IGCSE Biology Formula Practice
Worked Examples by Topic | Cambridge IGCSE Biology (0610)
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Calculating Magnification
Magnification = Image Size ÷ Actual Size
How to Use This Guide
- Study the formula — understand what each variable represents
- Follow the worked example — see how to apply the formula step-by-step
- Try the practice problem — click to reveal the answer
- Check units — always convert to the same units before calculating
- Check your tier — items marked (Extended) are Supplement content; Core candidates can skip them
1. Magnification Calculations
You must be able to find magnification, image size or actual size, working in millimetres. Converting between millimetres and micrometres (μm) is Extended.
The Magnification Formula
Magnification = Image Size ÷ Actual Size
M = I ÷ A
Remember: Magnification has no units — it's just a number (e.g., ×400)
Extended: 1 mm = 1000 μm
Finding Magnification (Extended: uses μm)
A cell measures 50 μm in real life. In a diagram, it appears as 10 cm. What is the magnification?
Finding Actual Size
A microscope image shows a chloroplast measuring 15 mm. The magnification is ×3000. What is the actual size?
Practice Problem (Extended: uses μm)
A red blood cell has an actual diameter of 7 μm. In a microscope image, it measures 28 mm. Calculate the magnification.
Click to reveal answer
Step 1: Convert 28 mm to μm: 28 × 1000 = 28,000 μm
Step 2: M = I ÷ A = 28,000 ÷ 7 = ×4000
2. Percentage Change (Osmosis)
Essential for osmosis experiments. Positive = gain (water entered), negative = loss (water left). Always divide by the INITIAL value.
The Percentage Change Formula
Percentage Change = (Final - Initial) ÷ Initial × 100
Positive result = increase (water gained by osmosis)
Negative result = decrease (water lost by osmosis)
Potato Chip in Water
A potato chip has an initial mass of 2.5 g. After being placed in distilled water for 30 minutes, its final mass is 3.0 g. Calculate the percentage change in mass.
Potato Chip in Concentrated Solution
A potato chip has an initial mass of 3.2 g. After 30 minutes in concentrated sugar solution, its final mass is 2.4 g. Calculate the percentage change.
Practice Problem
A potato cylinder has an initial length of 40 mm. After being in salt solution, its length is 34 mm. Calculate the percentage change.
Click to reveal answer
Step 1: Change = 34 - 40 = -6 mm
Step 2: -6 ÷ 40 × 100 = -15%
The potato lost water by osmosis because the salt solution was more concentrated than the potato cell contents (Extended: the solution had a lower water potential)
3. Rate Calculations
Used for photosynthesis (bubble counting), respiration, enzyme activity, and transpiration experiments. Rate = amount ÷ time.
The Rate Formula
Rate = Change ÷ Time
Used for: rate of photosynthesis, rate of respiration, rate of enzyme activity
Units: bubbles/min, cm³/min, mm/min, etc.
Rate of Photosynthesis
An aquatic plant produces 45 bubbles of oxygen in 3 minutes. Calculate the rate of photosynthesis.
Rate from Graph (Gradient)
A graph shows gas collected vs time. At 2 minutes, 10 cm³ was collected. At 6 minutes, 50 cm³ was collected. Calculate the rate.
Practice Problem
In an enzyme experiment, 8 cm³ of gas was produced in 40 seconds. Calculate the rate in cm³ per minute.
Click to reveal answer
Step 1: Rate = 8 ÷ 40 = 0.2 cm³/second
Step 2: Convert to per minute: 0.2 × 60 = 12 cm³/min
4. Genetic Ratios & Punnett Squares
Predict offspring ratios using Punnett squares. Key phenotypic ratios: 3:1 (Bb × Bb) and 1:1 (Bb × bb).
Key Genetic Ratios
Monohybrid Cross
In pea plants, tall (T) is dominant over short (t). Two heterozygous tall plants are crossed. What is the probability of a short offspring?
| T | t | |
| T | TT | Tt |
| t | Tt | tt |
Predicting Number of Offspring
From a cross Tt × Tt, if 80 offspring are produced, how many are expected to be short?
