Oxford Physics: PAT test discussion

@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.

Hmm sorry I'm not buying that. "t" here was a constant value which was used as a limit of the integration (that's what limit means, surely?)

So you integrate, presumably on some other plane or what have you, and your left with a constant with the same value as what we are changing ... so ... erm ... that's nothing?

Intuition is one thing; being able to do things properly is another. Either the question was poorly worded, or the expectations of the question were poorly understood.

for the circles question, if I got one of the radii wrong but the centres of both and the other radius right and correctly drew in all four tangents but was unable to work out their lengths, how many marks do you think that would be?

Anyone know about this?

t doesnt change it just makes tx a family of functions, thus t is a parameter, integrating with a parameter is perfectly fine

Your limits of integration can be anything - a variable, a function, a number.

What matters is you integrate a function with respect to x and your limits of integration involve t.

Anyone know about this?

Okay so you've lost me now: why is integrating with a parameter okay? I can't integrate the "function" x=at^2? What would that get me? That only maps out the values of x in the x-t plane surely? But I can integrate x with respect to t, that's fine (but still begs the question of why?)

So for the function (xt)^4, that to me looks like 1 variable and a constant; then, we integrate that to a constant ... okay ... and then boom it's a variable? Either this is some seriously fancy maths or my (and 2 separate maths teachers) understanding about the meaning of basic calculus is wrong.



You got 4 tangents? I nearly did that but I have this horrid feeling that they don't exist. Can anyone else say that they got 4 tangents?

4 tangents but 2 lengths

Okay so you've lost me now: why is integrating with a parameter okay? I can't integrate the "function" x=at^2? What would that get me? That only maps out the values of x in the x-t plane surely? But I can integrate x with respect to t, that's fine (but still begs the question of why?)

So for the function (xt)^4, that to me looks like 1 variable and a constant; then, we integrate that to a constant ... okay ... and then boom it's a variable? Either this is some seriously fancy maths or my (and 2 separate maths teachers) understanding about the meaning of basic calculus is wrong.



You got 4 tangents? I nearly did that but I have this horrid feeling that they don't exist. Can anyone else say that they got 4 tangents?

Yeah I'm not sure there would be two tangents? I asked my maths savy friend and he didn't seem to think so. Again we might have made a mistake though so I'm definitely willing to hear if someone thinks there are are indeed more than 2 tangents.

which of these values is wrong for how much each question was worth because this adds up to 101 not 100?

which of these values is wrong for how much each question was worth because this adds up to 101 not 100?

Okay so you've lost me now: why is integrating with a parameter okay? I can't integrate the "function" x=at^2? What would that get me? That only maps out the values of x in the x-t plane surely? But I can integrate x with respect to t, that's fine (but still begs the question of why?)

So for the function (xt)^4, that to me looks like 1 variable and a constant; then, we integrate that to a constant ... okay ... and then boom it's a variable? Either this is some seriously fancy maths or my (and 2 separate maths teachers) understanding about the meaning of basic calculus is wrong.



Yes but not when that "t" then must switch from a constant to a variable - that's not how it works. The only way it can work is if you move to a different plane or something but even then I can't really see how that'd work. You can integrate y=rootx ... or you could rearrange y=2at, and x=at^2 and integrate that way ... the key thing is that the x,y plane is determined by a third plane t, but integrating and differentiating t on the t plane is a different matter to that on the x-y plane.




You got 4 tangents? I nearly did that but I have this horrid feeling that they don't exist. Can anyone else say that they got 4 tangents?

Paramatics is 8 i think

Well say you want to integrate a general line from 0 to 1 , y=ax+b so integral y=a/2 x^2 +bx +c
Integral 0 to 1 = a/2 +b
a and b are not constants, but you did nothing illegal while integrating