Biology
Problem Solving Helpsheet : Calculations and Graphs
Averages
Generally, this involves adding the values present together and then dividing the
sum by the number of values.
You might also be asked to work out the average increase/decrease per given
unit of time (hour/minute/second). To do this you just need to work out the
total increase/decrease and then divide that value by the total number or
hours/seconds/minutes in the given time period.
Percentages
(New value ÷ Original value) x 100 = percentage
For example
400 moths in a woodland area are peppered variety and 600 are melanic variety.
What percentage of the moth population are peppered variety?
Total number of moths in area= 1000
Number that are peppered variety= 400
(New value ÷ original value) x 100
(400 ÷ 1000)
0.4
=
x
x 100
100
40%
Percentage change
Whether the question asks to work out a percentage increase or a percentage
decrease the calculation is the same.
You must first calculate the value of the change. And then calculate what
percentage of the original value this is using the method above for percentages
as follows:
(Actual decrease/increase ÷ original value) x 100 = percentage change
For example
Blood pressure decreases from 15 to 3 units as it moves from the capillaries
into the veins. Calculate the percentage decrease in blood pressure when blood
moves into the veins.
Step 1: what is the value of the change?
15 - 3 = 12
Step 2: what percentage is this change value of the original value?
(Actual decrease/increase ÷ original value) x 100 = percentage change
(12 ÷
15) x
100
0.8 x 100
= 80%
Ratios
You simplify a ratio by dividing both sides by the highest common factor
Example 1
Sam has 25 apples and 5 oranges
Q: Express in a whole number the ratio of oranges to apples that Sam has.
Oranges
:
Apples
5
:
25
(÷5) 1
:
5
(÷5)
Example 2
There is 145mg of maltose and 70mg of starch in a barley grain. (this
information may be given or may have to be extracted from a graph)
Q. Express in a whole number the ratio of starch to maltose in a barley grain
Starch
:
Maltose
70
:
145
(÷5) 14
:
29 (÷5)
Graph Drawing (easy marks if your get it right)
Daisy distribution in field
Average
number
of daisies
per m2
Distance from trees
P
Plot
Are all your points plotted accurately and neatly? (Line graphs
in Biology- Join the dots; Bar graphs- bars must be EXTREMELY neatly drawn to
get the mark)
L
Labels
Do all the axis have labels and does the graph have a title?
(if drawing a graph from data given in a table your axis should
Be labelled with the exact wording of the headings given in
the table)
U
Units
Have you included units in the labels where required?
Examples of units : meters (m), seconds (s), kilograms (Kg)
S
Scale
Have you used an appropriate scale for both axis that is
clearly and accurately marked?
Scales must go up in equal increments (e.g. 5, 10, 15, 20, 30 or
20, 40, 60, 80, 100 etc)
S
Size
provided?
Does your graph fill more than half the graph paper
WARNING: Only join your line to the origin (0,0) if that’s where the given
values start. The line doesn’t always have to be connected to the origin in
Biology.
For example
Graph relationships
If you are asked to describe the relationship between variables shown in a
graph you have to give specific details about the relationship and the values at
which the relationship changes (if it changes)
Example
Q
Using data from the graph,
describe the relationship between
the mass of nitrogen fertiliser
and the average mass of root
nodules per plant.
Sample answer
As the mass of fertiliser increased the average mass of root nodules per
plant decreases rapidly until the mass of fertiliser reaches 1g. After this
point the average mass of root nodules per plant continues to decrease but is
decreasing more slowly.