📚 Year 8 OCR Biology: Quick Reference Handbook of Formulas and Theorems | 八年级OCR生物：公式定理速查手册
This handbook collects the key formulas, equations and principles you need to revise for Year 8 OCR Biology. Use it as a rapid check when you tackle magnification questions, energy transfers or genetic crosses. Each section gives you the essential fact in bold, followed by a clear explanation.
本手册汇集八年级OCR生物需要复习的关键公式、方程和原理。当你要处理放大倍率、能量传递或遗传杂交问题时，可以用它快速查阅。每个小节先给出核心事实，再用简洁的文字加以解释。
1. Magnification Formula | 放大倍率公式
The magnification of a microscope image tells how many times larger the image appears compared to the real specimen.
显微镜图像的放大倍率表示图像比实际样本大多少倍。
Magnification = Image size / Actual size (M = I / A)
You can rearrange the formula using the triangle method: cover the quantity you want to find; I = M x A, A = I / M.
你可以用三角法转换公式：盖住想求的量；I = M × A，A = I ÷ M。
- Image size is measured in millimetres (mm) or micrometres (µm) – make sure units match.
- 图像大小以毫米或微米为单位——务必统一单位。
- Always convert so that image size and actual size share the same unit before calculating.
- 计算前必须将图像大小和实际大小转换为相同单位。
| Example | Calculation |
| Image size = 20 mm, actual size = 0.1 mm | M = 20 / 0.1 = 200 × |
If the answer is less than 1, you are looking at a reduction, not a magnification.
若答案小于1，则表示缩小而非放大。
2. Unit Conversions in Microscopy | 显微镜单位换算
Microscope measurements use millimetres (mm), micrometres (µm) and nanometres (nm). Always convert to the same unit before using the magnification formula.
显微镜测量使用毫米、微米和纳米。代入放大公式前必须统一单位。
1 mm = 1000 µm 1 µm = 1000 nm
To convert mm to µm, multiply by 1000; to convert µm to mm, divide by 1000.
毫米换算成微米乘以1000，微米换算为毫米除以1000。
| From | To | Operation |
| mm | µm | × 1000 |
| µm | mm | ÷ 1000 |
| µm | nm | × 1000 |
A typical plant cell is about 0.1 mm long, which is 100 µm. An organelle like a mitochondrion is about 1 µm, or 1000 nm, across.
典型植物细胞长约0.1 mm，即100 µm；线粒体等细胞器直径约1 µm，即1000 nm。
3. Surface Area to Volume Ratio | 表面积与体积比
As an organism (or a cube of agar) gets larger, its volume grows faster than its surface area. The surface area to volume ratio decreases.
生物体（或琼脂块）越大，其体积增长快于表面积，表面积与体积之比下降。
SA : V = Surface Area / Volume
For a cube of side length L: Surface area = 6L², Volume = L³, so SA:V = 6 / L.
对于边长为 L 的立方体：表面积 = 6L²，体积 = L³，故 SA:V = 6 / L。
A small cube (L = 1 cm) has a large SA:V (6:1); a large cube (L = 3 cm) has SA:V = 2:1. This affects how quickly substances diffuse in and out.
小立方体 (L = 1 cm) 的 SA:V 大 (6:1)；大立方体 (L = 3 cm) 的 SA:V 为 2:1，这影响物质进出扩散的速度。
Living things rely on a high SA:V for efficient exchange of oxygen, nutrients and waste. Single-celled organisms can rely on diffusion alone, while larger organisms need specialised exchange surfaces and transport systems.
生物依靠高SA:V 高效交换氧气、营养和废物。单细胞生物仅靠扩散即可，而较大生物需要特化的交换表面和运输系统。
4. Photosynthesis Equations | 光合作用方程式
Photosynthesis converts light energy into chemical energy stored in glucose. It takes place in chloroplasts.
