📚 Year 7 WJEC Biology: Formula & Theorem Quick Reference Guide | 七年级 WJEC 生物：公式定理速查手册
This quick reference guide pulls together the key formulas, word equations, and useful principles you will meet in Year 7 WJEC Biology. Understanding these relationships will help you explain how living organisms work, make accurate microscope measurements, and tackle ecology and genetics questions with confidence.
这份速查手册汇集了你在七年级 WJEC 生物课程中会遇到的关键公式、词汇方程和实用原理。理解这些关系将帮助你解释生物体如何运作，进行准确的显微镜测量，并自信地解答生态与遗传学问题。
1. Microscope Calculations | 显微镜计算
The total magnification of a light microscope is found by multiplying the eyepiece lens magnification by the objective lens magnification. This is the first formula you need to use regularly in the lab.
光学显微镜的总放大倍率由目镜放大倍率乘以物镜放大倍率得出。这是你在实验室中需要经常使用的第一个公式。
The formula is:
公式为：
Total Magnification = Eyepiece Magnification × Objective Magnification
总放大倍率 = 目镜放大倍率 × 物镜放大倍率
10 × 40 = 400×. This means the image you see appears 400 times larger than its real size.
例如，如果目镜放大 10 倍，物镜放大 40 倍，总放大倍率为 10 × 40 = 400 倍。这意味着你看到的图像比其实际大小大了 400 倍。
When you are asked to calculate the real size of a specimen, you can rearrange the idea of magnification. The relationship is:
当需要计算标本的实际大小时，可以重新排列放大关系。公式为：
Actual Size = Image Size ÷ Magnification
实际大小 = 图像大小 ÷ 放大倍率
Always make sure the image size and actual size are in the same units – micrometres (µm) or millimetres (mm) are the most common in school biology. Remember that 1 mm = 1000 µm.
务必确保图像大小和实际大小使用相同的单位——在学校生物中最常用的是微米 (µm) 或毫米 (mm)。请记住 1 mm = 1000 µm。
2. Surface Area to Volume Ratio | 表面积与体积比
Living organisms rely on diffusion to move substances in and out of cells. The surface area to volume ratio (SA:V) is a decisive factor in how quickly diffusion can happen. A large surface area compared to the volume allows efficient exchange of gases, nutrients, and waste.
生物体依靠扩散作用使物质进出细胞。表面积与体积比 (SA:V) 是决定扩散快慢的关键因素。与体积相比，较大的表面积可有效交换气体、营养物质和废物。
You do not need to calculate SA:V for irregular shapes, but understanding the principle is essential. For a cube, you can find the ratio like this:
你不需要计算不规则形状的 SA:V，但理解这一原理至关重要。对于立方体，可以这样计算：
| Cube side length / 立方体边长 | Surface area (6 × side²) / 表面积 (6 × 边长²) | Volume (side³) / 体积 (边长³) | SA:V / 表面积：体积 |
|---|---|---|---|
| 1 cm | 6 cm² | 1 cm³ | 6 : 1 |
| 2 cm | 24 cm² | 8 cm³ | 3 : 1 |
| 3 cm | 54 cm² | 27 cm³ | 2 : 1 |
Notice how the SA:V decreases as the organism or cell gets larger. This is why multicellular organisms need specialised exchange surfaces like lungs, gills, and the villi in the small intestine – they increase the surface area enormously.
请注意，随着生物体或细胞变大，SA:V 会减小。这就是多细胞生物需要肺、鳃和小肠绒毛等特化交换表面的原因——它们极大地增加了表面积。
3. Photosynthesis Word Equation | 光合作用词汇方程
Photosynthesis is the process plants and algae use to trap light energy and convert carbon dioxide and water into glucose and oxygen. The word equation is a simple way to summarise the starting materials and products.
光合作用是植物和藻类利用光能，将二氧化碳和水转化为葡萄糖和氧气的过程。词汇方程是总结反应物和生成物的简便方式。
Carbon dioxide + Water → Glucose + Oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
y chlorophyll in chloroplasts. The balanced symbol equation (6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂) is often taught later, but understanding this word model now prepares you for deeper study.
