Graphs

How to get an A in Junior Cert Science: Part 2 – the graphs

Since this science course was first examined in 2006 graph questions have become quite common.

There are different types of graph questions, and we will look at each of these different types in turn.

There is nothing scary here, and you have probably covered them all in maths anyway. It’s just that the science textbooks don’t seem to do a very good job of telling us why we have them in the first place, or why there are different types.

Why do we have graphs?

You won’t get asked this so you don’t have to learn it off by heart – I just thought you deserved to know.

There are many different reasons, but we’ll just look at two here.

Reason 1:

To see what the relationship is between two variables, e.g. between the extension of a string and the force which caused it.

Now assuming that a bigger force causes a bigger extension, the question is; are the two quantities directly proportional? i.e. if the size of the force doubles then the extension should be twice as much, if the force triples the extension will be three times as much etc.

Another way of saying this is that the two quantities increase at the same rate (as force is increased the extension increases at the same rate).

Or finally the scientific way of saying this is to say that the two quantities are directly proportional to each other (you must learn the phrase in italics off by heart because it gets asked a lot as you will see below).

To investigate this you would plot the results on a graph, and if the two quantities are directly proportional then you will find that if you draw a line through the points you will end up with a straight line through the origin (the origin is the (0,0) mark).

 

Reason 2:

In some graphs the slope of the line gives us some extra information (and you must know what this is).

There are only three graphs which fall into this category so make sure that you know each of them.

1. The slope of a distance-time graph corresponds to the speed (or velocity) of the moving object

2. The slope of a velocity-time graph corresponds to the acceleration  of the moving object

3. The slope of a voltage-current graph corresponds to the resistance of the resistor under investigation.

 

Note that for each of these graphs you will also get a straight line going through the origin, which verifies that the two quantities are directly proportional to each other.

 

Which brings us to our next problem – how do we calculate the slope of a line?

 

To calculate the slope of a line

Pick any two points (from the graph) and label one point (x1y1) and the second point (x2y2).

Make life easy for yourself by picking (0,0) as one of the points (assuming the line goes through the origin).

You must then use the formula:                                    

slope = (y2 – y1)/(x2 – x1)

Note that you can also find this formula on page 18 of the new log tables

Yo – Which axis is the y-axis?

Remember the yo-yo? It goes up and down right? Well so does the y axis (and it begins at zero) so y-zero = yo

Now that’s just freaky.

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

The following can be downloaded as a word document here

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.

 

 

Junior Cert Science – answering graph questions

Since this science course was first examined in 2006 graph questions have become quite common. If you know how to answer them they can be a source of very easy marks but if you’re not familiar with them you can similarly lose a lot of marks just by not knowing some simple rules. And remember there is no choice on the paper!

There are different types of graph questions and you have probably covered many of them in maths anyway. It’s just that the science textbooks don’t seem to do a very good job of telling us why we have them in the first place, or why there are different types.

The graphs you need to be familiar with:

  1. Distance-time graphs
  2. Velocity-time graphs
  3. Voltage-current graphs
  4. Force-extension graphs
  5. Cooling curves
  6. Solubility curves

As you can see these are almost all from the Physics section of the course, and unless you have practiced answering exam-questions they can seem rather intimidating. The link below is to a document which contains all recent exam questions on graphs at Higher Level and Ordinary Level and also includes the solutions. The nice thing is that once you’ve done one or two questions on a given graph they all tend to repeat after that.

There is lots of other advice on answering the graph question, but it’s all in the document itself.

Hope it’s useful!

Revision – Graphs

Junior Cert Science – Graphs and the phrase ‘directly proportional’

Usually there is at least one graph to draw on the Junior Cert Science paper, and if it’s in the Physics section then chances are it will be a straight line graph (the main exception is Cooling Curves). There’s nothing on the syllabus (that I’m aware of) that states that students are expected to know the significance of a straight line graph. In fact here’s a piece of research for you – next time you’re in class ask your students why we’re expected to bother with graphs in the first place. My bet is that very few will be able to give a convincing answer.

One reason we ‘bother’ with graphs is to establish a relationship between two variables; to use the correct jargon we want to see if the variables are ‘directly proportional’ to each other. Now that term ‘directly proportional’ is very important. In means in effect that the two variables are increasing at the same rate. For example if you are on a bicycle travelling at a steady speed of 10 m/s, then for every second that you cycle you will have travelled 10 m (d’oh), and if you travel for twice as long you will cover twice as much ground. If you travel for four and a half times as long, you will cover four and a half times the distance.
So again, the time and the distance covered are increasing at the same rate – they are directly proportional to each other.

The graph is our way of verifying this – it turns out that when you plot all the given data and you end up with a straight line which passes through (0,0) then we can state that the two variables are directly proportional to each other.

So why am I telling you all this now?
Because in the exam you may be asked to draw a graph and then say what the relationship is between the two variables. And if you don’t use the phrase ‘directly proportional’ in your answer then you probably won’t get full marks.
Now as I mentioned I have never seen this phrase highlighted in a Junior Cert textbook so you may well have heard it here first.

Now to help you I have compiled all the graph questions that have ever been asked at Junior Cert into one word document. You can find it on the revision page of thephysicsteacher here (it’s no.3 – Graphs). It also contains all the solutions to the questions, plus a list of do’s and don’ts.

Make sure you check it out before going into the exam. And if you’re reading this as a teacher please remember when photocopying to copy back-to-back and reduce two pages onto one. In doing so you reduce the amount of pages by a factor of 4.

Good luck!