光合作用将光能转化为储存在葡萄糖中的化学能，发生在叶绿体内。
Word equation:
文字方程式：
Carbon dioxide + Water → Glucose + Oxygen
(Light energy absorbed by chlorophyll is required)
（需要叶绿素吸收的光能）
Symbol equation:
符号方程式：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Glucose provides energy for respiration and can be converted into starch, cellulose or other substances.
葡萄糖为呼吸作用提供能量，并可转化为淀粉、纤维素等物质。
5. Aerobic Respiration Equations | 有氧呼吸方程式
Aerobic respiration releases energy from glucose using oxygen. It happens continuously in all living cells, mostly in mitochondria.
有氧呼吸利用氧气从葡萄糖中释放能量，在所有活细胞中持续进行，主要在线粒体中发生。
Word equation:
文字方程式：
Glucose + Oxygen → Carbon dioxide + Water (+ energy)
Symbol equation:
符号方程式：
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
The energy released is used for muscle contraction, keeping warm, active transport and building new molecules.
释放的能量用于肌肉收缩、保温、主动运输以及合成新分子。
6. Anaerobic Respiration | 无氧呼吸
When oxygen is insufficient, cells can respire anaerobically to release a smaller amount of energy quickly.
当氧气不足时，细胞可进行无氧呼吸，快速释放少量能量。
In animals:
在动物体内：
Glucose → Lactic acid (+ energy)
Lactic acid builds up in muscles, causing fatigue and cramps; it is later broken down when oxygen is available (oxygen debt).
乳酸在肌肉中积累导致疲劳和痉挛；待氧气充足时可被分解（氧债）。
In yeast (fermentation):
在酵母中（发酵）：
Glucose → Ethanol + Carbon dioxide (+ energy)
This reaction is used in baking (CO₂ makes dough rise) and brewing (ethanol production).
该反应用于烘焙（CO₂ 使面团膨胀）和酿造（生产乙醇）。
7. Energy Transfer in Food Chains (10% Rule) | 食物链中的能量传递 (10%法则)
At each trophic level in a food chain, only about 10% of the energy is transferred to the next level. The rest is lost as heat, movement, undigested material and waste.
食物链中每一营养级仅有约10%的能量传递至下一级，其余以热、运动、未消化物质和排泄物等形式散失。
Energy available to next level ≈ 0.10 × Energy at current level
This limits the length of food chains – rarely more than 4 or 5 trophic levels because there is insufficient energy to support further levels.
这限制了食物链的长度——通常不超过4到5个营养级，因为能量不足以支撑更多层级。
| Trophic level | Energy left (example in kJ) |
| Producer (grass) | 10 000 |
| Primary consumer (rabbit) | 1 000 |
| Secondary consumer (fox) | 100 |
| Tertiary consumer (eagle) | 10 |
8. Pyramids of Biomass | 生物量金字塔
A pyramid of biomass shows the total dry mass of living material at each trophic level. Because of energy loss, the biomass almost always decreases from producers upwards.
生物量金字塔表示每一营养级的生物干重总量。由于能量损失，生物量几乎总是从生产者向上一级递减。
The pyramid is always drawn to scale, with the producer bar at the bottom being the widest. In some aquatic ecosystems, the pyramid of numbers may appear inverted, but the pyramid of biomass still shows a decrease.
金字塔按比例绘制，底部生产者条最宽。在某些水生生态系统中数量金字塔可能倒置，但生物量金字塔依然递减。
Biomass at level n ≈ 0.10 × Biomass at level (n-1)
You can use the 10% rule to estimate biomass and explain why fewer predators can be supported.
你可以用10%法则估算生物量，并解释为何能支撑的捕食者更少。
9. Enzyme Activity and Temperature | 酶活性与温度
Enzymes are biological catalysts that speed up reactions. Their activity depends strongly on temperature.
酶是生物催化剂，能加速反应，其活性强烈依赖温度。
- At low temperatures, molecules move slowly and fewer enzyme-substrate collisions occur – activity is low.
