Download Mathematics for Biology 3

Formulae
We will assume that, as a successful GCSE maths candidate, you can already cope with this topic
so here are some questions as a reminder. If you find you can’t cope, then use a GCSE maths
revision guide to help you.
Questions to try (Formulae)
14.
Cardiac Output = Heart Rate x Stroke Volume
(heart)
(number of
(volume of blood
-1
beats min ) ejected at each beat/cm3)
Calculate the cardiac output for the following:
HR/beats min-1
60
95
128
a)
b)
c)
15.
SV/cm3
90
135
150
Using the formula from question 14, find the following values:
HR/beats min-1
SV/cm3
?
85
65
110
?
?
a)
b)
c)
Cardiac Output
units?
8250
10625
8450
16. Rearrange the following formula to allow calculation of the given subjects:
 = s + p
a) s = ?
b) p = ?
You should be able to do this even if
the formula appears meaningless!
Exam-style question (Formulae)
17. The table shows the (ooh, look!) ratio of the amount of water lost to the amount of oxygen
gained for two terrestrial animals, an annelid worm & an insect:
Organism
Ratio =
Annelid worm
Insect
Mass of water lost/mg g-1min-1
Volume of oxygen taken up/cm3 g-1min-1
2.61
0.11
Both the annelid and the insect take up oxygen at a rate of 2.5cm3 g-1min-1. Calculate the
rate at which water would be lost in meeting these requirements in:
a) the annelid
b) the insect
1
Arithmetic Means
The mean is one of three ways – mean, median & mode – which can be used to represent a whole
set of numbers. (Median & mode are more likely to feature in the ecology topics in A2.)
The mean (x) = the sum of the individual values (x)
the number of values (n)
e.g. 5, 2, 6, 2, 7, 3, 9, 1, 8, 9, 7, 10, 5, 9, 11, 7, 3, 4, 6
(x) = 114 = 6
19
Significant Figures (Sig. Fig.)
The number of significant figures gives us information about the accuracy of the data e.g. when
measuring the length of a specimen with a plastic ruler, you would not expect to include
fractions of millimetres accurately – compare this with the measurements you’d expect when
using a microscope & graticule.
The more figures you quote in your results, the more accuracy you claim so use only what is
reasonable from the equipment you use.
To count the number of sig. fig. remember two simple rules:

The first significant figure of any number is simply the first digit which isn’t a zero

The 2nd, 3rd, 4th, etc. significant figures follow on after the first, & include the zeroes
Questions to try (Sig. Fig.)
18. Calculate a mean from the following values:
Give your answer:
1.9
2.3
1.7
1.8
2.1
1.5
2.1
a) as shown on your calculator
b) to an appropriate number of sig. fig.
19. How many sig. fig. are there in the following numbers?
a) 1293
b) 136.2
c) 9.7
d) 0.348
e) 0.005 847 5
f) 8.3405 x 103
Once again, if you find these difficult, check a GCSE maths revision guide.
2
g) 3.00 x 10-6