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Advanced Higher Maths 2013-2014 :: Discussion and Help Thread

This poll is closed

How do you feel you have done in the paper?

Great, hoping for an A 17%

Could've done better, hoping for A/B 21%

Bad, hoping for B/C 24%

Totally messed it up, hoping for D or might fail38%

Total votes: 29

Hype en Ecosse

It's that time again. A new year has rolled around and a new era of mathematicians have taken up the subject. Every year, AH Maths proves to be our most popular discussion thread, so here I am to kick it off for the new year. It's been over a year since I've done maths, but I'll still be here to help out as best as I can!

What follows is a list of resources you might find useful, as well as possibly broken links (let us know if they are!)
Credit goes to Kelz_26, who compiled the original list years ago and has since left us. :sad:

Books:
Selected Books
Maths In Action 1
Maths In Action 2
Maths In Action 3
BrightRed Revision
Practice Papers
Practice Papers
Past Papers

Past Papers:
2001, 2002 and 2003
AH Pure and Applied Maths past papers (2001 - 2012)

Other Resources:
LOTS of Practice Questions
SQA AH Maths
Arrangement Documents
HSN Course Summary
Formulae
Notes
Scholar
HSN Forum
Revision Site
Checklist
Teejay
Online scientific calculator
Wolfram Alpha
Integrator
Timings & Outline for Unit 1
Timings & Outline for Unit 2
Timings & Outline for Unit 3
Unit 1 Practice NAB
Unit 2 Practice NAB
Specimen Question Paper with Marking Instructions

YouTube Channels
PatrickJMT
KhanAcademy
DLB Maths (past paper solutions and tutorials)

(edited 10 years ago)

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Reply 1

TheFOMaster

Original post by Hype en Ecosse

Here's a link to a site with all the past papers for the course.

Reply 2

Hype en Ecosse

Original post by TheFOMaster

Here's a link to a site with all the past papers for the course.

That's brilliant. Thanks!

Reply 3

TheFOMaster

Original post by Hype en Ecosse

That's brilliant. Thanks!

No problem! I'm pretty sure I saw it on here anyway, and I've had it bookmarked since from back when I did the course :moon:

Reply 4

JimmyGatz

I'm doing adv maths but only got a B in higher, going to be tough! The B could get appealed to an A as well

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Reply 5

RD208

Woo AH maths! We've already done binomial theorem from before the summer (of which I remember nothing haha) and are into improper and partial fractions. Our class is relatively huge - there's about 15 of us and most got band 1 A's :0

Here's hoping for an A. Good luck all :smile:

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Reply 6

Shengis14

Watching, I did it last year and got an A, so I might be able to help some people

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Reply 7

kylerfc

I am doing AH maths this year too! :smile:

We have already done some of the trig functions stuff with cosec etc though I can't really remember much of it!

Reply 8

Hype en Ecosse

Original post by kylerfc

I am doing AH maths this year too! :smile:

We have already done some of the trig functions stuff with cosec etc though I can't really remember much of it!

It's dead easy: 4 things to remember.

\sec x = \frac{1}{\cos x} \ \ \csc x = \frac{1}{\sin x} \ \ \cot x = \frac{1}{\tan x}

And remember from Higher:

\sin ^2x + \cos ^2 x = 1

divide by sine or cosine squared and you get a few magical new identities.

Reply 9

LionKing1

Original post by Hype en Ecosse

It's dead easy: 4 things to remember.

\sec x = \frac{1}{\cos x} \ \ \csc x = \frac{1}{\sin x} \ \ \cot x = \frac{1}{\tan x}

And remember from Higher:

\sin ^2x + \cos ^2 x = 1

divide by sine or cosine squared and you get a few magical new identities.

