📚 Year 11 Eduqas Science: Formula and Theorem Quick Reference Handbook | Year 11 Eduqas 科学：公式定理速查手册
This quick reference handbook gathers the essential formulas, equations and key theorems you need for Year 11 Eduqas Science. Whether you are revising for your GCSE Physics, Chemistry or Biology papers, having these relationships at your fingertips will help you tackle calculations, explain phenomena and check units with confidence. Use it alongside your class notes and past papers for the most effective revision.
这本速查手册汇集了 Year 11 Eduqas 科学课程所必需的核心公式、方程与关键定理。无论你正在为 GCSE 物理、化学还是生物考试复习，掌握这些关系式都能帮助你从容应对计算题、解释现象并自信地核对单位。请结合课堂笔记和历年真题使用，以获得最佳复习效果。
1. Speed, Distance and Time | 速度、距离与时间
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v = d / t
Average speed (v) equals distance travelled (d) divided by time taken (t). Speed is a scalar quantity measured in metres per second (m/s).
平均速率（v）等于经过的距离（d）除以所用时间（t）。速率是标量，单位为米每秒（m/s）。
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s = v × t
Distance (s) is the product of average speed and time. Always check that the units are consistent: if speed is in m/s, time must be in seconds.
距离（s）等于平均速率与时间的乘积。务必保持单位一致：若速率单位为 m/s，时间单位须为秒。
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average speed = total distance / total time
For journeys with several stages, use total distance and total time to find the overall average speed. (Equation given on the Eduqas equation sheet in this form.)
对于包含多个阶段的行程，使用总距离和总时间求平均速率。（Eduqas 公式表以此形式给出该公式。）
2. Acceleration and SUVAT Equations | 加速度与运动学方程
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a = (v - u) / t
ate of change of velocity. v = final velocity, u = initial velocity, t = time. Unit: m/s².
加速度（a）是速度的变化率。v = 末速度，u = 初速度，t = 时间。单位：m/s²。
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v = u + a t
This SUVAT equation links final velocity, initial velocity, acceleration and time. (Equation is provided on the equation sheet.)
该运动学方程联系了末速度、初速度、加速度和时间。（公式表提供此方程。）
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s = u t + ½ a t²
Displacement (s) can be found when acceleration is constant. The ½ a t² term accounts for speeding up or slowing down.
当加速度恒定时，可用此式求位移（s）。½ a t² 项用于体现加速或减速的过程。
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v² = u² + 2 a s
Useful when time is not given. All four SUVAT equations are listed on the Eduqas formula sheet for GCSE Physics.
当未给出时间时，该方程非常实用。所有四个运动学方程均列于 Eduqas GCSE 物理的公式表中。
3. Newton's Laws and Forces | 牛顿定律与力
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F = m a
Newton' = mass × acceleration. Force is measured in newtons (N), mass in kg, acceleration in m/s².
牛顿第二定律：合力 = 质量 × 加速度。力的单位是牛顿（N），质量单位为 kg，加速度单位为 m/s²。
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W = m g
l field strength (g). On Earth g ≈ 9.8 N/kg, but Eduqas often uses 10 N/kg for simplicity.
重量（W）= 质量 × 重力场强度（g）。地球表面 g ≈ 9.8 N/kg，但 Eduqas 考试通常为简化取 10 N/kg。
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Newton's Third Law: When two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction.
牛顿第三定律：当两个物体发生相互作用时，它们彼此施加的力大小相等、方向相反。
4. Momentum | 动量
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p = m v
is a vector quantity with unit kg m/s. In a closed system, total momentum before a collision equals total momentum after.
动量 = 质量 × 速度。动量是矢量，单位为 kg m/s。在封闭系统中，碰撞前的总动量等于碰撞后的总动量。
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F = Δp / t
Resultant force equals rate of change of momentum. This is a more general form of Newton's Second Law.
合力等于动量的变化率。这是牛顿第二定律更普遍的表达形式。
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The conservation of momentum principle is crucial for solving problems involving collisions and explosions. Remember to assign positive and negative directions.
动量守恒原理是解决碰撞和爆炸问题的关键。记得规定正方向和负方向。
5. Work, Energy and Power | 功、能与功率
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W = F d
ce moved in the direction of the force. Unit: joule (J). (Provided on the equation sheet.)
