Maths Skills

• PERCENTAGE UNCERTAINTY:

  (Uncertainty/Reading)*100

  
  

  WORKED EXAMPLE:

  A calculation of the maximum length of an organelle in an image. Using a ruler the image measures 4mm. You divide by the magnification (given to be 500) to give you 0.008mm. The question wants the answer in micrometres so you multiply 0.008mm by 1000 to get 8 micrometres.

  A ruler has an uncertainty of 1mm.

  The uncertainty = 1mm, so (1/4)*100 = 25%. You can then use this percentage to find the end uncertainty: 0.25*8 = 2 micrometres.
• To convert from ordinary to standard form, move the decimal point to the left or right until you have one digit in front of it. Count how many moves you have to make to achieve this. This tells you the correct power of 10 to write in the standard form number.

  
  

  For example:

  21834 becomes 2.1834 x 10⁴

  0.0385 becomes 3.85 x 10⁻²

  0.0020 becomes 2.0 x 10⁻³
• To multiply two numbers shown in standard form, multiply the two numbers together and then add the powers of 10.

  
  

  For example:

  (7 x 10²) x (2 x 10⁴) = 14 x 10⁶

  = 1.4 x 10⁷
• To divide two numbers shown in standard form, divide one number into the other and then subtract the powers of 10.

  
  

  For example:

  (8 x 10⁹) / (2 x 10⁵) = 4 x 10⁴

  (6 x 10⁴) / (3 x 10⁻³) = 2 x 10⁷
• To add or subtract two numbers in standard form, convert the numbers to ordinary form and then add or subtract in the usual way.
• Equation for calculating image size/actual size/magnification:

  IMAGE = ACTUAL × MAGNIFICATION

  ACTUAL = IMAGE ÷ MAGNIFICATION

  MAGNIFICATION = IMAGE ÷ ACTUAL
• S.A:V RATIO:

  Surface area ÷ volume
• Why use millions of cells in a measurement?


  To allow comparison as there is likely to be different amounts of cells in the samples.
• CALCULATING INDEX OF DIVERSITY:

  1. Calculate N(N-1) to find value A
  2. Calculate n(n-1) for each species
  3. Add these numbers together to find value B
  4. Divide

  (You are given the formula in the exam)
• Diameter = 2 × Radius.
• Area of a circle = π × r2
• Surface area = l * w * no. of sides
• Volume = l * w * h
• A logarithm is the power to which a base is raised.

  E.g. 3 x 10⁴ = the logarithm of this number is 4
• TO CONVERT A NUMBER TO LOG:

  1. press the log button on the calculator
  2. enter number (e.g. 1000)
  3. press =
  4. answer is given (e.g. in the case of 1000 the log would be 3)
• TO CONVERT A LOG TO A NUMBER:

  1. press shift and log
  2. enter the log (e.g. 3)
  3. press =
  4. answer is given (e.g. in the case of 3 the number would be 1000)
• Logs such as 5 x 10² are called 'logs to the base 10'.

  There are also 'natural logs', in which the base is 2.71 instead of 10.
• Natural logs are represented by the letters 'ln' on the calculator.

  (in reverse they are represented as 'e')
• Expressed mathematically, x is the logarithm of n to the base of bˣ.

  For example, 2³ = 8. Therefore, 3 is the logarithm of 8 to base 2.
• Logs are used for ease of graphing when dealing with large numbers, for example, bacteria colonies. Graph data ranging from 100 to 1 x 10⁸ would have a very large scale, which would be highly inaccurate. So, logs are used - for example, the graph scale would range from 2 to 5 instead of 100 to 10,000,000.

  However, when reading values from the graph you must convert the log back to a real number to be able to do calculations (shift + log on the calculator).
• % decrease = (change / the original) * 100.

  This is guaranteed to be somewhere on your exam papers.
• Complex maths questions are usually easier if broken down into constituent parts.

  E.g. "Calculate the rate of gas production in cm³ g⁻¹ min⁻¹ during the first 40 minutes of this investigation." = how many cm³ produced per gram of substrate per minute of the investigation.

  //

  In the example below, a simplified version would be "Every hour, each 1kg of fish requires 90cm³ of oxygen."