Mathematics – Irish Leaving Certificate

I recently mentioned that the brilliant Maths Emporium team have been busy with the filing cabinets! You will find many International GCSE Mathematics papers. The Mathematics Emporium is a free website intended for the use of teachers of mathematics in secondary schools, wherever they are located and regardless of what awarding body they use.

Maths Emporium International papers
Maths Emporium

On the subject of papers from beyond UK shores, from Ireland, we have the Irish Leaving Certificate Qualification.

Students normally sit the Junior Certificate exam at the age of 14 or 15, after 3 years of post-primary education and from the Graduate Recruitment Bureau A Level Equivalents Guide we see that An Irish Leaving Certificate is roughly equal to two-thirds of an A Level and is the main basis upon which places in universities, institutes of technology and colleges of education are allocated.

These qualifications with their very clear mark schemes provide us with another source of very useful examples. Once you have clicked the checkbox to verify that you have read, understood and accepted the terms and conditions, you can search for papers and mark schemes by subject. As well as marking notes, an excellent feature of these mark schemes is the model solutions provided.

For example, if we look at the Junior Certificate 2017 higher paper, question 6 is on Venn Diagrams; the mark scheme provides a model solution.

Looking at the 2017 Leaving Certificate paper, I see, for example, differentiation from first principles and De Moivre’s Theorem. Again, model solutions are provided as part of the mark scheme.

I mentioned the Project Maths site in a previous post, this is an Irish site supporting Mathematics teachers. These teacher resources are for Leaving Certificate students. A site well worth exploring, looking at Algebra we see for example under expressions:

Project Maths Student Resources Index
The student resources include many activities with accompanying GeoGebra files.
Project Maths Student Resources
Modulus Inequalities Project Maths

Integration and area

Junior Certificate resources are also available.

These whiteboard templates caught my eye, simply download the file, project it onto your whiteboard, use the interactive menu to choose the background you need and start writing!

Project Maths - Whiteboard Templates
Project Maths Ireland – Whiteboard Templates









Plans and Elevations

Needing some resources for Plans and Elevations this week – some great resources are…

Diagnostic Questions
A go-to site where I know I can find a quiz on any topic. Looking at the AQA Quiz Collection, we find – 2D Representations of 3D Shapes.
Diagnostic Questions AQA

A lovely (free) interactive 3d modelling tool to demonstrate plans and elevations is available in the Geometry collection on on the excellent MathsPad. MathsPad is a subscription site (a very reasonable subscription providing value for money in my personal opinion), you can search for Free resources and you will discover an excellent collection.

TES Resources
Plans & Elevations TES

This search returns many excellent (free) resources on TES on Plans and Elevations, note that these are TES Picks. The slide shown here is from a very clear PowerPoint, Plans and Elevations,  author, Fintan Douglas.

Dr Frost
Dr Frost Plans & Elevations
Another go-to site, from Dr Frost we have his Plans and Elevations resources. Dr Frost’s consistently high-quality resources include full solutions; you will also find plenty of challenges for students aiming at the highest grades.

SSDD Problems
SSDD Problem Triangular Prisms 2
SSDD Problems tagged Plans and Elevations are currently Triangular Prisms 2 and Triangular Prisms 3.

Don Steward
Don Steward
Many excellent challenges from Don Steward on Plans and Elevations.


GCSE Mathematics Revision (14-16)

With two of three UK GCSE Mathematics papers still to go at the time of writing, I can see the various revision pages are popular. The GCSE (14-16) Revision page has been updated since last year; notable additions include:

From David Morse, Maths4Everyone has a wonderful collection of high-quality resources, all freely available on TES Resources. Note all David’s fully worked exam questions by topic.
Inequalities & Regions David Morse
Also on Maths4Everyone, you will find a lovely collection of GCSE Revision Worksheets including a great set of SSDD revision questions. (See Craig Barton’s SSDD Problems site.)
SSDD Questions David Morse

From the Eduqas resource collection, we have Mathematics Take-Aways for Higher and Foundation. These attractively presented resources offer very useful revision indeed. Full solutions are provided.

Mathematics Take-Away - Eduqas
Mathematics Take-Away – Eduqas


On Maths Genie, you will find numerous resources by topic. Under Grade 7, for example, we have Inverse and Composite Functions. You will find some revision examples and also exam questions with solutions.

Maths Genie Functions

For centres offering International GCSE qualifications, you will find the brilliant Maths Emporium team have been busy with the filing cabinets.

Maths Emporium International papers

Maths Emporium

Note that all the exam boards add examination papers to their secure sites; these should, of course, be kept securely, they are intended only for teachers. They should not be shared.

Have you seen…? #3

… these GCSE lesson starters from Eduqas?

Starters - Eduqas
GCSE Starters – Eduqas

A starter, with a worked solution, is available for every day of the year. Starters are also available for Foundation Upper and Foundation Lower. (Select ‘Open resource’ under Files.)

Starter - Eduqas

Eduqas have a whole collection of Mathematics resources well worth exploring. I have used their lovely Rotations, Reflections and Enlargements demonstrations for many years! Looking at the collection, a very happy discovery, these Loci resources.


Loci Teaching Tool – NGfL Cymru

Appropriately for this time of year when so many students are revising for examinations, anyone for a Mathematics Take-Away? These attractively presented resources offer very useful revision indeed. Full solutions are provided.

Mathematics Take-Away - Eduqas
Mathematics Take-Away – Eduqas


Have you seen…? #2

…the famous equation poster contest from the excellent Math Careers site?

Do you have a favourite equation? Peter Alfeld of The University of Utah has a collection he thinks are important or intriguing. My personal favourite, Euler’s identity, is his first on the list.

                    eiπ = -1

For more on beautiful equations try the 17 equations that changed the world on the World Economic Forum where for each equation we have the following information:

  • What does it mean?
  • History
  • Importance
  • Modern use

Or from BBC Earth, have a look at “What is the most beautiful equation?

For UK school age students note the famous equation poster contest from the excellent Maths Careers site. This competition closes on Friday 8th June; winners in each age group will win an Android tablet. There will also be five ‘highly commended’ certificates awarded in each group.

I have added the competition details to Mathematics for Students.