📚 Year 10 CCEA Science: Formula & Theorems Quick Reference | Year 10 CCEA 科学：公式定理速查手册
Welcome to your one‑stop revision guide for all the essential formulas, laws and theorems covered in Year 10 CCEA Science. This handbook is designed to help you quickly find, understand and apply the key mathematical relationships that underpin physics, chemistry and biology at this level. Keep it handy when tackling past papers, homework or last‑minute revision.
欢迎来到 Year 10 CCEA 科学必背公式、定律和定理的一站式复习指南。这本手册旨在帮助你快速查找、理解和应用构成物理、化学和生物学核心的关键数学关系。在做历年真题、完成作业或考前突击时随时翻阅，事半功倍。
1. Motion & Forces | 运动与力
distance / time. It tells you how fast something is moving without considering direction.
速度是物体通过一段距离的快慢程度。平均速度公式为 速度 = 距离 / 时间。这个公式告诉你物体运动有多快，但不考虑方向。
Velocity differs from speed because it is a vector – ty: a = (v - u) / t, where v is final velocity, u is initial velocity and t is time taken.
速度与速率不同，速度是矢量，包含方向。加速度是速度的变化率：a = (v - u) / t，其中 v 是末速度，u 是初速度，t 是所用时间。
ass (kg) multiplied by acceleration (m/s²). This relationship helps you calculate how much force is needed to change an object’s motion.
牛顿第二定律通常写作 F = m × a。力（单位牛顿）等于质量（千克）乘以加速度（米/秒²）。这个关系可让你计算改变物体运动需要多大的力。
For weight, use W = m × g, where g is gravitational field strength (on Earth ~10 N/kg). Remember that mass is constant, but weight changes with gravity.
计算重力时，使用 W = m × g，其中 g 是引力场强度（在地球上约为 10 N/kg）。请记住，质量是恒定的，而重量随重力变化。
| Quantity 量 | Equation 方程 | Units 单位 |
|---|---|---|
| Speed 速度 | v = d / t | m/s |
| Acceleration 加速度 | a = (v - u) / t | m/s² |
| Force 力 | F = m × a | N (kg·m/s²) |
| Weight 重力 | W = m × g | N |
2. Energy & Work | 能量与做功
joules (J), force in newtons (N) and distance in metres (m). Work done equals the energy transformed.
做功是力使物体移动时转移的能量。公式为 W = F × d，其中功的单位是焦耳 (J)，力的单位是牛顿 (N)，距离的单位是米 (m)。所做的功等于转化的能量。
al energy gained by raising an object is GPE = m × g × h, where h is the change in height.
运动物体的动能由 KE = ½ × m × v² 给出。物体升高所获得的重力势能为 GPE = m × g × h，其中 h 是高度变化。
al to one joule per second. Efficiency = (useful output energy / total input energy) × 100%.
功率是能量转移的速率：P = E / t 或 P = W / t。功率的单位是瓦特（W），等于每秒一焦耳。效率 =（有用的输出能量 / 总输入能量）× 100%。
| Energy 能量 | Equation 方程 |
|---|---|
| Kinetic 动能 | KE = ½ m v² |
| Gravitational potential 重力势能 | GPE = m g h |
| Work done 做功 | W = F d |
| Power 功率 | P = E / t |
| Efficiency 效率 | η = (Eout / Ein) × 100% |
3. Waves & Light | 波与光
ed (v) is in metres per second, frequency (f) in hertz (Hz) and wavelength (λ) in metres. This applies to both sound and electromagnetic waves.
波动方程将波速、频率和波长联系在一起：v = f × λ。速度 (v) 的单位是米每秒，频率 (f) 的单位是赫兹 (Hz)，波长 (λ) 的单位是米。这适用于声波和电磁波。
For reflection, the law of reflection states that the angle of incidence equals the angle of reflection, measured from the normal line. For refraction, Snell’s law is introduced conceptually, but at this stage you use ray diagrams to show bending towards or away from the normal.
对于反射，反射定律指出入射角等于反射角，均从法线量起。对于折射，斯涅尔定律在概念上有所引入，但现阶段你只用光线图来表示向法线或远离法线的弯曲。
of frequency: T = 1 / f. This helps you calculate how long one complete wave cycle takes.
波的周期 T 是频率的倒数：T = 1 / f。这有助于计算完成一个完整波周期所需的时间。
4. Electricity Basics | 电学基础
ns constant: V = I × R. Voltage (V) in volts, current (I) in amperes, resistance (R) in ohms (Ω).
欧姆定律指出，在温度不变的条件下，通过导体的电流与导体两端的电压成正比：V = I × R。电压 (V) 的单位是伏特，电流 (I) 的单位是安培，电阻 (R) 的单位是欧姆 (Ω)。
or P = I² × R. The energy transferred in a circuit is given by E = P × t or E = V × I × t.
