back page crunchers

[mathguy]

OK guys, I'm assuming there are shortcuts to the back page crunchers. Is this true? I'm from a puny little 1A school, so you don't have to worry about helping the competition. I just know that they always look the same and people seem to blaze through them at practice meets!

[stupidityismygam]

usually it has trig identities

like half and double angles for tangent

then with sin and cos, these are popular

[unparseable or potentially dangerous latex formula], which just equals

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

then there is the ever so popular [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula]

[Kurt]

Also several like [unparseable or potentially dangerous latex formula], which is the same as the ABSOLUTE VALUE (crucial part, lol) of [unparseable or potentially dangerous latex formula].

They will also occasionally use [unparseable or potentially dangerous latex formula], which is the same as [unparseable or potentially dangerous latex formula].

[bradp]

How about all of the (maclaurin/taylor) series?

The only one i've figured out is

1/x - 1/[3x^3] + 1/[5x^5] - 1/[7x^7]

is arctan (1/x)

[AuSmith]

http://mathworld.wolfram.com/MaclaurinSeries.html

I think equations 5, 17, 11, 23, and maybe 13 come up.

[Kurt]

A lot of the series expansion problems don't converge quickly enough to be accurate within 2 significant digits after only 4-5 terms, so I always just plug those in.

[AuSmith]

[LeoG]

You will also have problems like


Log(.0479)+Log(7.79)+Log(2.19)+Log[(9.28)/(7.79)]

which is just equal to (.0479 x 7.79 x 2.19 x 9.28) / 7.79

Also there are some like sin(.969)/cos(.969) x sq.rt of 1-{sin(.425 x 1.6)}^2

which is equal to tan(.969) x cos(.425 x 1.6)

[polymath25]

I've also seen problems like

cos(.946-.687)-cos(.946+.687)

which equals 2sin(.946)sin(.687)

Of course by the time you recognize something like this, you probably could have been able to plug the original equation into the calculator and gotten your answer quicker.

[mathslug]

I agree with kurt. There's a problem on UIL B 2007 that doesnt converge fast enough. I think it was the arctan type series. The answer that the test demanded was .2 off of the answer you would've gotten had you done arctan(x).

Zack

[AuSmith]