做功（W）= 力 × 沿力方向移动的距离。单位：焦耳（J）。（公式表提供。）
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Eₖ = ½ m v²
tic energy = ½ × mass × (speed)². Both mass and speed affect kinetic energy significantly.
动能 = ½ × 质量 ×（速率）²。质量与速率都会显著影响动能的大小。
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ΔEₚ = m g Δh
ential energy = mass × g × change in height. (Given on the Eduqas Physics equation sheet.)
重力势能的变化 = 质量 × g × 高度变化。（Eduqas 物理公式表提供。）
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P = W / t or P = E / t
Power is the rate of energy transfer or work done. Unit: watt (W). 1 W = 1 J/s.
功率是能量转移或做功的速率。单位：瓦特（W）。1 W = 1 J/s。
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Efficiency = (useful output / total input) × 100%
Efficiency can be expressed as a percentage or a decimal. No real system is 100% efficient due to energy dissipation.
效率可用百分数或小数表示。由于能量耗散，任何真实系统的效率都不会达到 100%。
6. Electrical Quantities: Charge, Current, Voltage, Resistance | 电学量：电荷、电流、电压、电阻
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Q = I t
t × time. Charge is measured in coulombs (C), current in amperes (A), time in seconds (s).
电荷（Q）= 电流 × 时间。电荷单位为库仑（C），电流单位为安培（A），时间单位为秒（s）。
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V = I R
Ohm' Law: potential difference (V) = current × resistance. Resistance is measured in ohms (Ω).
欧姆定律：电势差（V）= 电流 × 电阻。电阻的单位为欧姆（Ω）。
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R = V / I
Resistance can be calculated from voltage and current. For ohmic conductors, the ratio V/I is constant at constant temperature.
电阻可通过电压与电流计算得出。对于欧姆导体，在温度恒定时 V/I 的比值保持不变。
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For series circuits: total resistance Rₜ = R₁ + R₂ + … for Eduqas, but you must know that adding resistors in parallel reduces total resistance.
串联电路：总电阻 Rₜ = R₁ + R₂ + …，各处电流相等。并联电路：并联支路越多，总电阻反而越小；Eduqas 不要求倒数公式，但须知道并联电阻会使总电阻减小。
7. Electrical Power and Energy | 电功率与电能
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P = I V
Electrical power = current × potential difference. (Equation sheet provides this formula.)
电功率 = 电流 × 电势差。（公式表提供此公式。）
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P = I² R
for components where V = I R holds. Useful for calculating heat dissipated in a resistor.
对于满足 V = I R 的元件，功率也可用此式表达。常用于计算电阻器上的散热。
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E = P t
e. Energy can be expressed in joules (J) or kilowatt-hours (kWh) for domestic electricity.
电能转移量 = 功率 × 时间。能量单位可用焦耳（J），家庭用电中也常用千瓦时（kWh）。
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E = Q V
Energy transferred = charge × potential difference. This links the charge–current equation with energy.
能量转移 = 电荷 × 电势差。该式将电荷–电流关系与能量联系起来。
8. Wave Properties | 波的性质
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v = f λ
velength. Frequency (f) is in hertz (Hz), wavelength (λ) in metres (m), wave speed in m/s.
波速 = 频率 × 波长。频率（f）单位为赫兹（Hz），波长（λ）单位为米（m），波速单位为 m/s。
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T = 1 / f
Period (T) is the time for one complete wave cycle. It is the reciprocal of frequency.
周期（T）是完成一次完整波动所需的时间，与频率互为倒数。
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s: oscillations are parallel to energy transfer (e.g. sound, ultrasound). Both obey v = f λ.
横波：振动方向与能量传递方向垂直（如光、电磁波、水波）。纵波：振动方向与能量传递方向平行（如声波、超声波）。两者均遵循 v = f λ。
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Reflection, refraction, diffraction and the electromagnetic spectrum are key qualitative topics; the wave equation is the main quantitative tool.
反射、折射、衍射和电磁波谱是重要的定性话题；波速方程则是主要的定量工具。
9. Radioactive Decay | 放射性衰变
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Half-life concept: time taken for the count rate (or number of nuclei) to halve.
Eduqas does not provide a half-life equation on the formula sheet; you use the graph or data to read half-life directly. You may need to calculate the fraction remaining after n half-lives as (½)ⁿ.
