1. A minimum of 10% of the marks in the exams involve maths.

2. Answer the questions on the sheet. You may use a calculator. No cheating – work in silence!

3. 1.29 2.68 3.8cm 3 4.a) 24.6 b) 1.45 c) 0.0000100 5.Mrs Eves – 24, Miss Jesusanmi – 8, Mr Walker – 4 6. 5 / 6 7.160 8.29.2

4. At least higher tier GCSE maths standard. This means that simple calculations do not count towards the 10%. The specification lists all the skills you need.

5. Use of standard form Ratios, fractions and percentages Power, exponential and logarithmic functions Significant figures Mean, median, mode, range, standard deviation Charts and graphs (including logarithmic scales) Probabilities Calculations of rate from results/graphs Use of equations Statistical tests Uncertainties and percentage errors Calculations of circumference, surface area and volume

6. You should be able to give answers to an ‘appropriate number of significant figures’. Use figures in the question to help you. Starting on the left, count from the first digit that is not a 0. When you get to the required number of sig. fig., look at the next digit. If it’s 0 to 4, round down. If it’s 5 to 9, round up. E.g. 0.048484848… is 0.05 to 1 sig. fig. or 0.048 to 2 sig. fig. or 0.0485 to 3 sig. fig.

7. Try the examples on the sheet – 3 minutes!

8. Number1 sig.fig.2 sig.fig.3 sig.fig. 124507100000 120000 125000 25.36430 25 25.4 0.025650.03 0.026 0.0257 6.79097 6.8 6.79

9. Calculators use the standard order of operations: Brackets Indices (or Orders) Division Multiplication Addition Subtraction This means your calculator might not do the sum you want. To get it right, press = after each part of the calculation (or make use of the brackets on your calculator!).

10. For the sum… 2 + 4 2 You might type in… 2 + 4 ÷ 2 = Which would give you… 4 Because your calculator ‘does’ BIDMAS. If you type… 2 + 4 = Then… ÷ 2 = You’ll get the right answer, which is… 3 Or, you could type… ( 2 + 4 ) ÷ 2 =

11. Try the examples on the sheet – 3 minutes!

12. 1.22 2.33 3.9

13. Mean = (sum of values)/(number of values) Median – put numbers in order and select ‘middle’ value Mode = most frequently occurring value Range = lowest and highest values (or highest – lowest) Try the example on the sheet – 5 minutes!

14. Mean = 19.9 Median = 19 Mode = 17 Range = 13 to 30 (or 17)

15. For a sample of data, standard deviation gives an indication of the spread of data around the mean. For now, if the standard deviations of two samples ‘overlap’, there is no significant difference between them. We’ll learn how to calculate standard deviation later in the year. Both curves show a normal distribution.

16. What information does the table above give us?

17. Overlap between ranges (mean ± s.d.) for Pudelpointers suggests no significant difference in heritability between tracking and searching. No overlap between ranges (mean ± s.d.) for Large Munsterlanders therefore these is a significant difference in the heritability of the tracking and searching. Tracking is influenced by genetic factors more than searching in Munsterlanders.

18. Powers – multiply the number by itself the number of times stated in the power, e.g. 2 3 = 2 x 2 x 2 = 8 This includes standard form, e.g. 5.2 x 10 3 = 5.2 x 10 x 10 x 10 = 5200 You should be able to convert numbers to and from standard form.

19. Includes a number (from 1 to <10) multiplied by 10 x (where x is any whole number, including negative numbers). You must retain the sig. fig. Try the examples on the sheet.

20. 1.243000 = 2.43 x 10 5 2.0.00123 = 1.23 x 10 -3 3.469100000 = 4.691 x 10 8 4.0.00001050 = 1.050 x 10 -5

21. Exponential functions – also involve powers, e.g. 2 x = 2 multiplied by itself x times

22. A single bacterium is allowed to grow and reproduce for 24 hours. If it can divide by binary fission once every 20 minutes, how many cells will be present after 24 hours? Answer: There will be (24 x 60) / 20 divisions = 72 divisions The total number of cells will be 2 72 = 4.722 x 10 21

23. We can use a logarithmic function to make it easier to accurately plot graphs of data that covers several orders of magnitude (i.e. very small numbers and very big numbers).

24. We generally use log 10 in Biology. With large numbers, we use standard form. This involves 10 x, where x is called the exponent. Log 10 y = x means 10 x = y So, we can use the log function to work out the exponent of a number.

