Year 11 CCEA Science: Quick Reference Formulas & Theorems | Year 11 CCEA 科学公式定理速查手册

📚 Year 11 CCEA Science: Quick Reference Formulas & Theorems | Year 11 CCEA 科学公式定理速查手册

This handbook brings together the essential formulas, equations and theorems required for Year 11 CCEA GCSE Science. Covering biology, chemistry and physics, the content is organised for rapid revision and consistent recall. Every key relationship is presented in both English and Chinese to support dual-language learners.

本手册汇集了 Year 11 CCEA GCSE 科学所需的核心公式、方程和定理。内容涵盖生物、化学和物理，按专题编排，方便快速复习和记忆。每个关键关系均以中英双语呈现，支持双语言学习。

1. Biology Key Equations and Concepts | 生物学关键公式与概念

Biology at this level requires understanding how to calculate magnifications and how to represent the processes of photosynthesis and respiration with word and symbol equations.

本阶段的生物学习要求掌握如何计算放大倍率，以及如何用文字和符号方程式表示光合作用与呼吸作用。

• Magnification = image size ÷ actual size — 放大倍率 = 图像尺寸 ÷ 实际尺寸 (单位一致)
• Photosynthesis word equation: carbon dioxide + water → glucose + oxygen — 光合作用文字方程式：二氧化碳 + 水 → 葡萄糖 + 氧气
• Symbol equation: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ — 化学方程式：6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
• Aerobic respiration word equation: glucose + oxygen → carbon dioxide + water (+ energy) — 有氧呼吸文字方程式：葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）
• Symbol equation: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O — 化学方程式：C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O

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2. Relative Mass and the Mole | 相对质量与摩尔

The mole concept connects the microscopic world of atoms to measurable laboratory quantities. Relative atomic mass and relative formula mass are foundations of quantitative chemistry.

摩尔概念将微观的原子世界与可测量的实验室量联系起来。相对原子质量和相对式量是定量化学的基础。

• Relative atomic mass, A_r — average mass of an atom compared to 1/12 of carbon-12 — 相对原子质量 A_r — 一个原子的平均质量与碳-12 的 1/12 相比较
• Relative formula mass, M_r — sum of A_r of all atoms in the formula — 相对式量 M_r — 化学式中所有原子的 A_r 之和
• Number of moles: n = m / M_r (mass m in grams) — 摩尔数：n = m / M_r（质量 m 以克为单位）
• Mass: m = n × M_r — 质量：m = n × M_r
• Number of particles = n × 6.02 × 10²³ — 粒子数 = n × 6.02 × 10²³

n = m ÷ M_r

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3. Concentration and Titration | 浓度与滴定

Solution concentration links the amount of solute to the volume of solvent. Titration calculations use the mole ratio from a balanced equation to find unknown concentrations.

溶液的浓度将溶质的量与溶剂的体积联系起来。滴定计算利用平衡方程式中的摩尔比来求得未知浓度。

• Concentration (mol/dm³): c = n / V — 浓度（mol/dm³）：c = n / V
• Mass concentration (g/dm³): c = mass / volume — 质量浓度（g/dm³）：c = 质量 / 体积
• Converting cm³ to dm³: divide by 1000 — cm³ 转换为 dm³：除以 1000
• Titration: m_av_a / m_bv_b = n_a / n_b — 滴定计算：(酸的摩尔数 × 体积) 与碱的比例由化学计量决定

c = n / V

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4. Percentage Yield and Atom Economy | 产率与原子经济性

These measures help chemists judge the efficiency and sustainability of a reaction. They are required to evaluate industrial processes in CCEA specifications.

这些指标帮助化学家判断反应的效率和可持续性。CCEA 考纲要求用它们评估工业过程。

• Percentage yield = (actual yield / theoretical yield) × 100% — 产率 =（实际产量 / 理论产量）× 100%
• Atom economy = (M_r of desired product / sum of M_r of all products) × 100% — 原子经济性 =（目标产物 M_r / 所有产物 M_r 总和）× 100%
• A higher atom economy reduces waste and improves sustainability — 原子经济性越高，废物越少，可持续性越好。

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5. Rate of Reaction | 反应速率

The rate of a chemical reaction measures how quickly reactants are used up or products are formed. It can be followed by mass loss, gas volume or colour change.

化学反应速率衡量反应物消耗或产物生成的快慢。可以通过质量损失、气体体积或颜色变化来跟踪。

• Mean rate = quantity of reactant used or product formed / time — 平均速率 = 反应物消耗量或产物生成量 / 时间
• For gas produced: rate = volume of gas / time (cm³/s) — 对气体生成：速率 = 气体体积 / 时间
• For mass loss: rate = mass lost / time (g/s) — 对质量损失：速率 = 损失质量 / 时间
• Factors: temperature, concentration, surface area, catalyst — 影响因素：温度、浓度、表面积、催化剂

rate = Δ quantity / Δ t

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6. Motion and Kinematics | 运动学

These equations describe uniform acceleration in a straight line. They are central to the CCEA physics unit on motion.

