📚 Year 9 CIE Science: Formula & Theorem Quick Reference Handbook | Year 9 CIE 科学：公式定理速查手册
This quick-reference handbook collects the essential formulas, laws, and key facts needed for Year 9 CIE Science. It covers Physics, Chemistry, and Biology in a concise, bilingual format – perfect for revision and exam preparation.
这本速查手册汇集了 Year 9 CIE 科学课程中必备的公式、定律和核心知识点。内容涵盖物理、化学和生物，采用中英对照的简洁形式，非常适合复习和备考使用。
1. Motion and Forces | 运动与力
Speed is the distance travelled per unit time. The formula is: v = d ÷ t, where v = speed, d = distance, and t = time. Units: m/s.
速度是单位时间内通过的距离。公式：v = d ÷ t，其中 v = 速度，d = 距离，t = 时间。单位：米/秒。
Acceleration is the rate of change of velocity: a = (v – u) ÷ t. u = initial velocity, v = final velocity. Unit: m/s².
加速度是速度的变化率：a = (v – u) ÷ t。u = 初速度，v = 末速度。单位：米/秒²。
Newton’s Second Law: Force = mass × acceleration (F = m a). Force is measured in newtons (N), mass in kg, acceleration in m/s².
牛顿第二定律：力 = 质量 × 加速度 (F = m a)。力的单位是牛顿 (N)，质量单位是千克，加速度单位是米/秒²。
Weight is the force due to gravity: W = m g. On Earth, g ≈ 9.8 N/kg (often rounded to 10 N/kg).
重量是由重力产生的力：W = m g。在地球上，g ≈ 9.8 N/kg（通常取整为 10 N/kg）。
Friction always opposes motion. It can be useful (e.g., brakes) or a problem (e.g., energy loss).
摩擦力总是阻碍运动。摩擦既可以有用（如刹车），也可能造成麻烦（如能量损失）。
2. Forces in Equilibrium and Hooke’s Law | 力的平衡与胡克定律
When forces are balanced, an object remains at rest or moves at constant velocity (Newton’s First Law).
当力平衡时，物体保持静止或匀速直线运动（牛顿第一定律）。
Hooke’s Law: The extension of a spring is directly proportional to the force applied, up to the limit of proportionality. F = k x, where k is the spring constant, x is extension.
胡克定律：在弹性限度内，弹簧的伸长量与施加的力成正比。F = k x，其中 k 是弹簧常数，x 是伸长量。
Resultant force: the single force that has the same effect as all the forces acting on an object. Calculated by vector addition.
合力：一个与物体受到的所有力作用效果相同的力。通过向量加法计算。
3. Energy and Work | 能量与功
Kinetic Energy: KE = ½ m v². m = mass (kg), v = speed (m/s), KE in joules (J).
动能：KE = ½ m v²。m = 质量 (kg)，v = 速度 (m/s)，动能单位是焦耳 (J)。
Gravitational Potential Energy: GPE = m g h. h = height (m). This is energy stored due to position.
重力势能：GPE = m g h。h = 高度 (m)。这是由于位置而储存的能量。
Work Done = Force × distance moved in the direction of the force: W = F d. 1 J = 1 N m.
做功 = 力 × 在力的方向上移动的距离：W = F d。1 J = 1 N m。
Power = Work done ÷ time taken: P = W ÷ t, or Energy transferred ÷ time. Unit: watt (W). 1 W = 1 J/s.
功率 = 做功 ÷ 时间：P = W ÷ t，或能量转移 ÷ 时间。单位：瓦特 (W)。1 W = 1 J/s。
Law of Conservation of Energy: Energy cannot be created or destroyed, only transferred or transformed. In any process, total energy remains constant.
能量守恒定律：能量既不会凭空产生，也不会凭空消失，只能转移或转化。在任何过程中，总能量保持不变。
4. Density, Pressure, and Moments | 密度、压强与力矩
Density = mass ÷ volume: ρ = m / V. Units: kg/m³ or g/cm³. 1 g/cm³ = 1000 kg/m³.
