1. Maths in Biology

2. Maths in Biology
There is always a calculation questions in the past papers
The mark schemes have the numerical answers, but are sometimes lacking in an explanation for how they reached those answers
Therefore, I have taken a selection of past paper questions involving calculations and written worked answers for those questions
Hope it is helpful!

3. Equations to learn

4. MAGNIFICATION = SIZE OF IMAGE SIZE OF OBJECT
PULMONARY VENTILATION = TIDAL VOLUME X VENTILATION RATE
CARDIAC OUTPUT = STROKE VOLUME X HEART RATE

5. Calculations

6. DIFFERENCE / ORIGINAL VALUE
Percentage increase
DIFFERENCE / ORIGINAL VALUE
Example – 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°C
37°C
0.5
4.0
10.5
1.0
10.7
32.5
ANSWER: The DIFFERENCE is 32.5 – 10.7 = 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)

7. Question: Jan 2013 – Q4(b)(ii)

8. 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 percentage
You 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 people
Therefore, the difference in the number of patients without diarrhoea after 1 day’s treatment is 60 – 5 = 55 55
NO UNITS NEEDED HERE!

9. 60 5

10. Question: June Q4 (a)
Look at the units!!! It will help you figure out what you need to calculate
6/30 = 0.2
0.2
6 arbitrary units (10-4)
30 minutes
There 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 minutes

11. 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

12. Heart rate = number of beats per minute
It takes 0.7 seconds to beat once
There are 60 seconds in a minute
60/0.7 = 85.7 beats per minute (could round to the nearest number = 86)
85.7
CARDIC OUTPUT = STROKE VOLUME X HEART RATE
Cardiac output is the volume of blood pumped by one ventricle if the heart in one minute
So 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 cm3
7970

13. HINT! Units: the clue to what you need to divide by what
Question: June 2011 Q4 (b)
HINT! Units: the clue to what you need to divide by what
dm3s-1 = dm3/s1
Volume of air breathed out by person A between 0 and 3 = 6.5 – 2.3 = 4.2 dm3
Rate 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-1
1.4

14. 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 minute
85.7

15. Question: Jan 2011 Q1 (d) rearranges to give: 0.42
MAGNIFICATION = SIZE OF IMAGE/measured size
SIZE OF OBJECT/actual size
rearranges to give:
SIZE OF OBJECT/actual size = SIZE OF IMAGE
MAGNIFICATION
Width of image = measure the distance between B and C with a ruler = 2.1 cm
You then need to convert this to μm as that is the units that the questions ask for.
1 cm = μm
2.1 cm = μm
Actual width = measured width/magnification =21 000/ = 0.42μm
0.42

16. Question: Jan 2011 Q3 (d) CARDIAC OUTPUT = STROKE VOLUME X HEART RATE
Stroke Volume = Cardiac Output/ Heart Rate
Answer is given in cm3
Stroke Volume = 5000/55 = 90.9 cm3
90.9

17. Question: Jan 2011 Q5 (b) 4 cm3 16 cm3
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.