Year 10 CAIE Biology Formula & Theorem Quick Reference Handbook

📚 Year 10 CAIE Biology Formula & Theorem Quick Reference Handbook | 公式定理速查手册

This comprehensive quick reference guide collects every essential formula, equation, and quantitative relationship you will encounter in the Year 10 CAIE IGCSE Biology course (0610/0970). Mastery of these mathematical and logical tools is critical for solving examination problems on magnification, energy flow, gas exchange, genetics and more. Each entry is explained succinctly with context, units, and typical applications. Use this handbook alongside past paper practice to build speed and accuracy.

这本全面的速查手册汇集了 Year 10 CAIE IGCSE 生物课程（0610/0970）中你会遇到的每一个核心公式、方程式和定量关系。掌握这些数学与逻辑工具对于解决放大倍数、能量流动、气体交换、遗传等考试题目至关重要。每条公式都配有简洁的语境说明、单位和典型应用。请在使用真题练习的同时参阅本手册，提高解题速度和准确度。

1. Magnification and Actual Size | 放大倍数与实际大小

Magnification measures how many times larger an image appears compared to the real object. The formula triangle is central to microscopy questions. Always ensure that image size and actual size share the same units before calculation. The standard unit for actual size is usually micrometres (µm) or millimetres (mm).

放大倍数衡量影像比实物大多少倍。这一公式三角形是显微镜考题的核心。计算前务必保证图像大小与实际大小单位一致。实际大小的常用单位是微米（µm）或毫米（mm）。

Magnification = Image size ÷ Actual size

放大倍数 = 图像大小 ÷ 实际大小

Image size often measured in mm with a ruler from a diagram.
图像大小通常用直尺从图中量取，单位为毫米。
Actual size is often given in µm; convert 1 mm = 1000 µm.
实际大小常以微米给出；转换关系为 1 mm = 1000 µm。

Worked example: If a cell image is 24 mm wide at a magnification of ×400, actual size = 24 ÷ 400 = 0.06 mm = 60 µm.

示例：若某细胞图像在 ×400 放大倍数下宽度为 24 mm，实际大小 = 24 ÷ 400 = 0.06 mm = 60 µm。

2. Fick’s Law for Diffusion | 扩散的菲克定律

Fick’s Law describes the rate of diffusion across a surface. In CAIE IGCSE Biology, you are expected to understand the factors affecting diffusion rate qualitatively and apply the proportionality relationship. The law highlights how exchange surfaces are adapted for efficiency.

菲克定律描述物质穿过表面扩散的速率。CAIE IGCSE 生物要求你定性理解影响扩散速率的因素并应用比例关系。该定律强调了交换表面如何进化适应以提高效率。

Rate of diffusion ∝ (Surface area × Concentration difference) ÷ Diffusion distance

扩散速率 ∝ (表面积 × 浓度差) ÷ 扩散距离

Large surface area increases the rate (e.g., alveoli, villi).
较大的表面积加快速率（如肺泡、绒毛）。
Greater concentration gradient speeds up diffusion.
浓度梯度越大，扩散越快。
Thin exchange surface reduces diffusion distance, raising the rate.
薄的交换表面缩短扩散距离，提高速率。

3. Photosynthesis and Aerobic Respiration Word Equations | 光合作用与有氧呼吸的文字方程式

Although word equations are often required, the balanced chemical equations help to visualise matter conversion. These are tested both as recall and as the basis for gas exchange experiments. Note the opposite directions of the two reactions.

虽然考试常要求文字方程式，但平衡的化学方程式有助于直观理解物质转化。这两条方程式既考查记忆也是气体交换实验的基础。注意两个反应方向相反。

Photosynthesis:

光合作用：

6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂

(Carbon dioxide + Water → Glucose + Oxygen, in the presence of light and chlorophyll)

(二氧化碳 + 水 → 葡萄糖 + 氧气，需光与叶绿素)

Aerobic Respiration:

有氧呼吸：

C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O

(Glucose + Oxygen → Carbon dioxide + Water, releasing energy as ATP)

(葡萄糖 + 氧气 → 二氧化碳 + 水，释放能量生成 ATP)

4. Efficiency of Energy Transfer and Biomass | 能量传递效率与生物量

In food chains, only a fraction of energy or biomass is passed to the next trophic level. The efficiency formula appears often in ecology calculations. Energy is lost through movement, heat, undigested material, and excretion. Efficiency explains the pyramidal shape of ecosystems.