密度 = 质量 ÷ 体积：ρ = m / V。单位：千克/米³ 或 克/厘米³。1 g/cm³ = 1000 kg/m³。
Pressure = Force ÷ Area: P = F / A. Unit: pascal (Pa), 1 Pa = 1 N/m². A larger area reduces pressure for the same force.
压强 = 压力 ÷ 面积：P = F / A。单位：帕斯卡 (Pa)，1 Pa = 1 N/m²。在相同的力下，面积越大压强越小。
Liquid pressure increases with depth: P = h ρ g, where h = depth, ρ = liquid density, g = gravitational field strength.
液体压强随深度增加而增大：P = h ρ g，其中 h = 深度，ρ = 液体密度，g = 重力场强。
Moment of a force = Force × perpendicular distance from pivot: M = F d. Unit: N m. Principle of moments: for a balanced object, total clockwise moment = total anticlockwise moment.
力矩 = 力 × 到支点的垂直距离：M = F d。单位：N m。力矩原理：平衡时，顺时针力矩之和 = 逆时针力矩之和。
5. Electricity | 电学
Current (I) is the rate of flow of charge: I = Q ÷ t. Unit: ampere (A), charge Q in coulombs (C), time in seconds.
电流 (I) 是电荷流动的速率：I = Q ÷ t。单位：安培 (A)，电荷 Q 单位库仑 (C)，时间单位秒。
Ohm’s Law: Voltage (potential difference) = Current × Resistance: V = I R. V in volts (V), I in A, R in ohms (Ω).
欧姆定律：电压（电势差）= 电流 × 电阻：V = I R。V 单位伏特 (V)，I 单位安培，R 单位欧姆 (Ω)。
In a series circuit: current is the same everywhere, total resistance Rtotal = R₁ + R₂ + …, and the supply voltage is shared.
串联电路中：电流处处相等，总电阻 R总 = R₁ + R₂ + …，电源电压被分压。
In a parallel circuit: voltage across each branch is the same, total current is the sum of branch currents, and total resistance is reduced (1/Rtotal = 1/R₁ + 1/R₂).
并联电路中：各支路电压相等，总电流等于各支路电流之和，总电阻降低 (1/R总 = 1/R₁ + 1/R₂)。
Electrical Power: P = I V, also P = I² R, P = V² / R. Energy transferred: E = P t (in joules) or E = I V t.
电功率：P = I V，也可写为 P = I² R，P = V² / R。电功（能量转移）：E = P t（焦耳）或 E = I V t。
6. Waves | 波动
Wave speed = Frequency × Wavelength: v = f λ. v in m/s, f in hertz (Hz), λ in metres (m).
波速 = 频率 × 波长：v = f λ。v 单位 m/s，f 单位赫兹 (Hz)，λ 单位米 (m)。
Transverse waves (e.g., light, water waves) have oscillations perpendicular to the direction of energy transfer. Longitudinal waves (e.g., sound) have oscillations parallel to it.
横波（如光、水波）的振动方向与能量传播方向垂直。纵波（如声波）的振动方向与传播方向平行。
Law of reflection: angle of incidence = angle of reflection. These are measured from the normal.
反射定律：入射角等于反射角。角度从法线量起。
Refraction occurs when a wave changes speed as it enters a new medium, causing it to change direction. For light, Snell’s law relates angles: n₁ sin θ₁ = n₂ sin θ₂.
折射是波进入新介质时速度改变而引起的方向变化。对于光，斯涅尔定律：n₁ sin θ₁ = n₂ sin θ₂。
7. Atomic Structure and the Periodic Table | 原子结构与元素周期表
Atoms consist of protons (+1 charge), neutrons (0 charge), and electrons (–1 charge). Protons and neutrons are in the nucleus; electrons orbit in shells.
