analysing spinning, throwing, and rotational skills.
转动运动由角位移、角速度和角加速度描述。这些量是线性运动学的角量对应物，对于分析旋转、投掷和转体技能至关重要。
ω = Δθ / Δt
α = Δω / Δt
v = r ω (tangential velocity)
A discus thrower increases angular velocity by extending the rotating radius during the wind-up, then transferring that rotational speed to the implement. Conservation of angular momentum (H = I × ω) explains why a spinning skater speeds up when pulling the arms in.
铁饼运动员通过在预摆阶段增大旋转半径来提高角速度，然后将该转动速度传递到器械上。角动量守恒 (H = I × ω) 解释了为什么旋转中的滑冰运动员收臂会加速旋转。
9. Energy Expenditure and METs | 能量消耗与代谢当量
Energy expenditure is often estimated using the Metabolic Equivalent of Task (MET), where 1 MET is approximately 3.5 mL O₂/kg/min at rest. The formula combines MET value, body mass, and time to estimate kilocalories burned.
能量消耗通常使用代谢当量 (MET) 估算，1 MET 约为静息时 3.5 mL O₂/kg/min。该公式结合 MET 值、体重和时间来估算消耗的千卡数。
1 MET = 3.5 mL O₂ · kg⁻¹ · min⁻¹
kcal ≈ MET × mass (kg) × time (h)
Jogging at 7 METs for 30 minutes by a 70 kg person expends roughly 7 × 70 × 0.5 ≈ 245 kcal. This formula appears in exercise prescription and nutritional planning questions.
一个 70 公斤的人以 7 METs 慢跑 30 分钟，能量消耗约为 7 × 70 × 0.5 ≈ 245 千卡。该公式出现在运动处方和营养计划试题中。
10. One-Repetition Maximum (1RM) and Training Loads | 一次重复最大值与训练负荷
1RM is the maximum load that can be lifted for one complete repetition of an exercise. Submaximal testing uses repetitions-to-fatigue equations to estimate 1RM safely. Common formulas include the Brzycki and Epley equations.
一次重复最大值 (1RM) 是指某个练习中能够完成一次完整重复的最大负荷。次最大强度测试使用疲劳前重复次数方程来安全估算 1RM。常用的有 Brzycki 和 Epley 方程。
Estimated 1RM = weight lifted / (1.0278 – 0.0278 × reps) (Brzycki)
If an athlete can lift 80 kg for 5 repetitions, estimated 1RM ≈ 80 / (1.0278 – 0.0278 × 5) ≈ 90 kg. Training zones are then prescribed as percentages of 1RM: e.g. strength at 80–95%, hypertrophy at 65–80%.
若运动员能用 80 公斤完成 5 次重复，估算 1RM ≈ 80 / (1.0278 – 0.0278 × 5) ≈ 90 公斤。然后训练区间按 1RM 百分比设定：如力量训练为 80–95%，肌肥大训练为 65–80%。
11. Cardiac Output, Stroke Volume, and the Fick Equation | 心输出量、每搏输出量与菲克方程
Cardiac output (Q) is the volume of blood pumped by the heart per minute. It is the product of heart rate (HR) and stroke volume (SV). The Fick principle relates oxygen consumption to cardiac output and arteriovenous oxygen difference.
心输出量 (Q) 是心脏每分钟泵出的血液量，等于心率 (HR) 与每搏输出量 (SV) 的乘积。菲克原理将耗氧量与心输出量和动静脉氧差关联起来。
Q = HR × SV
VO₂ = Q × (a-vO₂ diff)
During maximal exercise, an elite athlete might achieve a cardiac output of 25–35 L/min, supported by a high stroke volume (e.g. 150 mL) and heart rate (e.g. 200 bpm). The increase in a-vO₂ diff reflects greater oxygen extraction by active muscles.
在最大运动中，精英运动员的心输出量可达 25–35 L/min，这得益于较高的每搏输出量（如 150 mL）和心率（如 200 次/分）。动静脉氧差的增加反映了活动肌肉对氧的摄取增强。
12. Coefficient of Restitution and Elasticity | 恢复系数与弹性
The coefficient of restitution (e) measures the elasticity of a collision between two objects. It is the ratio of relative velocity after impact to relative velocity before impact, and it governs the behaviour of balls, rackets, and surfaces.
恢复系数 (e) 衡量两个物体碰撞的弹性，是撞击后相对速度与撞击前相对速度的比值，支配着球、球拍和场地表面的行为。
e = (v₂’ – v₁’) / (v₁ – v₂)
A perfectly elastic collision has e = 1 (e.g. idealised tennis ball on a rigid racket), while a perfectly inelastic collision has e = 0. Most sporting impacts have e between 0.5 and 0.9, affecting speed off the bat or club.
完全弹性碰撞 e = 1（如理想化的网球与刚性球拍），完全非弹性碰撞 e = 0。大多数运动撞击的 e 在 0.5 到 0.9 之间，影响球拍或球杆击球后的速度。
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