How to get an A in Applied Maths

It may not seem a big deal, but if you’re a teacher of Applied Maths then worked solutions – whether they be Department of Education marking schemes or full solutions – can be a life-saver.

The official marking schemes go back to 1995 but for some reason you can only get back to 2001 on the Department’s site

Over the course of the last couple of weeks one of my first-year Science students has been diligently giving up his lunch-times to scan in these earlier marking schemes which are not online (from 2000 – 1995), along with full solutions to 1994 and 1993.

These are all now available on the Applied Maths solutions page which is here.

Together with the existing older scanned in solutions it now forms almost a complete set of solutions going back 35 years.

Over the last couple of years I have converted the exam questions for all of these into Word format and these can be accessed here.

Alternatively I have incorporated the questions into a series of booklets (one per topic) where the questions are grouped by similarity. These booklets also contain introductions to the topics plus gradual lead-in questions taken from Ordinary Level papers.
Many of the questions have a ‘how-to-solve’ guide which gives you some help in answering the question without giving you the full solution (the full solution is available elsewhere).

As always, you can download these one document at a time or alternatively just send me a memory stick and I’ll copy them on and post them back.

Oh – and thanks to Eoin Robinson for all his help; If the resource is useful you might leave a comment and thank him!


Some of my favourite resources in my lab

1. An electronic labeller.
Not cheap. But very, very necessary.
This model allows for different size tape and different font sizes.
It also has a wide range of characters, including mathematical symbols.

2. Trays
More specifically, gratnell trays.
Durable, stackable, availabe in a range of sizes and colours.

3. Sweet boxes
More specifically haribo boxes. For storing all the small bits; everything from protractors to spatulas to  test-tubes.
They also act as little basins of water if need be. And they’re all completely free.

Applied Maths Resources

A bit late in the year perhaps, but for anyone out there studying (or teaching) Applied Maths it might be worth noting that I have uploaded a full set of exam questions in the Exam Material section of the website. These go from 2010 all the way back to 1970. I scanned them in from some old papers I had filed away and then converted them to Microsoft Word so that they can be easily incorporated into other documents (more on that later).

It was an interesting exercise in that up until that point I thought that Applied Maths was one of the very few subjects which required more than simply learning off past questions, but it turns out that if you are prepared to cover the full gamut of questions then almost every question you will see in the 2011 or 2012 paper will be very close in apperance to at least one question which has appeared in the past.

Because I have converted into Microsoft Word there is sure to be the odd typo along the way, which is why  on the same page you can have access to the original papers which I scanned in and uploaded (these only go back to 1976 because the quality of the 1975 – 1970 papers was simply too poor to read after scanning).

In the meantime I am working on a set of solutions for all these – some of which have already been provided by a colleague so it’s a case of trying to fill in the gaps but when I have them I intend to stick them up on the same page – stay tuned, but don’t hold your breath!

Sure to be of use to someone – try to avoid printing these if you can.

And good luck with the study.

Nuclear Physics Resouces

For anyone out there interested in educating themselves on all things nuclear. I teach this as two seperate chapters for Leaving Cert Physics. I would like to think that by studying the notes on the two chapters plus watching the associated links you would actually be in a position to answer any leaving cert questions on the topic.

You can download the word documents for the two chapters here (they’re chapters 30 and 31) and the links for the associated videos are beside them but I’ll put them here for convenience:
The Atom and Radioactivity
Fission,Fusion and NuclearEnergy

The nice thing (I think) is that the word documents contain every exam question that has ever appeared on that topic (broken into individual short questions) plus the solution to each question.
At least I think that’s cool.

It means not only can you put yourself in a postion to understand what’s happening in Japan at the moment but it should feel nice to know that you can do leaving cert Physics!

After all, it’s not rocket science (is it?)

Apart from that, the following video serves as a reasonably good source of information although it is by no means comprehensive and doesn’t list the potential dangers, which is what most people want to know.

Finally, a useful timeline of events is available from Mr Reid’s blog here

Normally we cover this topic towards the end of sixth year but this is the perfect time to introduce the concepts to fifth years; I wonder how many teachers chose not to alter their lesson plan because that’s just not the order in which it’s meant to be taught?

Leaving Cert Physics: Derivations

There are a total of 11 derivations on the Leaving Cert Physics syllabus:

1. Three equations of motion

2. F = ma

3. v = r w

4. Relationship between Periodic Time and Radius for a Satellite in Orbit

5. To show that any object that obeys Hooke’s Law will also execute SHM

6. Equation for a diffraction grating

7. Resistors in series and in parallel

8. F = Bqv

I have put the derivations together in a single word document, together with the year in which they have appeared on an exam paper.

It can be found on the revision page of

Hope it proves useful

Nice resources for atomic bonding

A rather unorthodox approach to revising atomic bonding:

It dovetails nicely with one of the many free resources from absorblearning – in this case an animation of an oxygen atom bonding (covalently) with two hydrogen atoms to form a water molecule.

