📚 Year 11 SQA Science: Quick-Reference Formula Handbook | Year 11 SQA 科学：公式定理速查手册
This handbook compiles the most important formulas, theorems, and key equations from Year 11 SQA Science, covering National 5 Physics, Chemistry, and Biology. Use it as a rapid revision tool to reinforce your understanding and solve problems efficiently.
本手册汇编了 Year 11 SQA 科学（苏格兰国家五级物理、化学和生物）中最关键的公式、定理与方程式，可作为快速复习的工具，帮助你巩固理解、高效解题。
1. Physics: Speed, Velocity and Acceleration | 物理：速率、速度与加速度
In National 5 Physics, you need to distinguish between scalar and vector quantities. Speed is the scalar rate of motion, while velocity includes direction. Acceleration is the rate of change of velocity.
在国家五级物理中，需要区分标量和矢量。速率是运动的标量快慢，速度则包含方向。加速度是速度变化的快慢。
average speed = distance / time v = d / t
This equation is used to find average speed when an object travels a known distance over a measured time. Rearranging gives d = v × t to find distance or t = d / v to find time.
此公式用于计算物体通过已知距离的平均速率。变形后可得距离 d = v × t 或时间 t = d / v。
acceleration = change in velocity / time a = (v – u) / t
Here v is final velocity, u is initial velocity, and t is the time taken. A negative acceleration indicates deceleration.
其中 v 为末速度，u 为初速度，t 为时间。加速度为负值表示减速。
2. Physics: Forces and Newton’s Laws | 物理：力与牛顿定律
Newton’s Second Law and weight calculations are fundamental. You must be able to resolve forces and apply the concept of resultant force.
牛顿第二定律和重力计算是基础内容。你必须能够分解力并运用合力概念。
force = mass × acceleration F = m × a
This tells us that a resultant force causes an object to accelerate. The unit of force is the newton (N). Use this relationship to find unknown mass or acceleration.
这告诉我们，合力会导致物体加速。力的单位是牛顿 (N)。利用这一关系可求未知质量或加速度。
weight = mass × gravitational field strength W = m × g
On Earth, g = 9.8 N/kg (often rounded to 10 N/kg for estimation). Weight is a force, so it is measured in newtons.
在地球表面，重力场强 g = 9.8 N/kg（估算时常取 10 N/kg）。重量是力，因此单位为牛顿。
3. Physics: Work, Energy and Power | 物理：功、能量和功率
Energy is never created or destroyed, only transformed. You must be comfortable calculating work done, gravitational potential energy, kinetic energy, and power.
能量既不会凭空产生也不会消失，只会相互转化。你需要熟练计算功、重力势能、动能和功率。
work done = force × distance W = F × d
Work is measured in joules (J). The distance must be in the direction of the force. Use this to relate energy transferred to a mechanical process.
功的单位是焦耳 (J)。距离必须沿着力的方向。此公式可将能量转移与机械过程联系起来。
gravitational potential energy = mass × g × height Ep = m × g × h
Ep is the energy stored due to an object’s position in a gravitational field. Use h for vertical height gained.
重力势能是物体因在重力场中的位置而储存的能量。h 表示上升的垂直高度。
kinetic energy = ½ × mass × velocity² Ek = ½ m v²
Kinetic energy depends on mass and the square of speed. When an object falls, Ep converts to Ek if air resistance is negligible.
动能取决于质量和速度的平方。不计空气阻力时，物体下落过程中 Ep 转化为 Ek。
power = energy / time P = E / t
Power is the rate of energy transfer, measured in watts (W). 1 W = 1 J/s. Use this to compare how quickly work is done.
功率是能量转移的速率，单位是瓦特 (W)。1 W = 1 J/s。可用于比较做功的快慢。
4. Physics: Electricity – Ohm’s Law and Circuits | 物理：电学 – 欧姆定律与电路
National 5 expects you to use Ohm’s Law, combine resistances, and calculate electrical energy or power. Remember the rules for series and parallel circuits.
