The RHS AH Maths Emporium

Thank you all so much for making the last day so memorable… amazing gifts and cards, all so thoughtfully chosen.  I’ll be blinking back a few tears when I think back on all this, I tell you.

So, that’s about it from me.  As a final thank you, here’s the photo you requested I upload for you.  Don’t we all look nice?  And, as a bonus, have a listen to the first five minutes or so of Mark Kermode reviewing films on Friday’s Simon Mayo show on Radio Five Live, and you’ll hear a shout-out to The Advanced Higher Class of RHS.  Fame for us all, at last!

Keep working hard at the Maths, and I’ll see you at the movies!

Two lessons to go before I head off into the sunset, so now is as good a time as any to say a big thank you to you all for your hard work, effort and enthusiasm over the years I’ve known you.  The blog will continue in the capable hands of Mrs C, and in the meantime I wish you all the very best.

Any chance of some cake?

Today we finished the content of Unit 1 with a quick note on rectilinear motion and integration. We then discussed some key questions in the philosophy of mathematics:

• what is maths?
• why is it useful?
• is maths discovered or invented?

Fascinating stuff. If you’re keen to read more about all, this you could do worse than look here (good old wikipedia). This page gives a lot more detail, and this one seems to come very much from a Platonistic viewpoint, which seems to be where we all are anyway. Sort of.

It is possible to do a joint degree in mathematics and philosophy; alternatively you may be able to study the philosophy of mathematics as part of a mathematics degree. The content can be pretty scary, so is usually only encountered in your third or fourth year of study.

Happy holidays – but make sure you study for the extension test on Wed 29 Oct!

exercise2-solutions

2002-ah-paper-d-solutions

2001-ah-paper-d-solutions

Please find some scanned solutions for practice papers. Click on the link and the file will take a couple of minutes to load. Sorry I didn’t write them, but there were lots. Hope you can read them.

Happy holidays

MrsC

Hope these are of some help

Outcome 2

^a)         (x-8)(x+2) over (x²+16)²

^b)        x⁴(2x+5) over (x+1)⁴

^c)         6-x over 6x²sq.rt(x-3)

^d)        2 cot 2x

^e)         30x²e^2x³

^f)         2e^x+2 (x+3)

^g)        x²(3sinx + xcosx)

Outcome 3

a)      ½ e^2x + 1/2x² + c

b)      1/3(x³-4)⁵+ c

c)      1/5 sin⁵x + c

d)     ½ ln(1+x²) + c

e)      –e^{cos x}

f)       1/30 (6+x³)¹⁰

g)      1/3 (1+x²)^3/2

mrs c

Hi Stuart
Have a look at the notes for Rectilinear Motion.
Q5) Remember that displacement differentiated gives velocity which when differentiated gives acceleration (and of course integrating takes you back the way!). So by starting off with a formula for acceleration we would have to integrate to get the velocity or speed. We then have to find the C value by substituting in t=0, v=0.
For the second part of the question we have to integrate the velocity to get the displacement etc.
Hope this helps you and the others who are stuck

Have they arrived yet?  Anyway, from my end, let me say the Higher results for all classes look pretty darn good.  Very impressive.  Congratulations to you all.

Heriot-Watt has started up a newsletter for their Actuarial Mathematics courses which you can find here.  It may be of interest to some of you if you are thinking of studying mathematics at university.  Actuarial mathematics is mostly statistical in nature, but the Advanced Higher in Applied Mathematics (Statistics) isn’t actually an entry requirement.

Admit it, you’ve always wondered this, haven’t you?  And not just because Doctor Who is on tonight…

Talking with the Applied Maths class the other day I asked if there were situations where a negative value for time had any meaning, and we agreed that there were (eg t=-5 could mean 5 seconds before you started measuring, sort of thing).  But few would doubt the essential, ahem, “left-to-rightness” of time itself.  I mean, it only flows one way, doesn’t it?

Well… there are novelists out there who have written books that run backwards (Martin Amis, for example – see, we can have learning and erudition in a maths blog!), and it’s long been a staple of science-fiction.  But what about the science or mathematics behind a backward-running world?

Take a look here and see what you think.

Now I’m not complaining or anything, but it’s fair to say that quite a few people have managed to miss quite a few lessons thus far in S6, all for very good reasons of course.  Hopefully you have managed to at least get copies of the notes you have missed thus far, but this post here is designed to lay down a marker as regards how far we have come with partial fractions.  Today in class we looked at algebraic long division, which is essential for the final type of pf we’ll be looking at next week.  If you missed today’s lesson, you could do worse than look here which is the summary page for the algebra section of Unit 1 on the SCHOLAR website.  (You should have your password for this site by now – if not, ask!)  Long division is explained in section 1.11, while all the partial fraction work we have done thus far can be found in sections 1.10.1 to 1.10.6 – it would be a very good idea to work through some of these exercises if you are at all unsure of the work you’ve missed.