Mike Hayden Maths

Welcome

Hello, and welcome to my website. I’m an experienced maths tutor with a degree in Applied Mathematics. With 5 years teaching experience I have helped students from several schools, colleges and companies to excel in their exams. Below you can find full details of my tutoring services and experience, feedback and testimonials, and samples of my notes and solutions. Simply call or email me at any time to set up a lesson.

Yours in Education
Michael Hayden B.Sc., Grad Dip

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

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.

How much do I charge?

€40 for a 1 hour lesson.

Rates for longer lessons, multiple lessons and groups are negotiable.

When am I currently available?

Mondays	20:00 - 21:00
Wednesdays	19:15 - 21:00
Saturdays	10:00 - 13:00

Which areas of college maths can I teach?

To see samples of solutions to exercises from some of the areas below simply click on the relevant link.

Statistics / Quantitative Analysis

- Measures of Central Tendency and Dispersion

- Linear Programming and Break-even Analysis

- Surveying and Sampling Methods

- Normal Distributions and Calculations

- Binomial, Poisson, Hypergeometric Distributions

- Confidence Intervals

- Correlations and Regression

- Hypothesis Testing

- Index Numbers (Laspeyre, Paasche, etc.)

Calculus / Engineering Maths

- Differentiation and Differential Equations

- Integration and Inititial Value Problems

Mature Students sitting Junior Cert Maths

- All material at Honours or Pass level

Mature Students sitting Leaving Cert Maths

- All material at Honours or Pass level

I am open to teaching other areas of mathematics and am constantly updating my skills. Simply contact me to see if I can help you. It is always useful if you can send lecture notes, tutorial questions or past exam papers by email so I can check what material is involved and your lecturer's method of teaching it.

Who can I teach?

- Junior Cert and Leaving Cert students at Ordinary or Higher Level

- University and College students (undergrad or postgrad)

- Professionals pursuing qualifications

- Adults returning education

Do I teach Leaving Cert Honours maths?

Absolutely. Below are links to pages containing several hundred of my solutions to questions from various Leaving Cert Honours textbooks. Please note that these solutions are geared towards 6th Year students who have developed a reasonable understanding of the topics. For help with the techniques involved please contact me to set up some lessons.

Topic	Questions
Algebra	5
Coordinate Geometry of the Line	11
Cubic Equations	4
Indices	2
Inequalities	16
Logarithms	4
Quadratic Equations	10
Simultaneous Equations	4

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!

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.

Which college courses have I dealt with in the past?

Institution	Course	Module	Year
Trinity College	Bachelor in Nursing Studies	Research Methods	1
UCD	Bachelor of Business and Law	Quantitative Analysis for Business	1
D.I.T.	B.Eng. in Mechanical Engineering	Engineering Mathematics	3
NCI	BA (Honours) in Business	Quantitative and Qualitative Analysis	1
I.T. Tallaght	B.Eng. in Energy and Environmental Engineering	Technical Maths 1	1
Griffith College	BA (Hons) in Business Studies	Quantitative Analysis for Business Decisions	1
DBS	Bachelor of Business	Business Mathematics and Research Techniques	1
The Open University	B.Sc. Information Technology and Computing	Open Mathematics (MU120)	n/a

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	c_f = 5
The cost of sending a text on the bundle service is called the variable cost per unit	c_v = 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:

Answer: The bundle service becomes worthwhile after a person sends their 84^th 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 83^rd text message	83 x 0.1 = €8.30	5 + 83 x 0.04 = 5 + 3.32 = €8.32
Amount spent after 84^th text message	84 x 0.1 = €8.40	5 + 84 x 0.04 = 5 + 3.36 = €8.36

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