Maths Skills in
Biology
The number of marks used to credit the relevant
Mathematical skills is no less than 20% of the total marks
for the qualification.
Those marks are allocated to questions and tasks related
to biology, chemistry and physics in a ratio of 1:2:3
Maths Skills In Biology
Learning outcomes:
• Analyse personal
strengths and
weaknesses in the
mathematical
components of
combined science.
• Revise mathematic
components that
you need to
complete your
combined science
GCSE
Read through the maths
skills you need for
combined science and
rate how you feel about
each one ‘Before
Lesson’
Maths Skills In Biology
Task:
Around the room are a series of information
sheets about a particular maths skill with
exam questions on the back.
Make your way around the room, read the
information and then answer the questions in
your books.
STRETCH: Come up with your own biology
linked question for each skill., complete with
a mark scheme
Comparing Data
When comparing two sets of data try to use:
‘as the ………… increases/decreases, the …………
increases/decreases’
Is the same relationship true for all the data or does
it start to level off after a certain number?
Use data to back up
your statement
As the distance from the light
increases, the production of gas
bubbles decreases. Going from 40
bubbles at 10cm to 5 at 40cm. e.g.
Distance from
light (cm)
Production of gas
bubbles/minute
10
40
20
20
30
10
40
5
Comparing Data
Exam Questions:
volume of sodium
hydrogencarbonate solution
added in cm3
volume of gas collected
in 1 hour
in cm3
0
1
5
2
10
Breathing rate
(breaths per
minute)
Length of time of
exercise (seconds)
Resting
46
30
53
4
60
55
15
5
90
63
20
6
25
6
120
65
30
6
150
73
180
77
1. Describe the effect of
increasing the volume of sodium
hydrocarbonate solution on the
volume of gas collected.
2. Describe the effect of the
length of exercise on the
breathing rate of a person.
Analysing Graphs
When comparing two sets of data on a graph try to use:
‘as the ………… increases/decreases, the …………
increases/decreases’
Is the same relationship true for the whole graph or
does it start to level off after a certain number?
Use data to back up
your statement
As the carbon dioxide levels increase
from 0 to 0.07, the rate of
photosynthesis increases. After 0.07
the rate of photosynthesis remains e.g.
constant at 20.
Analysing Graphs
Exam Questions:
1. Describe the trend shown in
the graph.
2. State the % risk of lung cancer
for a man who gave up smoking at 50.
3. Describe the relationship
between coronary heart
disease and age.
Drawing Tables
Title of each variable at
the top of each column
Time
(min)
Independent
variables in the
first column
arranged in
ascending order.
Units of measurements given in
the heading of the table
Volume of O2 released
(cm3)
1
2
at pH 3
1.4
2.7
at pH 6
1.6
3.2
3
4.2
5.6
4
5.9
5.7
Dependent variables in following
columns
Drawing Tables
Exam Questions:
1. A student recorded the change in oxygen levels in germinating peas
over a 30 minute period.
The results are shown below.
A 10 mins (−0.8) ml, 20 mins (−1.6) ml, 30 mins (−2.4) ml
B 10 mins (−0.1) ml, 20 mins (−0.1) ml, 30 mins (−0.1) ml
C No change
Draw a table for these results.
2. Some students investigated the effect of pH on the action of the
enzyme trypsin which breaks down a protein in milk. This turn the milk
into a clear colourless solution.
They set up 5 test tubes that each contained trypsin and milk at
either pH 5,6,7,8 or 9. Then they timed how many minutes it took for
the milk in each test tube to turn colourless. Design a table to record
the results for this investigation.
Calculating The Mean
12
13
14
11
12
12
13
Step 1- Total
12+13+14+11+12+12+13= 87
Step 2- Divide total by
number of pieces of data
87 ÷ 7 = 12.4
The mean is 12.4
If there are
any anomalous
results, remove
them before
calculating the
mean.
To calculate the mean you add up all of the numbers and
then divide them by how many pieces of data you have.
