📚 Formula and Theorem Quick Reference Manual | 公式定理速查手册
This quick reference manual brings together all the key formulas, theorems, and relationships you need for the CAIE Year 8 Science curriculum. Covering physics, chemistry, and biology, it helps you revise core concepts efficiently, understand how to apply each formula, and build confidence for your exams. Use it as a daily study companion or a last‑minute revision tool — every entry is kept concise and paired with a clear explanation.
这本速查手册汇集了 CAIE 8 年级科学课程中所有关键公式、定理与关系式。内容涵盖物理、化学和生物，帮助你高效复习核心概念，理解每个公式的应用，并建立考试信心。你可以把它当作每日学习伴侣或考前冲刺工具——每个条目都简明扼要，并配有清晰的解释。
1. Motion and Forces | 运动与力
otal time (t): v = d ÷ t. The SI unit is metres per second (m/s). In symbol form, we write v = d / t.
平均速度 (v) 等于总路程 (d) 除以总时间 (t)：v = d ÷ t。国际单位是米每秒 (m/s)。符号表达式为 v = d / t。
For a straight line on a distance–time graph, speed equals the gradient. Acceleration (a) is the change in velocity per unit time: a = (v − u) / t where u is initial velocity. The unit is m/s².
在路程—时间图中，直线部分的斜率就是速度。加速度 (a) 是单位时间内速度的变化量：a = (v − u) / t，其中 u 为初速度。单位是米每二次方秒 (m/s²)。
Newton’s second law states that force (F) equals mass (m) times acceleration (a):
牛顿第二定律指出力 (F) 等于质量 (m) 乘以加速度 (a)：
F = m × a
Force is measured in newtons (N), mass in kilograms (kg). An object at rest stays at rest, and an object in motion stays in motion at constant velocity unless acted upon by an unbalanced force (Newton’s first law).
力的单位是牛顿 (N)，质量的单位是千克 (kg)。物体在不受不平衡外力作用时，静止的保持静止，运动的保持匀速直线运动（牛顿第一定律）。
2. Density, Pressure and Moments | 密度、压强与力矩
Density (ρ) is mass per unit volume: ρ = m / V. The unit is kg/m³ or g/cm³. A less dense substance floats on a denser one.
密度 (ρ) 是单位体积的质量：ρ = m / V。单位是 kg/m³ 或 g/cm³。密度较小的物体会浮在密度较大的物质上。
Pressure (p) is the force applied per unit area: p = F / A l (Pa), where 1 Pa = 1 N/m². A larger area leads to a smaller pressure for the same force.
压强 (p) 是单位面积上承受的压力：p = F / A。单位是帕斯卡 (Pa)，1 Pa = 1 N/m²。相同的力作用在更大面积上会使压强减小。
equals the total anticlockwise moment. Moment = force × perpendicular distance from pivot: M = F × d.
力矩原理：物体处于转动平衡时，顺时针总力矩等于逆时针总力矩。力矩 = 力 × 到支点的垂直距离：M = F × d。
3. Energy, Work and Power | 能量、功与功率
Work done (W) measures energy transferred when a force moves an object: W = F × d, where d is the distance moved in the direction of the force. It is measured in joules (J).
功 (W) 衡量力使物体移动时传递的能量：W = F × d，其中 d 是沿力方向移动的距离。单位是焦耳 (J)。
Gravitational potential energy gained is Eₚ = m × g × h, where g ≈ 10 m/s² on Earth, h is the height change. Kinetic energy is Eₖ = ½ × m × v².
增加的重力势能为 Eₚ = m × g × h，地球上 g ≈ 10 m/s²，h 是高度变化。动能为 Eₖ = ½ × m × v²。
Power (P) is the rate of doing work or transferring energy: P = W / t or P = E / t. The unit is the watt (W), where 1 W = 1 J/s.
功率 (P) 是做功或传递能量的快慢：P = W / t 或 P = E / t。单位是瓦特 (W)，1 W = 1 J/s。
Energy cannot be created or destroyed — of conservation of energy). Efficiency = (useful energy output ÷ total energy input) × 100%.
能量既不能被创造也不能被消灭——只能从一种形式转化为另一种形式（能量守恒原理）。效率 = (有用能量输出 ÷ 总能量输入) × 100%。
4. Electricity and Magnetism | 电与磁
Electric current (I) is the flow of electric charge. It is measured in amperes (A). Voltage (V) is the energy transferred per unit charge, measured in volts (V). Resistance (R) is measured in ohms (Ω).
电流 (I) 是电荷的定向流动，单位是安培 (A)。电压 (V) 是每单位电荷传递的能量，单位是伏特 (V)。电阻 (R) 的单位是欧姆 (Ω)。
Ohm’s law: for a resistor at constant temperature, voltage equals current multiplied by resistance:
欧姆定律：在温度恒定时，电阻两端的电压等于电流乘以电阻：
V = I × R
cuits, the voltage across each branch is the same, and total current is the sum of branch currents.