电功率可用 P = V × I 或 P = I² × R 来计算。电路中转移的能量由 E = P × t 或 E = V × I × t 给出。
For components in series, total resistance Rtotal t is the same everywhere. For parallel circuits, the reciprocal of total resistance is 1/Rtotal /R₁ + 1/R₂, and the sum of branch currents equals the total current entering the junction.
对于串联元件，总电阻 Rtotal = R₁ + R₂ + ...，各处电流相等。对于并联电路，总电阻的倒数为 1/Rtotal = 1/R₁ + 1/R₂，各支路电流之和等于进入交汇点的总电流。
5. Atomic Structure & Radioactivity | 原子结构与放射性
An atom contains protons, neutrons and electrons. The atomic number (Z) equals the number of protons, which defines the element. The mass number (A) is the total of protons plus neutrons. In standard notation: ²³₁₁Na, meaning sodium has 11 protons and 12 neutrons.
原子包含质子、中子和电子。原子序数 (Z) 等于质子数，定义了元素种类。质量数 (A) 是质子数与中子数之和。在标准表示法中，²³₁₁Na 表示钠有 11 个质子和 12 个中子。
During alpha decay, the nucleus loses 2 protons and 2 neutrons, so the mass number decreases by 4 and the atomic number decreases by 2. Beta decay involves a neutron turning into a proton and emitting an electron; mass number stays the same, atomic number increases by 1.
在 α 衰变中，原子核失去 2 个质子和 2 个中子，因此质量数减少 4，原子序数减少 2。β 衰变则是一个中子转变为质子并发射一个电子；质量数保持不变，原子序数增加 1。
The half‑life of a radioactive isotope is the time taken for half the undecayed nuclei to decay. You can calculate the fraction remaining after n half‑lives as (1/2)ⁿ.
放射性同位素的半衰期是未衰变原子核衰变掉一半所需的时间。经过 n 个半衰期后剩余的比例可用 (1/2)ⁿ 来计算。
6. Chemical Reactions & Equations | 化学反应与方程式
s of reactants and products. The total mass of reactants equals the total mass of products – this is the Law of Conservation of Mass. For example: 2H₂ + O₂ → 2H₂O.
配平的化学方程式表示反应物与生成物的相对数量关系。反应物的总质量等于生成物的总质量 – 这就是质量守恒定律。例如：2H₂ + O₂ → 2H₂O。
In exothermic reactions, energy is released to the surroundings (ΔH negative). In endothermic reactions, energy is absorbed from the surroundings (ΔH positive). Bond breaking requires energy, bond making releases energy.
在放热反应中，能量向周围释放（ΔH 为负）。在吸热反应中，能量从周围吸收（ΔH 为正）。断裂化学键需要能量，形成化学键释放能量。
The rate of reaction can be followed by measuring the change in mass, volume of gas produced, or colour change over time. Factors affecting rate include temperature, concentration, surface area and catalysts.
反应速率可通过测量质量变化、产生气体的体积或颜色随时间的变化来跟踪。影响反应速率的因素包括温度、浓度、表面积和催化剂。
7. The Mole & Stoichiometry | 摩尔与化学计量
ole is the unit for amount of substance. One mole contains 6.02 × 10²³ particles (Avogadro' mass (g) / molar mass (g/mol). Molar mass is the relative formula mass expressed in grams.
摩尔是物质数量的单位。一摩尔包含 6.02 × 10²³ 个粒子（阿伏伽德罗常数）。摩尔数 n = 质量 (g) / 摩尔质量 (g/mol)。摩尔质量是用克表示的相对分子质量。
To calculate percentage yield: % cal yield) × 100. Atom economy = (mass of desired product / total mass of reactants) × 100%. These indicators are important in green chemistry.
计算产率：% 产率 =（实际产量 / 理论产量）× 100。原子经济性 =（所需产物的质量 / 反应物总质量）× 100%。这些指标在绿色化学中很重要。
es × 24. This allows you to convert between volume and moles in reactions involving gases.
在室温和常压 (RTP) 下，一摩尔气体占据 24 dm³。气体体积 V (dm³) = 摩尔数 × 24。这使你能够在对涉及气体的反应中在体积和摩尔数之间进行转换。
8. Acids, Bases & Salts | 酸、碱与盐
ation is the reaction between an acid and a base to form a salt and water: H⁺ + OH⁻ → H₂O.
酸在水中产生 H⁺ 离子，碱产生 OH⁻ 离子。pH 标度衡量酸性：pH 值越低，H⁺ 浓度越高。中和反应是酸与碱反应生成盐和水：H⁺ + OH⁻ → H₂O。
d = moles of base at the equivalence point. This links the mole concept to practical work.