这些方程描述匀加速直线运动，是 CCEA 物理运动学单元的核心。

• Speed: v = s / t (distance ÷ time) — 速率：v = s / t
• Acceleration: a = (v − u) / t — 加速度：a = (v − u) / t
• SUVAT equation 1: v = u + at — 方程 1：v = u + at
• SUVAT equation 2: s = ut + ½at² — 方程 2：s = ut + ½at²
• SUVAT equation 3: v² = u² + 2as — 方程 3：v² = u² + 2as
• v = final velocity, u = initial velocity, a = acceleration, t = time, s = displacement — 符号：v 末速度，u 初速度，a 加速度，t 时间，s 位移。

v² = u² + 2as

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7. Forces and Newton's Laws | 力与牛顿定律

Newton' nship between forces and motion. The second law provides the foundational equation F = ma.

牛顿三定律解释了力与运动的关系，第二定律给出了基础方程 F = ma。

• Newton I: An object remains at rest or in uniform motion unless acted upon by a resultant force — 牛顿第一定律：物体保持静止或匀速运动，除非有合力作用。
• Newton II: Resultant force = mass × acceleration — 牛顿第二定律：合力 = 质量 × 加速度
• Newton III: For every action there is an equal and opposite reaction — 牛顿第三定律：作用力与反作用力大小相等、方向相反。
• Weight: W = mg (g = 9.8 N/kg on Earth, often taken as 10 N/kg) — 重力：W = mg
• Resultant force: F_net = ma — 合力：F_net = ma

F = ma

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8. Energy, Work and Power | 能量、功与功率

Energy can be stored, transferred and conserved. These formulas link mechanical work, kinetic energy, gravitational potential energy and power.

能量可以被储存、传递和守恒。这些公式将机械功、动能、重力势能和功率联系起来。

• Work done: W = F × d (force × distance moved in direction of force) — 功：W = F × d
• Kinetic energy: E_k = ½mv² — 动能：E_k = ½mv²
• Gravitational potential energy: E_p = mgh — 重力势能：E_p = mgh
• Power: P = W / t or P = ΔE / t — 功率：P = 功 / 时间 或 P = 能量转移 / 时间
• Efficiency = (useful energy output / total energy input) × 100% — 效率 =（有用能量输出 / 总能量输入）× 100%
• Principle of conservation of energy: energy cannot be created or destroyed, only transferred — 能量守恒定律：能量不能凭空产生或消失，只能转化或转移。

E_k = ½mv²

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9. Electricity | 电学

Charge, current, voltage, resistance and power are linked through a small set of equations. They apply to both series and parallel circuits.

电荷、电流、电压、电阻和功率通过一小套方程相互关联，适用于串联和并联电路。

• Charge: Q = I t (coulombs, amperes, seconds) — 电荷量：Q = I t
• Ohm's law: V = I R — 欧姆定律：V = I R
• Power: P = I V — 电功率：P = I V
• Power from current and resistance: P = I² R — 另一种功率公式：P = I² R
• Energy transferred: E = P t = I V t — 电能：E = P t = I V t
• In series circuits: current constant, voltage splits; in parallel: voltage constant, current splits — 串联电路中电流相同，电压分配；并联电路中电压相同，电流分配。

P = I V

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10. Waves | 波

The wave equation links speed, frequency and wavelength. It is used for both electromagnetic waves and mechanical waves such as sound and water waves.

波动方程将波速、频率和波长联系起来，适用于电磁波和声波等机械波。

• Wave speed: v = f λ — 波速：v = f λ
• Frequency and period: f = 1 / T — 频率与周期：f = 1 / T
• v = speed (m/s), f = frequency (Hz), λ = wavelength (m) — v 波速，f 频率，λ 波长。
• All electromagnetic waves travel at 3.0 × 10⁸ m/s in a vacuum — 所有电磁波在真空中速度为 3.0 × 10⁸ m/s。

v = f λ

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11. Atomic and Nuclear Physics | 原子与核物理

Nuclear decay equations show how alpha and beta particles are emitted. Half-life describes the time for half of a radioactive sample to decay.

核衰变方程展示 α 和 β 粒子的发射。半衰期描述放射性样品衰变一半所需的时间。

• Alpha decay: mass number decreases by 4, atomic number decreases by 2 — α 衰变：质量数减 4，原子序数减 2
• Example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He — 例子：²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
• Beta decay: mass number unchanged, atomic number increases by 1 — β 衰变：质量数不变，原子序数加 1
• Example: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e — 例子：¹⁴₆C → ¹⁴₇N + ⁰₋₁e
• Half-life: the time taken for the radioactivity or number of nuclei to halve — 半衰期：放射性强度或原子核数减半所需的时间
• After n half-lives, fraction remaining = (½)ⁿ — 经过 n 个半衰期后：剩余比例 = (½)ⁿ

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12. Key Principles and Additional Useful Equations | 核心原理与补充实用公式

Several conservation laws and additional relationships underpin all of the sciences. Density, pressure and the kinetic particle model appear across the syllabus.

若干守恒定律和补充关系式是全部科学的基础。密度、压强和粒子运动模型在考纲中反复出现。

• Conservation of mass: total mass of reactants = total mass of products — 质量守恒：反应物总质量 = 生成物总质量
• Conservation of energy: total energy is constant in a closed system — 能量守恒：封闭系统中总能量保持不变
• Conservation of charge: total electric charge is the same before and after any process — 电荷守恒：任何过程前后总电荷量不变
• Density: ρ = m / V (kg/m³ or g/cm³) — 密度：ρ = m / V
• Pressure: p = F / A (Pa, N/m²) — 压强：p = F / A
• Kinetic particle theory: gas pressure arises from particles colliding with container walls; temperature increases the average kinetic energy — 粒子运动论：气体压强

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