国家五级要求运用欧姆定律、计算等效电阻以及电功或电功率。需牢记串联和并联电路规则。
voltage = current × resistance V = I × R
This relationship holds for ohmic conductors at constant temperature. Rearranging gives I = V / R or R = V / I.
该关系适用于恒温下的欧姆导体。变形可得 I = V / R 或 R = V / I。
charge = current × time Q = I × t
Use this when dealing with the quantity of charge passing a point in a circuit. Charge is measured in coulombs (C).
处理电路中通过某点的电荷量时使用此公式。电荷的单位是库仑 (C)。
electrical power = current × voltage P = I × V
Combining with Ohm’s Law gives P = I² R and P = V² / R. These are useful when you know only two quantities.
联立欧姆定律可导出 P = I² R 和 P = V² / R。当已知其中两个量时，这些形式很实用。
5. Physics: Waves and Radiation | 物理：波与辐射
Wave properties and nuclear radiation form a significant part of the specification. You must be able to use the wave equation and handle half-life calculations.
波的性质与核辐射是考试的重要组成部分。你需要熟练运用波动方程并进行半衰期的相关计算。
wave speed = frequency × wavelength v = f × λ
This applies to all waves, including sound, light, and water waves. Frequency is in hertz (Hz), wavelength in metres (m).
该公式适用于所有波，包括声波、光波和水波。频率单位为赫兹 (Hz)，波长单位为米 (m)。
period = 1 / frequency T = 1 / f
The period T is the time for one complete wave cycle. It is the inverse of frequency.
周期 T 是完成一次完整振动所需的时间，与频率互为倒数。
For nuclear half-life, the activity or count rate halves after each fixed time interval. No single formula is given; you must apply proportional reasoning.
对于核辐射半衰期，活度或计数率在每段固定时间后减半。没有单一公式，需要运用比例推理进行求解。
6. Chemistry: Mole and Concentration | 化学：摩尔与浓度
The mole concept is central to quantitative chemistry. You must be able to convert between mass, moles, and concentration, and use balanced equations to predict reacting quantities.
摩尔概念是定量化学的核心。你必须能在质量、摩尔和浓度之间进行转换，并运用配平方程式预测反应量。
number of moles = mass / molar mass n = m / M
Use the formula mass (in g/mol) calculated from the periodic table. This equation links the laboratory measurement (mass) to the chemical amount (moles).
使用由周期表算出的摩尔质量（g/mol）。该式将实验室测量值（质量）与化学上的“份数”（摩尔）联系起来。
concentration = number of moles / volume c = n / V
Concentration is usually expressed in mol/dm³. Remember to convert volume to dm³ if given in cm³ (1 dm³ = 1000 cm³).
浓度单位通常为 mol/dm³。若体积以 cm³ 给出，需换算为 dm³ (1 dm³ = 1000 cm³)。
7. Chemistry: Acids, Bases and Titrations | 化学：酸、碱与滴定
Neutralisation reactions and titration calculations are key skills. Understanding the relationship between hydrogen and hydroxide ions is essential for pH concepts.
中和反应与滴定计算是关键技能。理解氢离子与氢氧根离子的关系对掌握 pH 概念至关重要。
In a titration, the reaction H⁺ + OH⁻ → H₂O governs the stoichiometry. For monoprotic acids and monoacidic bases, the mole ratio is 1:1. This gives a useful rule:
在滴定中，反应 H⁺ + OH⁻ → H₂O 决定化学计量。对于一元酸和一元碱，摩尔比为 1:1，由此可得一个实用规则：
cₐ × Vₐ × nₐ = c_b × V_b × n_b (where n = number of H⁺ or OH⁻ per formula unit)
This allows you to find an unknown concentration or volume when the mole ratio is not 1:1. Always check the balanced equation first.