Calculating The Mean
Exam Questions:
1. Calculate the mean reaction
time.
3. Calculate the most appropriate
mean volume of oxygen produced
at pH 7.
2. Calculate the mean ADH level in
people without diabetes.
Mode & Median
Mode- The number which appears most often
in a set of numbers.
Median- The middle number when the data
set is placed in numerical order.
The mode is 12 because it
appears most often.
8,9,10,10,11,11,12,12,12,12,13
The median is 11 because it’s the
middle number
Mode & Median
Exam Questions:
2. A group of students
are investigating variation
in shoe size.
The results they
gathered are:
3,7,4.5,6,6,4.5,7,7.5,8,6,8
1. What is the modal group for both
sets of data represented above?
Calculate the mode and
the median of the data
they have collected.
Calculating Percentages
There are several methods to calculate percentages:
Method 1
1. Divide your number by 100
(this gives you 1%)
2. Multiply this number by the
percentage you want.
e.g. 45% of 560
(560 ÷ 100) x 45 = 252
Method 2
1. Write out your percentage
as a decimal (10% is 0.1 etc.)
2. Multiply this number by your
number.
e.g. 45% of 560 (45% is 0.45)
560 x 0.45 = 252
How to calculate what percentage one number is of
another. If you want to know what percent A is of B:
Divide A by B then multiply by 100
e.g. 14 animals out of 56 are mammals, what % is this?
(14 ÷ 56) x 100 = 25%
Calculating Percentages
Exam Questions:
1. Mayfly nymphs, caddis fly
larvae and stonefly larvae are
indicators of clean water.
Calculate the percentage of
organisms in stream A that are
clean water indicators.
2. One complete cell cycle in an onion cell takes 24 hours (1440
minutes). Mitosis takes up 30% of this time. The remainder of time
is spent in interphase.
Calculate the length of time, in minutes, an onion cell spends in
interphase.
Calculating Percentage Changes
To calculate the percentage change you need to do
the following:
Final value – starting value
starting value
A willow tree initially
has a mass of
2.27kg.
After 5 years it has
a mass of 76.74kg
76.74 – 2.27
2.27
x 100
x 100
= 3281 %
increase
Calculating Percentage Changes
Exam Questions:
1. Calculate the percentage change
in mass for chip 5.
2. Suggest why calculating a
percentage change is more useful
than calculating the change in mass in
this investigation
3. Calculate the missing
percentage change in mass.
Percentile Charts
Percentile charts show the percentage of readings below a
certain value.
99.6% of babies have
a mass below this
75% of babies have
a mass below this
25% of babies have
a mass below this
They are often used to compare the
growth of children against others at
the same age.
Percentile Charts
Exam Questions:
1. Calculate the difference in
height of an 11 year old male
in the 95th percentile and an
11 year old male in the 5th
percentile.
2. Explain what is meant by
the 95th percentile on this
graph.
3. What percentage of 20
year old males have a height
of 165cm or more?
Converting Units
Make sure you check
the units given to
you in the question
and the units you are
expected to give
your answer in.
To convert your units
do the calculation
shown in the diagram
e.g. going from mm to m
you divide the number
by 1000 6mm = 0.006m
Converting Units
Exam Questions:
1. Convert 34 millimetres into metres.
2. Convert 1034 nanometres into picometres.
3. Convert 6 000 000 seconds into microseconds.
4. Convert 87 nanoseconds into milliseconds.
5. The answer you get to a question is 0.15mm.
Give your answer in a) m
b) µm
c) nm
Standard Form
We show figures as numbers between 1 and 10
multiplied by a power of 10
The index number tells us
how many place values to
move the digit.
You do the reverse for a number smaller than 0 and end up
with a negative power.
Standard Form
Exam Questions:
1. Write the number 4540
million in standard form.
4. Which one of the following is
the same as 60 nanoseconds?
2. Write 0.00072 in standard
form.
3. Divide 80 million by 20 000.
Write your answer in
standard form.