25. pH is a measure of the relative concentration of H + ions in a solution. It is calculated as follows: pH = -log 10 [H + ] The contents of the stomach are found to have a H + ion concentration of 0.0001moldm -3. What is the pH? pH = -log 10 [0.0001] = 4 If the pH of the blood is 7, what is the concentration of H + ions? pH = -log 10 [H + ], so H + conc. = 10 -pH H+ conc. = 10 -pH = 10 -7 = 0.0000001moldm -3

26. pH is a measure of the relative concentration of H + ions in a solution. It is calculated as follows: pH = -log 10 [H + ] Remember: H + conc. = 10 -pH Try the examples on the sheet.

27. pH = -log 10 [H + ]H + conc. = 10 -pH 1.pH 3 2.pH 3.60 3.pH 8.33 1.1.0 x 10 -14 moldm 3 2.3.16 x 10 -7 moldm 3 3.5.62 x 10 -9 moldm 3

28. Select appropriate graph for your data: Bar chart Histogram Scatter graph/line graph Remember: Label the axes Include units Continuous scales (must allow for accurate plotting – no multiples of 3!) Best fit line is either straight (ruler!) OR curved (smooth!) You can look for correlation (positive or negative) and direct/inverse proportion.

29. For the next few slides, see if you can explain what each graph shows. Why has a particular type of graph been chosen?

31. Bar chart with standard deviation bars – which groups are significantly different?

33. Positive correlation – as the male head length increases, the female head length increases.

35. X-axis labelled in powers of 10, i.e. 10 -2, 10 -1, 10 0, 10 1, 10 2 …

36. The Institute of Biology says: ‘Graphs should be joined dot to dot with straight lines when the intermediate values can not be reliably predicted’. You will usually use a line of best fit.

43. What information does the graph tell us?

45. a)The heights of all the students in a class b)The eye colours of all the students in a class c)The number of bacterial cells growing in a test tube Be ready to explain your answers! 3 minutes!

46. a)The heights of all the students in a class Histogram b)The eye colours of all the students in a class Bar chart c)The number of bacterial cells growing in a test tube Line graph

47. Rate of reaction = 1. time taken for reaction OR: Rate of reaction = quantity of product formed. time taken for reaction Rate of movement = distance moved. time taken to move that distance …and so on. From a graph, rate = gradient of line Maximum rate = maximum gradient of line

50. 1. 1.4 (2 marks) 1 mark for 4.2 ÷ 3 2.

51. You should be able to simplify a ratio, e.g. 8:2 is the same as 4:1 144:12 is the same as 12:1 etc. In Biology, we usually express ratios in the form x:1, where x is any number (not necessarily an integer), or just as x, imagining the ‘:1’ part. Allows us to make comparisons more easily.

54. Need to understand how to interpret/use fractions. e.g. finding ½ of a number using formulae Nothing more difficult than GCSE! Answer the questions – 5 minutes!

55. 1.206.25 2.37/60 3.3/10 4.12/5 or 2 2 / 5

56. Calculate a percentage. Interpret percentages in tables and graphs. Calculate percentage increase/decrease: Percentage increase = final value – original value X 100 original value How would you calculate percentage decrease? Answer the questions – 10 minutes!

57. 1.69% 2.37 marks 3.84.4%

60. Image length = real length x magnification Pulmonary ventilation = tidal volume x ventilation rate Cardiac output = heart rate x stroke volume Need to recall, rearrange and use these. Index of diversity =N (N – 1) Σ n (n – 1) Where N = total number of organisms of all species, and n = total number of organisms of each species. Need to be able to use this to calculate index of diversity.

61. You should be able to visualise 3D shapes from 2D diagrams. Given formulae, calculate: Circumference and area of circles Surface areas and volumes of regular blocks and cylinders Circumference of a circle = 2 π r or π d Area of a circle = π r 2 Surface area of a shape = sum of areas of all sides Volume of a regular shape (prism) = area of cross-section x length Try the calculations – 5 minutes!

62. If a neurone has a mean diameter of 0.1mm and a length of 25cm, calculate the approximate volume of the neurone.

63. 1.a) 25.1cm b) 50.3cm 2 2. Area of cross-section = 7.85x10 -3 mm 2 Volume = 1.963mm 3

64. Calculations of % errors Calculations of standard deviation Statistics: X 2 (Chi-squared) – tests for differences between observed and expected results Spearman’s rank correlation coefficient – tests for correlation between two measurements from the same sample Student’s t-test – tests for differences between mean values