**I am emailing a link of this to everyone on the class list every week. 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.com and I will add you to the mailing list.**

## Continuous Assessment

You are identified by the last four digits of your student number unless you are winning the league. The individual quiz marks are out of 2.5 percentage points. Your best eight quizzes go to the 20% mark for quizzes. The R % column is your running percentage (for best eight quizzes), MPP is your Maple Percentage *Points* and the GPP is your Gross Percentage *Points* (for best eight quizzes and Maple). Most of the columns are rounded but column five, for quiz four, is correct.

S/N | Q1 | Q2 | Q3 | Q4 | Q5 | Q6 | Q7 | Q8 | Q9 | Q10 | Q11 | R % | QPP | MPP | GPP |

Kelliher | 3 | 3 | 3 | 2.5 | 100 | 10.0 | 3 | 13.0 | |||||||

3281 | 2 | 3 | 3 | 2.5 | 99 | 9.9 | 3 | 12.9 | |||||||

8335 | 2 | 3 | 2 | 2.5 | 98 | 9.8 | 3 | 12.8 | |||||||

5527 | 2 | 3 | 3 | 2.5 | 94 | 9.4 | 3 | 12.4 | |||||||

7878 | 2 | 2 | 2 | 1.9 | 85 | 8.5 | 3 | 11.5 | |||||||

1864 | 1 | 2 | 3 | 2.1 | 83 | 8.3 | 3 | 11.3 | |||||||

8403 | 2 | 1 | 2 | 2.5 | 82 | 8.2 | 3 | 11.2 | |||||||

8478 | 2 | 2 | 2 | 2.4 | 82 | 8.2 | 3 | 11.2 | |||||||

8416 | 2 | 1 | 2 | 2.5 | 80 | 8.0 | 3 | 11.0 | |||||||

4198 | 0 | 1 | 2 | 2.5 | 76 | 5.7 | 3 | 8.7 | |||||||

6548 | 2 | 1 | 2 | 2.5 | 73 | 7.3 | 3 | 10.3 | |||||||

8603 | 1 | 2 | 2 | 2.4 | 67 | 6.7 | 3 | 9.7 | |||||||

8556 | 1 | 1 | 2 | 2.2 | 66 | 6.6 | 3 | 9.6 | |||||||

2567 | 2 | 2 | 2 | 1.28 | 64 | 6.4 | 3 | 9.4 | |||||||

7209 | 2 | 1 | 2 | 0.5 | 54 | 5.4 | 3 | 8.4 | |||||||

2859 | 2 | 1 | 0 | 0.5 | 52 | 3.9 | 3 | 6.9 | |||||||

1852 | 1 | 1 | 2 | 1.5 | 50 | 5.0 | 3 | 8.0 | |||||||

9464 | 1 | 1 | 2 | 0.9 | 45 | 4.5 | 3 | 7.5 | |||||||

5546 | 0 | 0 | 1 | 1 | 42 | 2.1 | 3 | 5.1 | |||||||

7950 | 0 | 0 | 1 | 0 | 32 | 0.8 | 1.5 | 2.3 | |||||||

8455 | 0 | 1 | 1 | 0.7 | 29 | 2.9 | 3 | 5.9 | |||||||

5553 | 0 | 1 | 0 | 0 | 24 | 1.2 | 3 | 4.2 | |||||||

4775 | 1 | 0 | 1 | 0 | 24 | 1.8 | 3 | 4.8 |

The solutions to three of the quiz questions may be found in the notes. The only other question is done here: *Use *partial fractions *to decompose .* *I give two worked solutions with explanations.* **Standard Method** The first thing we must do is factorise the ‘bottom’ (denominator), . We multiply and look at the factors of eight which are and we can use and to rewrite :

Now to each factor in the bottom we can associate a term in the partial fraction expansion. Here we have distinct linear factors, which is Rule II:

.

Therefore, for the partial fraction expansion we need for all values of (the bottoms are the same).

If they are equal for all values of we can input values of into both of them to generate equations in and . For example, :

,

and ,

,

so the answer is

.

**Cover Up Method**

Because there is no in the factorisation I can use the Cover Up Method.

.

## Quiz 5 Question Bank

The question bank for Quiz 5 (in Week 7) is as follows:

- P. 58, Q. 1(iii) & (iv)*, 3, 4, 5** & 6

* there is a typo in the solution. The second term should be .

** there is a typo in the answer to Q.5(iii) – it should be rather than . The final answers will not be given on the quiz paper and neither is there any value in writing down the final answers alone — you will receive marks for full and correct solutions — but nothing for final answers without justification or skipping important steps. Please don’t learn off model solutions — you need to understand the material not just on a superficial level to do well later on. Quiz 5 runs from 19:15 to 19:30 *sharp *on Wednesday 18 March.

