DRAWING THE GRAPH
- You must use graph paper and fill at least THREE QUARTERS OF THE PAGE.
- Use a scale which is easy to work with i.e. the major grid lines should correspond to natural divisions of the overall range.
- LABEL THE AXES with the quantity being plotted, including their units.
- Use a sharp pencil and mark each point with a dot, surrounded by a small circle (to indicate that the point is a data point as opposed to a smudge on the page.
- Generally all the points will not be in perfect line – this is okay and does not mean that you should cheat by putting them all on the line. Examiners will be looking to see if you can draw a best-fit line – you can usually make life easier for yourself by putting one end at the origin. The idea of the best-fit line is to imagine that there is a perfect relationship between the variables which should theoretically give a perfect straight line. Your job is to guess where this line would be based on the available points you have plotted.
- Buy a TRANSPARENT RULER to enable you to see the points underneath the ruler when drawing the best-fit line. Make that a LONG transparent ruler. See next point.
- BE VERY CAREFUL drawing a line if your ruler is too short to allow it all to be drawn at once.
Nothing shouts INCOMPETENCE more than two lines which don’t quite match.
- DO NOT JOIN THE DOTS if a straight line graph is what is expected. Make sure that you know in advance which graphs will be curves.
- Note that examiners are obliged to check that each pint is correctly plotted, and you will lose marks if more than or two points are even slightly off.
- When calculating the slope choose two points that are far apart; usually the origin is a handy point to pick (but only if the line goes through it).
- When calculating the slope DO NOT TAKE DATA POINTS FROM THE TABLE of data supplied (no matter how tempting!) UNLESS the point also happens to be on the line.
If you do this you will lose beaucoup des marks and can kiss goodbye any chance of an A grade.
Do you understand why you cannot do this?
WHAT GOES ON WHAT AXIS?
To show one variable is proportional to another, the convention is to put the independent variable on the x–axis, and the dependant variable on the y-axis, (from y = fn (x), meaning y is a function of x). The independent variable is the one which you control.
If the slope of the graph needs to be calculated then we use a difference approach, one which often contradicts option one, but which nevertheless must take precedence. In this case we compare a formula (the one which connects the two variables in question) to the basic equation for a line: y = mx.
See if you can work out what goes on what axis for each of the following examples and in each case establish the significance of the slope of the graph (they get progressively trickier):
- To Show Force is proportional to Acceleration
- Ohm’s Law
- Snell’s Law
- Acceleration due to gravity by the method of free-fall
- Acceleration due to gravity using a Pendulum
- Frequency proportional to length
- Frequency proportional to tension
There is usually a follow-up question like the following;
“Draw a suitable graph on graph paper and explain how this verifies Snell’s Law”.
There is a standard response to this;
“The graph of Sin i against Sin r resulted in a straight line through the origin (allowing for experimental error), showing Sin i is directly proportional to Sin r, and therefore verifying Snell’s Law”.
If you are asked any questions to do with the information in the table, you are probably being asked to first find the slope of the graph, and use this to find the relevant information.
And always, always, label your axes.