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# Oxford Physics: PAT test discussion watch

1. i remeber equating the equations by using the identity (sinx)^2 +(cosx)^2 and ended up with something with the equation of a circle. i then let y equal 0 and found the x values
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2. how many marks would i get for the parametric if i only found one solution and forgot to generalize it ?
3. (Original post by cooltejaskd)
Now let's address the most crazy thing - waves question! What was that?!?! How the hell would you GRAPH such a thing?

Also, can anyone post answers to the other questions involved in the wave question? (Time period, velocity, frequency related)
Time period =2pi/w
V=wavelength*w/2pi
For the sketching I didn't rlly knw how to do it other than drawing 2 cos waves or different wavelengths and periods in their phase and graphically solving it over one wavelength. Mathematically seems right cus 2pi/wavelength and wt are both constants at a particular time. Not sure abt the frequency of the combined wave but to find the distance between points where no sound is heard u set the equation they gave to 0 n solve for the 2 values of x n subtract one from the other to get lambda1lambda2/lambda1 +lambda2
4. DrSebWilkes.... Could you please ask your 2nd year university friend what the answer is?

I do not want to argue about the method used. If the final answer is correct, oxford gives marks. RIGHT NOW... All that matters to me is the marks! So... Plz. Thanks.
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5. I think
X= a(wt - sin(t)) Y = a(sqrt(3) - 2cos(t))
since i remember having to put -1/6pi +2kpi in brackets when writing down the solutions for x
6. how many marks would i get for my method
for parametric using sin^2 + cos^2 =1
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7. (Original post by Tomyil12345)
Yes exacly, now if you ignore that you got t^13 by an integral you can diff. this with respect to t. Since t is a variable independent of x( otherwise they would have to state this) it doesn’t matter that you obtained that which you are diffirentiating by an integral
On one level it seems to make sense, but that's always the danger with calculus. If I have a variable x, and I integrate gravity with respect to distance from infinity to a point "R", then we know we get potential energy. If we assign a numerical value to R, then we get a numerical solution to "U" (since U=k/x). But if we then differentiate U with respect to R, then you're asking to stop making that "R", which had some pretend pre determined value to start changing and find out how it changes when we increase "R" by a little bit - but ... we just said it had a pre-determined value, so how can it change?

It might seem okay to you but what we've done is remove the meaning of what integration actually is; that's why to a mathematician what you have just done there is not allowed.

Now it goes without saying I really hope I'm wrong and we get marks for that, but at the end of the day it seems very strange that the people who literally work with maths for a living wouldn't know this seems a little dodgy.
8. (Original post by igcsesareeasy)
how many marks would i get for my method
for parametric using sin^2 + cos^2 =1
If the answer is corret full, otherwise depends how you applied it. Just stating it will be 0 marks i guess..
9. (Original post by Alexxcor)
how many marks would i get for the parametric if i only found one solution and forgot to generalize it ?
Probably most you got the whole method right apart from the final answer so yea
10. (Original post by DrSebWilkes)
On one level it seems to make sense, but that's always the danger with calculus. If I have a variable x, and I integrate gravity with respect to distance from infinity to a point "R", then we know we get potential energy. If we assign a numerical value to R, then we get a numerical solution to "U" (since U=k/x). But if we then differentiate U with respect to R, then you're asking to stop making that "R", which had some pretend pre determined value to start changing and find out how it changes when we increase "R" by a little bit - but ... we just said it had a pre-determined value, so how can it change?

It might seem okay to you but what we've done is remove the meaning of what integration actually is; that's why to a mathematician what you have just done there is not allowed.

Now it goes without saying I really hope I'm wrong and we get marks for that, but at the end of the day it seems very strange that the people who literally work with maths for a living wouldn't know this seems a little dodgy.
You dont have to assume t is constant just that it doenst depend on x, which i think is resonable,
11. (Original post by Tomyil12345)
You dont have to assume t is constant just that it doenst depend on x, which i think is resonable,
But you can't integrate to a variable [yet] ...

Look we're going around in the locus of:

$\dpi{120} \large |Z|=k \newline Z\epsilon \mathbb{C}, k\epsilon\mathbb{R}^{^{+}}$

The point is for everyone here, neither of us know the answer. As a guy standing up for maths and its importance, I'm telling you what you're doing isn't strictly speaking correct. So let's just move on.
12. (Original post by DrSebWilkes)
But you can't integrate to a variable [yet] ...

Look we're going around in the locus of:

$\dpi{120} \large |Z|=k \newline Z\epsilon \mathbb{C}, k\epsilon\mathbb{R}^{^{+}}$

The point is for everyone here, neither of us know the answer. As a guy standing up for maths and its importance, I'm telling you what you're doing isn't strictly speaking correct. So let's just move on.
Sorry i meant t is a parameter NOT a variable that would indeed be illegal
13. Multivariable calculus operates with derivatives and integrals in only one carteesian plane. Strictly speaking, i believe our method was wrong as we did not treat independent variables correctly but it luckily turned out to be alright because of the nature of the question.
14. (Original post by Tomyil12345)
Sorry i meant t is a parameter NOT a variable that would indeed be illegal
Hmm okay so this is where I definitely leave the comfort of my knowledge but surely integrating a parametric equation doesn't really solve anything? What would integrating in the t-plane do?

You got me interested now ...
15. How many marks were the calculus, parametric equations, air resistance and planets questions out of?
16. (Original post by Quantum42)
How many marks were the calculus, parametric equations, air resistance and planets questions out of?
9,9,7,9
17. (Original post by Alexxcor)
9,9,7,9
thanks. If for the air resistance one I did all of it except for calculating work done at the end, how many marks do you think that would be out of 7?
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18. (Original post by Quantum42)
thanks. If for the air resistance one I did all of it except for calculating work done at the end, how many marks do you think that would be out of 7?
3-4
19. (Original post by Quantum42)
thanks. If for the air resistance one I did all of it except for calculating work done at the end, how many marks do you think that would be out of 7?
I think 4/7 because the first two were pretty basic
20. @DrSebWilkes

Lol nice symbols.As a future physics student, you should really try to acquire intuition for what is asked of you. Only way you can integrate the function is if t isnt a function of x - then you take t^4 out of the integral. And there is no evidence why it would be expected of us to treat t as t(x). Differentiating shouldn't cause anyone any problems.

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