The student want to make 20 cm 3 of a 02 mol dm 3 sodium chloride solution using a 10 mol dm 3 sodium chloride solution and distilled water 10 mol dm 3 is five times the concentration of 02 mol dm ID: 1002322
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1. Starter Question:
2. Question: Jan 2011 Q5 (b) The student want to make 20 cm3 of a 0.2 mol dm-3 sodium chloride solution using a 1.0 mol dm-3 sodium chloride solution and distilled water. 1.0 mol dm-3 is five times the concentration of 0.2 mol dm-3 Therefore it needs to be diluted in the distilled water. So one part out of 5 needs to be the sodium chloride solution Final volume = 20 cm3. 20/5 = 4cm3 4 cm3 of sodium chloride solution to 16 cm3 of distilled water. 4 cm316 cm3
3. Maths for Biologists
4. Make sure you know…Mean – add up all values, divide by number of valuesMedian – middle or central value in a setMode – most common value
5. Equations to learn
6. MAGNIFICATION = SIZE OF IMAGE SIZE OF OBJECT PULMONARY VENTILATION = TIDAL VOLUME X VENTILATION RATECARDIAC OUTPUT = STROKE VOLUME X HEART RATEMITOTIC INDEX = number of cells undergoing mitosis total number of cellsINDEX OF DIVERSITY d= N(N-1) Σ(n(n-1)Make sure you can rearrange an equation!
7. Question: Jan 2011 Q1 (d)SIZE OF OBJECT/actual size = SIZE OF IMAGE MAGNIFICATION MAGNIFICATION = SIZE OF IMAGE/measured size SIZE OF OBJECT/actual sizerearranges to give:Width of image = measure the distance between B and C with a ruler = 2.1 cmYou then need to convert this to μm as that is the units that the questions ask for. 1 cm = 10 000 μm 2.1 cm = 21 000 μmActual width = measured width/magnification =21 000/50 000 = 0.42μm0.42
8. Question: June 2011 Q6 (c) We can see from the values in the table that one cardiac cycle occurs in 0.7 seconds. This can be seen from the changes in pressure. Both the left atrium and left ventricle have the same blood pressure values at 0 s and 0.7 s, indicating one whole cycle. There are 60 seconds in a minute 60/0.7 = 85.7 beats per minute85.7
9. Question: Jan 2012 Q5 (b)Same volume of blood in the right ventricle at time 0 s and 0.7 s, therefore one heart beat lasts 0.7 seconds.STROKE VOLUME – the volume of blood pumped out at each beat. This volume is the difference between the maximum volume of blood and the minimum volume of blood in the right ventricle in one cardiac cycle. 148 – 55 = 93 cm3
10. Heart rate = number of beats per minuteIt takes 0.7 seconds to beat once There are 60 seconds in a minute60/0.7 = 85.7 beats per minute (could round to the nearest number = 86)85.7CARDIC OUTPUT = STROKE VOLUME X HEART RATECardiac output is the volume of blood pumped by one ventricle if the heart in one minuteSo we have the HEART RATE from 5 (b)(i) We also need that the STROKE VOLUME = 93 cm3 (see previous slide for explanation)CARDIAC OUTPUT = 93 X 85.7 = 7970 cm37970
11. Question: Jan 2011 Q3 (d)CARDIAC OUTPUT = STROKE VOLUME X HEART RATEStroke Volume = Cardiac Output/ Heart RateAnswer is given in cm3Stroke Volume = 5000/55 = 90.9 cm3 90.9
12. Calculations
13. DifferenceTake one value away from the otherYou may have to read values from the graph before working out a difference
14. Percentage Increase/DecreaseWork out the difference between the valuesDivide this value by the initial valueTimes by 100You may get percentage increases that are greater that 100%
15. Percentage increaseDIFFERENCE / ORIGINAL VALUEExample – June 2013 Q 5 (b) Calculate the percentage increase in the mean rate of uptake of imatinib when the temperature is increased from 4°C to 37°C at a concentration of imatinib outside the cells of 1.0 µmol dm-3. Give your answer to one decimal place. 4°C37°C0.54.010.51.010.732.5ANSWER: The DIFFERENCE is 32.5 – 10.7 = 21.8. This is how much the mean uptake has increased with the increase in temperature. Now you want to calculate the percentage increase.PERCENTAGE INCREASE = (21.8 / 10.7) x 100 = 203.7% (to 1 decimal place)
16. Question: Jan 2013 – Q4(b)(ii)
17. Look at the graph (annotated on the next slide) - go to the time point of 1 day along the x-axis (horizontal axis)The question is asking for the number of patients, not percentageYou are told in the question that 100 patients are treated with each solution. Solution A – After 1 day 5% of people are without diarrhoea – 5% of 100 people is 5 people Solution B – After 1 day 60% of people are without diarrhoea – 60% pf 100 people is 60 peopleTherefore, the difference in the number of patients without diarrhoea after 1 day’s treatment is 60 – 5 = 5555 NO UNITS NEEDED HERE!
18. 605
19. Calculating RatesRates tell you how fast something is happeningAlways expressed per unit time e.g. g min-1, cm3 min-1Divide something by time
20. Question: June 2011 Q4 (b)Volume of air breathed out by person A between 0 and 3 = 6.5 – 2.3 = 4.2 dm3Rate at which person A breathed air out is the volume of air breathed out (4.2 dm3) divided by the time that it took to breath this volume out (3 seconds)Therefore, 4.2/3 = 1.4 dm3s-11.4HINT! Units: the clue to what you need to divide by whatdm3s-1 = dm3/s1
21. Calculating Rates from a GraphWork out the gradient of a line (you may need to draw a tangent if the line is a curve)Change in y divided by change in x
22. Look at the units!!! It will help you figure out what you need to calculate6 arbitrary units (10-4)30 minutes 6/30 = 0.20.2There are 4 arbitrary units of sodium ions still in the solution after 30 minutes. As it started at 10, then 6 arbitrary units of sodium ions must have been taken up in 30 minutesQuestion: June 2012 - Q4 (a)
23. RatiosDivide one number by the otherIf you wrote this ratio in full it would be 1.08:1If you write a ratio like this make sure you write it the correct way round!Remember! Surface area: volume ratio (surface area/volume) Concentration of sodium chloride solution / mol dm–3Mass of disc at start / gMass of disc at end / gRatio of mass at start to mass at end 0.0016.117.20.94 0.1519.120.20.95 0.3024.323.21.05 0.4520.218.71.08 0.6023.721.9 0.7514.913.71.09
24. Significant FiguresFollow instructions in the questionsIf no specific instruction given, use the same number of significant figures as the values in the question
25. Drawing a GraphChoose the right sort of graph:Continuous data – line graphDiscrete categoric data – bar chart (bars separated by gaps)Continuous categoric data (e.g. height categories) – histogram (bars not separated by gaps)IV on x axisLinear scaleLabel axes and include units separated by / or ()Plot points accuratelyDraw a neat ruled line to connect the points on a line graphDo not extrapolate beyond the data set
26. Standard DeviationStandard deviation gives you a measure of the spread of data around the mean.Bigger standard deviation means greater variety in the data68% of all measurements lie within 1 SDIf standard deviations overlap it shows that means may not be significantly different from one another
27. Standard deviation as error bars