原子由质子（+1 电荷）、中子（0 电荷）和电子（–1 电荷）组成。质子和中子在原子核内；电子在核外分层排布。
Atomic number (Z) = number of protons. Mass number (A) = number of protons + neutrons.
原子序数 (Z) = 质子数。质量数 (A) = 质子数 + 中子数。
Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. They have the same chemical properties.
同位素是同一种元素中质子数相同、中子数不同的原子。它们的化学性质相同。
Relative atomic mass (Ar) is the average mass of an atom of an element compared to 1/12 of the mass of a carbon‑12 atom.
相对原子质量 (Ar) 是元素一个原子的平均质量与一个碳‑12 原子质量的 1/12 之比。
Electron configuration: first shell holds up to 2 electrons, second and third shells hold up to 8. Group number often relates to outer‑shell electrons.
电子排布：第一层最多 2 个电子，第二、三层各最多 8 个。族数常与最外层电子数相关。
8. Chemical Bonding, Formulas, and Equations | 化学键、化学式与化学方程式
Ionic bonding: transfer of electrons from metal to non‑metal, forming oppositely charged ions held by electrostatic attraction. Example: NaCl.
离子键：金属向非金属转移电子，形成带相反电荷的离子，通过静电引力结合。例如：NaCl。
Covalent bonding: sharing of electron pairs between non‑metal atoms. Example: H₂O, CO₂.
共价键：非金属原子间共用电子对。例如：H₂O, CO₂。
Chemical formulas show the number and type of atoms in a substance. Subscripts indicate the number of atoms, e.g., H₂SO₄.
化学式表示物质中原子的种类和数目。下标数字表示原子个数，例如 H₂SO₄。
Relative formula mass (Mr) = sum of relative atomic masses of all atoms in the formula. Used for ionic and covalent compounds.
相对分子质量 (Mr) = 化学式中所有原子的相对原子质量之和。用于离子和共价化合物。
Percentage by mass of an element = (mass of element in one formula unit / Mr) × 100%.
某元素的质量分数 = (该元素在一个式单元中的质量 / Mr) × 100%。
Law of Conservation of Mass: total mass of reactants = total mass of products. Equations must be balanced: number of each atom is the same on both sides.
质量守恒定律：反应物的总质量 = 生成物的总质量。化学方程式必须配平：两边各原子个数相等。
9. Types of Chemical Reactions | 化学反应类型
Combustion: fuel + oxygen → carbon dioxide + water (+ energy). Example: CH₄ + 2O₂ → CO₂ + 2H₂O.
燃烧：燃料 + 氧气 → 二氧化碳 + 水（+ 能量）。例如：CH₄ + 2O₂ → CO₂ + 2H₂O。
Neutralization: acid + base → salt + water. Example: HCl + NaOH → NaCl + H₂O.
中和反应：酸 + 碱 → 盐 + 水。例如：HCl + NaOH → NaCl + H₂O。
Displacement: a more reactive metal displaces a less reactive metal from its compound. Example: Zn + CuSO₄ → ZnSO₄ + Cu.
置换反应：较活泼金属将较不活泼金属从其化合物中置换出来。例如：Zn + CuSO₄ → ZnSO₄ + Cu。
Decomposition: a compound breaks down into simpler substances, often by heating. Example: CaCO₃ → CaO + CO₂.
分解反应：一种化合物分解成更简单的物质，常在加热下进行。例如：CaCO₃ → CaO + CO₂。
Oxidation: gain of oxygen or loss of electrons. Reduction: loss of oxygen or gain of electrons. (OIL RIG: Oxidation Is Loss, Reduction Is Gain of electrons).
氧化：得氧或失电子。还原：失氧或得电子。(OIL RIG: Oxidation Is Loss, Reduction Is Gain).
10. Cells, Tissues, and Organ Systems | 细胞、组织与器官系统
All living things are made of cells. Differences between plant and animal cells: Plant cells have cell wall, chloroplasts, large vacuole; animal cells do not.
