beausoli
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hey, guys, how did you all do?

Did you find it alright? I thought it was ok. Could anyone remember the answers post their answers here. I will try my best to recall some of those.

If, luckily, Mr M comes here, could you pls post the right answers here? Thank you so much.

The question about binomial expansion, I got 1/3 for a, and 7/3 for b. Question 7, the one about integrate sinx and cosx, i got (pi/2-ln2)

The question about the value of 'P', i think it's question 9, I got -1,-4,5 for the values of p.

Question8, the one about water depth in the tank, i got 8.5 minutes for the value of t when x=0.5.

Somehow, I am not very comfortable with my answers....
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seanw
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I felt the paper was kind of easy, although, even though I got the same answers as you, I still feel uncomfortable. I was last to have my paper collected so i scribbled some down.. Not sure which are for which questions though.

pi/2 - ln2 integrating 4sinx/(sinx+cosx)

(2-ln3)/3 last integration question part 2

1/root3 last integration question part 1

7x-11y+4=0 implicit differentiation question

70.9 degrees question 1, direction between 2 vectors

(-64,16)(-1,1)(125,5) parameter question

8.5 mins rates question

a=1/3 and b=2 1/3 binomial question
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beausoli
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question one, the angle is 70.9 degree
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beausoli
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10 i)

I got (3^0.5)/3
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seanw
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(Original post by beausoli)
10 i)

I got (3^0.5)/3
Im fairly sure 1/root3 is correct, used the graphical calculator, got the same answer. Tan30

the integral ends up as sec^2, with the limits 30 and 0 degrees... tan30-tan0.

1-siny^2= cosy^2. (cosy^2)^(3/2)=cosy^3.

x= sin y
dx = cos y dy

so 1/((1-x)^(3/2)) dx becomes cosy/cosy^3 dy = secy^2 dy which = tany.

Limits were 1/2 and 0. sin30=1/2 sin0=0.

edit/ anddddddd after all that i realised 3^0.5 / 3 = 1/root3 lol :P It's been a long day, went back to bed, woke up 20 mins before the exam :X!

I'm sure Mr.M won't fail to deliver.
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beausoli
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yes

but tan30 is (3^0.5)/3

am i wrong here??
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beausoli
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Seanw,

What did you get for the one about proving that the vectors are screw...

I did prove that they don't intersect, but i feel i got the wrong answer for s and t, I think i got 0.6 for s, and 2.4 for t, then put these values into the third equation,
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beausoli
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By the one, remeber there is a question on partial fraction??

I got -1/x+2 and 2/x+1 (CAN'T REMEMBER EXACTLY WHAT'S ON THE BOTTOM)

so when you integrate it

I=-lnlx+2l+2lnlx+1l+k
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seanw
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(Original post by beausoli)
Seanw,

What did you get for the one about proving that the vectors are screw...

I did prove that they don't intersect, but i feel i got the wrong answer for s and t, I think i got 0.6 for s, and 2.4 for t, then put these values into the third equation,
Those values for s and t are correct. But for all the marks, you also need to prove they aren't parallel, I think. Skew is non parallel and non intersecting.

The equation for partial fractions was x/(x+2)(x+1) so 2/(x+1) - 1/(x+2) is correct.. as is the integration.
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beausoli
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yes..well, but if it's easy to see that the direction vectors are different, do you still need to prove it?

That was the question i asked my teacher this morning...she didn't give me an exact answer though
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beausoli
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well...two marks lost..lol
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beausoli
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what did you get for the first question, the one on the angle between two vectors?
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seanw
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arccos 3/root84? I think, something like that. 70.9 degrees ring a bell? I also had 360-70.9, but I don't think you need that do you?
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beausoli
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YES, thanks!!!!!!
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cultist17
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happily i seem to have got most of these. i appear to have made a mistake somewhere with the rates of change question though
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beausoli
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ok, so

there are Questions on

binomial expansion
diffrential equations
partial fraction
last integration question
integration involving 4sinx/sinx+coxs
prove(vectors)
angle between two vectors


what else? There are 10 questions in total

there is one question on the equation of normal, i think the gradient of normal i got was 7/11

so

y-1=(x-1)*(7/11)

11y-11=7x-7

so the equation should be: 7x-11y+4=0 ??????????/
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seanw
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(Original post by cultist17)
happily i seem to have got most of these. i appear to have made a mistake somewhere with the rates of change question though
I hate those questions about rates of change, so I wouldn't be surprised if I'm wrong. :/ dx/dt = krootx, then I think I ended up with t = 2/k rootx + c, and some really obscure values for k and c after solving simultaneously for t=0 x=2 and t=5 x=1.
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seanw
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(Original post by beausoli)
ok, so

there are Questions on

binomial expansion
diffrential equations
partial fraction
last integration question
integration involving 4sinx/sinx+coxs
prove(vectors)
angle between two vectors


what else? There are 10 questions in total

there is one question on the equation of normal, i think the gradient of normal i got was 7/11

so

y-1=(x-1)*(7/11)

11y-11=7x-7

so the equation should be: 7x-11y+4=0 ??????????/
Same.
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Nebuduck
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Well, Darn. Question 7 - I happily integrated it, got pi/2 - ln2, smiled, went on the question 8. Eventually got to the end of the paper. Was going to just relax with a big smile on my face, but thought "Why don't I go and check all my answers instead?". When I got around to checking question 7, for some reason I thought "What's this minus doing here? Surely that should be a plus!?" - and duly "corrected" it. Whoop de doo.

Apart from that, I think my answers tally pretty well with the rest of you. Personally, I thought that paper was absolutely great fun, which means of course that it was pretty darned tricky. I'm still pretty confident though (apart from that pi/2 - ln2, of course.)

Surely proving they don't intersect proves they aren't parallel at the same time - since you're just using the direction vector component of the vector equation, if the two vectors are parallel, the equations will all work out - and turn out to be true for all values of s and t. The fact that they don't work out tells you that they aren't parallel, and don't intersect.
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seanw
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(Original post by Nebuduck)
Surely proving they don't intersect proves they aren't parallel at the same time - since you're just using the direction vector component of the vector equation, if the two vectors are parallel, the equations will all work out - and turn out to be true for all values of s and t. The fact that they don't work out tells you that they aren't parallel, and don't intersect.
I'm not sure to be honest, I just do a method, don't really pay attention to the theory. Although, I think considering it's in 3 dimensions, that the vectors could be parallel even if they don't intersect.. and in that case they are NOT skew. skew lines do not intersect and are not parallel. If they aren't parallel, again, they can still intersect. So i guess you have to prove they don't intersect, and, aren't parallel.

So, basically, that could all be waffle, or could be true. Either way, you aren't going to lose anything so who cares?
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