化学符号版本更精确，但在七年级通常只要求你写出词汇方程，并解释光能被叶绿体中的叶绿素吸收。配平的符号方程 (6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂) 往往以后才会学到，但理解这个词汇模型现在就为你打下基础。
4. Respiration Word Equations | 呼吸作用词汇方程
Respiration releases energy for life processes from the breakdown of glucose. The two types you need to know are aerobic respiration (using oxygen) and anaerobic respiration (without oxygen). The word equations are different.
呼吸作用通过分解葡萄糖为生命活动释放能量。你需要了解的两种类型是有氧呼吸（使用氧气）和无氧呼吸（不使用氧气）。它们的词汇方程不同。
Aerobic respiration / 有氧呼吸
Glucose + Oxygen → Carbon dioxide + Water + Energy (ATP)
葡萄糖 + 氧气 → 二氧化碳 + 水 + 能量 (ATP)
Aerobic respiration happens continuously in most cells and provides a large amount of energy. It is why we breathe in oxygen and breathe out carbon dioxide.
有氧呼吸在大多数细胞中持续进行，并提供大量能量。这就是我们吸入氧气并呼出二氧化碳的原因。
Anaerobic respiration in animals / 动物中的无氧呼吸
Glucose → Lactic acid + Energy
葡萄糖 → 乳酸 + 能量
This occurs in muscles during vigorous exercise when oxygen supply cannot keep up with demand. Lactic acid build‑up causes muscle fatigue and can lead to cramp, but it is removed once extra oxygen becomes available again.
这种情况发生在剧烈运动时，当氧气供应跟不上需求时，肌肉中就会进行无氧呼吸。乳酸堆积会引起肌肉疲劳甚至抽筋，但当额外氧气再次可用时，乳酸会被清除。
Anaerobic respiration in plants and yeast / 植物与酵母的无氧呼吸
Glucose → Ethanol + Carbon dioxide + Energy
葡萄糖 → 乙醇 + 二氧化碳 + 能量
This version is important in fermentation, used to make bread and alcoholic drinks. The carbon dioxide makes bread rise, and the ethanol gives alcoholic beverages their character.
这个形式在发酵中很重要，用于制作面包和酒精饮料。二氧化碳使面包膨胀，乙醇赋予酒精饮料独特的风味。
5. The 10% Energy Rule in Food Chains | 食物链中的 10% 能量规则
When energy is transferred from one trophic level to the next, only about 10% of the energy is passed on. The rest is lost as heat from respiration, excreted as waste, or used in movement and growth that is not eaten by the next consumer.
当能量从一个营养级传递到下一个营养级时，只有大约 10% 的能量被传递下去。其余的以呼吸产热的形式散失、作为废物排出，或用于不被下一消费者食用的运动和生长。
This principle explains why food chains are usually short – there simply isn't enough energy to support many trophic levels. For example, 1000 kJ of energy in grass might support only about 100 kJ in a herbivore, and 10 kJ in a carnivore that eats the herbivore.
这一原理解释了为什么食物链通常很短——根本没有足够的能量支撑多个营养级。例如，草中 1000 kJ 的能量可能只会在食草动物中支撑约 100 kJ，而在以该食草动物为食的肉食动物中仅剩约 10 kJ。
You can use a simple energy pyramid or rule‑of‑thumb calculation:
你可以使用简单的能量金字塔或经验计算公式：
Energy at next level ≈ Energy at current level × 0.1
下一级的能量 ≈ 当前级的能量 × 0.1
6. Population Growth Formula | 种群增长公式
In ecology, population change can be modelled by looking at births, deaths and migration. The basic formula is:
在生态学中，种群变化可通过观察出生、死亡与迁移来建模。基本公式为：
Population change = (Births – Deaths) + (Immigration – Emigration)
种群变化 = (出生数 – 死亡数) + (迁入数 – 迁出数)
If the number of births plus immigrants is greater than the number of deaths plus emigrants, the population grows. If it is smaller, the population shrinks. This formula can be applied to any species, from bacteria in a flask to rabbits in a field.