Practice Problem
In mice, black fur (B) is dominant to brown fur (b). Two black mice, both Bb, are crossed and have 12 offspring. How many would you expect to have brown fur?
Click to reveal answer
Step 1: Bb × Bb gives 1 BB : 2 Bb : 1 bb
Step 2: Probability of brown fur (bb) = 1/4
Step 3: 12 × 1/4 = 3 offspring expected with brown fur
5. Surface Area to Volume Ratio
Explains why cells are small, why organisms need lungs/gills, and why small animals lose heat faster. As size increases, SA:V decreases.
SA:V Ratio for Cubes
Surface Area = 6 × side²
Volume = side³
SA:V = Surface Area ÷ Volume
Key concept: As organisms get larger, SA:V ratio decreases — this affects heat loss, gas exchange, and nutrient uptake
Comparing Cell Sizes
Calculate the SA:V ratio for a cube-shaped cell with sides of 2 μm.
Practice Problem
Calculate the SA:V ratio for a cube with 4 cm sides. Compare this to a 2 cm cube.
Click to reveal answer
4 cm cube: SA = 6 × 16 = 96 cm², V = 64 cm³, Ratio = 96 ÷ 64 = 1.5:1
2 cm cube: SA = 6 × 4 = 24 cm², V = 8 cm³, Ratio = 24 ÷ 8 = 3:1
The smaller cube has a higher SA:V ratio — this is why small organisms lose heat faster and can exchange gases more efficiently across their body surface.
6. Gas Exchange Values
You need to describe how inhaled and exhaled air differ in oxygen, carbon dioxide and water vapour (Core), and explain why they differ (Extended). The values below are typical figures.
Composition of Inhaled vs Exhaled Air
| Gas | Inhaled Air | Exhaled Air | Change |
|---|---|---|---|
| Oxygen (O₂) | 21% | 16% | ↓ 5% |
| Carbon dioxide (CO₂) | 0.04% | 4% | ↑ ~4% |
| Water vapour | Variable | Saturated | ↑ Increases |
Why these changes? (Extended)
- • O₂ decreases: Used in aerobic respiration in cells
- • CO₂ increases: Produced by aerobic respiration in cells
- • Water vapour increases: Evaporates from moist alveoli surfaces
Calculating Percentage Decrease
Calculate the percentage decrease in oxygen between inhaled and exhaled air.
Practice Problem
By how many times does the CO₂ concentration increase between inhaled and exhaled air?
Click to reveal answer
Calculation: 4% ÷ 0.04% = 100 times
CO₂ concentration increases 100-fold from inhaled to exhaled air
7. Heart Rate Calculations
Heart rate is measured as beats per minute (bpm). Often measured over 15 or 30 seconds and scaled up.
Heart Rate from Pulse
Heart Rate (bpm) = Number of beats ÷ Time (min)
A student counts 18 pulse beats in 15 seconds. Calculate the heart rate in beats per minute.
Practice Problem
After exercise, a student counts 36 pulse beats in 20 seconds. What is their heart rate?
Click to reveal answer
Step 1: 20 seconds = 20/60 = 1/3 minute
Step 2: 36 ÷ (1/3) = 36 × 3 = 108 bpm
Or: 36 × (60/20) = 36 × 3 = 108 bpm
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Frequently Asked Questions
How do I calculate magnification in IGCSE Biology?
Use the formula M = I ÷ A where M is magnification, I is image size, and A is actual size. Rearrange to find any unknown: Actual size = Image size ÷ Magnification. Always ensure units are the same before calculating. Core works in millimetres; converting between millimetres and micrometres (1 mm = 1000 μm) is Extended.
How do I calculate percentage change for osmosis experiments?
Use the formula: Percentage change = (Final value - Initial value) ÷ Initial value × 100. A positive result means increase (water gained), negative means decrease (water lost). For example, use it for the change in mass of potato pieces placed in solutions of different concentrations.
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