*** Mathematical Skills required ***

The following are formulae you must LEARN and be able to use or rearrange: 
- From Cell structure booklet -Magnification triangle to work out ACTUAL, IMAGE or MAGNIFICATION of an image. 

- From Transport in animals: Cardiac output triangle.

- From Biodiversity within a community: Index of diversity

- From Energy in ecosystems: Energy equations ENTERING the ecosystem and BETWEEN trophic levels. 

- From Inheritance: Chi-squared calculation

- From Populations: Hardy Weinberg 

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                                                                          *** Specification points ***

Arithmetic and numerical computations 

MS 0.1: Recognise and make use of appropriate units in calculations: 

* Convert between units, eg mm3 to cm3 as part of volumetric calculations. (Answers to tasks)

* Work out the unit for a rate, eg breathing rate

MS 0.2: Recognise and use expressions in decimal and standard form:

* Use of appropriate number of decimal places in calculations eg for a mean. (Markscheme)

* Carry out calculations and convert between numbers in standard and ordinary form, eg use of magnification, volumes (Markscheme)

* Understand standard form when applied to areas such as a size of organelle. 

* Convert between numbers in standard form and ordinary form 

* Understand that significant figures need retaining when making conversions between standard and ordinary form, eg 0.0050 mol dm–3 is equivalent to 5.0 × 10–3 mol dm–3

MS 0.3: Use ratios, fractions and percentages:

* Calculate  percentage change (Markscheme)

* Calculate surface area to volume ratio (See Induction homework in 4.1 Section- scroll down)

* Use scales for measuring

* Represent phenotypic ratios (monohybrid and dihybrid crosses)

MS 0.4: Estimate results:

* Estimate results to sense check that the calculate values are appropriate. 

MS 0.5: Use calculations to find and use power, exponential and log functions:

* Estimate the number of bacteria grown over a certain length of time. ( with PowerPoint)

* Apply logs to any given data. ( See M.S 2.5 for example activities)

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Handling Data 

MS 1.1: Use appropriate number of sig figs: 

* Report calculations to an appropriate number of significant figures given raw data quoted to varying numbers of significant figures (Answers)

* Understanding that calculated results can only be reported to the limits of the least accurate measurement

MS 1.2: Find arithmetic means: 

* Calculate or compare the mean, median and mode of a set of data (Answers)

MS 1.3: Construct ad interpret frequency tables and diagrams, bar charts and histograms. 

* Represent a range of data in a table with clear headings, units and consistent demical places 

* Interpret data from a variety of tables 

* Plot a range of data in an appropriate format eg enzyme activity over time as a graph.

* Interpret data from a variety of graphs eg explain an ECG graph. 

MS 1.4: Under simple probability:

* Use the terms probability and chance appropriately

* Understand the probability associated with genetic inheritance 

MS 1.5: Under the principle of sampling as applied to data: 

* Index of diversity. 

MS 1.6: Understands the term Mean, mode and median: 

* Mean, mode and median ( See MS 1.2 for worksheet and answers)

MS 1.7: Use a scatter diagram to identify a correlation between 2 variables: 

* Interpret a scattergram eg enviro factors on lung/cardiac disease. 

MS 1.8: Make order of magnitude calculations. 

* Magnification formula eg Magnification = size of image/size of real object. 

MS 1.9: Select and use a stats test: 

* Chi-squared to test significance of difference between O and E results. (Video activity sheet, answers to video activity, practice activity, answer to practice activity)

* Student T-test 

* Correlation coefficient- Spearman's rank. 

MS 1.10: Understand measures of dispersion include SD and range. 

* Comment on SD 

* Understand why standard deviation might be a more useful measure of dispersion for a given set of data (Worksheet) (Answers)

MS 1.11: Identify uncertainties in measurements and use simple techniques to determine uncertainty. 

* Calculate % error 

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Algebra

MS 2.1: Understand and use the symbols: =, <, <<, >>, >, ∝, .

MS 2.2: Change the subject of an equation 

* Re-arrange formula. 

MS 2.3: Substitute numerical values into algebraic equations. 

* Magnification triangle, cardiac output, index of diversity, etc. 

MS 2.4: Solve algebraic equations 

* Magnification triangle, cardiac output, index of diversity etc 

MS 2.5: Use logs in relation to quantities (Markscheme)

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Graphs

MS 3.1: Translate information between graph, numerical and algebraic forms:

* Understand that data may be represented in a number of formats 

MS 3.2: Plot 2 variables from experimental data 

* Select an appropriate format for plotting data, bar charts, histograms, graphs and scattergrams (Activity sheet 1, activity sheet 2, activity sheet 3)

MS 3.3: Understand that y-mx + c represents linear relationship. 

* Predict/sketch the shape of a graph with a linear relationship (Graph drawing rules)

MS 3.4: Determine the intercept of a graph 

MS 3.5: Calculate rate of change from graph showing linear relationship 

* Calculate rate from graph. (Answers) ANSWERS AT THE BOTTOM OF THIS PAGE

MS 3.6: Draw and use the slope of a tangent as a measure of rate of change 

* Method to measure the gradient of a point on a graph 

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Geometry and trigonometry

MS 4.1: Calculate circumference, SA and V of regular shapes

* Calculate the C and A of a cicrcle

* Calculate SA and C of prism, cylindrical prism and spheres 

* Calculate SA and V of cells. 

Induction homework covering MS 4.1

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We would recommend you buy a copy of the "Essential maths skills for A-level Biology" CGP revision guide.