Happy New Year


Janus the Roman god of beginnings, gates, transitions, time, duality, doorways, passages, and endings is usually depicted as having two faces, one looking to the future and the other to the past. Whether or not the month of January has actually been called after him, his image provides a good representation of this reflective time of the year.

From GMG’s perspective we can look back on the past year with satisfaction and forward to the new year with anticipation of further growth and development. Once again our exam students did us and themselves proud with the results they achieved.

We expanded our  offering with the launch of a the following online courses and resource packs:

Early in the new year we will add a resource for the new Junior Cert Business Studies course. June 2019 will be the first sitting of the exam with the common level paper in place of the separate ordinary and higher level papers up to this.

Wishing you a happy, peaceful and prosperous new year.

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Simple way to produce Trigonometric Table

I have been asked by a reader of this blog if I have any tricks to help remember values in the trigonometric table. Well, Mohamed, here is a way to produce a version of the table. You can easily add additional values to the simple table shown below by recalling the definitions of other functions.

Table of trig values


The steps to produce this are as follows:

  1. Draw a blank template for your table with six columns.
  2. Fill the cells of the first  row  with “angle” and the numbers 0,1,2,3, and 4 respectively.
  3. Divide across by 4.
  4. Get the square roots.
  5. Write each entry in simplest form.

You now have the sine values for angles of 0, 30, 45, 60, and 90 degrees.

Reverse the order of the results to get the corresponding cosine values.

Get the tangent values using tan = sin/cos.

If you want to extent the table to other values you can do so using:

cotan = 1/tan  = cos/sin          sec = 1/cos          cosec = 1/sin


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Work out rather than remember Trigonometric Formulae

If you can draw the picture, apply Pythagororas’ theorem and use similiar triangles you can work out the formulae.

Trigonometric Formulae

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GMG Launches Resource Pack for Leaving Cert Physics

LC Physics resource Pack

This resource includes:

A number of publications from Galway Maths Grinds:

Making the most of your Scientific Calculator

Time Management for Students

Google Search for Students

Making the most of the Formulae and Tables Booklet

Resources from the State Exams Commission website examinations.ie gathered here for convenient access:

Past exam papers

Marking Schemes

Advice from Chief Examinations Officer

Course Syllabus

Links to useful websites and video tutorials

Facility to download sheets of graph paper to print off.

Advice on how to prepare for and approach the examination

Some suggestions on how to remember things in physics


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A way to remember Physics Formulae related to Electricity

Distance Sppeed Time

It is not uncommon for students to make use of triangles like those shown on the left to help remember or quickly solve formulae based on equations of the form A=B.C or B=A/C.

While these can be quite useful as memory joggers, it would probably be too cumbersome for most people to try this method for remembering a lot of different formulae.

The use of the first letter of each word in a sentence or phrase to help recall an ordered list of items is another well used method of aiding memory. Ring Out Your Great Bells In Victory can be used to recall that the colours of the rainbow, the spectrum of white light, in increasing order of frequency, are Red Orange Yellow Green Blue Indigo and Violet.

The image below combines these two methods to help remember physics formulae relating to electricity.

Physics formulae - electricity

The top half is used to help explain the method implemented in the bottom half.

Step 1: draw five triangles laid out as shown.

Step 2: Add the letters




Step 3:  in three rows at the corners of the triangles. Make up a sentence to remember these letters in the given order. I have used

James Watt Can Justify

Clear Values And Serious Work

Acting Openly.

These stand for the units of measurement of different physical parameters as indicated in the bottom half of the image.





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New Course Launched – Resources for Junior and Leaving Cert Maths Students

Resources for Maths Students

GMG has today launched its online mini-course “Resources for Junior and Leaving Cert Maths Students“.

The purpose of this course to gather together in a cost-effective manner a number of publications of Galway Maths Grinds that are of value to students, particularly those studying for either the Junior Certificate or Leaving Certificate Maths exams, and to add further value by providing links to a number of other useful resources, such as a facility to download and print off graph paper.