在串联电路中，各处电流相等，总电阻等于各电阻之和：Rₜₒₜₐₗ = R₁ + R₂ + …。在并联电路中，各支路两端电压相等，总电流等于各支路电流之和。
Electromagnets: a current-carrying wire wrapped around an iron core produces a magnetic field. The strength can be increased by more turns of wire, larger current, or using a soft iron core.
电磁铁：绕在铁芯上的通电线圈产生磁场。增加线圈匝数、增大电流或使用软铁芯可增强磁性。
5. Atoms, Elements and Compounds | 原子、元素与化合物
All substances are made of atoms. An element consists of only one type of atom. A compound contains two or more types of atom chemically bonded together. A molecule is a group of atoms covalently bonded.
所有物质都由原子构成。元素仅由一种原子组成。化合物由两种或两种以上原子通过化学键结合而成。分子是由共价键结合的一组原子。
The atomic number is the number of protons in the nucleus. The mass number is the total number of protons plus neutrons. In a neutral atom, the number of electrons equals the number of protons.
原子序数等于原子核内的质子数。质量数等于质子数与中子数之和。在中性原子中，电子数等于质子数。
Electron arrangement: the first shell holds up to 2 electrons, the second and third shells up to 8 each. The group number in the periodic table indicates the number of electrons in the outermost shell (for groups 1–2 and 13–18).
电子排布：第一壳层最多容纳 2 个电子，第二、三壳层最多各 8 个。元素周期表中的族数（1–2 和 13–18 族）表示最外层电子数。
6. Chemical Reactions and Equations | 化学反应与方程式
nt A + Reactant B → Product C. Symbol equations use chemical formulae and must be balanced — the number of atoms of each element is the same on both sides.
文字方程式左侧是反应物，右侧是产物：反应物 A + 反应物 B → 产物 C。符号方程式使用化学式，必须配平——每种元素的原子数在两侧保持一致。
Conservation of mass: during a chemical reaction, the total mass of products equals the total mass of reactants. No atoms are created or destroyed; they are only rearranged.
质量守恒：在化学反应中，生成物的总质量等于反应物的总质量。原子不被创造或消灭，只是重新排列。
Rate of reaction can be increased by higher temperature, larger surface area, higher concentration (of solutions), or use of a catalyst. A catalyst speeds up a reaction without being used up.
反应速率可通过升高温度、增大表面积、提高溶液浓度或使用催化剂来提高。催化剂能加速反应，自身在反应前后质量不变。
base → salt + water), and displacement (more reactive metal displaces less reactive one).
常见反应类型：燃烧（燃料 + 氧气 → 二氧化碳 + 水）、中和（酸 + 碱 → 盐 + 水）以及置换反应（活泼金属置换出不活泼金属）。
7. Acids, Alkalis and pH Scale | 酸、碱与 pH 值
Acids produce hydrogen ions (H⁺) in water; alkalis produce hydroxide ions (OH⁻). The pH scale runs from 0 (strongly acidic) to 14 (strongly alkaline), with 7 being neutral.
酸在水中产生氢离子 (H⁺)；碱在水中产生氢氧根离子 (OH⁻)。pH 值范围从 0（强酸性）到 14（强碱性），7 为中性。
₂O(l). A salt and water are formed. Indicators such as litmus, universal indicator, and phenolphthalein change colour at different pH levels.
中和反应：H⁺(aq) + OH⁻(aq) → H₂O(l)。生成盐和水。指示剂如石蕊、通用指示剂和酚酞在不同的 pH 值下会改变颜色。
Common acids: hydrochloric acid (HCl), sulfuric acid (H₂SO₄), nitric acid (HNO₃). Common alkalis: sodium hydroxide (NaOH), potassium hydroxide (KOH).
常见的酸：盐酸 (HCl)、硫酸 (H₂SO₄)、硝酸 (HNO₃)。常见的碱：氢氧化钠 (NaOH)、氢氧化钾 (KOH)。
8. Cells and Life Processes | 细胞与生命活动
The cell is the basic unit of life. Plant cells contain a cell wall, chloroplasts, and a large central vacuole, which animal cells lack. Both have a nucleus, cytoplasm, and cell membrane.
细胞是生命的基本单位。植物细胞有细胞壁、叶绿体和大液泡，动物细胞没有。两者都含有细胞核、细胞质和细胞膜。
Diffusion is the net movement of particles from an area of higher concentration to an area of lower concentration, down a concentration gradient. Osmosis is the diffusion of water through a partially permeable membrane.