食物链中，只有一小部分能量或生物量传递至下一个营养级。效率公式经常出现在生态学计算中。能量因运动、散热、未消化物质及排泄而损失。效率解释了生态金字塔的形态。

Efficiency (%) = (Energy or biomass transferred to next level ÷ Energy or biomass available at previous level) × 100%

效率 (%) = （传递至下一级的能量或生物量 ÷ 上一级可用的能量或生物量）× 100%

Typical efficiency between trophic levels is about 10%.
营养级间的典型效率约为 10%。
Units must be the same (e.g., kJ, g/m²).
单位必须一致（如 kJ，g/m²）。

5. Respiratory Quotient (RQ) | 呼吸商

RQ indicates the type of substrate being respired and can be used to infer metabolic activity. It is derived from the volumes of carbon dioxide produced and oxygen consumed. Values for carbohydrates, lipids, and proteins differ. It is measured using a respirometer.

呼吸商（RQ）指示被呼吸的底物类型，可用于推断代谢活动。它由产生的二氧化碳体积与消耗的氧气体积之比得出。糖类、脂质和蛋白质的数值各有不同，可使用呼吸计进行测量。

RQ = Volume of CO₂ produced ÷ Volume of O₂ consumed

呼吸商 = 产生的 CO₂ 体积 ÷ 消耗的 O₂ 体积

Substrate	RQ value
Carbohydrate (葡萄糖)	1.0
Lipid (脂类)	~0.7
Protein (蛋白质)	~0.8–0.9

If RQ = 1.0, carbohydrate is the main fuel. During seed germination, a drop in RQ indicates lipid usage.

若 RQ = 1.0，主要燃料是糖类。种子萌发期间 RQ 下降表明脂类被利用。

6. Population Growth Rate | 种群增长速率

Populations change through births, deaths, immigration, and emigration. The population growth rate formula allows you to calculate the change in a closed or open population. This concept is vital for understanding bacterial growth curves and human population demography.

种群通过出生、死亡、迁入和迁出发生变化。种群增长速率公式可用来计算封闭或开放种群的变化。此概念对于理解细菌生长曲线及人口统计学至关重要。

Population growth rate = (Births – Deaths) + (Immigration – Emigration)

种群增长速率 = （出生数 – 死亡数） + （迁入数 – 迁出数）

If births + immigration > deaths + emigration, the population increases.
若出生+迁入 > 死亡+迁出，种群增长。
In the sigmoid growth curve, the rate eventually reaches zero at carrying capacity.
在 S 型生长曲线中，增长速率最终在环境容纳量处归零。

7. Cardiac Output | 心输出量

Cardiac output is the volume of blood pumped by the heart per minute. It brings together heart rate and stroke volume. Regular exercise can increase stroke volume and lower resting heart rate while maintaining cardiac output.

心输出量是心脏每分钟泵出的血液体积，它结合了心率与每搏输出量。经常运动可增大每搏输出量并在维持心输出量的同时降低静息心率。

Cardiac output (cm³/min) = Heart rate (beats/min) × Stroke volume (cm³/beat)

心输出量（cm³/min） = 心率（次/min） × 每搏输出量（cm³/次）

Average resting cardiac output ≈ 5 dm³/min (5000 cm³/min).
静息心输出量平均值约为 5 dm³/min (5000 cm³/min)。
During strenuous exercise, cardiac output can increase 4–5 times.
剧烈运动时心输出量可增至原来的 4–5 倍。

8. Genetic Probability – Punnett Square Ratios | 遗传概率 – 庞纳特方格比例

Monohybrid inheritance follows Mendel’s laws. The expected phenotypic and genotypic ratios emerge from random fertilisation of gametes. In CAIE IGCSE, you must predict outcomes using Punnett squares and interpret pedigree diagrams while applying the principle of probability.

