"Assume x is really small"

[myopic_owl22]

Hey there,
My teacher has been telling us that NESA will never make us solve for x in anything that requires more than a quadratic. In those situations with x^3 etc, we've been told to 'assume x is very small' and just equate it to zero if it has been added to something, and leave it as x if it's multiplied as it holds more significance.

I'm curious to hear if anyone else has heard similar information or other methods when solving such equations. Is there ever a situation when x isn't small and assuming it as such will give us a wrong value??? Thanks!

[david.wang28]

Hey there,
My teacher has been telling us that NESA will never make us solve for x in anything that requires more than a quadratic. In those situations with x^3 etc, we've been told to 'assume x is very small' and just equate it to zero if it has been added to something, and leave it as x if it's multiplied as it holds more significance.

I'm curious to hear if anyone else has heard similar information or other methods when solving such equations. Is there ever a situation when x isn't small and assuming it as such will give us a wrong value??? Thanks!

If x is not small, then just use the trusty quadratic formula no matter what. This is the get out of jail card for me. But for what you're saying, in your situation you should just equate the unknown concentration to zero, otherwise you would have to use the binomial theorem or Newton's method of approximation (which some students are just not capable of because they haven't done 3U maths).

[myopic_owl22]

If x is not small, then just use the trusty quadratic formula no matter what. This is the get out of jail card for me. But for what you're saying, in your situation you should just equate the unknown concentration to zero, otherwise you would have to use the binomial theorem or Newton's method of approximation (which some students are just not capable of because they haven't done 3U maths).

That's making more sense NESA (and everyone else) says that the new chem syllabus will be more math focussed, but yeah, they definitely wouldn't expect 3U from us! It's just a little hard to know if x is actually small or not... looks like I'll be using the quadratic formula a lot more. Thanks a lot for your advice!

[myopic_owl22]

Yep in that situation it seems that using the assumption method is easier. However the assumption method is ONLY valid if x is less than 5% than the initial concentration. Otherwise it will be incorrect.

Hope thats useful

Thanks for the reply! A quick follow up question, is there any way of knowing whether x is more or less than 5% of the initial concentration before we assume/ calculate with relevant equations? E.g. could we look at the keq and get a decent idea (i.e. if keq is really small, then the amount of products is small and therefore the amount that'll be made when establishing equilibrium (x) is insignificant)?

[myopic_owl22]

Thanks a bunch! Your explanation clears a lot of things up for me

[Aaron Lillis]

I have only found this to be relevant in common ion effect calculations