Newton's method for approximation q (1 Viewer)

[Joshmosh2]

For Newton's method for approximation, my teacher suggested that you should calculate the value for each component first, then sub into calculator, such as
f(a) = 3.223
f'(a) = 5.977
In her explanation, she said that if it is a three mark question, then one mark would be awarded for this calculation, before subbing into
a1 = a - f(a) / f'(a)

If you directly sub the approximation 'a' into the equation, without writing the values of the components, will you lose a mark?
The main problem i have with this is that it seems that your components are rounded off to 3 dec places, and could risk being slightly inaccurate
Thanks.

 

[Carrotsticks]

For Newton's method for approximation, my teacher suggested that you should calculate the value for each component first, then sub into calculator, such as
f(a) = 3.223
f'(a) = 5.977
In her explanation, she said that if it is a three mark question, then one mark would be awarded for this calculation, before subbing into
a1 = a - f(a) / f'(a)

If you directly sub the approximation 'a' into the equation, without writing the values of the components, will you lose a mark?
The main problem i have with this is that it seems that your components are rounded off to 3 dec places, and could risk being slightly inaccurate
Thanks.

The first mark is not awarded for the substitution. It is awarded to the computing of the first derivative (2009 HSC Q3 (b) (iii) and 2011 HSC Q2 (b)).

The second mark is awarded for demonstrating that you have some knowledge of Newton's Method ie: stating the formula, making some progress with the substitutions (in the marking criteria, they usually say "Makes substantial progress").

The third mark is awarded for a fully correct solution.

It has been said in the markers comments of previous years that students who simply substituted, without writing values, tended to be less successful with their responses. I am guessing that this is due to incorrect substitutions. However, if you do it correctly, you will not lose a mark.

Personally, I would avoid rounding off till the very end, for the same reason you stated. We don't want to be magnifying any degrees of error already had in your expressions.

 

[dan964]

For Newton's method for approximation, my teacher suggested that you should calculate the value for each component first, then sub into calculator, such as
f(a) = 3.223
f'(a) = 5.977
In her explanation, she said that if it is a three mark question, then one mark would be awarded for this calculation, before subbing into
a1 = a - f(a) / f'(a)

If you directly sub the approximation 'a' into the equation, without writing the values of the components, will you lose a mark?
The main problem i have with this is that it seems that your components are rounded off to 3 dec places, and could risk being slightly inaccurate
Thanks.

your best bet is to the keep the value in your calculator, but write the approximation as incomplete e.g. 3.223....

 

[obliviousninja]

Yea