HL maths questions

sd123

Right i've just a few things to ask and mention bout the HL course that my teacher seems to avoid when i say it to him.

1st of all i'm working very hard on an A1 and it really takes alot of work to get good at the c parts as im sure you all know. The only thing i have don other than the papers is doing out almost every question out of the less stress more success, both papers. If anyone has any other suggestions if your working on an A or if you already got one before please give them here.

2nd is just a small thing about the circle question on p2. Is it OK to differentiate the eqtn of a circle to get the slope and then sub in values for X and Y?

3rd: I think something should be worth noting about vector questions when asked for the angle between two vectors where the formula:
cosA=B.C/modBmodC is used. It is so much easier to draw a rough diagram with an I and J axis and get tan of the angle by putting the j component/ i component for both lines and then taking this away from 180 degrees. People who do applied maths will be very familiar with this but my maths teacher never mentioned it to us and its not mentioned in any marking schemes that i found. will marks be awarded for this approach in the LC? By the way this approach was much easier for 2 (c) (i) on the mock paper that evry1 was giving out about. i did this in about 6 lines in the mocks and got the right answer but only got attempt marks.

Finially, for now at least, is in Q 8 P2 which almost every one does. when asked to derive the maclaurin series for different things like ln(1+X). then the second part of the question says to get the general term and then use the ratio test. I know that everyone in my class just learned off the general terms, Un , but ive tried and get it hard. the other way is to derive them by using series ie top being geometric and bottom being arithmetic and using (ar to the power of n - 1 )/ a + (n-1)d and multiplying by (-1) to the power of -1 or other things. anyway the problem is that i can get it to work for all of them except sin x and cos x. A bit of help with this would be greatly appreciated.

any help with any of these or maybe your views would be great:D

Your Man

if you have text and tests some of the questions in the revison excercise are similar to c parts and some are i even more difficult, im goin for an a aswell and do a few of em.
the question about maclaurin-that way your doing it should work for all of them.
Circloe Question- all you would eventually get is another point on the circle which you can get in easier ways,
Not too sure about the vectors tbh, wouldnt be my best question

JC 2K3

sd123 wrote:

1st of all i'm working very hard on an A1 and it really takes alot of work to get good at the c parts as im sure you all know. The only thing i have don other than the papers is doing out almost every question out of the less stress more success, both papers. If anyone has any other suggestions if your working on an A or if you already got one before please give them here.

I'm fine just working off the papers, but I know there are books with LC maths questions in them you could get if you wanted.

sd123 wrote:

2nd is just a small thing about the circle question on p2. Is it OK to differentiate the eqtn of a circle to get the slope and then sub in values for X and Y?

Yes, but it likely wouldn't be any faster than the usual method.

sd123 wrote:

3rd: I think something should be worth noting about vector questions when asked for the angle between two vectors where the formula:
cosA=B.C/modBmodC is used. It is so much easier to draw a rough diagram with an I and J axis and get tan of the angle by putting the j component/ i component for both lines and then taking this away from 180 degrees. People who do applied maths will be very familiar with this but my maths teacher never mentioned it to us and its not mentioned in any marking schemes that i found. will marks be awarded for this approach in the LC? By the way this approach was much easier for 2 (c) (i) on the mock paper that evry1 was giving out about. i did this in about 6 lines in the mocks and got the right answer but only got attempt marks.

If you get the right answer and what you've done is clear then they can't take marks from you. Did you ask your teacher about it?

sd123 wrote:

Finially, for now at least, is in Q 8 P2 which almost every one does. when asked to derive the maclaurin series for different things like ln(1+X). then the second part of the question says to get the general term and then use the ratio test. I know that everyone in my class just learned off the general terms, Un , but ive tried and get it hard. the other way is to derive them by using series ie top being geometric and bottom being arithmetic and using (ar to the power of n - 1 )/ a + (n-1)d and multiplying by (-1) to the power of -1 or other things. anyway the problem is that i can get it to work for all of them except sin x and cos x. A bit of help with this would be greatly appreciated.

What is the problem with sinx and cosx?
For general terms I find the pattern is usually obvious.

fuinneamh

got a loan of a book called mathsbank of my teacher, around 20 questions on part (a)'s (b)'s and (c)'s on all the different topics, photocopied the part c's, standard is small bit lower than LC but is good revision the night before an exam.

sd123

Thanks to all who replied. any idea where i'd get that book Mathsbank. If anyone has any other ideas on different ways to do questions or any ideas you think might make some topics easier I'd love to hear them!:cool:

ZorbaTehZ

Mathsbank is not the best tbh, try and get something else if you can.

sd123

any ideas or recommendations there ZobraTehZ?

sd123

Ok I just want to check something about general terms. Every time I do out the Maclaurin series for cos X, I get Un= ((-1)to the power of n-1). (X to the power of 2n- 2)/(2n-2)! But the less stress more success gives a different general term. For sine X I get the same as above just replace 2n-2 with 2n-1. Am I right or is George Humphrey right?

Phaedrus25

The Magical Bag of Mathematical Tricks is brilliant. It explains everything you want and gives you loads of top class revision questions.

JC 2K3

sd123 wrote:

Ok I just want to check something about general terms. Every time I do out the Maclaurin series for cos X, I get Un= ((-1)to the power of n-1). (X to the power of 2n- 2)/(2n-2)! But the less stress more success gives a different general term. For sine X I get the same as above just replace 2n-2 with 2n-1. Am I right or is George Humphrey right?

Well you haven't told us what Less Stress More Sucess says.....

sd123

for cos X it replaces my (2n-2)s with (2n)

JC 2K3

2n is right, where are you getting 2n-2 from? Sure if n=0 then you get x^-2, and since the first term is 1 that makes no sense....

sd123

on top i got a=1 R= X^2 so ar^n-1 = 1(X^2)^n-1 which becomes X^2n-2
On bottom i got a=0 d=2 so a + (n-1)d becomes (2n-1)!
text and texts agrres with you and less stress for un but essential revision guide agrees with me.???????

JC 2K3

They're both right actually. Your one has n=1 for the first term and the other one has n=0 as the first term.

If n=0 is the first term then the formula ar^n-1 changes to ar^n and (a + d(n-1)) changes to (a + nd).

sd123

alright so the ratio test works equally as well for both right?

JC 2K3

yup

MathsManiac

JC 2K3 wrote:

If you get the right answer and what you've done is clear then they can't take marks from you. Did you ask your teacher about it?

It may depend on how the question is asked. You'll be giving an approximation, rather than an exact answer, which could be penalised if the question didn't ask for an approximate answer, (by saying something like "to the nearest degree").

e.g. angle between 2i+j and i+2j is arccos(4/5), which is approximately 37 degrees. Here I've given an exact answer, followed by an approximation.

Using your suggested method: arctan(1/2) is approx 26.565 degrees and arctan(2) is approx 63.435 degrees giving answer as approx 36.870 which again is approx 37 degrees.

At no point in the second solution did I give an exact answer to the question asked. (I could have, of course, by using the arctanA-arctanB formula.)

Depending on the context of the question, this failure to give the exact value might draw a penalty.