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STEP Prep Thread 2016 (Mark. II)

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To clarify one doubt that I have,

When you have cos(6x)=cos(4x), the solutions are 6x=4x+/-2nipi or 6x=2npi+/-4x? and for tan6x=tan4x, the solutions will always be 6x=4x+/-npi or 6x=npi+/-4x?
And how do you usually deduce for example the solutions of cosx=-(sqroot(3)/2), the solutions are sometimes, x=2npi+/-2pi/3 and sometimes it's x=npi+/-pi/3. Are there any tricks where writing the general form of these of questions. (I always get a bit confused at this).

n encompasses +- as it can be negative, the second one is correct
Second again
for cos x = something
you do
x= +-cos^-1 (something) + 2npi
for sin you do
x= sin-1 (something) + 2npi and (pi-sin-1(something)) + 2npi

tan is
x = tan-1(something) + npi

Sometimes you have to check all the solutions will work

(edited 7 years ago)

Reply 1501

Geraer100

Original post by ValerieKR

n encompasses +- as it can be negative, the second one is correct
Second again
for cos x = something
you do
x= +-cos^-1 (something) + 2npi
for sin you do
x= sin-1 (something) + 2npi and (pi-something) + 2npi

tan is
x = tan-1(something) + npi

Sometimes you have to check all the solutions will work

Okay thanks! In the question that I post, the first solutions are the ones that n encompasses +/-, so I am a bit confused :smile:

Reply 1502

Remyxomatosis

Original post by shamika

Yep, should be fine

thank you

Reply 1503

betterthanbarbs

I'm the only one doing STEP II in my school tomorrow. Finger crossed and hope I'd come out ok....
Liberation in 29 hrs..

Reply 1504

fa991

Original post by betterthanbarbs

I'm the only one doing STEP II in my school tomorrow. Finger crossed and hope I'd come out ok....
Liberation in 29 hrs..

Same here, I'll sure we'll be fine

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Reply 1505

Remyxomatosis

Original post by betterthanbarbs

I'm the only one doing STEP II in my school tomorrow. Finger crossed and hope I'd come out ok....
Liberation in 29 hrs..

Good luck

Since you're the only person doing the exam can you walk around the room?

Reply 1506

ComputerMaths97

If I don't get a U in STEP II I'll empty my bank account on results day to a charity

Reply 1507

krishdesai7

Original post by betterthanbarbs

I'm the only one doing STEP II in my school tomorrow. Finger crossed and hope I'd come out ok....
Liberation in 29 hrs..

Same here. I have my fingers crossed too. Good luck :smile:

Reply 1508

Geraer100

Good luck for tomorrow, guys!

Reply 1509

Gwenuin

Original post by Zacken

Please remove your post.

Uh.. why? Am I missing something here? :confused:

Reply 1510

student0042

STEP II 2014 Q4. Is arctan 1/x = π/2 - arctan x a common result that I should know? If so, are there corresponding ones for arcsin and arccos?

(edited 7 years ago)

Reply 1511

morgansmith

Heya, not used this thread before. Im not as clever as you lot haha, found step 1 quite hard, trying to figure out whether I got a grade 3 or scraped a grade 2. (Probably 3 lol)
For question 1, I proved it for 1,2,3, came back to disprove it for 4 at the end but ran out of time so only did half. for the second part I did part i and got it right and I started ii but didn't finish it, got to the part of expanding and stopped.

For wuestion 2, I did the differentiation part and completed part i correct, I started both ii and ii but didn get to the end. (Do you still get method marks even if u don't get to the answer)

Question 4 I only did part i but got it right.

Question 10 I got the method right could prove part i but that was an arithmetic error somewhere in my working but got the method right if that makes sense. Then used the given e in part ii and found out the 2 unknowns and if I can remember right, they are right according to the solutions on here.

Started question 3 but ran out of time right at the end so only managed to do the first graph.

What grade do you think this will be? Sorry didn't complete as many as these people ahahab

Reply 1512

fa991

Original post by student0042

STEP II 2014 Q4. Is arctan 1/x = π/2 - arctan x a common result that I should know? If so, are there corresponding ones for arcsin and arccos?

Well it's a particular case of arctan(a) + arctan(b) = arctan(a+b/1-ab) which is a very handy formula. I don't think there are equivalents for sin and cos but i may well be mistaken

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Reply 1513

Euclid2718

Hi all,

I just wanted to wish all of you all the best for STEP 2 tomorrow (for those taking it).
I'd also like to say thanks to all of you, I've found this thread (and it's precursor) really useful these past few months (sorry for not contributing myself).

Anyway, thanks,
Nathan

Good luck everyone!

Original post by ComputerMaths97

If I don't get a U in STEP II I'll empty my bank account on results day to a charity

Please send all monies to the shamika foundation.

Reply 1516

username1162972

Original post by fa991

Cosx=sin(pi/2-x) so you can find a arcosx +arcsinx aswell. Take care of periodicity aswell when handling this stuff.

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Reply 1517

TheWiseMan

Original post by ComputerMaths97

If I don't get a U in STEP II I'll empty my bank account on results day to a charity

Every adversity, every failure, every heartache carries with it the seed of an equal or greater benefit.
-Napoleon Hill

Reply 1518

ComputerMaths97

Original post by TheWiseMan

Every adversity, every failure, every heartache carries with it the seed of an equal or greater benefit.
-Napoleon Hill

My benefit is that I'll never take STEP again.

And I'll never underestimate the difficulty of an exam.

Reply 1519

Zacken

Original post by Gwenuin

Uh.. why? Am I missing something here? :confused:

You can't discuss the exam till 24 after you've sat the exam in the UK. Bear this in mind for STEP II as well.

Original post by student0042

STEP II 2014 Q4. Is arctan 1/x = π/2 - arctan x a common result that I should know? If so, are there corresponding ones for arcsin and arccos?

Yes, pretty much - there are similar ones for arcsin and arccos: arccos x + arcsin x = pi/2

hint: think of a right angled triangle.

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STEP Prep Thread 2016 (Mark. II)

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