HINT: There are 1 000 000 000
nanoseconds in a second.
Ratios & Fractions
Ratios show the relationship between two amounts.
e.g. if we had 5 trees in a field, 3 oak and 2 willow the
ratio is 3:2 – for every 3 oak trees there are 2 willow.
Fractions show the number of parts of a whole.
The fraction of oak trees is
trees only 3 are oak.
3
5
because out of our 5
If you can you should always simplify your answers
2
4:2 becomes 2:1 & becomes ½ etc.
4
Ratios & Fractions
Exam Questions:
1. A female with genotype Dd and
a male with genotype Dd for
sickle cell disease are about to
start a family. Complete the
Punnett square to show the
possible genotypes.
2. Give the ratio of potential offspring
with sickle cell to those without.
3. Give the probability (as a fraction) that their offspring is a
carrier for the disease.
4. What percentage chance is there that the child will have
sickle cell disease?
Variation
Discontinuous
The data can only be a
limited set of values e.g.
blood group, eye colour.
Frequency bar charts for
discontinuous data should
have gaps between the bars.
Continuous
The data can be any
value in a range e.g.
height, mass.
Frequency bar charts for
continuous data should have
no gaps between the bars.
Variation
Exam Questions:
1. Tick 2 boxes to best describe the variation shown by
plants of variety A.
2. Explain in detail the difference
between continuous and discontinuous
variation, using examples from the human
body.
Using Equations
Magnification:
How to
Calculate
Units
Image size
Magnification
Magnification
Image size ÷
actual size
Actual Size
Image size ÷
magnification
mm, etc.
Image Size
Actual size x
magnification
mm, etc.
Actual size
I
A
M
Using Equations
Exam Questions:
1. The width of the
labelled cell is 6mm. The
cell has been magnified 750
times.
Calculate the actual width
of this cell in mm.
2. The myelin sheath of
this neurone is 250nm in
thickness. Calculate the
magnification of this
electron micrograph.
Using Equations
Cardiac Output:
How to Calculate
Units
Cardiac
output
Stroke volume x
Heart rate
Litres/
min
Stroke
volume
Cardiac output ÷
Heart rate
Litres/
beat
Heart
rate
Cardiac output ÷
stroke volume
Beats/
min
Using Equations
Exam Questions:
1. Calculate the
heart rate after 4
weeks of training.
2. When the running speed
is 22km h-1, the stroke
volume is 0.18 dm3.
Calculate the cardiac output
of the runner at this speed.
Using Equations
BMI:
in Kilograms (Kg)
Mass
BMI =
Height2
in Metres (m)
e.g. a person with mass
78kg and height 1.80m
has a BMI of
78 ÷ 1.82
78 ÷ 3.24
= 24.07
They are in a healthy
range.
Using Equations
Exam Questions:
1. Calculate the body mass index for a person with a body mass of
78kg and a height of 1.7m.
2. Use the chart to find their BMI
category
A underweight
B normal range
C overweight
D obese
3. A man has a mass of 105kg and
a height of 1.84. Calculate his BMI.
Using Equations
Estimating Population Size:
Counting all the organisms in an area is often
impossible so we take samples using randomly placed
quadrats to estimate population size:
Number of
Population
= organisms in all x
size
quadrats
Total size of area where
organism lives
Total area of quadrats
Using Equations
Exam Questions:
1. In a 1m2 quadrat on a rocky shore there are 50 limpet shells.
The total area of rocks is 450m2. Estimate the population size of
limpets on rocks.
2. Explain why it would be better to estimate the population size
from a mean number of limpets from several randomly placed
quadrats.
3. 1m2 quadrats were used to gather the data above in a woodland
area of 25000m2. Estimate the population size of violets.
Answer Time
Using the modelled answer booklet, mark your
answer to the questions.
Make sure you correct anything
that you got wrong!
Maths Skills In Biology
Fill in the ‘After
Lesson’ section of the checklist, rating
how you feel about each topic now.