单基因遗传遵循孟德尔定律。预测的表现型和基因型比例源自配子的随机受精。CAIE IGCSE 考试要求你会用庞纳特方格预测结果，解读遗传谱系图并应用概率原理。

Parental genotypes	Expected phenotypic ratio
Heterozygous × Heterozygous (Tt × Tt)	3 dominant : 1 recessive
Heterozygous × Homozygous recessive (Tt × tt)	1 dominant : 1 recessive
Homozygous dominant × Homozygous recessive (TT × tt)	All dominant

Probability is independent for each offspring; ratios apply to large numbers of offspring.

概率对每个子代独立；比例适用于大量子代。

9. Q₁₀ Temperature Coefficient for Enzyme Activity | 酶活性温度系数 Q₁₀

The Q₁₀ value describes how much the rate of an enzyme‑controlled reaction increases when the temperature rises by 10 °C. In the range between 0 °C and the optimum temperature, Q₁₀ is typically around 2, meaning the rate doubles for each 10 °C rise. Beyond the optimum, denaturation causes the rate to plummet.

Q₁₀ 值描述温度每升高 10 °C 时酶控反应速率增加多少。在 0 °C 到最适温度之间，Q₁₀ 通常约为 2，即每升温 10 °C 速率翻倍。超过最适温度后，变性导致速率骤降。

Q₁₀ = (Rate at T + 10 °C) ÷ (Rate at T)

Q₁₀ = （温度 T + 10 °C 时的速率） ÷ （温度 T 时的速率）

If Q₁₀ = 2, rate doubles per 10 °C rise. Useful for interpreting enzyme graphs.
若 Q₁₀ = 2，每升温 10 °C 速率翻倍。可用于解读酶活性图。

10. Water Potential and Percentile Change | 水势与百分比变化

Osmosis problems often require calculating the percentage change in mass or length of plant tissue immersed in solutions. A negative percentage means water loss (plasmolysis), while a positive percentage indicates water gain (turgid). The sign and magnitude help determine the water potential of the external solution.

渗透作用题常要求计算浸泡在不同溶液中的植物组织质量或长度的百分比变化。负百分比表示失水（质壁分离），正百分比表示吸水（胀大）。符号和幅度有助于确定外部溶液的水势。

% Change = [(Final value – Initial value) ÷ Initial value] × 100%

变化百分比 = [(终值 – 初值) ÷ 初值] × 100%

Mass or length can be used; always state units clearly.
可使用质量或长度；务必清晰标明单位。
A 0% change suggests the solution is isotonic to the tissue.
0% 变化表明溶液与组织等渗。

11. Rate of Reaction, Uptake, or Production | 反应速率、吸收速率或产率

Many investigations involve measuring how fast a process occurs. The general rate formula is applied in photosynthesis experiments (oxygen bubbles per minute), transpiration (distance moved by air bubble per time), or product formation.

许多实验涉及测量过程发生的快慢。通用的速率公式适用于光合作用实验（每分钟氧气气泡数）、蒸腾作用（气泡移动距离/时间）或产物生成。

Rate = Quantity of change ÷ Time taken

速率 = 变化量 ÷ 所花时间

Common units: cm³/min, mm/s, bubbles/min.
常用单位：cm³/min, mm/s, 气泡数/min。
Calculate from a tangent on a graph to find instantaneous rate.
通过曲线上的切线计算瞬时速率。

12. Essential Constants and Unit Conversions | 重要常数与单位换算

Conversions between units of length, mass, and volume are frequently needed in calculations spanning microscopy, physiology, and ecology. Memorising these will save time and prevent mistakes in exams.

长度、质量和体积单位之间的换算在显微镜学、生理学及生态学计算中频繁使用。熟记这些换算关系可节省时间，避免考试出错。

Prefix / Unit	Equivalent
1 cm	10 mm
1 mm	1000 µm
1 µm	1000 nm
1 dm³	1000 cm³
1 litre (L)	1 dm³ = 1000 cm³
1 g	1000 mg
1 kg	1000 g

Also remember: temperature in biology is expressed in °C; human body temperature ≈ 37 °C; optimum for many plant enzymes ≈ 20–30 °C.

还需牢记：生物学温度用 °C 表示；人体体温约 37 °C；许多植物酶的最适温度约为 20–30 °C。

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Year 10 CAIE Biology Formula & Theorem Quick Reference Handbook | 公式定理速查手册