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Maths C3 questions

I just had a couple of questions to ask you from one of the C3 Solomon papers that I did today:

1) Question 3b) from here:

http://www.school-portal.co.uk/GroupDownloadFile.asp?GroupId=1152244&ResourceId=3992025

Would we be asked something like this in the real exam?

2) Also, on question 5a) from the exact same paper, I sketched the graph in but I put in only two 'curve things' , I didn't put in the third curve. If you look at the mark scheme (below), it will be a bit more clear what I am talking about. Would this be an issue? Other than that I sketched in both of the other two curves, the coordinates of the stationary points as given in the MS and also the equations of the asymptotes, would that have been enough to pick up all the 5 marks? Also if you don't mind me asking do you know where the third curve comes from ? My usual method is to draw the graph of sec x and then to work out what happens as the transformations are taking place? Is there an easier method? Thanks.

http://www.school-portal.co.uk/GroupDownloadFile.asp?GroupId=1152244&ResourceId=3992013


thanks!

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Reply 1
Original post by laurawoods
I just had a couple of questions to ask you from one of the C3 Solomon papers that I did today:

1) Question 3b) from here:

http://www.school-portal.co.uk/GroupDownloadFile.asp?GroupId=1152244&ResourceId=3992025

Would we be asked something like this in the real exam?


I've not seen it, though I don't see why not. . .

Original post by laurawoods

2) Also, on question 5a) from the exact same paper, I sketched the graph in but I put in only two 'curve things' , I didn't put in the third curve. If you look at the mark scheme (below), it will be a bit more clear what I am talking about. Would this be an issue? Other than that I sketched in both of the other two curves, the coordinates of the stationary points as given in the MS and also the equations of the asymptotes, would that have been enough to pick up all the 5 marks? Also if you don't mind me asking do you know where the third curve comes from ? My usual method is to draw the graph of sec x and then to work out what happens as the transformations are taking place? Is there an easier method? Thanks.

http://www.school-portal.co.uk/GroupDownloadFile.asp?GroupId=1152244&ResourceId=3992013
thanks!


The third curve is there because it is sec(xπ6)\sec(x - \frac{\pi}{6}) not just sec(x)\sec(x) :smile:
Reply 2
Original post by laurawoods
I just had a couple of questions to ask you from one of the C3 Solomon papers that I did today:

1) Question 3b) from here:

http://www.school-portal.co.uk/GroupDownloadFile.asp?GroupId=1152244&ResourceId=3992025

Would we be asked something like this in the real exam?

2) Also, on question 5a) from the exact same paper, I sketched the graph in but I put in only two 'curve things' , I didn't put in the third curve. If you look at the mark scheme (below), it will be a bit more clear what I am talking about. Would this be an issue? Other than that I sketched in both of the other two curves, the coordinates of the stationary points as given in the MS and also the equations of the asymptotes, would that have been enough to pick up all the 5 marks? Also if you don't mind me asking do you know where the third curve comes from ? My usual method is to draw the graph of sec x and then to work out what happens as the transformations are taking place? Is there an easier method? Thanks.

http://www.school-portal.co.uk/GroupDownloadFile.asp?GroupId=1152244&ResourceId=3992013


thanks!


For question 1, instead of wondering whether it will come up why not just learn it? Its not too hard.

You want ln(y) < 0 I.e y < 1. Differentiate you equation and find the minimum point, which will serve as a counter example
Reply 3
Original post by joostan
I've not seen it, though I don't see why not. . .



The third curve is there because it is sec(xπ6)\sec(x - \frac{\pi}{6}) not just sec(x)\sec(x) :smile:


Hmm but??? That third curve , I still don't understand...do you have an easier method for sketching these sorts of curves because when I did by my method (described in the OP) , I didn't get it? Which point gets mapped to that third curve? :smile: ANy guidance would be helpful ! thanks!

I had a go at one C4 question paper today and and I came across this question no 6:
http://www.school-portal.co.uk/GroupDownloadFile.asp?GroupId=1152243&ResourceId=3992062

Pls can you check if my working out is correct?
*integral sign* t(t+1) (-2t) dt (ON TOP OF *integral sign* I HAD 0 AND ON BOTTOM ROOT 2)
*integral sign* (-2t^3 -2t^2) dt
[-2t^4/ 4 - 2t^3/ 3 ]

Then subbing in 0 gave 0. so 0- ({6+4sqrt2}/ 3)
Reply 4
Original post by laurawoods
Hmm but??? That third curve , I still don't understand...do you have an easier method for sketching these sorts of curves because when I did by my method (described in the OP) , I didn't get it? Which point gets mapped to that third curve? :smile: ANy guidance would be helpful ! thanks!

