Implicit Differentiation - to cover or not to cover ?

[fisherpearse]

At LCHL if asked to find the slope of a circle students can avoid having to use Implicit Differentiation by writing the equation in (x-h)^2 + (y-k)^2 = r ^2 format and rearranging to get the explicit equation before differentiating ? Correct ? So I don't need to cover Implicit DIfferentiation ???

Regards,

Pearse

[Mark Campion]

I was under the impression that implicit differentiation was off the course. 
Do you happen to know if LCH students can be asked to find the general term of a cubic pattern?

tks

mark

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[fisherpearse]

The syllabus document says "use differentiation to find the slope of a tangent to a circle" but it doesn't mention Implicit Differentiation. If not given the point of tangency one way to do this is using Implicit Differentiation. If given the point of tangency you can get the slope of the radius line and work from there.

The latest version of Active Maths has included a section on Implicit Diff.

I'm just wondering if it can be avoided in all cases by rearranging.

As for Cubic patterns, again there's no specific mention in the syllabus, but I can't find a specific mention of Quadratic patterns either and I'm pretty sure they're on the syllabus. I cover them anyway.

Pearse

[Mark Campion]

If they're not given the point of tangency they can still express the function explicitly and say that dy/dx = plus or minus 1/2(r^2 - x^2)^-1/2(-2x)

agree re cubic...i guess whatever is in the JC can be examined so quadratic are in

m

[Eamonn - TheMathsTutor]

Hi Pearse,

After a bit of debate on this at a branch meeting of the IMTA last October, I contacted the NCCA and received the following response from Rachel Linney:

"Implicit differentiation will not be examined. There may be questions asked that could be solved using implicit differentiation but since there is no requirement for learners to formally engage with implicit differentiation only problems that permit alternative solution strategies will appear on the paper."

Hope that helps.

Regards,

Eamonn

[fisherpearse]

Eamonn,

thanks for that - good to know.

Pearse

[fisherpearse]

Mark,

yes that's the way I was doing the tangent without Implicit.

Re cubic they could be asked a cubic pattern question where Tn=an^3+bn^2+cn+d and set up such that b,c or d = 0 - then it's a question of three linear simultaneous equations which is in the syllabus document. So yes I also cover cubics. Also cover third difference = 6a + 2.

Pearse 

[sarah]

Want to reignite this question. Just had a look at the Deb mock and question on paper 1 gives equation of circle followed by the Question.......find dy/dx in terms of x and y.
Would this suggest question must be done using implicit as to rewrite as y= and differentiate explicitly would result in dy/dx in terms of x.

What do we think? To cover or not?

[Mark Campion]

I wouldn't bother cover implicit diff unless you have a few spare classes at the end of May

just get them to complete the square and rearrange.

and if you are going to do implicit with them, consider using the christian bros method attached.

m

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[Eamonn - TheMathsTutor]

In general I wouldn't pay too much attention to the mock papers as they have no official standing.

[Fergal O'Neill]

Hi folks, If I remember correctly, the earlier version of Active Maths 4, Book 1, had a supplement added to it for Chapter 13 (Differential Calculus I), which contained Implicit Differentiation because it became examinable from 2015 onwards albeit only in relation to using it to find the slope of a tangent to a circle.

_________________________
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Naas

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[fisherpearse]

Sarah,

I'll be showing my class how to write / rewrite the equation in (x-h)^2 + (y-k)^2 - r^2 format then isolate y and differentiate in the normal way. 

The course is long enough without adding to it unnecessarily.

NCCA have confirmed to IMTA that Implicit Differentiation will not be required (see earlier post from Eamon).

Maybe suggest to DEB that the final version of the mock paper has this question in (X-h)^2..... format.

Pearse

[Ronan Downes]

Why not show it to them?

Why restrict their use of calculus to single-valued functions? 

The level of calculus is essentially an elementary introduction to the subject and where a skill can be useful in the Leaving cert and on in to their mathematical careers how can you not show it to them? It only takes a few minutes and a few examples.

Ronan

Yours Sincerely,

Ronan Downes

email: ronan...@gmail.com

mobile:+353868140362

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[Mary Timmons]

Speaking of mocks has anyone got the papers yet? My school still hasn't decided on companies yet! 

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