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AS CAIE Biology: Quick Reference Handbook of Formulas and Principles | AS CAIE 生物：公式定理速查手册

2026-07-25 16:03 · 本文部分内容由AI辅助创作

📚 AS CAIE Biology: Quick Reference Handbook of Formulas and Principles | AS CAIE 生物：公式定理速查手册

This comprehensive handbook is a rapid revision tool for AS Level Biology students following the CAIE syllabus (9700). It distils the essential formulas, principles, and quantitative relationships that appear frequently in Paper 1, Paper 2, and Paper 3 assessments. From magnification calculations to the chi-squared test, mastering these core concepts will sharpen your problem-solving skills and deepen your understanding of biological processes. Use this guide to reinforce your knowledge and boost your exam confidence.

这本综合手册是为学习CAIE大纲（9700）的AS生物学生准备的快速复习工具。它提炼了试卷一、试卷二和试卷三中经常出现的重要公式、原理和定量关系。从放大率计算到卡方检验，掌握这些核心概念将提升你的解题能力，并加深你对生物过程的理解。使用本指南巩固知识，增强考试信心。

1. Magnification and Size Calculations | 放大率与尺寸计算

Magnification is the ratio of an image's size to the actual size of the specimen. The fundamental formula is:

Magnification = Image size ÷ Actual size

Rearranging gives: Actual size = Image size ÷ Magnification and Image size = Magnification × Actual size nsure units are consistent; convert measurements to the same unit, typically micrometres (µm) or millimetres (mm), where 1 mm = 1000 µm.

放大率是图像大小与样本实际大小的比值。基本公式为：放大率 = 图像尺寸 ÷ 实际尺寸。变形可得：实际尺寸 = 图像尺寸 ÷ 放大率，以及图像尺寸 = 放大率 × 实际尺寸。务必保持单位一致；将测量值转换为相同单位，通常为微米(µm)或毫米(mm)，其中1 mm = 1000 µm。

ures 25 mm and the actual cell diameter is 0.05 mm, the magnification is 25 ÷ 0.05 = 500×.

示例：如果一个细胞图像测量为25 mm，而实际细胞直径为0.05 mm，则放大率为25 ÷ 0.05 = 500×。

2. Surface Area to Volume Ratio | 表面积与体积比

As an organism or cell increases in size, its surface area (SA) increases as the square of linear dimensions, while volume (V) increases as the cube. Consequently, the SA:V ratio decreases. For a cube of side length l:

SA = 6l², V = l³, SA:V = 6 / l

This principle explains why large organisms need specialised transport systems (e.g. circulatory systems) and why cells are small to allow efficient diffusion. A high SA:V ratio maximises exchange of materials with the environment.

随着生物体或细胞体积增大，表面积按线性尺寸的平方增加，而体积按立方增加，因此SA:V比值下降。对于边长为l的立方体：SA = 6l²，V = l³，SA:V = 6/l。这个原理解释了为什么大型生物需要专门的运输系统（例如循环系统），以及为什么细胞必须小以进行高效扩散。高SA:V比能最大化与环境间的物质交换。

3. Cardiac Output, Stroke Volume & Heart Rate | 心输出量、每搏输出量与心率

Cardiac output (CO) is the volume of blood pumped by each ventricle per minute. It is determined by stroke volume (SV) – the volume pumped per beat – and heart rate (HR) – the number of beats per minute.

Cardiac output = Stroke volume × Heart rate
CO = SV × HR

O ≈ 4.9 dm³ min⁻¹. During exercise, both SV and HR can increase, raising CO significantly.

心输出量(CO)是每个心室每分钟泵出的血液体积。它由每搏输出量(SV，每次心跳泵出的体积)和心率(HR，每分钟心跳次数)决定。心输出量 = 每搏输出量 × 心率。典型单位：CO用dm³ min⁻¹，SV用dm³ (或cm³)，HR用次/分钟。静息成年人均值：SV ≈ 0.07 dm³ (70 cm³)，HR ≈ 70次/分钟，CO ≈ 4.9 dm³ min⁻¹。运动时，SV和HR均可增加，显著提高CO。

4. Minute Ventilation, Tidal Volume & Breathing Rate | 每分钟通气量、潮气量与呼吸频率

Minute ventilation (also called pulmonary ventilation) is the total volume of air moved into the lungs per minute. It is the product of tidal volume (TV) – the volume of air per breath – and breathing rate (BR) – the number of breaths per minute.

Minute ventilation = Tidal volume × Breathing rate
(dm³ min⁻¹) = (dm³ breath⁻¹) × (breaths min⁻¹)

At rest, tidal volume is about 0.5 dm³ and breathing rate is about 12 breaths min⁻¹, giving a minute ventilation of ~6.0 dm³ min⁻¹. During vigorous activity, both can increase severalfold.