## Academic Learning Centre

I am waiting for an update on the issue of day students taking over the evening session.

## Week 6

No classes next week but we will have a Maple night on April 1 in the normal rooms.

## Maple Labs

We have a Maple Lab Wednesday 18 March. **Group 1 – Starts at 18:00 and Finishes at 20:50:** Wednesdays 18:00-19:05 – Maple Lab in room C219 Wednesdays 19:15-19:30 – Weekly Quiz in C212 Wednesdays 19:30-20.50 – Theory class in room C212 **Group 2 – Starts at 19:15 and Finishes at 22:00:** Wednesdays 19:15-19:30 – Weekly Quiz in C212 Wednesdays 19:30-20:50 – Theory class in room C212 Wednesdays 20.55-22:00 – Maple Lab in room C219 As you can see here you can download a student copy of Maple. Some students said that they were unable to open the file I sent in their Maple 17 — this is strange as I am actually using Maple 16!

## Week 5

In Week 5 we finished off Partial Differentiation and used it to look at Error Analysis.

## Week 7

In Week 7 we will finish off Error Analysis and look at some numerical methods of solving equations and evaluating integrals. In Maple, we will look at Partial Differentiation and Error Analysis.

## Study

Please feel free to ask me questions about the exercises via email or even better on this webpage. Anyone can give me exercises they have done and I will correct them. I also advise that you visit the Academic Learning Centre.

## Continuous Assessment

The Continuous Assessment is broken into Weekly Quizzes (20%) and Maple (10%). There will be *eleven** *weekly quizzes and your eight best results will count (so 2.5% per quiz from eight quizzes). You will receive an email (i.e. this one) on Thursday/Friday detailing the examinable exercises. Maple consists of five labs and a Maple Test in the sixth lab. Satisfactory participation in labs gives you 1.5% and the Maple Test is worth 2.5%. More on this in the coming days.

## Student Resources

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

## 10 comments

Comments feed for this article

March 16, 2015 at 5:04 pm

StudentHi J.P.,

Having trouble with these two questions; would you point me in right direction?

March 16, 2015 at 5:12 pm

J.P. McCarthyQ.3 (ii)

Everything is correct up until the final line .

Q.6

When you are differentiating with respect to you are keeping constant. Hence is also constant.

Therefore if you are using the product rule you would have

.

…yes your derivative of was incorrect. However, as you can see there is no real need here for the product rule as it is “constant” times “function” and you just need to use

… you pull out the constant.

All you need here is

.

This should make things more straightforward.

Regards,

J.P.

March 16, 2015 at 5:31 pm

StudentHi J.P.,

Just stuck on question 4 – I’m getting a different answer then from the book – am I right in saying we need to use both product rule and chain rule (chain for the ). I have done it both ways still not working.

Regards.

March 16, 2015 at 5:35 pm

J.P. McCarthyUsing a product rule

.

Get back to me if this doesn’t find your problem.

Regards,

J.P.

March 16, 2015 at 5:36 pm

StudentHi J.P.,

I am having trouble with Q3 part 2 , Could you point me in right direction .

March 16, 2015 at 5:39 pm

J.P. McCarthyYou are not using the Chain Rule properly.

We have so using the Chain Rule we have

.

Regards,

J.P.

March 23, 2015 at 9:47 am

StudentHi J.P.,

Would you point me in right direction for Q.4?

Thanks.

March 23, 2015 at 9:51 am

J.P. McCarthyFirstly I should say that the numbers are ridiculous — errors of 0.1 m would have been more appropriate. Also I have no error in — you interpreted this correctly.

Secondly, when you are differentiating with respect to and , note that because is constant so is .

i.e. you should have

,

and similar for .

Regards,

J.P.

March 23, 2015 at 9:55 am

StudentHi J.P.,

Just having trouble with the first part of Q.2 on P.65. Do i bring the below the line above and when I do this, do i need a product rule for .

I’m getting an answer of 21!!

Regards.

March 23, 2015 at 10:11 am

J.P. McCarthyYou have a number of options.

As written,

,

is a fraction as so you need the Quotient Rule (http://en.wikipedia.org/wiki/Quotient_rule) to differentiate it.

However, when you are differentiating with respect to , note that the top is a constant…therefore we can write

and differentiate as follows using the Chain Rule:

.

However if you do that you might note that you could have originally written

and used the product rule for differentiating with respect to .

This is a general situation. Suppose you have a function that is a fraction

.

Now you can use the Quotient Rule or else write

and use the Product Rule.

Regards,

J.P.