The GMG documents included are:

  • Making the most of your Scientific Calculator
  • Time Management for Students
  • Google Search for Students
  • Junior Certificate Geometry Theorems
  • Making the most of the Formulae and Tables Booklet
  • How to Study Maths

The advantages for students of the “course” format over getting individual PDF documents to download include:

  • A lower price, by almost 30%, for the bundle compared to getting the individual documents separately.
  • Can access on-line any time to either download or view online compared to having one time access only to allow download to your own device.
  • Will automatically have access to any further updates or additions to the course.
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GMG launches Online Time Management Course

Personal Effectiveness is a measure of an individual’s overall ability to perform various tasks and activities in his or her educational and life endeavours. There are practical, straightforward skills and strategies needed to excel in the various realms in life. These personal effectiveness skills include amongst others; personal goal setting, time management, study skills, organization, problem solving, decision-making and efficient use of various tools and resources at ones’ disposal. The development of these skills allows individuals to become more capable, competent, and confident in themselves and their performance, and help them to be better able to reach the goals they set for themselves.

At Galway Maths Grinds we provide information and strategies to help individuals to make the most of their talents and abilities. Individuals can use these simple strategies and techniques to make the very most of their learning activities.

While you can not beat working one on one with an experienced mentor, we can only help a limited number of students in this manner. To cater for others we have a number of publications that can be purchased online and downloaded as PDF files.

Today we launch our Effective Time Management course which students can follow online at their own pace.

It launches at an introductory price of €23.37  until November 1st when it will revert to the normal price of €61.50.

If you are curious about the odd pricing, it is because we are using an American platform to host the course and it requires the course to be priced as a whole number of euro before VAT is added. VAT of 23% is then added because we are based in Ireland.  So the  €23.37  is made up of a pre VAT price of  €19 plus 23% VAT.



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The Greek Alphabet

When learning new material in subjects like maths, physics and other science subjects we not only encounter new concepts, but new notation and language.  The letters of the Greek alphabet are often used to represent different things in these subjects. They can cause a little confusion when first encountered, particularly the distinctions between upper and lower case versions of the same letters. So I thought it useful to provide a copy of the alphabet here.

Greek Alphabet

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Back to School – How do I Succeed?

Now that the summer holidays have ended and students are back to school there will be mixed feelings. The extra freedom of the holidays has vanished for another little while, but all the activities you take part in with your school friends start up again.  A big question for students and parents is what can I do to make the most of my time at school for the coming year?  While the question may be particularly pertinent for students in exam years, it applies to all.

There will be lots of advise from lots of different people. Much of it good advise and some maybe a bit questionable. You could feel overwhelmed with it all if you do not keep it in perspective. You have lots of subjects to study, but not everyone is actually taught how to learn most effectively. So brushing up on effective study skills would be a great help.

But this question; what can I do to make the most of my time at school for the coming year?, can be applied to any aspect of your life, not just academic studies. A broader question is what can I do to make the most of the time I have in my life? In fact there is a lot you can do.

I would suggest that the first skills to master for studying effectively  are the same skills to be mastered to be successful in any aspect of your life. What are they? –  Effective Time Management skills. The number one set of life skills that most people do not learn to master are basic time management skills. Time management is effectively management of your self so that you figure out what is important to you. It involves doing the right things at the right time, in the right way to achieve the goals that you have chosen for yourself. It does  not need to be complicated, but it does require a little thought and effort. And a little coaching from someone with experience can make a great difference to how quickly and easily you develop the skill set.

Galway Maths Grinds has produced an online Time Management course that goes live at the end of September. Students will be able to follow the course at the own pace, and by doing the simple assignments in the course workbook end up on completion with their own personalised time management system that they can apply to any aspect of their lives.






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GMG arrangements for Ed Sheeran Concerts

All classes are as normally scheduled. We remind clients of Galway Maths Grinds on Friday evening and Saturday to keep the car pass you were issued in the car when coming to class. It might be a good idea to put it in the car now rather than risk forgetting it on the day. Have the pass on the dash of the car as you approach a control barrier and you will be waved through.

Note also that a one way traffic system will be in place in accordance with the details on the map below. The direction of traffic flow will be from Threadneedle Road down Dr Mannix Road and towards the Prom via Rockbarton Road or Dalysford Road. Click on the map to see a larger version.

Traffic system for concerts

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