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.

## Test

The test will take place at 3 pm in WGB G 05 next Friday 2 November in Week 6.

I would’ve intended that everything up to and including section 2.2 is examinable for the test.

You can find the tests I set for the last two years after Exercise Sheet 1 — which is itself after page 49. Also there is a sample from last year here.

As we will not have covered continuity, we will not be able to do the questions two as they are phrased. However we have covered limits.

I will make some brief remarks on these tests now.

### “MS2001: Test 1 A Solutions”

1. Note that we have only done Q. 1(a) using the Alternate Solution given. This question is worth 5/12.5 = 40%; the thinking being that to be of passing standard you must be able to do this ‘exercise’ question.
2. In light of us not covering Continuity on time, the first part of question could read “Find $\displaystyle\lim_{x\rightarrow 0}f(x)$ or else explain why it does not exist.” To answer this you would have to look at the left- and right-hand limits and invoke Proposition 2.1.3. The second part might ask you “for what values of $a\in\mathbb{R}$ does $\displaystyle\lim_{x\rightarrow 1} f(x)$ exist”, and you would once more have to invoke Proposition 2.1.3. This question is worth 4/12.5 = 32%; the thinking being to get a first you should be able to do the ‘exercise’ question, and this, an ‘exam’ question.
3. For Q. 3 of the test, you need to know and understand the following definitions: even, odd, increasing, decreasing, quadratic, roots, polynomial, rational function, absolute value, limit, one-sided limit. 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. You get one mark for one right, two marks for two right and three plus a bonus half-mark for all three right.

### “MS2001: Test 1 A and 1 B Q 3”

I will not ask you for a definition in question two. Again the question could be “Find $\displaystyle\lim_{x\rightarrow 0}g(x)$ or else explain why it does not exist” and “for what value(s) of $k$ does $\displaystyle \lim_{x\rightarrow -1}g(x)$ exist?”

## Lectures

We are in the middle of section 2.3.

## Tutorials

Remember you can ask whatever you want in tutorials. If you have questions about the test or past exam papers work away.

### Tutorial 4 Question Bank

Question 10 from Exercise Sheet 1 (after page 59 in the notes)

Questions 5, 6 (i), (ii), (iii), 7  from Exercise Sheet 2 — but don’t worry about removable and essential discontinuities (we are using the terms skip-discontinuity and blow-up) (after page 62 in the notes)

Question 1 from MS2001: Exercises (before page 63 in the notes)

Questions 23, 31- 37 from the Additional but Harder Exercises for Definitions I (just before page 60 in the notes).

### Tutorial 3 Question Bank

Question 9 from Exercise Sheet 1 (after page 59 in the notes)

Questions 1 – 4 from Exercise Sheet 2 (after page 62 in the notes)

Questions 4 from MS2001: Exercises (before page 63 in the notes)

Questions 27 – 30 from the Additional but Harder Exercises for Definitions I (just before page 60 in the notes).

### Tutorial 2 Question Bank

Questions 4, and 6 – 8 from Exercise Sheet 1 (after page 59 in the notes).

Questions 1 – 3 from MS2001: Exercises (before page 63 in the notes)

Questions 17 – 22 and 24 – 26 from the Additional but Harder Exercises for Definitions I (just before page 60 in the notes).

### Tutorial 1 Question Bank

Questions 1, 2 and 5 from Exercise Sheet 1 (after page 59 in the notes).

Questions 1 to 16 from the Additional but Harder Exercises for Definitions I (just before page 60 in the notes).