当摩尔比不是 1:1 时，此关系式可用来求未知浓度或体积。务必先配平方程式再使用。
The pH scale runs from 0 (strongly acidic) to 14 (strongly alkaline). In National 5, you are not required to calculate pH using logarithms, but you should know that pH = -log₁₀[H⁺] for higher study.
pH 标度从 0（强酸）到 14（强碱）。国家五级不要求用对数计算 pH，但可了解 pH = -log₁₀[H⁺] 以备后续学习。
8. Biology: Microscopy and Magnification | 生物：显微镜与放大倍数
Cell biology questions often require you to calculate magnification, actual size, or image size from micrographs. The formula is simple but must be applied carefully.
细胞生物学考题常要求根据显微照片计算放大倍数、实际大小或图像大小。公式简单，但应用时必须细心。
magnification = image size / actual size M = I / A
All sizes must be in the same unit. Typically, image size is measured in mm or cm, and actual size in µm or nm. Convert using 1 mm = 1000 µm.
所有长度必须使用相同单位。通常图像尺寸以 mm 或 cm 给出，而实际尺寸以 µm 或 nm 给出。记住 1 mm = 1000 µm 进行换算。
Remember: magnification has no units. If a cell image is 5 cm long and the actual cell is 50 µm, first convert 5 cm to 50,000 µm, then M = 50,000 / 50 = 1000×.
注意：放大倍数无单位。若细胞图像长 5 cm，实际细胞长 50 µm，先将 5 cm 转为 50,000 µm，得 M = 50,000 / 50 = 1000×。
9. Biology: Photosynthesis and Respiration | 生物：光合作用与呼吸作用
These two key biochemical processes are often described through word and chemical equations. You must be able to recall reactants, products, and the energy changes involved.
这两大生化过程常用文字和化学方程式描述。必须能回忆出反应物、生成物及伴随的能量变化。
Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Light energy is absorbed by chlorophyll to convert carbon dioxide and water into glucose and oxygen. This is an endothermic process.
叶绿素吸收光能，将二氧化碳和水转化为葡萄糖和氧气。这是一个吸热过程。
Aerobic respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
Glucose is broken down using oxygen to release carbon dioxide, water, and energy (ATP). This occurs in mitochondria and is exothermic.
葡萄糖在氧气作用下分解，释放二氧化碳、水和能量 (ATP)。该过程发生在线粒体中，为放热反应。
For practical experiments, you may need to relate gas exchange to these equations, e.g., oxygen uptake or carbon dioxide release.
在实验中，可能需要联系这些方程式来分析气体交换，如氧气的吸收或二氧化碳的释放。
10. Biology: Genetics and Monohybrid Crosses | 生物：遗传学与单基因杂交
Understanding inheritance patterns requires you to apply Mendel’s principles. Use Punnett squares to predict genotype and phenotype ratios.
理解遗传规律需要运用孟德尔原理。使用旁氏表预测基因型与表现型比例。
In a monohybrid cross between two true-breeding parents (e.g., TT × tt), all F₁ offspring are Tt. Crossing two F₁ heterozygotes (Tt × Tt) gives a genotype ratio of 1 TT : 2 Tt : 1 tt and a phenotype ratio of 3 dominant : 1 recessive.
纯合亲本杂交（如 TT × tt），F₁ 代全为 Tt。两个 F₁ 杂合子杂交 (Tt × Tt)，基因型比为 1 TT : 2 Tt : 1 tt，表现型比为 3 显性 : 1 隐性。
For sex determination, the cross XX × XY produces a theoretical 1:1 ratio of female to male offspring.
性别决定中，XX × XY 的杂交理论上雌雄后代比例为 1:1。
Remember that predicted ratios are probabilistic. Real results may vary due to chance, especially with small sample sizes.
记住预测比例是概率性的。实际结果可能因偶然性而偏离，尤其是在样本较小时。
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