AQA A2 Mathematics MPC4 Core 4 - 9th June 2015 [Discussion &amp; unofficial markscheme]

for the questions where you expand an equation, there is sometime question that asks you for the range or something where the answer is like |x|<2, for example, I don't understand how they find out, please help

Reply 1324

Original post by hamza3256

Thanks.
One last question: for the questions where you expand an equation, there is sometime question that asks you for the range or something where the answer is like |x|<2, for example, I don't understand how they find out, please help.

Binomial expansion okay so say you get given (3+x)^0.5 well to expand it using the formula you must divide by 3 so you get like 3^0.5(1+x/3)^0.5 now for a standard equation like (1+x)^0.5 the range is always -1 < x < 1 all you do now is sub x/3 for x so

-1 < x/3 < 1 and now that hoes to
-3<x<3

The modulus is just another way of writing the above so just stick to what I said you will be ok

Reply 1325

Cattie2312

Hi can anyone help me with how you prove sin3x, cos3x and tan3x using the addition formulas? Thanks!!!!

Reply 1326

hamza3256

Original post by YoloSwagginz

Binomial expansion okay so say you get given (3+x)^0.5 well to expand it using the formula you must divide by 3 so you get like 3^0.5(1+x/3)^0.5 now for a standard equation like (1+x)^0.5 the range is always -1 < x < 1 all you do now is sub x/3 for x so

-1 < x/3 < 1 and now that hoes to
-3<x<3

The modulus is just another way of writing the above so just stick to what I said you will be ok

Thanks but I could not understand where do you get the x/3 from?

Reply 1327

student0042

7

I'm going now, good luck to everyone.

Reply 1328

Original post by hamza3256

Thanks but I could not understand where do you get the x/3 from?

Do you use the formula 1 + an ... Etc

Reply 1329

Original post by Cattie2312

Hi can anyone help me with how you prove sin3x, cos3x and tan3x using the addition formulas? Thanks!!!!

Is there a paper that has this question cause I've never seen it

Reply 1330

2014_GCSE

3

Original post by YoloSwagginz

Is there a paper that has this question cause I've never seen it

There isn't one, but people think it's going to come up. I don't know how you would tackle it exactly though.

sin3x = 2sin2xcosx
=4sinxcos^2x

Maybe?

Reply 1331

hamza3256

Original post by YoloSwagginz

Do you use the formula 1 + an ... Etc

OH! I get it now. Thanks, I am actually very tired, so couldn't understand it, but now I do.

Gud luck for the exam!.

Reply 1332

Original post by hamza3256

Thanks but I could not understand where do you get the x/3 from?

If you are given a problem like (3-x)^-1

In order to expand it you need a 1 instead of a 3 so in order to get rid of it in the bracket you simply divide out and then put the 3 outside the bracket with the same power sooo

(3^-1)(1-x/3)^-1 = (3-x)^-1

Reply 1333

Original post by 2014_GCSE

There isn't one, but people think it's going to come up. I don't know how you would tackle it exactly though.

sin3x = 2sin2xcosx
=4sinxcos^2x

Maybe?

I'm pretty sure we don't get asked proofs and also to integrate or differentiate that will be easy

Reply 1334

Original post by 2014_GCSE

There isn't one, but people think it's going to come up. I don't know how you would tackle it exactly though.

sin3x = 2sin2xcosx
=4sinxcos^2x

Maybe?

Well I'd write it as sin2xcosx * cos2xsinx

Now you need double angle for both cos and sin which is simply 2sinxcosx and cos^2x - sin^2x now sub them in then how far do you go? Cause now we can start using the basic sin^2 + cos^2 = 1

Reply 1335

username1103136

Original post by 2014_GCSE

There isn't one, but people think it's going to come up. I don't know how you would tackle it exactly though.

sin3x = 2sin2xcosx
=4sinxcos^2x

Maybe?

It's definitely come up at least once, you just do, for example cos3x = cos (2x+x) (for use in cos2xcosx-sin2xsinx) and solve as normal. It asks you to find it because sometimes we get asked to solve sin^2x, which you need to rearrange your solution to find and then integrate that :smile:

(edited 8 years ago)

Reply 1336

student0042

7

Original post by 2014_GCSE

There isn't one, but people think it's going to come up. I don't know how you would tackle it exactly though.

sin3x = 2sin2xcosx
=4sinxcos^2x

Maybe?

sin(2x+x) = sin(2x)cos(x) + cos(2x)sin(x)[br]sin(3x) = (2sin(x)cos(x))cos(x) + (1-2sin^2(x))sin(x)[br]sin(3x) = 2sin(x)cos^2(x) + sin(x) - 2sin^3(x)[br]sin(3x) = 2sin(x)(1-sin^2(x)) + sin(x) - 2sin^3(x)[br]sin(3x) = 2sin(x) - 2sin^3(x) + sin(x) - 2sin^3(x)[br]sin(3x) = 3sin(x) - 4sin^3(x)

Usually the question will ask show that

sin(3x) = 3sin(x) - 4sin^3(x)

or similar.

(edited 8 years ago)

Reply 1337

datpr0

Original post by 2014_GCSE

There isn't one, but people think it's going to come up. I don't know how you would tackle it exactly though.

sin3x = 2sin2xcosx
=4sinxcos^2x

Maybe?

Hi! I just showered and I decided to check the thread on my phone one last time before I go to sleep, so this is my actual final post for today^^.

I don't believe it's ever been in an exam but it's definitely in the textbook.

It's actually pretty simple to solve; you start by rewriting sin3x as sin(x + 2x). Then you just use the formula in the booklet for sin(A + B) and rewrite sin(x + 2x) in that form (where A = x and B = 2x). After that point it all becomes standard stuff :wink:

.

Alright! Sleep (for real)! Good luck guys, I guess I'll see everyone on here after the exam.

(edited 8 years ago)

Reply 1338