Year 11 AQA Biology: Formula & Key Concepts Quick Reference | AQA 生物：公式定理速查手册

📚 Year 11 AQA Biology: Formula & Key Concepts Quick Reference | AQA 生物：公式定理速查手册

This article distils the essential equations, principles and numerical relationships you must master for the AQA GCSE Biology exams. From magnification and microscopy conversions to cardiac output, BMI, diffusion principles and energy‑transfer efficiency – every formula is presented with worked‑style explanation and paired bilingual commentary to strengthen your recall and application skills.

本文提炼了AQA GCSE 生物学考试必须掌握的核心公式、原理和数量关系。从放大倍率与显微镜单位换算，到心输出量、BMI、扩散原理以及能量传递效率，每一项公式都配以解析式说明和双语对照讲解，帮助你强化记忆与运用能力。

1. Magnification & Image Size | 放大倍数与图像尺寸

Magnification describes how many times larger an image appears compared to the real object. The relationship is captured by the equation: Magnification = Image size ÷ Actual size. Rearrange as needed: Actual size = Image size ÷ Magnification, or Image size = Magnification × Actual size. Always ensure both sizes are in the same unit before calculating.

放大倍数表示图像与实际物体相比放大了多少倍。三者关系由公式概括：放大倍数 = 图像尺寸 ÷ 实际尺寸。可按需变形：实际尺寸 = 图像尺寸 ÷ 放大倍数，或图像尺寸 = 放大倍数 × 实际尺寸。计算前务必统一单位。

• No units are attached to magnification – it is a pure number.
• 放大倍数没有单位，是一个纯数值。

M = I / A

2. Microscopy Unit Conversions | 显微镜单位换算

Microscope measurements frequently move between millimetres (mm), micrometres (µm) and nanometres (nm). The conversion factors are: 1 mm = 1000 µm, 1 µm = 1000 nm. Therefore, 1 mm = 1 000 000 nm. When substituting into the magnification formula, convert all lengths to the smallest unit or to the same unit first.

显微镜测量常需在毫米（mm）、微米（µm）和纳米（nm）之间转换。换算关系为：1 mm = 1000 µm，1 µm = 1000 nm。因此 1 mm = 1 000 000 nm。代入放大公式前，先将所有长度统一成相同单位（通常为最小单位）。

• To convert mm → µm, multiply by 1000.
• 毫米转换为微米，乘以 1000。
• To convert µm → mm, divide by 1000.
• 微米转换为毫米，除以 1000。

1 mm

= 1 000 µm

= 1 000 000 nm

3. Enzyme Activity & Rate of Reaction | 酶活性与反应速率

The rate of an enzyme‑catalysed reaction can be expressed as: Rate = Change in product (or substrate) ÷ Time. For example, if 10 cm³ of oxygen is produced in 50 seconds, the rate is 10 ÷ 50 = 0.2 cm³/s. Units must match the measured quantity per unit time, e.g. cm³/s, g/min.

酶催化反应的速率可表示为：速率 = 产物（或底物）变化量 ÷ 时间。例如，若 50 秒内产生 10 cm³ 氧气，则速率为 10 ÷ 50 = 0.2 cm³/s。单位须与测量量匹配，如 cm³/s、g/min。

Temperature and pH affect shape of the active site. The Q₁₀ temperature coefficient is not formally required at GCSE but you can describe it qualitatively: rate roughly doubles for every 10 °C rise until the enzyme denatures.

温度与 pH 会影响活性位点构象。Q₁₀ 温度系数在 GCSE 不作定量要求，但可定性描述：在酶变性前，温度每升高 10 °C，反应速率大致翻倍。

Rate = Quantity ÷ Time

4. Photosynthesis Equation & Factors | 光合作用方程与影响因素

The word equation: carbon dioxide + water → glucose + oxygen. The balanced symbol equation: 6 CO₂ + 6 H₂O → C₆H₁₂O₆ + 6 O₂, driven by light energy absorbed by chlorophyll. Light intensity, CO₂ concentration and temperature are limiting factors; the rate is governed by the factor in shortest supply.

文字方程：二氧化碳 + 水 → 葡萄糖 + 氧气。平衡符号方程：6 CO₂ + 6 H₂O → C₆H₁₂O₆ + 6 O₂，由叶绿素吸收光能驱动。光照强度、二氧化碳浓度和温度是限制因素；反应速率由最不足的因素决定。

For practical measurement, you can calculate rate of photosynthesis as oxygen production (e.g. number of bubbles per minute or volume of gas per minute).

在实际测量中，可用氧气产量（如每分钟气泡数或每分钟气体体积）计算光合作用速率。

6 CO₂ + 6 H₂O → C₆H₁₂O₆ + 6 O₂

5. Aerobic & Anaerobic Respiration Equations | 有氧与无氧呼吸方程

Aerobic respiration: glucose + oxygen → carbon dioxide + water (+ energy). Symbol: C₆H₁₂O₆ + 6 O₂ → 6 CO₂ + 6 H₂O. Energy is released as ATP.

有氧呼吸：葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）。符号：C₆H₁₂O₆ + 6 O₂ → 6 CO₂ + 6 H₂O。能量以 ATP 形式释放。

Anaerobic respiration in animals: glucose → lactic acid (+ energy). In plants and yeast (fermentation): glucose → ethanol + carbon dioxide (+ energy). Lactic acid causes muscle fatigue; ethanol has industrial uses.