'Dead easy' you havin a laugh :zomg:

Reply 10

Proud_Student

Doing it too...got a B in Higher so im going to have to work my ass off if I want an A/B D:

Reply 11

Legii

Original post by LionKing1

'Dead easy' you havin a laugh :zomg:

The way my teacher taught us to remember was that

cot x = 1/tan x
cosec x = 1/sin x
sec x = 1/cos x

just look at the 3rd letter :wink:

Reply 12

FizzicsGuy

Started Integration by substitution today, it's not that bad :biggrin:

Reply 13

CSM1996

Original post by FizzicsGuy

Started Integration by substitution today, it's not that bad :biggrin:

We got given notes to copy of them and it looks really confusing, probably because our teacher hasn't gone through it or done anything on it, we just got given some examples :lol:

He said it's not bad though, so hopefully it should be fine (I'm starting it tomorrow :tongue:

)

Reply 14

Proud_Student

Had double maths today..some of the most horrible things iv ever seen...we were asked alter on if we had any advance highers we regretted picking and we all go "Maths" haha

I cant get my head around binomial's number

Reply 15

Hype en Ecosse

Original post by Proud_Student

You mean binomial expansion? Or the binomial coefficient?

Reply 16

Proud_Student

Original post by Hype en Ecosse

You mean binomial expansion? Or the binomial coefficient?

The coefficient sorry for being so unclear ><

I understood it to an extent but i was baffled by where all the numbers were coming from ><

Reply 17

Hype en Ecosse

Original post by Proud_Student

The coefficient sorry for being so unclear ><

I understood it to an extent but i was baffled by where all the numbers were coming from ><

Oh, now this is a fun one! Right. I'm going to show you the cheat method first. The cheat method comes from looking at something called Pascal's triangle. Let's look at Pascal's triangle!

So, every row starts with a 1 and ends with a 1, but what about all the numbers in between? Well, they're just the two numbers "above" it added together. Like in the 3rd row, look at the two numbers above - that's 1+1, so the coefficient we've got is 2.
Let's go one row down. 1, 3, 3, 1. Look at the two numbers above the 3! 1+2 = 3.

One more row... 1, 4, 6, 4, 1. Look at the 4. It's the two numbers above, 1 + 3, added together. The 6, the two numbers above are 3 and 3...6. This works AAAALLLL the way down Pascal's triangle. And these are the coefficients of your terms. Which row you pick depends on what power of n your term

(x + y)^n

that you have. So...if you've got n = 0, you take the first row. n = 1 is the second row, n = 2 is the third row, n = 3 is the fourth row and so on...and in that row is the coefficient for all your terms. Let's have a look at those first few, for example:

(x + y)^0 = 1 \\ (x + y)^1 = x + y \\ (x + y)^2 = x^2 + 2xy + y^2 \\ (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3

Look at the co-efficients of those expanded terms, they all correspond with a row of Pascal's triangle depending on what our value for n, don't they? PatrickJMT explains this all really well. But we're still stuck with the question...where do those numbers come from!? Why does the triangle work?

This is explained through the "proper" way.

We've got our notation:

\displaystyle \binom{n}{k}

, this is pronounced "n choose k" for whatever weird reason. So we've got n choose k, and what that's short for is another fancy expression:

\displaystyle \binom{n}{k} = \dfrac{n!}{(n-k)!k!}

, now that's a big complicated expression, but what does it mean? Well, I'm going to assume you understand factorials and what the factorial sign means (let me know if you don't!), so how do we know what n and k is?

n, fortunately, stays the same. It's whatever our bracket was raised to, wasn't it? So in our expression

(x + y)^2

, n = 2. But what's k? K is just whatever term it is! So the first term is k = 0, the second term is k = 1, the third term is k = 2...etc...

So when we look at our binomial expansion, we've got

\displaystyle\binom{2}{0}

for the first term...

\displaystyle\binom{2}{1}

for the second term...

\displaystyle\binom{2}{2}

for the third term. And when n = k, that's when we stop.
So for whatever term we're looking at, it's got its own value for k (and they all have the same value of n), we just take those numbers, and plug them into our expression above:

\dfrac{n!}{(n-k)!k!}

and out pops the binomial coefficient! All of your numbers for your binomial coefficients come from plugging in combinations of n and k into this expression!