Equations (AQA A-Level Biology): Revision Notes
Equations
Mathematical equations are essential tools in A-Level Biology that allow you to calculate specific values from known data. You need to understand how to substitute values into formulae and rearrange equations to find unknown quantities.
Substituting into equations
Substitution involves replacing symbols in an equation with actual numerical values, then performing calculations in the correct order to find your answer.
You don't need to understand how equations are derived, but you must be able to use them correctly. Focus on learning the substitution process and applying the formulas accurately.
Understanding symbols and terms
Each symbol in an equation represents a specific quantity. For example, in ecological studies, you might use Simpson's Index of Diversity:
The symbols mean:
- N = total number of individual organisms in the survey
- n = number of individuals of each different species
- Σ = sum of (add together all the values that follow)
- Brackets = calculations that must be completed first
Order of operations
When substituting values, always solve brackets first. For instance, means you multiply N by the result of .
Critical Rule: Always complete calculations inside brackets before any other operations. This is the most common source of errors in equation work.
Worked Example: Simpson's Index Calculation
Consider plant species data where you've counted:
- Species A: 22 plants
- Species B: 30 plants
- Species C: 25 plants
- Species D: 23 plants
- Total plants (N) = 100
Step 1: Calculate for each species:
- A:
- B:
- C:
- D:
Step 2: Calculate for each species:
- A:
- B:
- C:
- D:
Step 3: Find :
Step 4: Substitute into the equation:
Rearranging equations
Sometimes you know all values except one. You can rearrange the equation (change the subject) to calculate the unknown term. This skill is particularly useful in microscopy calculations.
Magnification relationships
The basic magnification equation is:
Equation Triangle Technique: A triangle diagram helps visualise rearrangements. Cover the unknown quantity with your finger, and the remaining parts show how to calculate it.
Using equation triangles
From the basic equation, you can derive:
Worked Example: Microscopy Calculation
A mitochondrion measures 41 nm in a photograph taken at ×34,000 magnification. What is its actual size?
Step 1: Identify the unknown (real size) and rearrange:
Step 2: Substitute values:
Step 3: Convert to appropriate units: Since mitochondria are extremely small, convert to micrometres (μm):
Unit Consistency: Always ensure measurements use consistent units before substituting. Convert different units to the same scale to avoid errors in your calculations.
Estimating results
When gathering data or making measurements, estimate your expected result beforehand. This helps you judge whether your calculated answer is reasonable and identifies potential errors in your working.
Key Points to Remember:
- Always solve brackets first when substituting values into equations
- Check that all measurements use the same units before calculating
- Rearrange equations by covering the unknown quantity to see the calculation needed
- Estimate your expected answer to verify your final result makes sense
- Show each step of your working clearly, including units throughout