I've been having a mental battle with Q1 G on the same paper (2011), thinking you have to somehow translate/transform the graph, then find the area underneath using some means. However finally looking at the solutions, I have no idea what they are talking about and how they have got to certain inequalities. Anyone can explain?
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TheFuture001
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 26102013 19:34

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 26102013 19:48
(Original post by TheFuture001)
Yeah thanks, I got it! I had ended with a quadratic earlier on, but I discarded it as meaningless since I thought the P's and A's were just x's and y's in the end. I didn't expect to do that.
@dutchmaths, I'm not sure I really like your method aha. For example, to my eyes the first option after subbing in looks like it could probably be true, just by thinking of how large the number could get.
if we say the rectangle has sides x and y, then the P^3 is
(2x+2y)^3
= 8x^3 + 24x^2y + 24xy^2 + 8y^3
i would think that this is greater than the area xy for all values of x and y, which makes the first inequality P^3 > A seem like the answer
Ive probably made a mistake somewhere, cause the people who design these papers arent exactly stupid 
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 26102013 20:00
(Original post by MelvyW)
Hey guys, Im quite new to this, and i have managed this question, but i think there is potential mistake in the question.
if we say the rectangle has sides x and y, then the P^3 is
(2x+2y)^3
= 8x^3 + 24x^2y + 24xy^2 + 8y^3
i would think that this is greater than the area xy for all values of x and y, which makes the first inequality P^3 > A seem like the answer
Ive probably made a mistake somewhere, cause the people who design these papers arent exactly stupid
If we set then
and
So we can get provided  that is provided 
Sayonara
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 26102013 20:00
Does anyone know where the answering space for the questions (that are not multiple choice) will be?
I usually take up a lot of space for my working out.
And, what does A(theta) and B(pi/2 * theta) mean on question 4?
http://www.maths.ox.ac.uk/system/fil...e/0/test07.pdf
Is A and B a constant, function or what? 
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 26102013 20:04
(Original post by Noble.)
No, that inequality is not always true.
If we set then
and
So we can get provided  that is provided
I very much doubt i could something like that out in exam though . 
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 26102013 20:08
(Original post by Sayonara)
Does anyone know where the answering space for the questions (that are not multiple choice) will be?
I usually take up a lot of space for my working out.
And, what does A(theta) and B(pi/2 * theta) mean on question 4?
http://www.maths.ox.ac.uk/system/fil...e/0/test07.pdf
Is A and B a constant, function or what? 
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 26102013 20:10
(Original post by MelvyW)
Ahh okay i see. Thanks!
I very much doubt i could something like that out in exam though .
This is why you can instantly discount (b) as a potential answer, as once you apply some thought to it you realise how utterly absurd it is. It's suggesting as a possible answer, yet you can make an area of less than 1 with a perimeter of more than one (i.e. a 3x0.25 box has area <1 yet perimeter 6.5) and clearly a number less than one squared is also less than one, yet the number on the RHS is bounded below by 1. 
TheFuture001
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 26102013 21:05
(Original post by MelvyW)
Hey guys, Im quite new to this, and i have managed this question, but i think there is potential mistake in the question.
if we say the rectangle has sides x and y, then the P^3 is
(2x+2y)^3
= 8x^3 + 24x^2y + 24xy^2 + 8y^3
i would think that this is greater than the area xy for all values of x and y, which makes the first inequality P^3 > A seem like the answer
Ive probably made a mistake somewhere, cause the people who design these papers arent exactly stupid
I'd suggest you try this method too, I'll hint you. With the two equations you have, eliminate either x or y and see what happens. And don't be scared off seeing x's/y's and P's and A's in the same equation like I did
Q1 G in the following paper http://www.mathshelper.co.uk/Oxford%...est%202011.pdf I am having trouble with. The solutions claim 1 <= x^2  1 <= 0 . How they came to this conclusion, and what follows, I can not understand. I would appreciate at least a hint in the correct understanding, thanks!Last edited by TheFuture001; 26102013 at 21:19. 
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 26102013 21:27
(Original post by Noble.)
Well, it is somewhat intuitive. When you see a potential answer that says "If you cube the perimeter, it'll always be greater than the area" the first thing that should spring to mind is "Well, what if the perimeter is less than 1? Then when we cube it, it's going to be even smaller". This is partially why I, subconsciously, chose to use in the notation because is typically used to denote a very small value (it doesn't necessarily have to be, but in analysis the arguments are only really interesting for small ).
