HSC Extension 1 Mathematics Predictions / Thoughts (1 Viewer)

Trebla

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A remark on Q13c)ii).

It had a nice trap where you had to recognise that f'(x) and g'(x) are undefined at the points (1,0) and (-1,0) but these are points where the f(x) and g(x) are defined.

So technically speaking you can only say that since their derivatives are



then



Therefore you can only really claim that



This would suggest that simply substituting in say x = 1 to find c has some rigour issues as it doesn't quite fit that domain (even though it works out).

I think the intended solution was for students to recognise that since




then f(x) and g(x) share common points at x = -1 and x = 1.

From part (i), they have the same gradient behaviour in the domain -1 < x < 0 but have a common point at x = -1 on the "edge" of that domain. This means that



Similarly, they have the same gradient behaviour in the domain 0 < x < 1 but have a common point at x = 1 on the "edge" of that domain. This means that

Alternatively, you can just
- Prove f(1) = g(1) and f(-1) = g(-1) where the derivative is undefined
- Then solve for c in f(x) = g(x) + c, for one (or more) chosen x-values where the derivative is defined (e.g. x = 0.5)
 

beetree1

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Solutions are on the facebook HSC Discussion Group 2020!
 

thomson2354

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Xanthi

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Alternatively, you can just
- Prove f(1) = g(1) and f(-1) = g(-1) where the derivative is undefined
- Then solve for c in f(x) = g(x) + c, for one chosen x-value where the derivative is defined (e.g. x = 0.5)
Surely this recognition that -1 is not part of the derivative domain is not necessary, although important for rigour?
 

MrGresh

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Surely this recognition that -1 is not part of the derivative domain is not necessary, although important for rigour?
You would think so...

Also, I both proved that f(1)=g(1) and also proved by trigonometry that f(x)=g(x) using the triangle

Do i get full marks?
 

Xanthi

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You would think so...

Also, I both proved that f(1)=g(1) and also proved by trigonometry that f(x)=g(x) using the triangle

Do i get full marks?
If the triangle proved the left side I.e for x<0 by having a triangle opening to the left, then you should?
 

thomson2354

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88 looks about right.

Here is the equation: 50+0.7143*MARK (out of 70), rounded to nearest integer.

Note: Only use this equation for marks > 40
Yo can u give an example please.. my tiny brain can’t compute🤣
 

catha230

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does anyone remember how many mark 13c is? Thanks in advance!
 

catha230

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if its the f(x)=g(x) one then part i (the diff) was 4 marks and the proving theyre equal was 3, so 7 total
Since I did not have the cases or check the region whatsoever, I only integrated it and subbed x=1/2, what do you reckon I would get for it?
 

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