### Maths for AS Biology File

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Have a title and use over half the page.
Needs to show trends.
Put the independent variable on the X-axis.
Dependent variable goes on the Y-axis.
Have linear axes that start at the origin 0,0.
Show axis breaks with a jagged line.
Use a sensible scale.
Label axes with EXACTLY what they show and
give UNITS.
Plot points with PRECISION.
Given value x 100
Possible value
As with your test results when you calculate your
percentage;
What you got!
x 100 = Percentage Score.
Full possible marks
Percentages allow comparison of proportions where the
total value may vary! One test might be longer than
another so possibly more marks are available or one
population may be larger than another.
Find the difference = Final value – initial value.
Difference
Initial value
x 100 = % change.
% change may be an increase or decrease.
It can be several hundred % if the final value is
much bigger ( or smaller) than the initial value.
A minus value is a % decrease and a positive
value is a % increase.
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Mean is the type of average used in biology so call it
by this name.
Add all the values together then divide by the number
of values used.
If there are a number of values contributing to the
mean then Standard Deviation (SD) which is the mean
variation of points about the mean value can be
calculated.
The larger the number of similar values (sample size)
the smaller the S.D.
SD gives an idea of the spread of the data; so how
varied were the data points that contribute to the
mean.
When SD value are taken into account the mean
points may indicate overlap. One should question
whether they are different!
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If you measure the time for something to
happen than you can calculate the rate.
E.g. if during an enzyme reaction a measuring
cylinder filled with gas in 20s at optimum
temperature, but than at 10 degrees lower
temperature, takes 40s to fill the measuring
cylinder with gas then the first experiment
was faster so went at a higher rate.
Repeat the experiment to calculate a mean
time.
Start by calculating your mean time.
1/mean time in seconds = Mean Rate.
If you have a volume or value use that,
otherwise use 1.
What is the significance of using 1?
You are using it as a whole arbitrary unit. In
other words one whole reaction process.
It might signify the end point of a completed
reaction or in the example one full measuring
cylinder/test tube of gas.
1/20 = 0.05 arbitrary units per second
Or
1/40 = 0.025 arbitrary units per second.
As we have used the same arbitrary units our
results are comparable.
However we have decimal places to plot – not
always easy!
1000/20 = 50 arbitrary units (x1000) per second
Or
1000/40 = 25 arbitrary units (x1000) per second.
As we have used the same arbitrary units for all of
our values our results are still comparable but now
easier to plot as whole numbers.
Now on your Y-axes label you will have to
remember to add a multiplication factor (x1000) in
the units. As well as calling it a MEAN RATE.
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If you measure pulse then you know how fast
the heart is beating. Each time the left ventricle
CONTRACTS the blood pressure increases as the
blood surges into the aorta and pushes the
blood already there forward (Mass flow).
This pressure is referred to as HYDROSTATIC
PRESSURE. Each high value is SYSTOLE and lower
value (occurring between contractions) is
DIASTOLE.
Blood pressure is a result of ventricular
contraction.
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You can easily measure pulse by placing a
finger on an artery and noting how frequently
the artery bulges over a period of time.
Generally pulse is measure in beats per
minute [bpm] or; beats per minute or;
beats/min or; beats min-1.
If you measure pulse for a shorter time you
will have to use seconds [s]. This can then be
converted to bpm.
More accurately measure with a digital pulse
meter. The disadvantage of this is that it
measures pulse over a set period of time and
it may increase or decrease during this time.
Size of image = Magnification
Real object size
This is simply a ratio of sizes, so there are no units
BUT THE SAME UNITS MUST BE USED IN THE TOP
AND BOTTOM LINES OF THE EQUATION.
Actually MAG. is a measure of how many times the
real thing would fit into the enlargement.
Crucial to the calculation is the use of the SAME
UNITS for the image and the object. Generally it
is easier to convert mm measured (image) into
um by MULTIPLYING by 1000.
IF YOU ARE GIVEN AN IMAGE IT SHOULD EITHER
HAVE A MAGNIFICATION OR SCALE BAR.
If you are given an Image and MAG and need to
calculate the real size then the equation must
be rearranged (very simply);
Real object size = Image size ÷ Mag. Again
the units must be the same for the image and
the object.
Using Scale Bars is easy as they are just like rulers!
 Measure the SCALE BAR using a ruler in
millimetres.
 Look at the value of the scale bar (given in
micrometers) and divide it by the number of mm
measured.
 This is the value for each mm on the ruler.
 Measure the designated distance on the image and
multiply the value for each mm by the number of
millimetres measured.
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Always attempt calculations – they are not
that scary and often give EASY marks!!!
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