When to use "by inspection" as a reason? (1 Viewer)

[Giant Lobster]

What exactly is the threshold of simplicity of things where they can be 'summoned' with the reason "by inspection"? I know for equating coefficients in operations such as decomposition into partial fractions can be "by inspection" but what other examples are there?
Im hoping that using this effectively may save me some time, especially in things like geometry, if possible...

 

[spice girl]

firstly, NEVER use 'by inspection' in geometry. otherwise, i must say i've never used 'by inspection' as any reason for something equalling another. 'by inspection' is really another way of saying 'btw, i've skipped some steps'. if i tend to skip steps, i'd just go ahead and do it without telling them anyway. just don't skip important steps.

methinks 4u hsc isn't that hard to be worth skipping that many steps to the point that u lose marks. if u really want to save time u should invest some studying time looking for shorter alternate methods instead.

 

[turtle_2468]

to add to spice girl's post, the only situation I can think of where it is non-dodgy is when you correlate real and imagniary coeff...
eg x=4+3i = (a+2b)+bi
so by inspection a+2b=4 and b=3.
you could just write correlating..

 

[Toodulu]

also when you factorise something?

 

[Giant Lobster]

i see... hmmm
what about applications in graphs? Sometimes there are the darndest things where itll take 4 lines to properly explain but its pretty obvious? (i cant think of any examples atm tho)

 

[turtle_2468]

Factorising you normally can state without actually writing anything down unless it's non-obvious (ie you can't expand it out without say at least 10 terms), in which case you should probably put a line in the middle.
Graphs: Yes. for example, "from the graph, as there is a part above the x-axis and the graph is continuous at all points, with the graph going to -(infinity) as x approaches inf and -inf, by inspection there are at least 2 roots. That was far too long as well..

 

[Giant Lobster]

heh yeah.. well thanks anyway