I am emailing a link of this to everyone on the class list every Friday afternoon. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.ie and I will add you to the mailing list.

## Notes

As of 29 September: MATH6000 notes.

Also an E-Book: Engineering Mathematics by John Bird.

## Test Notice

Your first assessment will be on Wednesday 10 October in Week 4. The exact time will depend on your class group and will be communicated to you this week. The test will be a 45 minute, multiple-choice test (15 questions equally-weighted questions) and calculators will not be permitted.

A sample, which is also up on Blackboard and will be given to you Monday, may be found here.

Do not miss this first assessment. The policy on missed assessments is very strict in CIT as you can see here.

## Exercises

Quite apart from the exercises in the notes, there are also exercise sheets on Blackboard. The new ones this week are

I will give you a copy of both on Monday, along with a copy of the sample assessment.

Common Entry Science: Next Week we will work on the sample assessment mostly.

Biosciences: Your ‘other’ tutor may work with you on the sample assessment or the exercise sheets. I shall work with you on exercises in the notes. If you do not know what tutorial group you are in please consult here.

Computing: Tim Buckley will work with you on the sample assessment or the exercise sheets. I shall work with you on exercises in the notes. If you do not know what tutorial group you are in please consult here.

If you are having serious difficulty with doing exerices for MATH6000 Essential Maths, particularly long multiplication and division (as you will have to do some in the first assessment), then please visit the Academic Learning Centre where they will sort you out as best they can free of charge. The timetable may be found here.

## In-class Issues

### Significant Figures

We never spoke about significant figures but they did pop up in the Basic Calculations sheet.

Round each of the following: 78.96385, 54.0052, 9.4845,3$\pi$ , $\sqrt{18}$ and 0.23456 to:
(a) 3 decimal places.
(b) 1 decimal places.
(c) 3 significant figures.
(d) The nearest whole number.

Most people could handle (a), (b) and (c) but had no experience of (c). Significant figures refers to the somehow important digits in a number that indicate it’s magnitude with a varying level of detail (precision). For example, if you woke up one day with €10,023,323.78 in the bank you would say to yourself “great, I’ve got ten million euro in the bank”.

We might be asked to evaluate a number to, say, three significant figures. What this means is that you take the first three digits with the first non-zero digit in the decimal representation with rounding. The symbol $\approx$ denotes “is approximately“. For example, $\pi\approx 3.14$.

E.g.

$78.96385\approx 79.0$ to three significant figures.  We start with 78.9 but the 0.06 rounds the 0.9 up to a one and hence the 78 to a 79.

$54.0052\approx 54.0$ to three significant figures.

$9.4845\approx 9.49$ to three significant figures. We start with 9.48 but the 0.0005 rounds the 0.004 to a 0.005 which in turn rounds the 0.08 to a 0.09.

$3\pi\approx 9.424777961$ using a calculator so $3\pi\approx 9.43$ to three significant figures.

$\sqrt{18}\approx 4.242640687$ using a calculator so $\sqrt{18}\approx 4.24$ to three significant figures.

$0.23456\approx0.235$.

### Ratio and Proportion Question

We never did an example like Q. 7 on the Blackboard Ratio and Proportion sheet.

If three people can complete a task in six hours, how long will it take five people to complete
the same task, assuming the work rate remains constant?

Most of us can probably get the solution using a trial and error method but here we will present a slicker method to get to the answer.

First note that if there are three people working for six hours then it takes $3\times6=18$ man hours to complete the job.

So now we divide the 18 man hours it will take to do the job by the number of people:

$\displaystyle \frac{18}{5}=3.6$

So each man has 3.6 hours’ share of the work to do and if they work at a constant rate the job will be done in that time: 3.6 hours.

## Calculator Use

If you have not used a scientific calculator in a while or are not sure how to operate one please consult this guide.

## Ratio and Proportion Notes for Common Entry Science

I messed up here and had ye doing questions on ratio and proportion before we covered it in class. However ye were so good at these questions I decided that doing a lecture on them would have been a waste of time. However if anybody has fallen through the net the completed notes may be found here.