如果出生数与迁入数之和大于死亡数与迁出数之和，则种群增长；反之则种群萎缩。这个公式适用于任何物种，从烧瓶里的细菌到田野里的兔子皆如此。
Year 7 often looks at simple predator‑prey cycles where the populations of foxes and rabbits, for example, rise and fall in a linked pattern. The formula helps students see that populations do not just magically increase – they are driven by measurable rates.
七年级通常会观察简单的捕食者-猎物周期，例如狐狸和兔子的数量呈现出联动的升降规律。这个公式帮助学生理解，种群数量并非凭空增长，而是由可衡量的比率驱动的。
7. Estimating Population Size by Sampling | 通过取样估计种群大小
When you cannot count every organism in a habitat, you can use quadrats to sample. The estimation formula is:
当你无法数清栖息地中的每一个生物时，可以使用样方进行取样。估算公式为：
mated population = (Mean number per quadrat ÷ Area of one quadrat) × Total area of habitat
估计种群数 = (每个样方的平均数量 ÷ 单个样方面积) × 栖息地总面积
ed daisy population = (12 ÷ 0.5) × 200 = 24 × 200 = 4800 daisies. Remember to use random sampling and put the quadrat in several positions to get a reliable mean.
例如，若你随机投掷一个 0.5 m² 的样方若干次，计算每次放样中雏菊的平均数量为 12 朵，而整片田地面积为 200 m²，则估计雏菊数量 = (12 ÷ 0.5) × 200 = 24 × 200 = 4800 朵。记得采用随机取样并在多个位置放置样方，以获得可靠的平均值。
8. Diffusion Rate Principles | 扩散速率原理
Diffusion is the net movement of particles from a region of higher concentration to a region of lower concentration. While there is no single formula required at Year 7, the rate of diffusion is influenced by three main factors that you can think of as a relationship:
扩散是粒子从高浓度区域向低浓度区域净移动的过程。虽然在七年级不要求记忆单一的公式，但扩散速率受三个主要因素影响，你可以把它们看作一种关系：
Rate of diffusion ∝ (Surface area × Concentration difference) ÷ Diffusion distance
扩散速率 ∝ (表面积 × 浓度差) ÷ 扩散距离
This means diffusion is faster when the surface area is larger, the concentration gradient is steeper, and the distance particles must travel is shorter. This explains why alveoli in the lungs are tiny and numerous, with very thin walls – they maximise surface area and minimise the diffusion distance for oxygen and carbon dioxide.
这意味着，当表面积更大、浓度梯度更陡峭且粒子需要穿行的距离更短时，扩散速率更快。这就解释了为什么肺中的肺泡又小又多，而且壁极薄——它们最大化了表面积，并把氧气和二氧化碳的扩散距离降至最低。
9. Transpiration Rate Calculation | 蒸腾速率计算
Transpiration is the loss of water vapour from the leaves of a plant. Using a potometer, you can estimate the rate of water uptake, which closely follows transpiration rate under controlled conditions. The calculation is straightforward:
蒸腾作用是植物叶片散失水蒸气的过程。使用蒸腾计，你可以估算吸水速率，在受控条件下该速率与蒸腾速率密切相关。计算方法很简单：
Transpiration rate = Distance moved by air bubble ÷ Time taken
蒸腾速率 = 气泡移动的距离 ÷ 所用时间
es, the rate is 24 ÷ 30 = 0.8 mm per minute. You can then compare how different conditions – light, wind, humidity – . Typically, bright light and wind increase transpiration, while high humidity reduces it.
如果气泡在 30 分钟内移动了 24 mm，则速率为 24 ÷ 30 = 0.8 mm 每分钟。接着你可以比较不同条件——光照、风、湿度——如何影响该速率。通常情况下，强光和风会加快蒸腾作用，而高湿度则会减缓它。
10. Simple Genetic Ratios from Monohybrid Crosses | 单因子杂交的简单遗传比例
When you study inheritance, you use Punnett squares to predict the probability of offspring having certain traits. In Year 7 WJEC, you are likely to meet the 3:1 ratio and the 1:1 ratio from single‑gene crosses with dominant and recessive alleles.