所有生物由细胞构成。动植物细胞的区别：植物细胞有细胞壁、叶绿体、大液泡；动物细胞没有。
Magnification = Image size ÷ Actual size. Always in the same units. Example: a cell image 5 cm long, actual cell 0.05 cm long → magnification = 100×.
放大倍数 = 图像尺寸 ÷ 实际尺寸。单位需一致。例如：细胞图像长5 cm，实际细胞长0.05 cm → 放大倍数 = 100×。
Diffusion: net movement of particles from a region of high concentration to low concentration. No energy required. Osmosis is the diffusion of water through a partially permeable membrane.
扩散：微粒从高浓度区域向低浓度区域的净移动。不需要能量。渗透是水通过半透膜的扩散。
Organ systems: groups of organs working together. Examples: digestive system (mouth → oesophagus → stomach → small intestine → large intestine), circulatory system (heart, blood vessels).
器官系统：多个器官协同工作。例如：消化系统（口腔 → 食道 → 胃 → 小肠 → 大肠），循环系统（心脏、血管）。
11. Photosynthesis and Respiration | 光合作用与呼吸作用
Photosynthesis word equation: Carbon dioxide + Water → Glucose + Oxygen, in the presence of light and chlorophyll.
光合作用文字方程式：二氧化碳 + 水 → 葡萄糖 + 氧气，需要光和叶绿体。
Symbol equation: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂. It is an endothermic reaction, converting light energy to chemical energy.
符号方程式：6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂。它是吸热反应，将光能转化为化学能。
Aerobic respiration: Glucose + Oxygen → Carbon dioxide + Water + Energy (ATP). Symbol: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O (+ energy).
有氧呼吸：葡萄糖 + 氧气 → 二氧化碳 + 水 + 能量 (ATP)。符号：C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O (+ 能量)。
Anaerobic respiration in animals: Glucose → Lactic acid (+ some energy). In yeast: Glucose → Ethanol + Carbon dioxide (+ energy). Fermentation is used in baking and brewing.
动物无氧呼吸：葡萄糖 → 乳酸 (+ 少量能量)。酵母无氧呼吸：葡萄糖 → 乙醇 + 二氧化碳 (+ 能量)。发酵用于烘焙和酿造。
Breathing and gas exchange: Inhalation brings oxygen into lungs; exhalation removes CO₂. Alveoli provide a large surface area for diffusion.
呼吸与气体交换：吸气将氧气带入肺；呼气排出二氧化碳。肺泡提供了巨大的扩散表面积。
12. Genetics and Ecology | 遗传学与生态学
DNA is a double‑helix molecule carrying genetic information. A gene is a section of DNA that codes for a protein. Alleles are different forms of a gene.
DNA 是携带遗传信息的双螺旋分子。基因是编码蛋白质的 DNA 片段。等位基因是基因的不同形式。
Monohybrid cross: Using a Punnett square, predict genotype and phenotype ratios. Example: Tt × Tt → TT, Tt, tT, tt → ratio 1:2:1 genotype, 3:1 phenotype if T is dominant.
单性状杂交：运用旁氏方格预测基因型和表现型比例。例如 Tt × Tt → TT, Tt, tT, tt → 基因型比例 1:2:1，若 T 为显性，则表现型比例 3:1。
Natural selection: Individuals with advantageous traits are more likely to survive and reproduce, passing those traits to offspring. Leads to evolution.
自然选择：具有有利性状的个体更可能存活并繁殖，将这些性状传递给后代。这导致进化。
Food chains show feeding relationships. Energy is transferred; only about 10% passes to the next trophic level. Food webs show interconnected chains.
食物链展示取食关系。能量传递时，只有约 10% 进入下一营养级。食物网展示彼此关联的链。
Pyramid of numbers/bio‑mass: The number or mass of organisms at each trophic level. Producers are at the base; top predators at the apex.
数量/生物量金字塔：各营养级生物的数量或质量。生产者位于底部；顶级掠食者在顶端。
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