每分钟通气量是每分钟吸入肺部的空气总体积，等于潮气量(TV，每次呼吸的空气体积)与呼吸频率(BR，每分钟呼吸次数)的乘积。每分钟通气量 = 潮气量 × 呼吸频率。静息时，潮气量约0.5 dm³，呼吸频率约12次/分钟，因此每分钟通气量约为6.0 dm³ min⁻¹。剧烈活动时，两者均可增加数倍。

5. Water Potential (ψ) and Its Components | 水势及其组成

Water potential (ψ) is a measure of the tendency of water to move from one region to another. It is affected by solute concentration and pressure. Pure water at standard temperature and pressure has a ψ of zero. In solutions, ψ is usually negative because solutes lower water potential. The relationship is:

ψ = ψₛ + ψₚ

where ψₛ is the solute potential (osmotic potential) and ψₚ is the pressure potential. In plant cells, ψₛ is typically negative due to dissolved solutes in the vacuole. The cell wall exerts an inward pressure, making ψₚ positive when the cell is turgid. Water moves from regions of higher (less negative) ψ to lower (more negative) ψ across a selectively permeable membrane.

水势(ψ)衡量水从一个区域向另一个区域移动的趋势。它受溶质浓度和压力的影响。标准温度和压力下的纯水水势为零。在溶液中，由于溶质降低水势，ψ通常为负值。关系式为：ψ = ψₛ + ψₚ，其中ψₛ是溶质势（渗透势），ψₚ是压力势。在植物细胞中，由于液泡中的溶质，ψₛ通常为负。当细胞处于质壁分离复原时，细胞壁施加向内压力，使ψₚ变为正值。水通过选择性透膜从较高（较不负）水势区域向较低（较负）水势区域移动。

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6. Respiratory Quotient (RQ) | 呼吸商

The respiratory quotient is the ratio of carbon dioxide produced to oxygen consumed during respiration. It provides information about the substrate being respired.

RQ = Volume of CO₂ produced ÷ Volume of O₂ consumed

Typical RQ values:

SubstrateRQ
Carbohydrate (e.g. glucose)1.0
Lipid~0.7
Protein~0.9

呼吸商是呼吸作用中产生的二氧化碳与消耗的氧气体积之比。它能提供呼吸底物的信息。RQ = 产生的CO₂体积 ÷ 消耗的O₂体积。典型RQ值：碳水化合物（如葡萄糖）为1.0；脂质约0.7；蛋白质约0.9。数值越接近1.0，表明碳水化合物为主要底物；低于1.0则指示脂质或蛋白质被利用。

7. Mitotic Index | 有丝分裂指数

The mitotic index is a measure of the proportion of cells undergoing mitosis in a tissue. It is used to assess the rate of cell division and is often applied in the study of meristems or in cancer diagnosis.

Mitotic index = (Number of cells in mitosis ÷ Total number of cells) × 100

prophase, metaphase, anaphase, telophase), divide by the total number of cells in the field of view, and multiply by 100. For example, if 12 out of 200 cells are in mitosis, the mitotic index is (12/200) × 100 = 6%.

有丝分裂指数是衡量组织中正在分裂的细胞所占比例的指标，用于评估细胞分裂速率，常用于研究分生组织或癌症诊断。有丝分裂指数 = (正在有丝分裂的细胞数 ÷ 细胞总数) × 100。高有丝分裂指数表明快速生长。计算时，在显微镜下观察染色切片，计数可见染色体的细胞（前期、中期、后期、末期），除以视野中的细胞总数，再乘以100。例如，若200个细胞中有12个处于有丝分裂，则有丝分裂指数为 (12/200) × 100 = 6%。

8. Chi-Squared (χ²) Test | 卡方检验

The chi-squared test is a statistical tool used to determine whether there is a significant difference between observed and expected results in genetic crosses or other frequency data. The formula is:

χ² = Σ (O - E)² / E

d sum all values. Compare the calculated χ² with a critical value from a chi-squared table at the appropriate degrees of freedom (df = number of categories - 1). If χ² exceeds the critical value at p=0.05, the null hypothesis (that there is no significant difference) is rejected, suggesting the deviation is not due to chance alone.

卡方检验是一种统计工具，用于判断遗传杂交或其他频率数据中观察值与期望值之间是否存在显著差异。公式为：χ² = Σ (O - E)² / E，其中O为观察频数，E为期望频数，Σ表示所有类别求和。计算每组的(O - E)，平方后除以E，并将所有值相加。将计算出的χ²值与卡方表中相应自由度(df = 类别数 - 1)的临界值进行比较。若χ²大于p=0.05的临界值，则拒绝零假设（无显著差异），表明偏差不仅仅由偶然造成。

9. Genetic Ratios: Mendel's Laws | 遗传比例：孟德尔定律

Mendelian genetics provides predictable phenotypic and genotypic ratios in monohybrid and dihybrid crosses when alleles segregate and assort independently. Key ratios to remember: