📚 IB & CIE Biology: Calculation Practice | IB CIE 生物计算题专项训练
Calculation questions are a key component in both IB and CIE Biology examinations. From microscopy to genetics, and from ecology to physiology, mastering the common calculations can boost your confidence and save time during exams. This article provides a structured training of the most frequently tested calculation types, complete with formulas, worked examples, and essential tips.
计算题是 IB 和 CIE 生物考试中的重要组成部分。从显微镜操作到遗传学，从生态学到生理学，掌握常见的计算能够增强你的信心，并节省考试时间。本文提供了一套结构化的高频计算题型训练，包含公式、实例和关键提示。
1. Magnification and Actual Size | 放大倍数与实际尺寸
Magnification is how much larger an image appears compared to the real object. The core formula is:
放大倍数是指图像与真实物体相比放大的程度。核心公式为：
Magnification = Image size ÷ Actual size
Image size is the measured length of the specimen in the drawing or micrograph, while actual size is its true length. You must convert both to the same units before dividing.
图像尺寸是绘图或显微照片中测量到的标本长度，实际尺寸即其真实长度。计算前必须将两者转换为相同单位。
le: A red blood cell is drawn as 4.5 cm on a photomicrograph, but its real diameter is 7.5 µm. Convert 4.5 cm to µm: 4.5 cm = 45,000 µm. Then Magnification = 45,000 µm ÷ 7.5 µm = 6000×.
示例：一个红细胞在显微照片中被绘制为4.5 cm，但其真实直径为7.5 µm。将4.5 cm换算成µm：4.5 cm = 45,000 µm。则放大倍数 = 45,000 µm ÷ 7.5 µm = 6000×。
size given magnification, rearrange the formula: Actual size = Image size ÷ Magnification.
若题目已知放大倍数求实际尺寸，可变形公式：实际尺寸 = 图像尺寸 ÷ 放大倍数。
2. Haemocytometer Cell Counting | 血细胞计数板细胞计数
For the large central square (1 mm²), the volume is 0.1 mm³ (= 10⁻⁴ mL). The key formula:
血细胞计数板用于估算细胞浓度。标准的改良牛鲍计数板具有已知深度（0.1 mm）和网格面积。对于中央大方格（1 mm²），体积为0.1 mm³（= 10⁻⁴ mL）。关键公式为：
Cells per mL = Average count per large square × Dilution factor × 10⁴
= 10⁴ × 0.1 mm³. Always count multiple squares and calculate the mean to improve accuracy.
因子10⁴来源于1 mL = 10⁴ × 0.1 mm³。务必计数多个方格并计算平均值以提高准确性。
cell count in one large square is 28. Concentration = 28 × 5 × 10⁴ = 1.4 × 10⁶ cells mL⁻¹.
例题：一份酵母培养液上样前稀释了5倍。一个大方格内的平均细胞数为28。浓度 = 28 × 5 × 10⁴ = 1.4 × 10⁶ cells mL⁻¹.
If you count several smaller squares, first convert to the equivalent for one large square (e.g., 16 small squares from a 25-square grid).
如果你计数了几个小方格，需先换算成一个大方格对应的细胞数（比如从25格计数板中的16个小方格推算）。
3. Serial Dilutions | 连续稀释
Serial dilutions are performed to obtain a very low concentration of a solution step by step. The key relationship is:
连续稀释是通过逐步操作获得极低浓度溶液的方法。关键关系式为：
C₁V₁ = C₂V₂
C₂ and V₂ are the concentration and volume after dilution. Dilution factor (DF) = V₂ / V₁.
其中C₁和V₁是母液的浓度与体积，C₂和V₂是稀释后的浓度与体积。稀释倍数（DF）= V₂ / V₁。
. C₁V₁ = 4.0 × 2 = 8 mmol. C₂ = 8 mmol / 10 mL = 0.8 mol dm⁻³. Dilution factor = 10/2 = 5.
示例：将2 mL 4.0 mol dm⁻³ NaCl溶液加入到8 mL水中。总体积V₂ = 10 mL。C₁V₁ = 4.0 × 2 = 8 mmol。C₂ = 8 mmol / 10 mL = 0.8 mol dm⁻³。稀释倍数 = 10/2 = 5。
e serial dilutions, multiply the dilution factors of each step: Total DF = DF₁ × DF₂ × ...
进行多次连续稀释时，将每一步的稀释倍数相乘：总稀释倍数 = DF₁ × DF₂ × ...
4. Genetic Probability | 遗传概率
Genetic crosses require the product rule (multiply probabilities of independent events) and the sum rule (add probabilities of mutually exclusive events). For a dihybrid cross, you can use Punnett squares or the branched-line method.
遗传交配要用乘法法则（独立事件概率相乘）和加法法则（互斥事件概率相加）。对于双杂合交配，可使用庞纳特方格或分支法。
Example: In a cross AaBb × AaBb, what is the probability of offspring having genotype Aabb? The gene pairs are unlinked. Probability of Aa from Aa × Aa = 1/2; probability
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