There are over 100 other free resources like this from the same site (you can see more on the right-hand side of the pages).
It would be ideal if one could link directly to the resourse but instead you have to click on the icon on the top left to arrive at the required distination. Just as well it’s worth the trip.
The plan is put links to most of these in the relevant junior chemistry page of

Junior Cert Physics Resources


I have tended to neglect the Junior Cert end of

Hopefully this has now been rectified. Or at any rate it’s a start.
The interactive links were there already but not easily accessable, and were all on one long page.
The section which took longest to prepare was the ‘Tips for Teachers’ section. Hopefully this will prove useful to Biology and Chemistry teachers, and any new teachers, particularly hdip and trainee teachers.
Being more organised may also encourage me to be a bit more adventurous with the investigative approach rather than just telling students what to do for each so-called ‘experiment’.

I had my own school in mind with our own resources, but tried to be as general as possible.
The links on top are as likely to take you  into a parallel universe as anywhere else, but that’s for another day.

I am particularly proud of the ‘Teachers’ Tips’ column; each section of the Junior Physics syllabus has been teased out seperately with comments which I hope prove useful. Having everything itemised like this means I can follow this guide as I teach them myself and alter sections as needs be. Perhaps others may even get involved and offer constructive criticism on sections which they approach differently.

As with all advice, it is more a work in progress than a finished product. I would like to include a set of equipment for each section which teachers could cross-check in advance, along with a suggested length of time for teaching each chapter and sub-topic.
Next up would be a set of higher-order questions and a variety of teaching approaches, with particular emphasis on Assessment for Learning.

Electricity in particular requires special attention. It is one of the most popular topics on the exam paper and I imagine one of the trickiest to teach for the non-specialist teacher.

But it’s a start.

Feel free to download them to your own pc and adapt them to suit your own school needs. 

Dissection – great fun entirely

I have been experiencing a renaissance in my teaching life ever since I decided to embrace my ignorance on all issues biological (still can’t learn to love Chemistry unfortunately, but there may still be time).

We did heart dissections the other day.

I spent an evening searching for related videos on youtube. I am a firm advocate of the notion that unless you have been ‘prepped’ in terms of what to look for,you may well end up looking at an amorphous mess. In other words both the student and the teacher can be looking at the same object and see two completely different things. Discovery Learning obviously has its place, but as a teacher it’s all about knowing when to mix and match.

As usual there was a lot of sifting to be done before ending up with final list. As always, this is a labour of love.

Along the way I picked up the following nuggets:

  1. Each day your body makes 200 billion new blood cells.
  2. White blood cells live for two weeks, Red blood cells live four months.
  3. You have about 5 litres of blood in your body; when you donate blood you are giving up about half a litre.
  4. Your heart pumps about 70 times a minute, which equates to over 100,000 times a day!
  5. When exercising your heart-rate doubles to about 140 times a minute.
  6. Your heart is about the size of an apple.
  7. Blood takes about 35 seconds to make a round trip when relaxed, or 15 seconds when exercising.
  8. Heart Disease is Ireland’s number one cause of death.
  9. Irish women have almost twice the rate of death from heart disease as the EU average.
  10. The difference between a Heart Attack and a Stroke:
    Both are a result of blocked arteries: In a heart attack the blocked arteries are feeding the heart muscles, and those muscles are not getting the oxygen and nutrients they need to function.
    With a stroke, the blocked arteries are in the brain, and those brain cells are not getting what they need to function… depending on where in the brain it occurs, different functions are affected (e.g., speech, writing ability, and so on…)
    A third place where blocked arteries occur is in the lungs… then it is called a pulmonary embolism.

Ms Salter gave me a crash course on the dissection itself the day before, so I knew just about enough to set the troops on their way. They had an absolute ball, so why is this not a  mandatory activity? Why should non-specialist teachers like me get away with not doing such a memorable activity with my students?

I have since been informed that we can get hold of hearts which have all the tubes coming out of them, which should be much more educational.
I did tape the students doing the dissection itself, but accidentally taped over it. Sorry!
If doing it again I would  tell the students that their task is to teach another group about what they have learned. It tends to focus the mind!

I have put the youtube links on my website here.

Particle Physics and the LHC: some useful resources

The Large Hardon Collider is due to be turned on this day next week (Wednesday, 10th of September), so it’s not a bad time to put together some useful resources to show to the troops to give them some idea of what it’s all about.

At just under 5 minutes, the Large Hadron Rap isn’t a bad place to start:

The ‘rappers’ mention dark energy and dark matter; comprising 96% of the universe between them, they can’t be directly measured, but their influence is immense. Find out more by watching Patricia Burchat speak at TED:

Want more? Try ‘Most of the Universe is Missing

Mary Mulvihill over at Science@Culture reminds us that BBCRadio 4 is devoting the entire day to the event. Watch Dara O’Briain, among others, give his rather unique take on the event. Not a big fan of homeopathy or Deepak Chopra is our Dara. He does appear to be a fan of Physics though; ‘wonder how he got on with Science in school? He strikes me as someone I’d have to keep on when it came to handing out chemicals!


This link is to the CERN website.

Over on Teacher’s TV you can watch Brian Cox present ‘In Search of Giants’; three 15 minute programs:

The Building Blocks of Matter

The Hunt for the Higgs

The Forces of Nature

Finally for teachers, there are various free resources, including posters, available here.