## Test 2

Thursday 23 November at 09:00 in the usual lecture venue. You will be given a copy of these tables. Based on Chapter 3, samples at the back of Chapter 3 and also here (Q. 4 has a typo — it should be ). I strongly advise you that attending tutorials alone will not be sufficient preparation for this test and you will have to devote extra time outside classes to study aka do exercises.

## Week 10

We started Chapter 4 by looking at integration by parts. We started looking at completing the square.

## Week 11

We will look at completing the square and work.

## Week 12

We will look at centroids and centres of gravity.

## Week 13

There is an exam paper at the back of your notes — I will go through this on the board in the lecture times (in the usual venues):

- Monday 16:00
- Tuesday 09:00
- Thursday 09:00

We will also have tutorial time in the tutorial slots. You can come to as many tutorials as you like.

- Monday at 09:00 in E15
- Monday at 17:00 in B189
- Thursday at 12:00 in B180

## Study

Please feel free to ask me questions about the exercises via email or even better on this webpage.

## Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc.

## 4 comments

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November 21, 2017 at 8:22 am

StudentHi J.P.,

Could you correct these for me please and tell me how to do Q4 aswell.

Thanks a lot.

November 21, 2017 at 8:34 am

J.P. McCarthyRegarding Q. 1, and it is not true that

If you divide above and below you by you get:

.

Regarding Q. 2, area doesn’t come into it at all.

Regarding Q. 3, you have the slope correct but note the question doesn’t ask for anything more.

Regarding Q. 4 you need to know that:

increases with .

decreases with .

For Q. 5, you lose one mark for not including the unit. After that, please round the error to one significant figure (because using the differential is a rough approximation):

and match the precision (because beyond this is within margin of error: no decimal places in this case) with the calculated value:

,

so your answer reads

.

Regards,

J.P.

November 21, 2017 at 4:03 pm

StudentJ.P.,

I’m one of your maths student and was wondering if you could help with the question we were doing for tutorial. It’s question 5 of the last Test 2 paper you sent us. I’ve attempted it and just wanted to see if I was right and if not if you could show or tell me where I went wrong please.

November 21, 2017 at 4:20 pm

J.P. McCarthyThe error is never going to be zero, so you have certainly gone wrong. I don’t see how you get zero or where you calculated the partial derivatives.

Solution: We have . We have measurements and .

Our best guess for , which we denote by , is given by:

.

We approximate the error in this calculation, due to the error in the measurements of and using differentials:

.

We therefore need to differentiate partially with respect to and . The quickest way is to rewrite:

. Thus we get:

and

.

Alternatively, using the Quotient Rule on :

, and

.

Therefore

.

Evaluating the derivatives at the measurements:

The absolute value of is , so

.

It is good practise to round this to one significant figure because it is a rough approximation (not applicable here) and also, with the calculation, , to match the precision: in this case two decimal places: everything beyond the second decimal place is within the margin of error.

Answer therefore,

.

This question is missing context that would tell us the units. If there are units they must be included.

Regards,

J.P.