GCSE OCR Biology: Calculation Practice Questions | GCSE OCR 生物：计算题专项训练

📚 GCSE OCR Biology: Calculation Practice Questions | GCSE OCR 生物：计算题专项训练

Calculations are a key part of the GCSE OCR Biology specification. From magnification to enzyme rates and population estimates, mastering these skills will boost your exam confidence.

计算是 GCSE OCR 生物学考试的关键部分。从放大倍数到酶反应速率和种群估算，掌握这些技能将提升你的考试信心。

1. Magnification and Size Calculations | 放大倍率和尺寸计算

Magnification = Image size ÷ Actual size

The magnification formula relates the size of an image to the actual size of the specimen. Both values must have exactly the same unit before you substitute them into the equation.

放大倍数公式将图像大小与标本的实际大小联系起来。两数值在代入公式前必须使用完全相同的单位。

Unit conversions are crucial: 1 mm = 1000 µm; 1 µm = 1000 nm. For example, 0.02 mm = 0.02 × 1000 = 20 µm. Write very small numbers in standard form, e.g. 0.001 mm = 1×10⁻³ mm.

单位换算至关重要：1 mm = 1000 µm；1 µm = 1000 nm。例如，0.02 mm = 0.02 × 1000 = 20 µm。将极小的数字写成标准形式，如 0.001 mm = 1×10⁻³ mm。

Worked example: A photograph shows a mitochondrion with an image length of 30 mm. The actual length is 6 µm. First convert 30 mm to µm: 30 mm = 30 × 1000 = 30000 µm. Then Magnification = 30000 µm ÷ 6 µm = ×5000.

例题：一张照片显示一个线粒体，图像长度为 30 mm。实际长度为 6 µm。首先将 30 mm 转换为 µm：30 mm = 30 × 1000 = 30000 µm。然后放大倍数 = 30000 µm ÷ 6 µm = ×5000。

To find actual size, rearrange the formula: Actual size = Image size ÷ Magnification. If the magnification is ×400 and the image measures 12 mm, actual size = 12 mm ÷ 400 = 0.03 mm, which is 30 µm.

求实际大小时，重新排列公式：实际大小 = 图像大小 ÷ 放大倍数。如果放大倍数为 ×400，图像大小为 12 mm，则实际大小 = 12 mm ÷ 400 = 0.03 mm，即 30 µm。

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2. Rate of Enzyme-Controlled Reactions | 酶控反应速率计算

Rate = Quantity of product formed ÷ Time taken

Enzyme reactions are often followed by measuring the volume of gas produced, mass lost, or colour change. Always match the units to the readout – cm³ for volume, g for mass.

酶反应通常通过测量产生的气体体积、质量损失或颜色变化来追踪。单位需与读数匹配 —— 体积用 cm³，质量用 g。

Example: 45 cm³ of oxygen is produced in 5 minutes. Rate = 45 cm³ ÷ 5 min = 9 cm³/min. If the question asks for the rate in cm³/s, divide again by 60: 9 ÷ 60 = 0.15 cm³/s.

例题：5 分钟内产生 45 cm³ 氧气。速率 = 45 cm³ ÷ 5 min = 9 cm³/min。如果题目要求以 cm³/s 表示速率，再除以 60：9 ÷ 60 = 0.15 cm³/s。

When plotting a graph of volume against time, the initial rate is found from the steepest straight section. Pick two well-separated points on that section, calculate (change in volume) ÷ (change in time).

绘制体积-时间图像时，从最陡的直线部分求初始速率。在该部分取两个相距较远的点，计算 (体积变化) ÷ (时间变化)。

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3. Rate of Oxygen Production in Photosynthesis | 光合作用产氧速率计算

Rate = Volume of O₂ produced ÷ Time

In the classic pondweed (Elodea) practical, the number of bubbles per minute gives a quick estimate, but a gas syringe provides more reliable volume data. The same rate formula applies.

在经典的水生植物（伊乐藻）实验中，每分钟气泡数可快速估算，但气体注射器能提供更可靠的体积数据。相同的速率公式适用。

If 2.4 cm³ of oxygen is collected in 8 minutes, rate = 2.4 ÷ 8 = 0.3 cm³/min. To express this in mm³/min, multiply by 1000: 0.3 × 1000 = 300 mm³/min.

如果 8 分钟内收集到 2.4 cm³ 氧气，速率 = 2.4 ÷ 8 = 0.3 cm³/min。若用 mm³/min 表示，乘以 1000：0.3 × 1000 = 300 mm³/min。

Exam questions often link the rate to limiting factors. A graph that rises quickly and then plateaus suggests a limiting factor such as carbon dioxide or light intensity.

考题常将速率与限制因素联系起来。快速上升后趋于平缓的曲线暗示存在限制因素，如二氧化碳浓度或光照强度。

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4. Heart Rate and Cardiac Output | 心率和心输出量计算

Cardiac Output = Heart Rate × Stroke Volume

Cardiac output is the volume of blood pumped by one ventricle each minute. Heart rate is in beats per minute (bpm) and stroke volume is usually in ml per beat. Cardiac output is then expressed in ml/min or L/min.

心输出量是一个心室每分钟泵出的血液量。心率单位为次/分钟 (bpm)，每搏输出量通常以 ml/次给出。心输出量则以 ml/min 或 L/min 表示。

Worked example: Heart rate = 75 bpm, stroke volume = 80 ml. Cardiac output = 75 × 80 = 6000 ml/min. To convert to litres, divide by 1000: 6.0 L/min.

例题：心率 = 75 bpm，每搏输出量 = 80 ml。心输出量 = 75 × 80 = 6000 ml/min。转换为升，除以 1000：6.0 L/min。

If a question gives cardiac output and one other variable, rearrange: Stroke volume = Cardiac output ÷ Heart rate, or Heart rate = Cardiac output ÷ Stroke volume.

若题目给出心输出量和另一变量，可变形为：每搏输出量 = 心输出量 ÷ 心率，或心率 = 心输出量 ÷ 每搏输出量。

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5. Estimating Population Size: Capture-Recapture | 标记重捕法估算种群数量

N = (M × C) ÷ R

N = estimated total population; M = number captured, marked and released in the first sample; C = total number captured in the second sample; R = number of marked individuals in the second sample.

N = 估计种群总数；M = 第一次捕获、标记并释放的数量；C = 第二次捕获的总数；R = 第二次捕获中有标记的个体数。

Key assumptions: no births, deaths, immigration or emigration between samples; the marks do not affect survival or recapture chance; thorough mixing has occurred.

关键假设：两次采样间无出生、死亡、迁入或迁出；标记不影响生存或重捕概率；标记个体已被充分混合。

Worked example: 40 woodlice are caught, marked with a tiny spot of paint and released. Two days later, 50 woodlice are caught, of which 10 have marks. Estimated population N = (40 × 50)

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