酸的浓度可使用稀释公式 C₁V₁ = C₂V₂ 计算，或使用滴定数据：在等价点，酸的摩尔数等于碱的摩尔数。这将摩尔概念与实验操作联系起来。
carbonate → salt + water + carbon dioxide. Knowing these patterns helps predict products.
酸的常见反应：酸 + 金属 → 盐 + 氢气；酸 + 碳酸盐 → 盐 + 水 + 二氧化碳。掌握这些规律有助于预测产物。
9. Cell Biology & Transport | 细胞生物学与运输
ze / Actual size. This is essential when using microscopes. Remember to convert all units to the same scale (usually µm or mm).
放大倍数使用以下公式计算：放大倍数 = 图像大小 / 实际大小。使用显微镜时这条公式至关重要。记得将所有单位换算为相同的尺度（通常为 µm 或 mm）。
Diffusion is the net movement of particles from a region of high concentration to low concentration, down a concentration gradient. Osmosis is the diffusion of water across a partially permeable membrane from a dilute to a more concentrated solution.
扩散是粒子从高浓度区域到低浓度区域的净移动，沿浓度梯度进行。渗透是水通过半透膜从较稀溶液向较浓溶液的扩散。
Active transport requires energy (ATP) to move substances against their concentration gradient. In plants, root hair cells use active transport to absorb mineral ions from soil.
主动运输需要能量 (ATP) 使物质逆浓度梯度移动。在植物中，根毛细胞利用主动运输从土壤中吸收矿质离子。
10. Photosynthesis & Respiration | 光合作用与呼吸作用
is: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂. Light energy is converted into chemical energy in glucose.
光合作用的文字方程式：二氧化碳 + 水 → 葡萄糖 + 氧气，在光和叶绿素存在的条件下。配平的化学方程式为：6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂。光能在葡萄糖中转化为化学能。
O₆ + 6O₂ → 6CO₂ + 6H₂O. Anaerobic respiration in animals produces lactic acid; in yeast, it produces ethanol and carbon dioxide.
有氧呼吸利用氧气从葡萄糖中释放能量：葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）。化学简式为 C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O。动物体内的无氧呼吸产生乳酸；在酵母中，则产生乙醇和二氧化碳。
The inverse square law is sometimes investigated in the context of light intensity and photosynthesis rate: Light intensity ∝ 1/d². Doubling the distance from a light source reduces intensity to a quarter.
在研究光强与光合作用速率时有时会涉及平方反比定律：光强度 ∝ 1/d²。与光源的距离加倍，光强降至四分之一。
11. Ecology & Energy Transfer | 生态学与能量传递
Efficiency = (energy in biomass at one level / energy in biomass at the level below) × 100%. Typically only about 10% of energy is passed on.
营养级之间能量传递的效率可用以下公式计算：效率 =（一个营养级的生物质所含能量 / 上一营养级的生物质所含能量）× 100%。通常只有大约 10% 的能量被传递到下一级。
Pyramids of biomass show the total dry mass of organisms at each trophic level, while pyramids of energy show the energy content. The shape is nearly always a pyramid because energy is lost at each transfer.
生物质金字塔显示每个营养级生物的总干质量，而能量金字塔显示所含能量。其形状几乎总是呈金字塔形，因为每次能量传递都会有损耗。
d use the formula: estimated population = (number in first capture × number in second capture) / number marked in second capture for capture‑recapture.
样方和样线等采样技术有助于估算种群数量。你可以为收集到的数据计算平均数、众数和中位数，并使用标记重捕法公式：估算种群数量 =（第一次捕获数 × 第二次捕获数）/ 第二次捕获中标记个体数。
12. Key Equations Summary Table | 关键方程汇总表
The following table brings together the most important mathematical relationships from across the Year 10 CCEA Science syllabus. Use it as a rapid checklist before exams.
下表汇集了 Year 10 CCEA 科学课程大纲中最重要的数学关系。可作为考前快速核对清单使用。
| Topic 专题 | Equation 方程 |
|---|---|
| Speed | v = d / t |
| Acceleration | a = (v - u) / t |
| Force | F = m a |
| Weight | W = m g |
| Work done | W = F d |
| Kinetic energy | KE = ½ m v² |
| GPE | GPE = m g h |
| Efficiency | η = (Eout / Ein) × 100% |
| Wave speed | v = f λ |
| Ohm’s law | V = I R |
| Power (electricity) | P = V I |
| Energy transferred | E = V I t |
| Moles | n = mass / Mᵣ |
| Gas volume (RTP) | V = n × 24 dm³ |
| Concentration (dilution) | C₁V₁ = C₂V₂ |
| Magnification | M = image size / actual size |
| Photosynthesis | 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ |
| Respiration (aerobic) | C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O |
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