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# Thread for 2015 S6 Leavers Watch

1. (Original post by Hype en Ecosse)
I'll do you one better. I'll show you how it's derived!

Suppose we have a completely RANDOM trapezoid. I've chosen this one at random.

Now, let's do what you did. Let's split it up into 2 triangles and a rectangle (we can't assume height is the same size as length, so it's not a square necessarily) by drawing vertical lines.

So our left triangle - it has height , and I'm going to call its length .

Our right triangle has the same height, but is shorter - I'll call it length

Now our rectangle also has height, h, but I'll call this length

The entire bottom side of our trapezoid MUST be the lengths of the two triangles plus the length of the square, right? So I'll call this longer length then

Now we know the area of a triangle, it's 1/2 base x height, yeah? So we have two different bases: x and y.

Area of the two triangles must be: , and our rectangle area is simply

So to get the total area of the trapezoid, we add them all together like you did in the exam:

This is the area of a trapezoid, but it's not very pretty is it? Let's fix that: Take out h as a common factor, since it's in all of them!

Now the next step is trickier to see, but we can actually take out 1/2 as a common factor, let's see if you see the trick:
- I've taken a half out as a factor of each of the terms, which means I have to double everything inside the bracket to keep it correct. You can see that this is true simply by expanding the bracket out - you get what you had at the start again!

Now the next step is easy:
- we've just rewritten 2b_1 is all. You know, like 2x = x + x, same deal here.

Remember what we said at the start? We said that the longest side of the trapezoid is . We have that inside the bracket! So let's substitute it in, yeah?

. And there we go. That's the area of a trapezoid by using the length of the two parallel lines, but we can make it a little bit prettier by moving things around a little and putting the 1/2 back in the bracket:

TADA! The area of a trapezoid as you were taught at standard grade!

You don't actually have to remember very many "area of..." formulas. You could honestly just remember the area of a square - and then you can prove the area of a lot of other shapes (the triangle, then the trapezoid for example) from that, as long as you can take some simple little logical steps! I had no idea what the area of a trapezium was, but just decided I'd work it out there.
WOW! That all made sense! Thanks so much for going through the trouble of showing me this . I've always just remembered the formula and that was it but now I understand how one gets to that formula - wish I had you as a math teacher, because that was quite cool. Is this how math progresses or is it the same mundane memorisation game it was in standard grade?
2. (Original post by Princepieman)
WOW! That all made sense! Thanks so much for going through the trouble of showing me this . I've always just remembered the formula and that was it but now I understand how one gets to that formula - wish I had you as a math teacher, because that was quite cool. Is this how math progresses or is it the same mundane memorisation game it was in standard grade?
Maths involves more understanding as you progress up the levels. Higher Maths requires more understanding than SG; AH involves more than Higher. Tertiary level maths is almost 100% understanding. This is why many mathematicians hate secondary school mathematics - it's the exact opposite to the subject that they love.

You're not going to do proofs at Higher, but that proof I did there didn't involve any skills past first year! You can certainly chose to prove a lot of what you learn. They teach you a tool at Higher Maths called "completing the square" and you can use that to prove the quadratic formula, which is always a fun proof.
AH Maths involves a lot of "show that...", "prove that...", "from first principles..." questions. It's really fun and that's the stuff I enjoyed doing, but there is still a hefty bit of memorisation involved.

Hopefully ukd is still around () if you end up taking up AH Maths - he's really good at encouraging you to understand the material you're simply asked to accept. I know a little bit of maths past AH level simply because ukd pushed me. I don't do anything related to maths at all at uni!

You know how you have to know two trig identies for credit? , and you can prove both of them with stuff you'll have learned at Standard Grade. They're both proved using the same logic. Do you want to give it a try? We can give you a hint if you get stuck.
3. (Original post by Hype en Ecosse)
Maths involves more understanding as you progress up the levels. Higher Maths requires more understanding than SG; AH involves more than Higher. Tertiary level maths is almost 100% understanding. This is why many mathematicians hate secondary school mathematics - it's the exact opposite to the subject that they love.

You're not going to do proofs at Higher, but that proof I did there didn't involve any skills past first year! You can certainly chose to prove a lot of what you learn. They teach you a tool at Higher Maths called "completing the square" and you can use that to prove the quadratic formula, which is always a fun proof.
AH Maths involves a lot of "show that...", "prove that...", "from first principles..." questions. It's really fun and that's the stuff I enjoyed doing, but there is still a hefty bit of memorisation involved.