I had a go at one C4 question paper today and and I came across this question no 6:
http://www.school-portal.co.uk/GroupDownloadFile.asp?GroupId=1152243&ResourceId=3992062

Pls can you check if my working out is correct?
*integral sign* t(t+1) (-2t) dt (ON TOP OF *integral sign* I HAD 0 AND ON BOTTOM ROOT 2)
*integral sign* (-2t^3 -2t^2) dt
[-2t^4/ 4 - 2t^3/ 3 ]

Then subbing in 0 gave 0. so 0- ({6+4sqrt2}/ 3)

It's a translation of +π6+ \frac{\pi}{6} parallel to the x-axis.

The area looks good - except that it should be positive, not negative :smile:
Reply 5
Original post by joostan
It's a translation of +π6+ \frac{\pi}{6} parallel to the x-axis.

The area looks good - except that it should be positive, not negative :smile:


Oh yes, sorry I made a mistake it was 0- (-6+sqrt2/ 3 )

but, have you had a look at the MS ? why do they go into the trouble of getting rid of the negative sign and then swapping around the limits when without that itself you end up with the correct positive area?
Reply 6
Original post by joostan
It's a translation of +π6+ \frac{\pi}{6} parallel to the x-axis.

The area looks good - except that it should be positive, not negative :smile:


hello, so for the area question is my method right?
Reply 7
Original post by laurawoods
hello, so for the area question is my method right?

I haven't no.
Your method is correct, some prefer to do that - it really doesn't matter :smile:
Reply 8
Original post by laurawoods
I just had a couple of questions to ask you from one of the C3 Solomon papers that I did today:

1) Question 3b) from here:



thanks!


That is a lovely question - you need to solve the quadratic for any value between 0 and e, as long as the number inside the log is less than e the log will be negative :smile: and yes it would be well wthin their rights to set that as a question
Reply 9
Original post by natninja
That is a lovely question - you need to solve the quadratic for any value between 0 and e, as long as the number inside the log is less than e the log will be negative :smile: and yes it would be well wthin their rights to set that as a question


Are you sure about the bold? :wink:
Reply 10
Original post by joostan
Are you sure about the bold? :wink:


cool thanks!
Reply 11
Original post by joostan
Are you sure about the bold? :wink:


Oops meant less than 1 :P and not negative (then you get a complex number out the log :P)
Reply 12
Original post by joostan
I haven't no.
Your method is correct, some prefer to do that - it really doesn't matter :smile:


pls can u comment on this question too?

http://www.thestudentroom.co.uk/showthread.php?t=2350011&p=42598332
Reply 13


Provided you attain the correct solution, and your working is clear and correct you probably won't be penalised :smile:
Reply 14
Original post by joostan
Provided you attain the correct solution, and your working is clear and correct you probably won't be penalised :smile:


No I just wanted to know if taking logs was correct method?
Reply 15
Original post by laurawoods
No I just wanted to know if taking logs was correct method?


Personally, I'd try to avoid having a double ln, but it's up to you :smile:
Reply 16
Original post by joostan
Personally, I'd try to avoid having a double ln, but it's up to you :smile:


so r u saying u would rather taken logs like me?
Reply 17
Original post by laurawoods
so r u saying u would rather taken logs like me?


No, for 7c) I'd have done something similar to the mark scheme.
Reply 18
Original post by joostan
No, for 7c) I'd have done something similar to the mark scheme.


hmm,so is taking logs incorrect in any way ? sorry it seems like i am asking the same question again and again but sorry i am not yet getting definite answers . Because i did not get double ln.
Reply 19
Original post by laurawoods
hmm,so is taking logs incorrect in any way ? sorry it seems like i am asking the same question again and again but sorry i am not yet getting definite answers . Because i did not get double ln.


Like I said, provided your working is correct, then you should be ok.
Are you still doing 7)c) ???
Taking ln of both sides would be very messy indeed.

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