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Advanced Higher Maths 2011-2012 : Discussion and Help
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I extracted the number correctly yes, but i wasn't sure because everyone else was dividing by 7 rather than 7^k
i got 3412
i got 3412
also do you get follow through marks in AH, the reason I ask is Q8.
My working: (i am going to use T instead of theta)
x=4sinT
sinT=x/4
T=sin^-1(x/4)
dT/dx=1/(1-(x/4)^2)^0.5) should be dT/dx=1/(4(1-(x/4)^2)^0.5))
dT/dx=4/(16-x^2)^0.5 should be dT/dx=1/(16-x^2)^0.5
dx = ((16-x^2)^0.5)/4 dT should be dx = (16-x^2)^0.5 dT
then
limits: 0>sin^-1(0)=0 and 2>sin^-1(2/4)=pi/6
integral of (16-x^2)^0.5 dx between 0 and 2
= I of (16-x^2)^0.5 * ((16-x^2)^0.5)/4 dT between 0 and pi/6
= I of (16-x^2)/4 between 0 and pi/6
= I of (16-(4sinT)^2)/4
= I of (16-16(sin^2)T)/4
= 4 * I of (1-(sin^2)T)
= 4 * I of (cos^2)T
= 4 * I of (0.5cos2T + 0.5)
= 2 * I of (cos2T + 1) dT (i had limits and dT on every line)
= 2 * (0.5sin2T + T) between pi/6 and 0
= sin2T + 2T between pi/6 and 0
= sin(pi/3) + (pi/3)
= (root 3)/2 + pi/3
i have checked, this is exactly a quarter of the answer. would i get follow through marks or not, would the marking stop straight after i incorrectly differentiated or would i just lose a mark? thanks
My working: (i am going to use T instead of theta)
x=4sinT
sinT=x/4
T=sin^-1(x/4)
dT/dx=1/(1-(x/4)^2)^0.5) should be dT/dx=1/(4(1-(x/4)^2)^0.5))
dT/dx=4/(16-x^2)^0.5 should be dT/dx=1/(16-x^2)^0.5
dx = ((16-x^2)^0.5)/4 dT should be dx = (16-x^2)^0.5 dT
then
limits: 0>sin^-1(0)=0 and 2>sin^-1(2/4)=pi/6
integral of (16-x^2)^0.5 dx between 0 and 2
= I of (16-x^2)^0.5 * ((16-x^2)^0.5)/4 dT between 0 and pi/6
= I of (16-x^2)/4 between 0 and pi/6
= I of (16-(4sinT)^2)/4
= I of (16-16(sin^2)T)/4
= 4 * I of (1-(sin^2)T)
= 4 * I of (cos^2)T
= 4 * I of (0.5cos2T + 0.5)
= 2 * I of (cos2T + 1) dT (i had limits and dT on every line)
= 2 * (0.5sin2T + T) between pi/6 and 0
= sin2T + 2T between pi/6 and 0
= sin(pi/3) + (pi/3)
= (root 3)/2 + pi/3
i have checked, this is exactly a quarter of the answer. would i get follow through marks or not, would the marking stop straight after i incorrectly differentiated or would i just lose a mark? thanks
Original post by PW7
also do you get follow through marks in AH, the reason I ask is Q8.