This is why you can instantly discount (b) as a potential answer, as once you apply some thought to it you realise how utterly absurd it is. It's suggesting as a possible answer, yet you can make an area of less than 1 with a perimeter of more than one (i.e. a 3x0.25 box has area <1 yet perimeter 6.5) and clearly a number less than one squared is also less than one, yet the number on the RHS is bounded below by 1.
I realise you are expected to do all workings for the multiple choice in the space underneath each part. So how are you expected to answer the 15 mark questions.
Is there a question paper bookl and and answer book. are you given say x pages for all of the longer questions. or is it y pages for each of the 15 mark questions. and do they give a certain amount of space for each part of a question dependednt on how much space they think it should take up, or a set amount. Or is there 1 big space for the whole of the q
cheers 
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 26102013 22:06
(Original post by IceKidd)
Youve sat this exam so could you explain the format of the answer book please.
I realise you are expected to do all workings for the multiple choice in the space underneath each part. So how are you expected to answer the 15 mark questions.
Is there a question paper bookl and and answer book. are you given say x pages for all of the longer questions. or is it y pages for each of the 15 mark questions. and do they give a certain amount of space for each part of a question dependednt on how much space they think it should take up, or a set amount. Or is there 1 big space for the whole of the q
cheers 
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 26102013 22:30
(Original post by TheFuture001)
The solutions claim 1 <= x^2  1 <= 0 . How they came to this conclusion, and what follows, I can not understand. I would appreciate at least a hint in the correct understanding, thanks! 
fizzy pops
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 26102013 23:42
Hi, does anyone have any tips on how to approach questions, because sometimes I just look at questions and don't even know where to start! Any help would be much appreciated! Thanks XD!

Sayonara
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 27102013 00:10
(Original post by MelvyW)
From what i understand A(theta) just means the area A. The area is dependent on the value of theta, and hence A(theta)
You said that A and B would be dependent on theta, but I don't understand how it is used in this context:
A(theta) = B(0.5pi  theta)
I find that this notation is very unclear and most likely there was quite a few people who sat this MAT paper losing marks due to this. 
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 27102013 01:33
(Original post by Sayonara)
I find that this notation is very unclear and most likely there was quite a few people who sat this MAT paper losing marks due to this. 
TheFuture001
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 27102013 09:55
(Original post by Sayonara)
Thanks for the reply but I find your explanation very unclear.
You said that A and B would be dependent on theta, but I don't understand how it is used in this context:
A(theta) = B(0.5pi  theta)
I find that this notation is very unclear and most likely there was quite a few people who sat this MAT paper losing marks due to this. 
TheFuture001
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 27102013 10:09
(Original post by RichE)
What are the limits of the integral  and so the bounds for x?
I think I understand now, the graph shows for x=1, f(x)=0, so if you square f(x), 0, and take off 1 the limit is 1, yes? Using the same logic for x=0 and x=1, the upper limit becomes 0. Is this the correct way to think about this? 
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 27102013 11:12
(Original post by TheFuture001)
I think I understand now, the graph shows for x=1, f(x)=0, so if you square f(x), 0, and take off 1 the limit is 1, yes? Using the same logic for x=0 and x=1, the upper limit becomes 0. Is this the correct way to think about this?
x is a number between 1 and 1.
So x^2 is a number between 0 and 1
and x^2  1 is a number between 1 and 0.
We now need to work out what f(x^21) is. The function f is made up of different "rules" depending on the input. From the graph we can see that f is the rule "add 1" for inputs between 1 and 0.
So f(x^21) = (x^21) + 1 = x^2.
So it is x^2 you need to integrate between 1 and 1. 
applesquash
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 27102013 12:33
(Original post by fizzy pops)
Hi, does anyone have any tips on how to approach questions, because sometimes I just look at questions and don't even know where to start! Any help would be much appreciated! Thanks XD!
Haha might not have been that helpful, just my two cents. Could you give an example of one of those questions? 
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 27102013 13:50
(Original post by RichE)
.(Original post by Noble.)
.
Since Oxford has the MAT already is this the same. Is there also a small test for any of the colleges so that some of your interview involves discussing your answers to some of these problems. Or is there no test/problem sheet for any college? 
TheFuture001
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 27102013 14:32
(Original post by RichE)
At no point should you be squaring f(x). All you need to understand is what the function f(x^21) equals.
x is a number between 1 and 1.
So x^2 is a number between 0 and 1
and x^2  1 is a number between 1 and 0.
We now need to work out what f(x^21) is. The function f is made up of different "rules" depending on the input. From the graph we can see that f is the rule "add 1" for inputs between 1 and 0.
So f(x^21) = (x^21) + 1 = x^2.
So it is x^2 you need to integrate between 1 and 1.
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