2006 State questions

[bradp]

-------------------------

http://texasmath.org/DL/MA/MA06S.pdf


22) Find the digit in the ten-thousandth place of the sum of the series
1 - 2 + (2/3) - (4/45) + (2/315) ....
I'm assuming it's a taylor/maclaurin (w/e) deal but i don't know which one

23) ??

59) not sure what the area of the triangles are (besides the center one, obviously

[AuSmith]

Actually, do we ever have to use Taylor series? All Maclaurin is is a Taylor with center at x=0. In a Taylor series with center of convergence at a, you have (x-a) sprout up everywhere.

22) Yea, I don't like this one. The pattern looks unclear. First, I looked for a series to fit... maybe one with Bernoulli numbers. Didn't work. Next, I hoped maybe since [unparseable or potentially dangerous latex formula], that it was just a maclaurin with fractions in lowest terms. Then, I tried fitting x=2/3... hrm

23) I get 11.6

59) Say [unparseable or potentially dangerous latex formula]. Take away the 3 squares and middle triangle. Now, move two of the remaining triangles along the bold lines. It makes a single triangle. The squares of the sides of this triangle are [unparseable or potentially dangerous latex formula]... No, nevermind. Try again. Look at any one of the angles of the center triangle. The opposite angle is supplementary (sum of the 4 is 360, minus the two right angles), and has the same sine. It also has the same two adjacent legs. Therefore, the areas of the 4 triangles are the same.

[stupidityismygam]

23) you prove it is a rhombus....and you can solved using pythag

you get the side of the rhombus is 29/7...and the height is 3


so the area is 87/7

[suchenzang]

23) For the ease of explanation, label the rectangle that has sides parallel to the sides of the paper as ABCD with A as the upper left hand corner and BCD going clockwise. Then label the overlapping rectange as DEBF where E is the top corner and F is the lowest one. Label the intersection on the top as X (so that you have line AXB). AD and EB have a length of 3. Assign x as the length of AX. Then you have XB = 7-x. After using the Pythagorean Theorem you then get: [unparseable or potentially dangerous latex formula]. Solve, and you get x = 2.857. The shaded area would then be (7-2.857)*3 = 12.4 (E)

[suchenzang]

JINX! sort of... except i lost.

[stupidityismygam]

[AuSmith]

[AuSmith]

Ohhh... I just got what I did wrong.

23) draw a diagonal on the rhombus. [unparseable or potentially dangerous latex formula] is half of the acute angle in the rhombus (I did inverse sine for some reason).

[unparseable or potentially dangerous latex formula] where s is the side of the rhombus. You want 3s.

[AuSmith]

[bradp]

it's a hexagonal sequence !

[AuSmith]

And it's hexagonal!

[stupidityismygam]

and how exactly does that help??

though

IT IS HEXAGONAL!!

[Michael T]

It's #!

EDIT:...pwnt.

fine, fine.

IT'S HEXAGONAL!!!!!!!! :P

[AuSmith]

[suchenzang]

[stupidityismygam]

dang...too clever

i didnt see that

[bradp]

cosine.. thanks

not sure why i didn't figure that out

[Kurt]

I doubt Dr. White is going to put any REALLY crazy series on the math test...

If it starts with a 1, I usually check e^x and cosx first. If it doesn't start with a 1, I check sinx. There's also the random [unparseable or potentially dangerous latex formula], etc. he might put on there.

...I just want him to put the expansion of the error function on there! :D

[zefuri]

woah im glad im not on the math team

[stupidityismygam]

sadly...i dont know those...

though i pretend like i do...

yay for randomly trying one of those and guessing...

[Kurt]

The ones I listed are particularly nice (and easy to derive):

Well, it's easy to see this expansion:

[unparseable or potentially dangerous latex formula]

Since [unparseable or potentially dangerous latex formula], we can just integrate the expansion to see what the series expansion for [unparseable or potentially dangerous latex formula] is.

So [unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula] has a similar derivation:

[unparseable or potentially dangerous latex formula],

and [unparseable or potentially dangerous latex formula], so

[unparseable or potentially dangerous latex formula]

[AuSmith]