My working: (i am going to use T instead of theta)
x=4sinT
sinT=x/4
T=sin^-1(x/4)
dT/dx=1/(1-(x/4)^2)^0.5) should be dT/dx=1/(4(1-(x/4)^2)^0.5))
dT/dx=4/(16-x^2)^0.5 should be dT/dx=1/(16-x^2)^0.5
dx = ((16-x^2)^0.5)/4 dT should be dx = (16-x^2)^0.5 dT
then
limits: 0>sin^-1(0)=0 and 2>sin^-1(2/4)=pi/6
integral of (16-x^2)^0.5 dx between 0 and 2
= I of (16-x^2)^0.5 * ((16-x^2)^0.5)/4 dT between 0 and pi/6
= I of (16-x^2)/4 between 0 and pi/6
= I of (16-(4sinT)^2)/4
= I of (16-16(sin^2)T)/4
= 4 * I of (1-(sin^2)T)
= 4 * I of (cos^2)T
= 4 * I of (0.5cos2T + 0.5)
= 2 * I of (cos2T + 1) dT (i had limits and dT on every line)
= 2 * (0.5sin2T + T) between pi/6 and 0
= sin2T + 2T between pi/6 and 0
= sin(pi/3) + (pi/3)
= (root 3)/2 + pi/3
i have checked, this is exactly a quarter of the answer. would i get follow through marks or not, would the marking stop straight after i incorrectly differentiated or would i just lose a mark? thanks
My working: (i am going to use T instead of theta)
x=4sinT
sinT=x/4
T=sin^-1(x/4)
dT/dx=1/(1-(x/4)^2)^0.5) should be dT/dx=1/(4(1-(x/4)^2)^0.5))
dT/dx=4/(16-x^2)^0.5 should be dT/dx=1/(16-x^2)^0.5
dx = ((16-x^2)^0.5)/4 dT should be dx = (16-x^2)^0.5 dT
then
limits: 0>sin^-1(0)=0 and 2>sin^-1(2/4)=pi/6
integral of (16-x^2)^0.5 dx between 0 and 2
= I of (16-x^2)^0.5 * ((16-x^2)^0.5)/4 dT between 0 and pi/6
= I of (16-x^2)/4 between 0 and pi/6
= I of (16-(4sinT)^2)/4
= I of (16-16(sin^2)T)/4
= 4 * I of (1-(sin^2)T)
= 4 * I of (cos^2)T
= 4 * I of (0.5cos2T + 0.5)
= 2 * I of (cos2T + 1) dT (i had limits and dT on every line)
= 2 * (0.5sin2T + T) between pi/6 and 0
= sin2T + 2T between pi/6 and 0
= sin(pi/3) + (pi/3)
= (root 3)/2 + pi/3
i have checked, this is exactly a quarter of the answer. would i get follow through marks or not, would the marking stop straight after i incorrectly differentiated or would i just lose a mark? thanks
You do get follow through, so you'll lose whatever the marks alocated to the bit you got wrong and then you'll get the rest as long as you've used your result correctly.
Think I got about 64%: damn, really wanted an A 
Original post by ukdragon37
You do get follow through, so you'll lose whatever the marks alocated to the bit you got wrong and then you'll get the rest as long as you've used your result correctly.
oh ok cheers, was thinking i was going to lose 4 or 5 marks for one tiny mistake
Having marked it using ukdragon I am at 71%, I need an A to get in to Uni. For the binomial expansion question I expanded it using the whole triangle technique thing (never got round to learning how to do this properly) I think I did so correctly, but I didn't notice/understand what it meant by the general term in the expansion, do you think I can get 2/3 or just 1/3?
Also, for the maclaurins expansion, I did it by finding the derivative and setting it to 0 etc. for the (1+e^x)^2 part, I have no idea why I did this, but do you think I'd get any marks for it?
I would be so grateful to anyone that could help me, I'm so worried at the moment that I won't be getting in to uni just now predominately for a few stupid mistakes!
Also, for the maclaurins expansion, I did it by finding the derivative and setting it to 0 etc. for the (1+e^x)^2 part, I have no idea why I did this, but do you think I'd get any marks for it?
I would be so grateful to anyone that could help me, I'm so worried at the moment that I won't be getting in to uni just now predominately for a few stupid mistakes!
Original post by csawc
Having marked it using ukdragon I am at 71%, I need an A to get in to Uni. For the binomial expansion question I expanded it using the whole triangle technique thing (never got round to learning how to do this properly) I think I did so correctly, but I didn't notice/understand what it meant by the general term in the expansion, do you think I can get 2/3 or just 1/3?
Also, for the maclaurins expansion, I did it by finding the derivative and setting it to 0 etc. for the (1+e^x)^2 part, I have no idea why I did this, but do you think I'd get any marks for it?
I would be so grateful to anyone that could help me, I'm so worried at the moment that I won't be getting in to uni just now predominately for a few stupid mistakes!
Also, for the maclaurins expansion, I did it by finding the derivative and setting it to 0 etc. for the (1+e^x)^2 part, I have no idea why I did this, but do you think I'd get any marks for it?
I would be so grateful to anyone that could help me, I'm so worried at the moment that I won't be getting in to uni just now predominately for a few stupid mistakes!
From looking at past marking schemes for that type of binomial question you get no marks for expanding out the whole thing (usually).
I'm pretty sure you'll get marks for the other question though because it did say 'hence, or otherwise...' and do you mean that you had found f(0), f'(0), f''(0), f'''(0) and so on?
(edited 11 years ago)
Think I am around 68-70% so hoping the cut offs are generous!
Couple of questions, how many marks would I lose in each situation?:
Q3 I found one of the roots which was the complex conjugate and drew the argand diagram for the two roots I had found
Q8 I found the limits and did the substitution and then stopping
Q13 I found dy/dx okay but got one sign the wrong way round for the second derivative. This sort of also screwed up my two points of inflexion which I had worked out using the wrong second derivative. Would I still get the marks for that part of the question?