当你学习遗传学时，会使用庞纳特方格预测后代具有某些性状的概率。在七年级 WJEC 课程中，你很可能会遇到由显性和隐性等位基因控制的单基因杂交所产生的 3:1 比例和 1:1 比例。
- Monohybrid cross between two heterozygous parents (e.g., Bb × Bb): the expected phenotype ratio is 3 dominant : 1 recessive. This is Mendel's famous ratio.
- 两个杂合亲本的单因子杂交（例如 Bb × Bb）：预期的表型比例为 3 显性 : 1 隐性。这就是孟德尔著名的比例。
- Monohybrid cross between a heterozygous and a homozygous recessive individual (Bb × bb): the expected phenotype ratio is 1 dominant : 1 recessive. This is sometimes called a test cross ratio.
- 一个杂合个体与一个纯合隐性个体的单因子杂交 (Bb × bb)：预期的表型比例为 1 显性 : 1 隐性。这有时被称为测交比例。
It is important to remember that these ratios are probabilities, not guarantees. In a small family, the observed numbers might not match exactly. But over many offspring, the patterns become clear.
重要的是要记住，这些比例是概率而非保证。在较小的家庭中，观察到的数字可能不完全匹配。但在大量后代中，规律就会显现出来。
11. Heart Rate and Exercise Recovery | 心率与运动恢复
Although not a formula in the strict mathematical sense, the relationship between physical effort and heart rate is a key idea. You can calculate your recovery heart rate to see how quickly the body returns to resting conditions after exercise.
虽然严格来说不算是数学公式，但体力付出与心率之间的关系是一个关键概念。你可以计算自己的恢复心率，了解运动后身体恢复到静息状态的速度。
Recovery heart rate = Heart rate just after exercise – Heart rate after rest period
恢复心率 = 运动刚结束后的心率 – 休息一段时间后的心率
A common simple investigation: measure heart rate immediately after two minutes of stepping exercise, then again after two minutes of rest. The bigger the drop, the quicker the recovery, which is a sign of good fitness. This links back to aerobic respiration – a fitter person delivers oxygen to muscles more efficiently and removes lactic acid faster.
一个常见的简单探究是：在两分钟踏步运动后立即测量心率，然后在休息两分钟后再次测量。下降的幅度越大，恢复得越快，这是良好体能的标志。这与有氧呼吸联系紧密——体能更好的人能更有效地向肌肉输送氧气，并更快地清除乳酸。
12. Energy Calculation from Food | 食物中的能量计算
In nutrition and digestion topics, you may carry out a food burning experiment to compare the energy content of different foods. The energy transferred to water can be estimated using the idea of specific heat capacity, although you are not expected to use the full equation in Year 7. A simplified version is often introduced:
在营养与消化专题中，你可能会进行食物燃烧实验来比较不同食物的能量含量。传递给水的能量可以利用比热容的概念来估算，不过在七年级并不要求使用完整的公式，通常会引入简化版本：
Energy (J) ≈ 4.2 J/g°C × mass of water (g) × temperature rise (°C)
能量 (焦耳) ≈ 4.2 J/g°C × 水的质量 (克) × 上升温度 (°C)
= 6300 J. This energy came from the food sample, and you can compare how much of the food' nergy per gram. This experiment links to the idea that food provides fuel for respiration.
例如，如果 50 克水温从 20 °C 升高到 50 °C，所吸收的能量约为 4.2 × 50 × 30 = 6300 J。这一能量来自食物样品，你可以比较燃烧掉的食品质量，计算出每克食物所含的能量。该实验联系到食物为呼吸作用提供燃料的概念。
Year 7 students are expected to describe the method, identify variables, and understand that a lot of energy is lost to the surroundings, making the result lower than the true energy content shown on food labels.
七年级学生应能描述实验方法，识别变量，并理解大量能量会散失到周围环境中，导致结果低于食物标签上标示的真实能量含量。
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