Eduqas 不提供半衰期公式；须通过图表或数据直接读取半衰期。你可能需要计算经过 n 个半衰期后剩余的比例：(½)ⁿ。
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Radioactive decay is random and cannot be sped up by external conditions. Safety precautions include distance, shielding and limiting exposure time.
放射性衰变是随机的，不受外界条件影响。安全防护措施包括保持距离、使用屏蔽和限制暴露时间。
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Background radiation comes from natural sources (radon, cosmic rays) and artificial sources (medical, nuclear). Count rate is measured in counts per second.
背景辐射来自天然来源（氡气、宇宙射线）和人工来源（医疗、核能）。计数率以每秒计数为单位。
10. The Mole and Molar Mass | 摩尔与摩尔质量
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n = m / M
ar mass (g/mol). Molar mass is the relative formula mass (Mᵣ) expressed in grams per mole.
物质的量（摩尔数 n）= 质量（g）÷ 摩尔质量（g/mol）。摩尔质量即相对化学式量（Mᵣ）以 g/mol 为单位的数值。
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not required to reproduce this number, but you should know it underpins the mole concept.
1 摩尔任何物质均含有阿伏伽德罗常数的粒子数（6.02 × 10²³）。无需背下该数值，但应理解它是摩尔概念的基础。
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Number of moles = volume of gas (dm³) / 24 (at room temperature and pressure, r.t.p.)
At r.t.p., one mole of any gas occupies 24 dm³. This allows conversion between gas volume and amount of substance.
在常温常压下，1 摩尔任何气体的体积为 24 dm³。该关系可实现气体体积与物质的量之间的换算。
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Always check units: mass in grams, volumes in dm³, concentration in mol/dm³. Solid masses may also be given in kilograms – convert to grams first.
务必留意单位：质量用克（g），体积用 dm³，浓度用 mol/dm³。若固体质量以千克给出，需先转换为克。
11. Concentration and Titration | 浓度与滴定
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c = n / V
c) = number of moles ÷ volume of solution in dm³. Units: mol/dm³ (often written mol dm⁻³).
浓度（c）= 物质的量 ÷ 溶液的体积（dm³）。单位：mol/dm³（常写作 mol dm⁻³）。
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for 1:1 ratios). For other ratios, use the balanced equation to scale the moles correctly.
在滴定中，对于 1∶1 的反应：cₐcᵢd × Vₐcᵢd = cₐₗₖₐₗᵢₙₑ × Vₐₗₖₐₗᵢₙₑ。若化学计量数不同，需根据配平后的方程式对物质的量进行相应的倍数换算。
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moles = c × V (in dm³)
Rearrange the concentration equation to find the number of moles used in a reaction. If volume is given in cm³, divide by 1000 to convert to dm³.
重新整理浓度公式即可求出反应所用物质的量。若体积以 cm³ 给出，需除以 1000 换算为 dm³。
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lso be expressed in g/dm³. The link: concentration (g/dm³) = concentration (mol/dm³) × Mᵣ.
浓度还可用 g/dm³ 表示。换算关系：浓度（g/dm³） = 浓度（mol/dm³）× Mᵣ。
12. Biological Calculations: Magnification and Biomass | 生物计算：放大率与生物量
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Magnification = image size / real size
Magnification is a ratio; it has no units. Both image size and real size must be in the same unit (typically mm or µm).
放大率是一个比值，无单位。图像尺寸与实际尺寸须使用同一单位（通常用 mm 或 µm）。
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Real size = image size / magnification. Remember to convert units where 1 mm = 1000 µm. Always show your working.
实际尺寸 = 图像尺寸 ÷ 放大率。注意单位换算：1 mm = 1000 µm。务必展示计算过程。
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= (biomass transferred to next trophic level / biomass available at previous level) × 100%
Only about 10% of biomass is typically transferred between trophic levels because of respiration, uneaten parts and excretion. This limits the length of food chains.
通常只有约 10% 的生物量能传递至下一营养级，因为呼吸作用、未被取食的部分以及排泄都会造成能量损耗。这限制了食物链的长度。
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Percentage change = (final value – initial value) / initial value × 100%. This appears in many biology practical questions, including osmosis and enzyme activity.
变化率 =（最终值 – 初始值）÷ 初始值 × 100%。该计算广泛出现在渗透作用、酶活性等生物实验题中。
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