Thanks for your help!
Couple of questions, how many marks would I lose in each situation?:
Q3 I found one of the roots which was the complex conjugate and drew the argand diagram for the two roots I had found
Q8 I found the limits and did the substitution and then stopping
Q13 I found dy/dx okay but got one sign the wrong way round for the second derivative. This sort of also screwed up my two points of inflexion which I had worked out using the wrong second derivative. Would I still get the marks for that part of the question?
Thanks for your help!
Does anyone know how to do qu12? I tried to do it for 20 minutes but had no idea where to start? 
What parts do you differentiate?
What parts do you differentiate?For q13, I never used the quotient rule for d2y/dx2 so i ended up with 2t/2+t which i think is still correct so would i get the 8 marks, i still got +/- sqrt(3) and min and max?
Does anyone know where I can find marking schemes for the older AH Stats papers? I looked on the SQA website and they only seemed to have marking schemes for Mechanics for 2005-2006.
Original post by Marcus4004
Prob in both cases, one mark. 
(if you showed the working to get to 3412.)
(if you showed the working to get to 3412.)really?? thank yo i hope so! probs looking at a solid B now
i messed up quite a lot of the questions but hoping for followthrough marks 
Original post by Marcus4004
Prob in both cases, one mark. (if you showed the working to get to 3412.)
(if you showed the working to get to 3412.)I got 412 as well i just divided by 7 until i got an answer smaller than 7.... how do you get the 3 at the start???
70% at best for me, pretty annoyed cause I was really hoping for an A, all of my weakest subjects came up and none of strongest did. If there was a second order inhomogeneous ODE, finding the inverse of a 3x3 matrix or any of the high marking questions from 06-10 I would have been virtually guaranteed a band 1. I'm probably re-applying for uni next year (for physics) so I was really hoping for a good A... Plus my sister got a band 1 last year so there's a bit of sibling rivalry haha.
Original post by laughylolly
Does anyone know where I can find marking schemes for the older AH Stats papers? I looked on the SQA website and they only seemed to have marking schemes for Mechanics for 2005-2006.
Not sure if this is the correct thread to discuss these optional papers but anyhow since you ask and others also...
http://www.educationscotland.gov.uk/nationalqualifications/curriculumareas/mathematics/adviceandsupport.asp for STATISTICS n MECHANICS stuff
but couldn't actually find past-papers there!
also my own web site: http://www.tomctutor.com/start-1
and please could you kill (delete) the vampires as they are slowing down the thread
referesh especially for low-bandwidth users!
(edited 11 years ago)
Original post by tomctutor
Not sure if this is the correct thread to discuss these optional papers but anyhow since you ask and others also...
http://www.educationscotland.gov.uk/nationalqualifications/curriculumareas/mathematics/adviceandsupport.asp for STATISTICS n MECHANICS stuff
but couldn't actually find past-papers there!
also my own web site: http://www.tomctutor.com/start-1
and please could you kill (delete) the vampires as they are slowing down the thread
referesh especially for low-bandwidth users!
http://www.educationscotland.gov.uk/nationalqualifications/curriculumareas/mathematics/adviceandsupport.asp for STATISTICS n MECHANICS stuff
but couldn't actually find past-papers there!
also my own web site: http://www.tomctutor.com/start-1
and please could you kill (delete) the vampires as they are slowing down the thread
referesh especially for low-bandwidth users!
There isn't a thread for AH Applied maths and I know people who look here used to take it so more likely to get some help here? It's still AH maths technically...
But thank you!
And really? No one has said they've caused any problems before... (And I've had them there for a year or so "/)
Original post by erinkad
I'm guessing that I'm the only person on here that thought the paper was really difficult! I attempted nearly all the questions but I thought it was a lot harder than previous years
No you are not. I found it really hard as well as did most of the people in my class. I got over 93% in my prelim but hoping to scrape an A in this! Need it for uni!
Original post by whylime
No you are not. I found it really hard as well as did most of the people in my class. I got over 93% in my prelim but hoping to scrape an A in this! Need it for uni!
What kind of uni would specify an A in advanced maths?
Original post by Mr Dangermouse
What kind of uni would specify an A in advanced maths?
Most English unis for a science subject actually, as they see it as the equivalent to an A in A2 maths. (In fact AH is closer to A2 further maths)
Original post by ukdragon37
Most English unis for a science subject actually, as they see it as the equivalent to an A in A2 maths. (In fact AH is closer to A2 further maths)
I reckon it's better compared to an AS in FM. There's a bunch more DEs and potential for groups, and more fun stuff floating around in the later FM stuff(some boards at least).
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