动物体内的无氧呼吸：葡萄糖 → 乳酸（+ 能量）。植物和酵母（发酵）：葡萄糖 → 乙醇 + 二氧化碳（+ 能量）。乳酸导致肌肉疲劳；乙醇有工业用途。

C₆H₁₂O₆ + 6 O₂ → 6 CO₂ + 6 H₂O

Animals: glucose → lactic acid

Fermentation: glucose → ethanol + CO₂

6. Cardiac Output & Heart Rate | 心输出量与心率

Cardiac output is the volume of blood pumped by the heart per minute. It equals the stroke volume (volume per beat) multiplied by heart rate: Cardiac output (cm³/min) = Stroke volume (cm³/beat) × Heart rate (beats/min). Typical resting values: stroke volume ~70 cm³, heart rate ~70 bpm, giving cardiac output ~4900 cm³/min.

心输出量是心脏每分钟泵出的血液体积，等于每搏输出量（每次心跳泵血量）乘以心率：心输出量（cm³/min）= 每搏输出量（cm³/次）× 心率（次/分）。安静时的典型值：每搏输出量约 70 cm³，心率约 70 bpm，得心输出量约 4900 cm³/min。

You can rearrange to find stroke volume if cardiac output and heart rate are known.

若已知心输出量和心率，可变形求出每搏输出量。

CO = SV × HR

7. Body Mass Index (BMI) | 身体质量指数

BMI is a simple indicator of healthy weight status. It is calculated as: BMI = Mass (kg) ÷ Height² (m²). The result is expressed in kg/m². For adults, a BMI between 18.5 and 24.9 is considered healthy; below 18.5 is underweight, 25‑29.9 overweight, and 30 or above obese. Note – BMI does not distinguish between muscle and fat, so it has limitations.

BMI 是反映体重健康状态的简易指标，公式为：BMI = 体重（kg）÷ 身高²（m²），单位 kg/m²。对成人而言，BMI 在 18.5–24.9 为健康范围；低于 18.5 为过轻，25–29.9 为超重，≥30 为肥胖。注意，BMI 无法区分肌肉与脂肪，因此存在局限。

BMI = weight (kg) / [height (m)]²

8. Diffusion – Fick’s Law Principles | 扩散 – 菲克定律原理

Fick’s law describes the factors affecting the rate of diffusion across a membrane: Rate of diffusion ∝ (Surface area × Concentration difference) ÷ Thickness of membrane. A larger surface area, a steeper concentration gradient, and a thinner exchange surface all increase the rate. This principle explains why exchange organs are adapted with folded membranes, a rich blood supply, and very thin walls.

菲克定律说明影响扩散速率的因素：扩散速率 ∝（表面积 × 浓度差）÷ 扩散距离。更大的表面积、更陡的浓度梯度和更薄的交换表面都会提高扩散速率。这一原理解释了气体交换器官为何具有褶皱膜、丰富血供和极薄的壁。

Rate ∝ (SA × ΔC) / distance

9. Sampling & Population Estimation | 取样与种群估算

For sessile organisms, quadrats provide an estimate of population size: Estimated population = (Mean count per quadrat) × (Total area ÷ Quadrat area). For motile organisms, the capture‑mark‑recapture method uses: Estimated population = (Number in first sample × Number in second sample) ÷ Number of marked individuals recaptured. These are estimates only; assumptions must be stated, e.g. no migration, no births/deaths between samples.

对于固着生物，样方估算种群数量：估计种群数 =（每个样方平均数量）×（总面积 ÷ 样方面积）。对于活动生物，采用捉放法：估计种群数 =（第一次捕捉数 × 第二次捕捉数）÷ 第二次中已标记个体数。这些都只是估计值，须说明假设条件，如样本间无迁移、无出生死亡等。

N = (n₁ × n₂) / m

10. Energy Transfer & Efficiency | 能量传递与效率

As energy flows through an ecosystem, only a fraction is transferred from one trophic level to the next. Efficiency of energy transfer = (Energy in the higher trophic level ÷ Energy in the lower trophic level) × 100. Typical efficiency is around 10%. Losses occur through respiration, waste, uneaten parts and heat.

能量流经生态系统时，只有一小部分从某一营养级传递到下一级。能量传递效率 =（较高营养级的能量 ÷ 较低营养级的能量）× 100。典型的传递效率约 10%。能量因呼吸、排泄、未食部分和散热而损失。

Efficiency (%) = (E_out / E_in) × 100

11. Bacterial Growth Calculations | 细菌生长计算

Bacteria reproduce by binary fission; under ideal conditions population doubles every division time. The number of bacteria after n divisions = Starting number × 2ⁿ. For example, starting with 1 bacterium, after 6 divisions you have 2⁶ = 64. You may need to calculate divisions from elapsed time: n = Total time ÷ Division time.

细菌通过二分裂繁殖，理想条件下每隔一个分裂时间数量翻倍。n 次分裂后细菌数 = 起始数量 × 2ⁿ。例如，起始 1 个细菌，经 6 次分裂得 2⁶ = 64 个。可能需要根据经过时间求分裂次数：n = 总时间 ÷ 分裂时间。

Final number = initial × 2ⁿ

12. Osmosis & Water Potential | 渗透与水势

Osmosis is the net movement of water molecules from a region of higher water potential to a region of lower water potential through a partially permeable membrane. Pure water has the highest water potential (set at 0 kPa); adding solute lowers water potential (more negative values). Water potential is a key concept when predicting water movement in plant and animal cells.

渗透是水分子通过部分透性膜从水势较高区域向水势较低区域的净移动。纯水的水势最高（设为 0 kPa）；加入溶质会降低水势（越负越低）。在预测动植物细胞的水分移动时，水势是一个关键概念。

• Turgor pressure develops when a plant cell is placed in a hypotonic solution; water enters by osmosis.
• 植物细胞置于低渗溶液中产生膨压，水分通过渗透流入。
• Animal cells may burst (lysis) if too much water enters.
• 动物细胞若吸水过多可能胀破（溶血）。

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