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

## Test 1

Firstly, some good news. I am going at a different pace to last year so in fact we have covered everything we need to do for Test 1 already. All of Chapter 1 and Sections 2.1, 2.2 and 2.3 of Chapter 2 are all that will be examinable in Test 1. This means that Section 2.4 Continuity on Closed Intervals and Chapter 4 Differentiability are not  examinable.

Please find the Sample, Test 1 A and Test 1 B (second two with solutions).

Question 1 will be taken from the exercise sheets, Question 2 from a past exam paper, and Question 3 will be on definitions. Q.1 is worth 4/12.5 or 32%, Q. 2 is worth 5/12.5 or 40% and Q. 3 is worth 3.5/12.5 or 28% (1 correct = 1 mark, 2 correct = 2 marks, 3 correct = 3 marks + 0.5 mark bonus).

For Q. 3 of the test, you need to know the following definitions: even, odd, increasing, decreasing, quadratic, roots, polynomial, rational function, absolute value, limit, one-sided limit, continuous at a point, continuous, composition. Q.3 is a harder question and the thinking behind this is that you can get 72% a bare first if you get all of Q.1 and Q.2 — but you will have to be even better than this to get a higher mark.

## Next Week

Therefore we are going to have a period of revision before Test 1. This Monday we will start with Chapter 4, on Wednesday I will go through the sample test and we will have an additional tutorial instead of a lecture on Monday 24.

## This Week

In lectures, we covered from (but not including) Proposition 2.1.5 to (and including) Definition 3.1.1.

In the tutorial we answered exercises Q. 8 (iv), 9 (ii) & (iii).

## Supplementary Notes

The proof of Proposition 2.3.6.

## Problems

You need to do exercises – all of the following you should be able to attempt. Do as many as you can/ want in the following order of most beneficial:

### Wills’ Exercise Sheets

Q.10 from Exercise Sheet 1.

Q. 1 – 9 from Exercise Sheet 2.

### More Exercise Sheets

Section 2 from Problems.

### Past Exam Papers

Q. 1(b), 3(a) from Summer 2010.

Q. 1(b) from Autumn 2010.

Q. 1(b), 2(b) from Summer 2009.

Q. 1(b) from Autumn 2009.

Q. 1(b), 3 from Summer 2008.

Q. 1(b), 2, 3(a) from Autumn 2008.

Q. 1(a) from Summer 2007.

Q. 1(a), (b), 2 from Autumn 2007.

Q. 2(a), 3(b) from Summer 2006.

Q. 2(b), 3(a) from Autumn 2006.

Q. 2(b), 3 from Summer 2005.

Q. 2(b), 3 from Autumn 2005.

Q. 1(b), 3 from Summer 2004.

Q. 1(b), 2(b) from Autumn 2004.

Q. 1(b), 2(b) from Summer 2003.

Q. 1(b), 2 from Autumn 2003.

Q. 1(b) from Summer 2002.

Nothing from Summer 2001.

Q. 3(b) from Summer 2000.

### From the Class

1. Write a definition for $\lim_{x\rightarrow-\infty}f(x)=K$.
2. Prove Proposition 2.3.2.
3. Prove Corollary 2.3.3.
4. Find a lower bound for $|x^2+4x+4|$ on $(-1,2)$ using algebraic techniques only (reverse triangle inequality or Proposition 1.1.4).