What are my qualifications?

Honours Degree in Applied Mathematics and Computing from the University of Limerick

Postgraduate Diploma in Applied Computing from Dublin Institute of Technology

Who can I teach?

Junior Cert and Leaving Cert students at Ordinary or Higher Level

University and College students (undergrad or postgrad)

Professionals pursuing further qualifications

Adults returning to sit school exams

Students preparing to sit the GMAT or SAT exams

Where can I teach?

I can travel to your home, college or office in most areas on the south side of Dublin within the M50 ring.

Availability

I generally give lessons on weekday evenings, between 7pm and 9pm. Simply email me with your preferred time and I'll let you know if I'm available.

Testimonials

Below is a small selection of the feedback I have received from students and parents. Permission is sought prior to publishing of any quotes, texts or emails.

"Hi Mike, take a bow! Sophie got a B in her maths. Well done to both of you. Talk soon." - Father of Junior Cert Honours Level student.

“Hey, fantastic news, just got my results and I got an A1 in maths! Thanks for all your help!” - Chris, Leaving Cert Ordinary Level student

"I learned more about algebra in that hour than I would in a month in school" - Alex, Junior Cert Honours Level student.

"Hi Mike, just wanted to let u know that I got 490 and Trinity still offered me a place. I actually did better in the Maths section than in the verbal section! It was the toughest exam ever. Thank you for everything. I could not have done it without ur help." - Annie, MBA entrance exam student.

"Hi Mike, delighted to say that I passed both my maths re-sits. Many thanks for your invaluable help - I couldn't have done it without you!" - Paul, DIT Mechanical Enginereering student.

"Just got the results of our Quantitative Analysis group project Mike, 85%, really happy with that, thanks for all your assistance" - Paul, UCD Business and Law student.

Leaving Cert Honours Maths

Below are links to pages containing hundreds of my solutions to Leaving Cert Honours questions. You can also click here to access my new advanced search facility which allows you to narrow down the types of questions you are interested in. Please note that these solutions are geared towards students who have developed a reasonable understanding of the topics. For help with the fundamentals please contact me to set up some lessons.

TopicQuestions
Algebra5
Coordinate Geometry of the Line11
Cubic Equations4
Indices2
Inequalities16
Logarithms4
Quadratic Equations10
Simultaneous Equations4

This section of my website is currently under construction and my solutions for the other topics on the course will appear here shortly. Scanning and uploading the notes is a time-consuming process so please bear with me.

Sample Exam Solution - Break Even Analysis


You are considering changing from a pay-as-you-go mobile phone text service to using a text bundle offer. Currently you pay 10c per text. The Text Bundle offer costs €5 to set up and 4c per text after that. At what volume of texts is it worthwhile signing up to the bundle offer? Illustrate with a graph as well as calculating the exact volume.

Solution with detailed notes

 

The number of texts where the pay-as-you-go service costs the same as the bundle service is known as the break-even point. It is easiest to first use a formula to work this out, and then use our data to produce a graph.

 

First lets identify our different costs and set up some variables to represent these costs. All figures are in €.

 

The cost of signing up to the bundle service is called the fixed cost cf = 5
The cost of sending a text on the bundle service is called the variable cost per unit cv = 0.04
The cost of sending a text on the old pay-as-you-go service is called the price per unit p = 0.1
The number of texts where both services cost the same is called the break-even volume V = ?

 

We then use the following formula to find V:

 

vformula

 

Answer: The bundle service becomes worthwhile after a person sends their 84th text message.

 

Notice that we didn't round 83.333 down to 83 like we usually would in a mathematics problem. To explain why this is lets compare the pay-as-you-go service to the bundle service at 2 different stages:

 

  Pay-as-you-go Bundle
Amount spent after 83rd text message 83 x 0.1 = €8.30 5 + 83 x 0.04 = 5 + 3.32 = €8.32
Amount spent after 84th text message 84 x 0.1 = €8.40 5 + 84 x 0.04 = 5 + 3.36 = €8.36

 

After the 83rd text message, the pay-as-you-go option is still cheaper, but after the 84th message the bundle service becomes the cheaper option.

 

Now lets illustrate the problem with a graph (we will explain how to draw the graph in a moment):

 

breakevengraph

 

The fixed cost of the bundle is simply a horizontal line across the €5 mark. To get the point of intersection between the lines representing the total cost of the bundle and the total pay-as-you-go cost, i.e. the break-even point, we need a pair of coordinates. The x-co-ordinate is simply V which we calculated above, i.e. 83.333. The y-coordinate is the pay-as-you-go cost at this point, i.e. 83.333 x 0.1 = 8.3333. The graph clearly demonstrates how the pay-as-you-go option line is lower (i.e. cheaper) up to the break-even point and then the bundle becomes cheaper.