Hopefully ukd is still around () if you end up taking up AH Maths - he's really good at encouraging you to understand the material you're simply asked to accept. I know a little bit of maths past AH level simply because ukd pushed me. I don't do anything related to maths at all at uni!

You know how you have to know two trig identies for credit? , and you can prove both of them with stuff you'll have learned at Standard Grade. They're both proved using the same logic. Do you want to give it a try? We can give you a hint if you get stuck.
I'll probably have to try that later, right now I'm stuffing my face with Ben and Jerry's because of how exhausted I am. It's also a little treat for finishing the math exams
4. Woo, got tickets to go and see Macklemore
5. Hey! Have you guys seen this? http://www.invergordonacademy.org.uk...-documents.asp
It has the answers to the 2013 Exam Papers for Maths. Turns out I've done pretty good
Hey! Have you guys seen this? http://www.invergordonacademy.org.uk...-documents.asp
It has the answers to the 2013 Exam Papers for Maths. Turns out I've done pretty good
Yup, I've seen it.
Hey! Have you guys seen this? http://www.invergordonacademy.org.uk...-documents.asp
It has the answers to the 2013 Exam Papers for Maths. Turns out I've done pretty good
I can barely remember my answers but one ive noticed might be wrong like the camera one 9b credit I because it says 0.35x+6+4.25 but x was greater than 12 and the first 12 costed the 6 which is in the equation thus it should be 0.35(x-12) should it not? Oh well I did quite good, noticed I've made a few mistakes but nothing dire aha!

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8. 9 on both papers are mistakes.
9. (Original post by Bromaldehyde)
9 on both papers are mistakes.
Wow really? You sure? Because those were one of the only ones I got wrong. Apart from the very last one, because I forgot to square the 2x
Wow really? You sure? Because those were one of the only ones I got wrong. Apart from the very last one, because I forgot to square the 2x
I'd confirm for you if I could see a copy of the paper?
Wow really? You sure? Because those were one of the only ones I got wrong. Apart from the very last one, because I forgot to square the 2x
That's what's going round on twitter at least.
12. (Original post by TheFOMaster)
I'd confirm for you if I could see a copy of the paper?
Wish I had it but only the answers are available from that site. Kind of dumb

(Original post by Bromaldehyde)
That's what's going round on twitter at least.
You mean the answers are wrong right? Not the actual question. Probably a stupid question, but just checking haha.
14. (Original post by Bromaldehyde)
9 on both papers are mistakes.
I cannot find any mistakes in the answer to question 9 of paper 2. Would you point out the mistake and show your correct answer?
15. (Original post by gooday)
I cannot find any mistakes in the answer to question 9 of paper 2. Would you point out the mistake and show your correct answer?
I haven't checked them, I can't remember my answers now and I'm certainly not going to do them again, that's just what I was told by friends. If that's correct then that's fine.
16. (Original post by Bromaldehyde)
I haven't checked them, I can't remember my answers now and I'm certainly not going to do them again, that's just what I was told by friends. If that's correct then that's fine.
Upload the paper so us year-aboves can check?
17. (Original post by Hype en Ecosse)
Upload the paper so us year-aboves can check?
Sure, I'll scan it in in a few hours.
18. (Original post by Bromaldehyde)
Sure, I'll scan it in in a few hours.
Just question 9 in both papers would be cool, so that I can check if the answers are right or not.
19. (Original post by Bromaldehyde)
Sure, I'll scan it in in a few hours.
Would you kindly upload paper 1 as well?
20. I remember the question from paper 2 q 9b basically it wa talking about photography and how much a package would cost and asked you to create a formula for it:
The first 12 photos cost 0.50 pounds
Every photo after cost 0.35 pounds
A CD containing the photos cost 4.25
Let x represent the number of photos and create a formula in pounds etc where x > 12 and a CD is bought.

So....

12x0.50 = 6 pounds
C= 6 + 0.35(x-12) + 4.25
C= 6 + 0.35x - 4.20 + 4.25
C= 6 + 0.35x + 0.05
C= 6.05 + 0.35x

But the marking scheme states it is

C= 6 + 0.35x + 4.25
C= 0.35x + 10.25 which is wrong.

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