AIBU to ask if anyone can solve this Maths question?

[Hydrangea444]

DD is doing Further Maths A-Level and is stuck on this question.

Oh why didn't I think of that! Oh hang on, it's Saturday night! I imagine her Maths teacher is enjoying his weekend.
Actually, Mumsnet has provided help with a fair few Maths questions she was stuck on in the past. Never underestimate the power of Mumsnet!

I don’t know much about maths, but I imagine it’s not going to help her to simply know the answer. She needs guidance on whatever about it she is finding difficult. From maybe er I dunno, a teacher?
That's literally what she's doing though. Nobody is just going to say '17' and then say nothing else.

The A levels start next week.

Seems to me it's not just Maths you don't know much about.

Which it is she struggling with? She needs to differentiate the first equation. If she's struggling with the arcsin bit she can Google the rules for differentiating arcsin.
She then needs to simplify the equation until it resembles a number multiplied by the stuff in brackets. (That number is the constant k)

17

😂

I hope it is now. You would be a genius, unappreciated in your own lifetime.

Than you so much!

Ooh I love maths, I'm away to get a pen and paper. Except when it's my own dd she's a dick that doesn't listen.

My Ds 17 is giving it a go, he's just done his higher maths exam and is hoping to do advanced higher in S6...me and DD 19 don't have a clue!

She needs to look up the differential of arcsin - it's a standard one - and if she has a formula sheet for the exam it might be in there - otherwise she should Google it (and make herself a list of differentials to remember as part of her revision!). Then she needs to use chain and product rules to differentiate that first part.

She should then have something which she can manipulate algebraically until she gets the required result.

My DD had a go but has come back saying this is very complicated and she can't do it... she is sitting her A levels starting next week so either she has a problem or it is just a very hard question!! I am thinking the second option. Sorry not to be more helpful

Ugh too hard for me and DS is out. With respect to the PP with the Y10, it is way, way, way beyond those introduction to calculus videos. Very tricky.

It has been a very long time since I did A level further maths but I think she needs to use the product rule and the chain rule.

Thanks so much to your DD for having a look at it though 😀

Thank you. DD seems to think she is doing all the required steps but isn't getting to what is the right answer.

a)
y=(4x-3)sqrt(-8(2x^2-3x+1)) + arcsin(4x-3)
y=(4x-3)sqrt(-(16x^2-24x+8)) + arcsin(4x-3)
y=(4x-3)sqrt(-[(4x-3)^2-1]) + arcsin(4x-3)
y=(4x-3)sqrt(1-(4x-3)^2) + arcsin(4x-3)

let u=4x-3
y=u.sqrt(1-u^2) + arcsin(u)
dy/du=(1-u2)(1/2) + u(1/2)(1-u2)(-1/2).(-2u)+(1-u2)-(1/2)
dy/du=2(1-u2)(1/2)

dy/dx=dy/du . du/dx = 2(1-(4x-3)2)(1/2) . 4 = 16sqrt(2).sqrt(-2x^2 + 3x - 1))
k=16sqrt(2)

b)
I = y/k evaluated between 1,1/2
=arcsin(1) - arcsin(-1)
=0

Thanks. One bottle of Chateau Latour under. So apologies for any errors.

That's what I was gonna say 🤓

Have to confess I'm a lecturer in a mathematical subject with numerous maths degrees and professional qualifications and I don't fancy that

Tell her to use the product rule and chain rule to differentiate the first part of the expression and look up the derivative of arcsin (not a clue, frankly).

There's two reasons that the answer is included in part a: to give them something to aim for, and so they can do part b even if part a eludes them.

I have no idea about the further maths syllabus but if that's a past paper question I can't imagine it was fully answered by many! So the stronger students will have scored well by eking out as many attempt marks as possible, and by not skipping part b.

Or maybe it's super easy and I'm on a stupid Saturday night!

Even then I would struggle 🤣

@LovelyJubbly1234 feeling much more energetic than me tonight

Find out how to differentiate arcsins.

use that to do the two parts of the top sum separately, because differentials add. You will probably find that once you’ve differentiated the arcsin it will give you that square-root bit. That will give you K.

for the second bit, it’s asking you to integrate what you’ve just discovered dy over dx was. There’s a factor of k you’ll need to substitute out.

(c) not me, someone who likes maths.

My husband says he will do it and explain tomorrow. He’s an aerospace engineer ! I’ll revert back if no answer by then and he takes a look

Niche

Thank you so much! DD said that you have solved it uding a completely different method to the one she had used. That's fantastic!

U = 4x - 3

Chain rule for differentiation

I suppose BODMAS doesn't cut it anymore? 😊