# Separation of Powers Worksheet

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```					                                 Variation Project
Worksheet

The aim of this project is to investigate the type of variation that exists between two variables.
You will need to gather several sets of measurements of the variables. Begin by choosing
two variables to measure – either from the suggestions below or from ideas of your own.

Data that can be collected with straightforward measurements:

   the speed of travel (s) and the time (t) taken to cover a set distance
   the width (w) and length (l) of a rectangle of fixed area
   the distance covered (d) by travelling at a fixed speed for different amounts of time (t)
   the weekly wage (w) and hours (h) worked at a set rate of pay
   the circumference (C) of a circle and its diameter (d)
   the cost of staying in a hotel (c) and the number of days (d) stayed.

Data that requires specialist equipment, further research or the use of second-hand
information from other sources:

 the weight bearing capacity of beam (W) and its length (l)
 the voltage (V) in an electric circuit of fixed resistance and the current flowing (I)
the resistance (R) in an electric circuit of fixed voltage and the current flowing (I)
the force (F) of attraction between two bodies and the distance of separation (d)
 the distance (d) an object will fall and the time (t) of falling
 the volume (V) of a gas in a container at a constant temperature and the pressure (P)

Part 1

1. Record your data in a spreadsheet file. (Click on the 'Variation Project' tab below to see a
sample).

2. Plot the data using the graph wizard.
a) Choose the XY (Scatter) graph.
b) Choose the first option (the one with the points only – no lines through them.)
c) Here is a sample:

60
width     length
(cm)       (cm)                                  50

12          4
length (cm)

40
24          2                                   30
8          6                                   20
3         16                                   10
48          1                                   0
1         48                                        0   10   20       30         40   50   60
4         12                                                      w idth (cm )
Part 2

You now need to decide on the type of variation – is it direct, inverse or a rule that involves
powers?

 direct variation exists between m and n if the graph of m against n is a straight
line through the origin. (m  n or m = kn)
 if inverse variation exists between m and n, the product of m and n will be
constant (mn = k). Test for this by multiplying the two sets of values in the column
 if the rule requires powers, experiment with different formulas in column D of
k 2
the spreadsheet. For example, if you suspect that the rule is of the type m = /n ,
2
then n m should be constant for all your m and n values. (Make allowance for
experimental error when deciding if a set of values is constant.)

You can also use Excel to determine the equation of a line of best fit through your data
points.

 Click on the graph. Doing this will add the Chart menu to the menu bar at the
top of the screen.
 Go to Chart … Add trendline … Type. (Choose Linear if the points seem to fit
a straight line, Power if they don't.)
 Click on the line on your graph with the right mouse button. Go to Format
Trendline … Options and tick the Display equation on chart option.

Part 3
Conclusion

 Write a rule connecting the two variables and show how it fits one pair of your
values.
 Print out your tabulated data and graph.
 Summarise the type of variation that exists between the two variables.
Variation Project
Enter your data in a table like this one.
Use the Graph Wizard to plot a scatterplot of the data.

first variable     second
(m)        variable (n)        axb
1         12               4
2          6               2
3         18               6
4         48              16
5          3               1
6         21               7
7         36              12
8
9
10

```
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