Magnification Relationship
Ensure consistent units (e.g., convert µm to mm) before calculating.
Magnification = Image size / Actual size Actual size = Image size / Magnification Cambridge International A Level 9700
🧬 International A Level Biology Formula Sheet 2025
Quantitative relationships for microscopy, transport, genetics, ecology and statistics — organised for Cambridge 9700 papers.
Microscopy Transport Genetics Ecology
Handle Biology Calculations with Confidence
Although Biology is concept-based, Cambridge exams expect precise quantitative work. Use this formula sheet to keep magnification calculations, water potential, genetic ratios and statistical tests at your fingertips.
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Microscopy & cell measurement calculations
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Water potential and gas exchange relationships
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Population genetics and inheritance maths
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Ecological diversity and productivity formulas
Microscopy & Cellular Measurements
Scale Bar Calculations
Magnification = Measured scale bar length (on image) / Actual scale bar value (given).
Eyepiece Graticule
Calibrate using stage micrometer: 1 graticule unit = Stage micrometer length / Number of graticule divisions.
Surface Area : Volume Ratio
Express in simplest ratio form to compare different organisms or sizes.
SA:V = Surface area / Volume Transport & Physiology
Water Potential Relationships
Ψ total water potential, Ψs solute potential, Ψp pressure potential. C concentration (mol dm⁻³), R 8.31 J mol⁻¹ K⁻¹, T temperature (K). Ψp is positive in turgid cells.
Ψ = Ψs + Ψp Ψs = −CRT Transpiration Rate
Volume in cm³ (or cm³ converted from distance × area); time in minutes or seconds to give rate units.
Rate = Volume of water lost / Time Cardiac Output
Stroke volume (SV) in cm³ per beat, heart rate (HR) in beats per minute; cardiac output reported in dm³ min⁻¹.
Cardiac output = Stroke volume × Heart rate Ventilation Rate
Tidal volume (TV) in dm³ per breath, breathing rate (f) in breaths per minute.
Ventilation rate = Tidal volume × Breathing rate Fick’s Law of Diffusion
Greater surface area (A) and concentration gradient (ΔC) increase rate; greater thickness (d) reduces rate.
Rate ∝ (Surface area × Difference in concentration) / Thickness Genetics & Population Biology
Monohybrid & Dihybrid Ratios
Use Punnett squares to show genotype combinations. Expected phenotypic ratios: Monohybrid (3:1), Dihybrid (9:3:3:1) for heterozygous crosses.
Chi-squared Test for Genetic Ratios
O observed counts, E expected counts. Compare χ² with critical value at degrees of freedom = categories − 1.
χ² = Σ [(O − E)² / E] Hardy-Weinberg Equilibrium
p = dominant allele frequency, q = recessive allele frequency. Conditions: large population, random mating, no selection/migration/mutation.
p + q = 1 p² + 2pq + q² = 1 Mutation Rate (qualitative)
Rate = Number of mutations / Total number of genes examined × Time. Use data to compare relative rates.
Linkage & Recombination Frequency
Recombinants are offspring with new allele combinations; frequency < 50% indicates linkage.
Recombination frequency (%) = (Number of recombinants / Total offspring) × 100 Ecology & Ecosystems
Population Density
Area in m² (terrestrial) or volume in m³ (aquatic) for consistent units.
Density = Number of organisms / Area (or volume) sampled Mark-Release-Recapture (Lincoln Index)
Assumptions: even mixing, no immigration/emigration, marks remain.
Estimated population size = (Number marked in first sample × Number in second sample) / Number of marked recaptured Simpson’s Diversity Index
n = number of individuals in each species, N = total individuals.
D = 1 − Σ [n(n − 1) / N(N − 1)] Net Primary Productivity
GPP = Gross Primary Productivity, R = Respiratory losses.
NPP = GPP − R Energy Transfer Efficiency
Energy measured in kJ; compare trophic levels to discuss losses.
Efficiency (%) = (Energy transferred to next level / Energy available at previous level) × 100 Human Physiology & Health
Body Mass Index (BMI)
Use classification ranges: <18.5 underweight, 18.5–24.9 healthy, etc.
BMI = Mass (kg) / Height² (m²) Waist-to-Hip Ratio
Thresholds: >0.85 (women) or >0.90 (men) linked to higher cardiovascular risk.
WHR = Waist circumference / Hip circumference Energy Content of Food
Specific heat capacity of water = 4.18 kJ kg⁻¹ K⁻¹ (or 4.18 J g⁻¹ K⁻¹).
Energy (kJ) = (Mass of water × Specific heat capacity × Temperature rise) / Mass of food burned Water Potential in Medical Contexts
Compare solution Ψ to cell Ψ to predict red blood cell swelling/lysis or plant cell plasmolysis.
Statistics & Practical Skills
Mean, Median & Mode
Mean = Σx / n; median is middle value; mode is most frequent. Choose appropriate measure for data set.
Standard Deviation
x individual value, x̄ sample mean, n number of samples. Use sample standard deviation for Cambridge practical papers.
s = √[Σ (x − x̄)² / (n − 1)] Standard Error & Confidence Intervals
s sample standard deviation, n number of replicates, x̄ sample mean. Mention overlap of confidence intervals when comparing treatments.
Standard error (SE) = s / √n 95% CI ≈ x̄ ± 1.96 × SE Percentage Error
Absolute error usually half the instrument resolution; report result to same precision.
Percentage error = (Absolute error / Measured value) × 100% Calibration Curve Interpolation
Plot absorbance vs concentration, draw line of best fit, use measured absorbance to read unknown concentration.
How to Use This Formula Sheet
Boost your Cambridge exam confidence with these proven study strategies from our tutoring experts.
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Quote Formula + Units
Write the relevant formula before substitution and track units carefully — especially for water potential and gas calculations.
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Support Conclusions with Stats
When presenting practical conclusions, use calculated means, standard deviations and χ² to justify claims.
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Check Biological Plausibility
Sense-check your final values against typical biological ranges (e.g., realistic cell sizes, population counts).
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Link Numbers to Processes
After calculations, explain the biological mechanism behind the result to collect explanation marks.
Master Quantitative Biology with Expert Help
Practise Cambridge-style data analysis, planning and evaluation with specialist tutors who guide you through the calculations and the biology behind them.
Matches the quantitative requirements of Cambridge International AS & A Level Biology (9700), including practical assessment expectations.
Always specify significant figures based on instrument precision and indicate biological context in written answers.