How many marks would I get for this? (1 Viewer)

[elbatiolpxeho]

2007 3U HSC

1. (c) Differentiate tan^-1(x⁴) with respect to x. (2)

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Would I get full marks if I just wrote 4x³/(1+x⁸) instead of going 'let u=x²...'?

 

[blackops23]

i suppose no... you write "***answer***, as d[1/a tan-1f(x)]/dx = f'(x)/[a^2 + (f(x))^2], where a=1, and f(x)=x^4

Basically write the rule from the integral table as your reasoning.

 

[UnrealAnchovies]

i suppose no... you write "***answer***, as d[1/a tan-1f(x)]/dx = f'(x)/[a^2 + (f(x))^2], where a=1, and f(x)=x^4

Basically write the rule from the integral table as your reasoning.

Yeah but he's technically doing that in his answer...

 

[Drongoski]

ohex ... I like the way

you can be so backward!

 

[davidbarnes]

Yes

 

[Drongoski]

2007 3U HSC

1. (c) Differentiate tan^-1(x⁴) with respect to x. (2)

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Would I get full marks if I just wrote 4x³/(1+x⁸) instead of going 'let u=x²...'?

So someone who is good, answer is immediate. Yet there is a risk you may miss out on the full marks for not showing the derivation.

Edit

Which reminds me of the great French mathematician Galois, who died tragically at 20 following a duel. It seems he failed to gain entrance into the then best maths institution in France, the Ecole Polytechnique, apparently because he failed to show his workings to what must have been bleedingly obvious to him.

 

[jet]

If it's one mark, then sure, but if there is more than one mark allocated to the question, then just writing down the final result is not enough. There will be marks allocated to completing steps between the question and the final answer.

E.g. in this question one of the marks is allocated to either recognising that you use the chain rule, or something similar. You need to let them know what you're thinking so that the marker is happy giving you the mark. My answer would be something similar to



Yes, simply writing out the answer saves time, but then if you come back to check for mistakes it's harder to properly check every step you did if they aren't explicitly written out on the page.

 

[Drongoski]

+ 1

 

[OmmU]

As long as you get the right answer, you get all the marks.

 

[blackops23]

If it's one mark, then sure, but if there is more than one mark allocated to the question, then just writing down the final result is not enough. There will be marks allocated to completing steps between the question and the final answer.

E.g. in this question one of the marks is allocated to either recognising that you use the chain rule, or something similar. You need to let them know what you're thinking so that the marker is happy giving you the mark. My answer would be something similar to



Yes, simply writing out the answer saves time, but then if you come back to check for mistakes it's harder to properly check every step you did if they aren't explicitly written out on the page.

do you HAVE to show derivation, or can't you just use your standard table of integrals?

 

[Trebla]

2007 3U HSC

1. (c) Differentiate tan^-1(x⁴) with respect to x. (2)

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Would I get full marks if I just wrote 4x³/(1+x⁸) instead of going 'let u=x²...'?

Yes, you would get full marks. If anyone has ever seen the "sample answers" for the 2009 papers there was hardly any working shown. Also if you look at the marking criteria it says 2 marks are awarded for the "correct answer". Of course, with more complicated ones it would be better to show working as some form of insurance.

 

[ZachBC_94]

If all they wanted was the answer to all the questions, then there wouldn't be any, show that A = B questions. They want to see the process as well as the result. In some cases, the result will be the most insignificant part