扩散是粒子从高浓度区域向低浓度区域沿浓度梯度的净运动。渗透是水通过半透膜的扩散过程。
s: glucose → lactic acid (+ less energy). In yeast: glucose → ethanol + carbon dioxide (+ energy).
呼吸作用从食物中释放能量。有氧呼吸：葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）。人体无氧呼吸：葡萄糖 → 乳酸（+ 较少能量）。酵母菌无氧呼吸：葡萄糖 → 乙醇 + 二氧化碳（+ 能量）。
9. Photosynthesis and Plant Nutrition | 光合作用与植物营养
Photosynthesis is the process by which green plants use sunlight to make food:
光合作用是绿色植物利用光能制造养分的过程：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Carbon dioxide and water, in the presence of chlorophyll and light, produce glucose and oxygen. The rate is affected by light intensity, carbon dioxide concentration and temperature.
在叶绿素和光照条件下，二氧化碳与水反应生成葡萄糖和氧气。光合作用速率受光照强度、二氧化碳浓度和温度影响。
Plants use glucose for respiration, converting it into starch for storage, cellulose for cell walls, and proteins when combined with nitrate ions from the soil.
植物利用葡萄糖进行呼吸作用，将其转化为淀粉储存起来，形成细胞壁的纤维素，并与土壤中的硝酸根离子结合合成蛋白质。
Minerals: nitrates are needed for proteins and growth; magnesium is a component of chlorophyll. Lack of these causes yellowing of leaves and stunted growth.
矿物质：硝酸盐用于合成蛋白质和供生长；镁是叶绿素的组成成分。缺乏这些元素会导致叶片发黄、生长迟缓。
10. Ecosystems, Food Chains and Cycles | 生态系统、食物链与循环
nsumer → secondary consumer → tertiary consumer. Arrows show the direction of energy flow.
食物链表示能量从一个生物体传递到下一个生物体：生产者 → 初级消费者 → 次级消费者 → 三级消费者。箭头指示能量流动的方向。
In a food web, many food chains overlap. If one organism’s population changes, it affects others through interdependence. Predators and prey have cyclical population changes.
在食物网中，多条食物链相互重叠。一种生物数量变化会通过相互依存关系影响其他生物。捕食者与被捕食者的数量呈周期性变化。
The carbon cycle: carbon dioxide is removed from the air by photosynthesis and returned by respiration, combustion, and decomposition. Fossil fuels are a long-term store of carbon.
碳循环：光合作用从空气中吸收二氧化碳，呼吸作用、燃烧和分解又将其释放。化石燃料是碳的长期储存形式。
The water cycle: evaporation, transpiration, condensation, precipitation, and collection maintain the continuous movement of water on, above, and below the Earth’s surface.
水循环：蒸发、蒸腾、凝结、降水和汇集使水在地表、地下和大气间持续循环运动。
11. Genetics and Inheritance Basics | 遗传与遗传基础
Genes are sections of DNA that carry the instructions for characteristics. They are located on chromosomes in the nucleus. Humans have 46 chromosomes arranged in 23 pairs.
基因是携带性状指令的 DNA 片段，位于细胞核内的染色体上。人类有 46 条染色体，排列成 23 对。
Alleles are different forms of the same gene. Dominant alleles mask recessive alleles. Homozygous means two identical alleles; heterozygous means two different alleles for a trait.
等位基因是同一基因的不同形式。显性等位基因掩盖隐性等位基因。纯合指一对相同的等位基因；杂合指一对基因中有两个不同的等位基因。
A Punnett square can predict the probability of offspring inheriting a certain genotype. Sex determination: females have XX chromosomes, males have XY.
庞尼特方格可以预测子代出现某种基因型的概率。性别决定：女性为 XX，男性为 XY。
12. Space, Seasons and Gravity | 太空、季节与引力
The Earth orbits the Sun once every 365.25 days (a year). The Moon orbits the Earth roughly every 28 days. Day and night are caused by the Earth’s rotation on its axis every 24 hours.
地球绕太阳公转一周约为 365.25 天（一年）。月球大约每 28 天绕地球一周。昼夜由地球每 24 小时自转一周引起。
The seasons result from the tilt of the Earth’s axis (about 23.5°) as it orbits the Sun. When the Northern Hemisphere tilts towards the Sun, it experiences summer; away, winter.
四季是由于地球自转轴倾斜约 23.5° 绕日公转造成的。北半球朝向太阳时为夏季；远离时为冬季。
Gravitational force keeps planets in orbit. Weight (W) is the gravitational force on an object: W = m × g l field strength (≈ 10 N/kg on Earth). Mass is constant, but weight changes with location.
引力使行星保持轨道运行。重量 (W) 是作用在物体上的引力：W = m × g，其中 g 是引力场强度（地球上约 10 N/kg）。质量恒定，但重量随位置变化。
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