- 低温下分子运动慢，酶–底物碰撞少——活性低。
- As temperature rises, activity increases until it reaches an optimum (usually around 37 °C for human enzymes).
- 随温度升高，活性增加直至达到最适温度（人体酶约37 °C）。
- Above the optimum, the enzyme’s active site denatures (changes shape), so the substrate no longer fits – activity drops sharply and irreversibly.
- 超过最适温度，酶活性部位变性（形状改变），底物不再契合——活性急剧且不可逆地下降。
Rate of reaction ∝ collision frequency (up to optimum)
This principle applies to all enzymes, including those in digestion and photosynthesis.
这一原理适用于所有酶，包括消化和光合作用中的酶。
10. Punnett Squares and Genetic Ratios | 旁氏表与遗传比例
A Punnett square predicts the possible genotypes of offspring when two parents are crossed for a single gene (monohybrid cross).
旁氏表可预测单基因杂交时（单因子杂交）后代可能的基因型。
For a gene with two alleles, dominant (B) and recessive (b): if both parents are heterozygous (Bb), the Punnett square gives genotype ratios:
对一个具有显性 (B) 和隐性 (b) 等位基因的基因，若双亲均为杂合 (Bb)，旁氏表给出的基因型比为：
BB : Bb : bb = 1 : 2 : 1
The phenotype ratio for a completely dominant trait is:
完全显性性状的表型比为：
Dominant phenotype : Recessive phenotype = 3 : 1
If one parent is homozygous dominant (BB) and the other homozygous recessive (bb), all offspring are Bb (100% dominant phenotype).
若一方为纯合显性 (BB)，另一方为纯合隐性 (bb)，所有后代均为 Bb（100% 显性表型）。
Probabilities can be expressed as fractions, decimals or percentages. A Punnett square shows the chance of each outcome per fertilisation.
概率可用分数、小数或百分数表示。旁氏表显示每次受精出现某种结果的机会。
11. Calculating Percentage Change | 百分比变化计算
In biology experiments (e.g. osmosis in potato chips, measuring enzyme activity), you often need to find the percentage change in mass or length.
在生物实验（如马铃薯渗透实验、酶活性测定）中，常需计算质量或长度的百分比变化。
Percentage change = (Final value – Initial value) / Initial value × 100%
A positive result means an increase; a negative result means a decrease. Always subtract the initial value from the final value.
正值表示增加，负值表示减少。永远用终值减去初值。
| Initial mass | Final mass | Change |
| 5.0 g | 6.2 g | ((6.2 – 5.0) / 5.0) × 100% = +24% |
| 5.0 g | 4.6 g | ((4.6 – 5.0) / 5.0) × 100% = –8% |
Using percentage change makes it easier to compare results when the starting values differ.
当初始值不同时，利用百分比变化更易比较结果。
12. Factors Affecting Diffusion | 影响扩散的因素
Diffusion is the net movement of particles from a region of higher concentration to a region of lower concentration. The rate of diffusion is described by three key factors, captured in the relationship:
扩散是粒子从高浓度区域向低浓度区域的净移动。其速率可用三个关键因素描述，概括为以下关系：
Rate ∝ (Surface area × Concentration difference) / Diffusion distance
- Surface area – a larger surface allows more particles to cross at once (e.g. alveoli in lungs).
- 表面积 – 表面积越大，同时通过的粒子越多（如肺的肺泡）。
- Concentration gradient – a steeper gradient makes diffusion faster.
- 浓度梯度 – 梯度越陡，扩散越快。
- Diffusion distance – the thinner the barrier, the shorter the distance and the quicker the diffusion.
- 扩散距离 – 屏障越薄，距离越短，扩散越快。
Temperature also increases the kinetic energy of particles, speeding up diffusion.
温度增加粒子的动能，也会加快扩散。
These principles explain why organisms have adaptations such as flattened leaves, extensive root hairs and thin exchange surfaces.
这些原理解释了为何生物具有扁平叶片、大量根毛和薄交换面等适应性特征。
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