How to get 100% in your Leaving Cert Physics exam. Part 2: Answering Graph Questions

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.
• 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.
• 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.
• 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 de marks and can kiss goodbye any chance of an A grade.

What goes on what axis?

Option one

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.

Option two

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 (they get progressively trickier):

1. To Show Force is proportional to Acceleration
2. Ohm’s Law
3. Snell’s Law
4. Acceleration due to gravity by the method of free-fall
5. Acceleration due to gravity using a Pendulum

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.

How to get 100% in your Leaving Cert Physics exam. Part 1: Section A

Section A counts for 30% of your overall mark and is the easiest section to pick up full marks. There are about 24 experiments but many of them are minor variations on each other. Stop wasting time trying to predict which ones will come up and just learn them all. Take one or two per night and make sure you can answer every question on each experiment from past papers. In particular you need to use the following as a checklist for each experiment.

(i)     Draw a fully labelled diagram which includes all essential apparatus (have you included the apparatus necessary to obtain values for both variables?).

(ii)   Be able to state how the two sets of values were obtained (this is a very common question).

(iii) Describe what needs to be adjusted to give a new set of data

(iv) Write down the relevant equation if there is one associated with the experiment.

(v)   Be able to state how the data in the table will need to be adjusted.

(vi) Know what goes on each axis.

(vii)           Know how to use the slope of the graph to obtain the desired answer.

(viii)         Be able to list three sources of error/precautions.

Misc Points

• The graph question is usually well worth doing.
• Learn the following line off by heart as the most common source of error: “parallax error associated with using a metre stick to measure length / using a voltmeter to measure volts etc”.
• Make sure you understand the concept of percentage error; it’s the reason we try to ensure that what we’re measuring is as large as possible.
• There is a subtle difference between a precaution and a source of error – know the distinction.
• When asked for a precaution do not suggest something which would result in giving no result, e.g. “Make sure the power-supply is turned on” (a precaution is something which could throw out the results rather than something which negates the whole experiment).
• To verify Joule’s Law does not involve a Joulemeter
• To verify the Conservation of Momentum – the second trolley must be at rest.
• To verify the laws of equilibrium – the phrase ‘spring balance’ is not acceptable for ‘newton-metre’.
• To measure the Focal length of a Concave Mirror or a Convex Lens.
Note that when given the data for various values of u and v, you must calculate a value for f in each case, and only then find an average. (As opposed to averaging the u’s and the v’s and then just using the formula once to calculate f). Apparently the relevant phrase is “an average of an average is not an average”.

I have a document here which containts exam questions on every experiment which has ever appeared on a past paper from 2002 to 2010 (Higher Level and Ordinary Level) – this should be your bible for Section A over the coming weeks. Solutions are also included.

Now get back to work.

More to come.